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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 13543 was started by koen on vdheijden-arch,
Sat Jan 14 20:02:31 2017
The command was "prover9 -f logic_b.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file logic_b.in
formulas(sos).
x * (y * z) = (x * y) * z.
x * I = x.
x * inv(x) = I.
end_of_list.
formulas(goals).
(all x I * x = x).
(all x inv(inv(x)) = x).
(all x inv(x) * x = I).
(all x all y x * y = y * x).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x I * x = x) # label(non_clause) # label(goal). [goal].
2 (all x inv(inv(x)) = x) # label(non_clause) # label(goal). [goal].
3 (all x inv(x) * x = I) # label(non_clause) # label(goal). [goal].
4 (all x all y x * y = y * x) # label(non_clause) # label(goal). [goal].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
x * (y * z) = (x * y) * z. [assumption].
x * I = x. [assumption].
x * inv(x) = I. [assumption].
I * c1 != c1. [deny(1)].
inv(inv(c2)) != c2. [deny(2)].
inv(c3) * c3 != I. [deny(3)].
c5 * c4 != c4 * c5. [deny(4)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
No predicates eliminated.
============================== end predicate elimination =============
Auto_denials:
% assign(max_proofs, 4). % (Horn set with more than one neg. clause)
WARNING, because some of the denials share constants,
some of the denials or their descendents may be subsumed,
preventing the target number of proofs from being found.
The shared constants are: I.
Term ordering decisions:
Predicate symbol precedence: predicate_order([ = ]).
Function symbol precedence: function_order([ I, c1, c2, c3, c4, c5, *, inv ]).
After inverse_order: Function symbol precedence: function_order([ I, c1, c2, c3, c4, c5, *, inv ]).
Unfolding symbols: (none).
Auto_inference settings:
% set(paramodulation). % (positive equality literals)
Auto_process settings: (no changes).
5 x * (y * z) = (x * y) * z. [assumption].
kept: 6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
kept: 7 x * I = x. [assumption].
kept: 8 x * inv(x) = I. [assumption].
kept: 9 I * c1 != c1. [deny(1)].
kept: 10 inv(inv(c2)) != c2. [deny(2)].
kept: 11 inv(c3) * c3 != I. [deny(3)].
kept: 12 c5 * c4 != c4 * c5. [deny(4)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
7 x * I = x. [assumption].
8 x * inv(x) = I. [assumption].
9 I * c1 != c1. [deny(1)].
10 inv(inv(c2)) != c2. [deny(2)].
11 inv(c3) * c3 != I. [deny(3)].
12 c5 * c4 != c4 * c5. [deny(4)].
end_of_list.
formulas(demodulators).
6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
7 x * I = x. [assumption].
8 x * inv(x) = I. [assumption].
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.02 seconds.
given #1 (I,wt=11): 6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
given #2 (I,wt=5): 7 x * I = x. [assumption].
given #3 (I,wt=6): 8 x * inv(x) = I. [assumption].
given #4 (I,wt=5): 9 I * c1 != c1. [deny(1)].
given #5 (I,wt=5): 10 inv(inv(c2)) != c2. [deny(2)].
given #6 (I,wt=6): 11 inv(c3) * c3 != I. [deny(3)].
given #7 (I,wt=7): 12 c5 * c4 != c4 * c5. [deny(4)].
given #8 (A,wt=9): 13 x * (I * y) = x * y. [para(7(a,1),6(a,1,1)),flip(a)].
given #9 (T,wt=6): 16 x * inv(I) = x. [para(8(a,1),13(a,1,2)),rewrite([7(2)]),flip(a)].
given #10 (T,wt=10): 14 x * (inv(x) * y) = I * y. [para(8(a,1),6(a,1,1)),flip(a)].
given #11 (T,wt=7): 19 I * inv(inv(x)) = x. [para(8(a,1),14(a,1,2)),rewrite([7(2)]),flip(a)].
============================== PROOF =================================
% Proof 1 at 0.02 (+ 0.00) seconds.
% Length of proof is 12.
% Level of proof is 6.
% Maximum clause weight is 11.000.
% Given clauses 11.
1 (all x I * x = x) # label(non_clause) # label(goal). [goal].
5 x * (y * z) = (x * y) * z. [assumption].
6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
7 x * I = x. [assumption].
8 x * inv(x) = I. [assumption].
9 I * c1 != c1. [deny(1)].
13 x * (I * y) = x * y. [para(7(a,1),6(a,1,1)),flip(a)].
14 x * (inv(x) * y) = I * y. [para(8(a,1),6(a,1,1)),flip(a)].
19 I * inv(inv(x)) = x. [para(8(a,1),14(a,1,2)),rewrite([7(2)]),flip(a)].
21 x * inv(inv(y)) = x * y. [para(19(a,1),6(a,2,2)),rewrite([7(2)])].
22 I * x = x. [para(19(a,1),13(a,2)),rewrite([21(5),13(4)])].
23 $F. [resolve(22,a,9,a)].
============================== end of proof ==========================
% Redundant proof: 27 $F. [back_rewrite(9),rewrite([22(3)]),xx(a)].
% Disable descendants (x means already disabled):
9x
given #12 (T,wt=5): 22 I * x = x. [para(19(a,1),13(a,2)),rewrite([21(5),13(4)])].
given #13 (A,wt=10): 15 x * (y * inv(x * y)) = I. [para(8(a,1),6(a,1)),flip(a)].
given #14 (T,wt=4): 28 inv(I) = I. [para(22(a,1),8(a,1))].
given #15 (T,wt=8): 26 x * (inv(x) * y) = y. [back_rewrite(14),rewrite([22(5)])].
============================== PROOF =================================
% Proof 2 at 0.02 (+ 0.00) seconds.
% Length of proof is 14.
% Level of proof is 8.
% Maximum clause weight is 11.000.
% Given clauses 15.
2 (all x inv(inv(x)) = x) # label(non_clause) # label(goal). [goal].
5 x * (y * z) = (x * y) * z. [assumption].
6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
7 x * I = x. [assumption].
8 x * inv(x) = I. [assumption].
10 inv(inv(c2)) != c2. [deny(2)].
13 x * (I * y) = x * y. [para(7(a,1),6(a,1,1)),flip(a)].
14 x * (inv(x) * y) = I * y. [para(8(a,1),6(a,1,1)),flip(a)].
19 I * inv(inv(x)) = x. [para(8(a,1),14(a,1,2)),rewrite([7(2)]),flip(a)].
21 x * inv(inv(y)) = x * y. [para(19(a,1),6(a,2,2)),rewrite([7(2)])].
22 I * x = x. [para(19(a,1),13(a,2)),rewrite([21(5),13(4)])].
26 x * (inv(x) * y) = y. [back_rewrite(14),rewrite([22(5)])].
30 inv(inv(x)) = x. [para(8(a,1),26(a,1,2)),rewrite([7(2)]),flip(a)].
31 $F. [resolve(30,a,10,a)].
============================== end of proof ==========================
% Redundant proof: 33 $F. [back_rewrite(10),rewrite([30(3)]),xx(a)].
% Disable descendants (x means already disabled):
10x
given #16 (T,wt=5): 30 inv(inv(x)) = x. [para(8(a,1),26(a,1,2)),rewrite([7(2)]),flip(a)].
============================== PROOF =================================
% Proof 3 at 0.02 (+ 0.00) seconds.
% Length of proof is 15.
% Level of proof is 9.
% Maximum clause weight is 11.000.
% Given clauses 16.
3 (all x inv(x) * x = I) # label(non_clause) # label(goal). [goal].
5 x * (y * z) = (x * y) * z. [assumption].
6 (x * y) * z = x * (y * z). [copy(5),flip(a)].
7 x * I = x. [assumption].
8 x * inv(x) = I. [assumption].
11 inv(c3) * c3 != I. [deny(3)].
13 x * (I * y) = x * y. [para(7(a,1),6(a,1,1)),flip(a)].
14 x * (inv(x) * y) = I * y. [para(8(a,1),6(a,1,1)),flip(a)].
19 I * inv(inv(x)) = x. [para(8(a,1),14(a,1,2)),rewrite([7(2)]),flip(a)].
21 x * inv(inv(y)) = x * y. [para(19(a,1),6(a,2,2)),rewrite([7(2)])].
22 I * x = x. [para(19(a,1),13(a,2)),rewrite([21(5),13(4)])].
26 x * (inv(x) * y) = y. [back_rewrite(14),rewrite([22(5)])].
30 inv(inv(x)) = x. [para(8(a,1),26(a,1,2)),rewrite([7(2)]),flip(a)].
34 inv(x) * x = I. [para(30(a,1),8(a,1,2))].
35 $F. [resolve(34,a,11,a)].
============================== end of proof ==========================
% Redundant proof: 37 $F. [back_rewrite(11),rewrite([34(4)]),xx(a)].
% Disable descendants (x means already disabled):
11x
given #17 (T,wt=6): 34 inv(x) * x = I. [para(30(a,1),8(a,1,2))].
given #18 (A,wt=12): 25 x * (y * (inv(x * y) * z)) = z. [back_rewrite(18),rewrite([22(7)])].
given #19 (T,wt=8): 36 inv(x) * (x * y) = y. [para(30(a,1),26(a,1,2,1))].
given #20 (T,wt=9): 42 x * inv(y * x) = inv(y). [para(15(a,1),36(a,1,2)),rewrite([7(3)]),flip(a)].
given #21 (T,wt=10): 47 inv(x * y) = inv(y) * inv(x). [para(42(a,1),36(a,1,2)),flip(a)].
============================== STATISTICS ============================
Given=21. Generated=238. Kept=36. proofs=3.
Usable=11. Sos=0. Demods=10. Limbo=0, Disabled=32. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=199. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=32 (0 lex), Back_demodulated=25. Back_unit_deleted=0.
Demod_attempts=1855. Demod_rewrites=422.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
Megabytes=0.09.
User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
SEARCH FAILED
Exiting with 3 proofs.
Process 13543 exit (sos_empty) Sat Jan 14 20:02:31 2017
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