TSTP Solution File: GRP440-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:19:06 EDT 2022
% Result : Unsatisfiable 1.58s 1.90s
% Output : Refutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP440-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 13 10:48:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.58/1.90 ============================== Prover9 ===============================
% 1.58/1.90 Prover9 (32) version 2009-11A, November 2009.
% 1.58/1.90 Process 21538 was started by sandbox2 on n029.cluster.edu,
% 1.58/1.90 Mon Jun 13 10:48:10 2022
% 1.58/1.90 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21384_n029.cluster.edu".
% 1.58/1.90 ============================== end of head ===========================
% 1.58/1.90
% 1.58/1.90 ============================== INPUT =================================
% 1.58/1.90
% 1.58/1.90 % Reading from file /tmp/Prover9_21384_n029.cluster.edu
% 1.58/1.90
% 1.58/1.90 set(prolog_style_variables).
% 1.58/1.90 set(auto2).
% 1.58/1.90 % set(auto2) -> set(auto).
% 1.58/1.90 % set(auto) -> set(auto_inference).
% 1.58/1.90 % set(auto) -> set(auto_setup).
% 1.58/1.90 % set(auto_setup) -> set(predicate_elim).
% 1.58/1.90 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.58/1.90 % set(auto) -> set(auto_limits).
% 1.58/1.90 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.58/1.90 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.58/1.90 % set(auto) -> set(auto_denials).
% 1.58/1.90 % set(auto) -> set(auto_process).
% 1.58/1.90 % set(auto2) -> assign(new_constants, 1).
% 1.58/1.90 % set(auto2) -> assign(fold_denial_max, 3).
% 1.58/1.90 % set(auto2) -> assign(max_weight, "200.000").
% 1.58/1.90 % set(auto2) -> assign(max_hours, 1).
% 1.58/1.90 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.58/1.90 % set(auto2) -> assign(max_seconds, 0).
% 1.58/1.90 % set(auto2) -> assign(max_minutes, 5).
% 1.58/1.90 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.58/1.90 % set(auto2) -> set(sort_initial_sos).
% 1.58/1.90 % set(auto2) -> assign(sos_limit, -1).
% 1.58/1.90 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.58/1.90 % set(auto2) -> assign(max_megs, 400).
% 1.58/1.90 % set(auto2) -> assign(stats, some).
% 1.58/1.90 % set(auto2) -> clear(echo_input).
% 1.58/1.90 % set(auto2) -> set(quiet).
% 1.58/1.90 % set(auto2) -> clear(print_initial_clauses).
% 1.58/1.90 % set(auto2) -> clear(print_given).
% 1.58/1.90 assign(lrs_ticks,-1).
% 1.58/1.90 assign(sos_limit,10000).
% 1.58/1.90 assign(order,kbo).
% 1.58/1.90 set(lex_order_vars).
% 1.58/1.90 clear(print_given).
% 1.58/1.90
% 1.58/1.90 % formulas(sos). % not echoed (2 formulas)
% 1.58/1.90
% 1.58/1.90 ============================== end of input ==========================
% 1.58/1.90
% 1.58/1.90 % From the command line: assign(max_seconds, 300).
% 1.58/1.90
% 1.58/1.90 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.58/1.90
% 1.58/1.90 % Formulas that are not ordinary clauses:
% 1.58/1.90
% 1.58/1.90 ============================== end of process non-clausal formulas ===
% 1.58/1.90
% 1.58/1.90 ============================== PROCESS INITIAL CLAUSES ===============
% 1.58/1.90
% 1.58/1.90 ============================== PREDICATE ELIMINATION =================
% 1.58/1.90
% 1.58/1.90 ============================== end predicate elimination =============
% 1.58/1.90
% 1.58/1.90 Auto_denials:
% 1.58/1.90 % copying label prove_these_axioms_2 to answer in negative clause
% 1.58/1.90
% 1.58/1.90 Term ordering decisions:
% 1.58/1.90
% 1.58/1.90 % Assigning unary symbol inverse kb_weight 0 and highest precedence (5).
% 1.58/1.90 Function symbol KB weights: a2=1. b2=1. multiply=1. inverse=0.
% 1.58/1.90
% 1.58/1.90 ============================== end of process initial clauses ========
% 1.58/1.90
% 1.58/1.90 ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.90
% 1.58/1.90 ============================== end of clauses for search =============
% 1.58/1.90
% 1.58/1.90 ============================== SEARCH ================================
% 1.58/1.90
% 1.58/1.90 % Starting search at 0.01 seconds.
% 1.58/1.90
% 1.58/1.90 ============================== PROOF =================================
% 1.58/1.90 % SZS status Unsatisfiable
% 1.58/1.90 % SZS output start Refutation
% 1.58/1.90
% 1.58/1.90 % Proof 1 at 0.92 (+ 0.01) seconds: prove_these_axioms_2.
% 1.58/1.90 % Length of proof is 64.
% 1.58/1.90 % Level of proof is 25.
% 1.58/1.90 % Maximum clause weight is 41.000.
% 1.58/1.90 % Given clauses 44.
% 1.58/1.90
% 1.58/1.90 1 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C))))))) = D # label(single_axiom) # label(axiom). [assumption].
% 1.58/1.90 2 multiply(multiply(inverse(b2),b2),a2) != a2 # label(prove_these_axioms_2) # label(negated_conjecture) # answer(prove_these_axioms_2). [assumption].
% 1.58/1.90 3 inverse(multiply(A,multiply(multiply(B,multiply(C,multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(B,D)))))),multiply(multiply(E,F),inverse(multiply(V6,multiply(A,F))))))) = V6. [para(1(a,1),1(a,1,1,2,2,1,1))].
% 1.58/1.90 4 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),C),inverse(multiply(D,multiply(E,C))))),D)))) = E. [para(1(a,1),1(a,1,1,2,2,2))].
% 1.58/1.90 12 inverse(multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(inverse(A),multiply(multiply(inverse(C),D),inverse(multiply(E,multiply(F,D))))),E)),F)))) = C. [para(4(a,1),1(a,1,1,2,2,2))].
% 1.58/1.90 18 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(D,multiply(A,C)))))) = inverse(multiply(E,multiply(F,multiply(multiply(inverse(F),multiply(multiply(inverse(E),multiply(multiply(D,V6),inverse(multiply(V7,multiply(V8,V6))))),V7)),V8)))). [para(3(a,1),4(a,1,1,2,2,1,2,2)),flip(a)].
% 1.58/1.90 540 multiply(A,multiply(B,multiply(multiply(inverse(B),C),inverse(multiply(inverse(D),multiply(A,C)))))) = D. [para(18(a,2),12(a,1))].
% 1.58/1.90 676 inverse(multiply(A,multiply(B,multiply(C,inverse(multiply(D,multiply(A,multiply(E,multiply(multiply(inverse(E),F),inverse(multiply(inverse(C),multiply(inverse(B),F)))))))))))) = D. [para(540(a,1),1(a,1,1,2,2,1))].
% 1.58/1.90 1280 inverse(multiply(inverse(A),multiply(A,multiply(B,inverse(multiply(C,B)))))) = C. [para(18(a,1),676(a,1,1,2,2,2,1,2)),rewrite([12(16)])].
% 1.58/1.90 1398 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(C,inverse(multiply(D,C)))),D))) = A. [para(1280(a,1),18(a,1,2,2,2)),rewrite([12(23)])].
% 1.58/1.90 1427 inverse(multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(C,A)))))) = C. [para(1280(a,1),676(a,1,1,2,2,2,1,2,2,2,2)),rewrite([1398(9)])].
% 1.58/1.90 1431 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D)))) = inverse(B). [para(1280(a,1),1280(a,1,1,2,2,2))].
% 1.58/1.90 1709 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)))) = D. [para(1427(a,1),1280(a,1,1,2,2,2))].
% 1.58/1.90 1720 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,C)))),multiply(D,multiply(inverse(D),B)))) = C. [para(1427(a,1),1427(a,1,1,2,2,2))].
% 1.58/1.90 1791 multiply(A,multiply(B,multiply(inverse(B),inverse(multiply(inverse(C),A))))) = C. [para(1398(a,1),540(a,1,2,2,1)),rewrite([1398(10)])].
% 1.58/1.90 1824 multiply(A,multiply(B,multiply(multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(multiply(D,E)))),D)),E))) = A. [para(1427(a,1),1398(a,1,2,2,1,2,2))].
% 1.58/1.90 1941 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),multiply(D,multiply(inverse(D),C))) = A. [para(1280(a,1),1791(a,1,2,2,2))].
% 1.58/1.90 1952 multiply(multiply(A,multiply(inverse(A),inverse(multiply(B,inverse(C))))),multiply(D,multiply(inverse(D),B))) = C. [para(1427(a,1),1791(a,1,2,2,2))].
% 1.58/1.90 2093 multiply(multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(C)),inverse(multiply(inverse(D),C))),B)))),D) = A. [para(1791(a,1),1941(a,1,2))].
% 1.58/1.90 2304 multiply(inverse(A),multiply(A,multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))) = B. [para(1431(a,1),12(a,1,1,2,2,1,2,1,2,1,1)),rewrite([12(15)]),flip(a)].
% 1.58/1.90 4295 multiply(A,multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))) = A. [para(1398(a,1),1824(a,1,2,2,1,2,1,2,2,1)),rewrite([1398(15)])].
% 1.58/1.90 4326 multiply(A,multiply(multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(multiply(C,D)))),C)),D)) = inverse(multiply(inverse(E),multiply(E,multiply(multiply(F,multiply(inverse(F),inverse(V6))),V6)))). [para(1824(a,1),1709(a,1,1,2,2,1,2,2,1)),flip(a)].
% 1.58/1.90 4339 multiply(multiply(A,multiply(B,inverse(multiply(multiply(inverse(inverse(multiply(C,multiply(multiply(inverse(C),multiply(multiply(D,multiply(inverse(D),inverse(multiply(E,F)))),E)),F)))),inverse(inverse(V6))),B)))),V6) = A. [para(1824(a,1),2093(a,1,1,2,2,1,1,2,1))].
% 1.58/1.90 4482 multiply(multiply(A,multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(C))),C))),multiply(D,multiply(inverse(D),inverse(inverse(E))))) = E. [para(4295(a,1),1791(a,1,2,2,2,1))].
% 1.58/1.90 4486 multiply(A,multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B)))) = A. [para(4295(a,1),1941(a,1))].
% 1.58/1.90 4515 multiply(A,multiply(inverse(A),multiply(multiply(B,multiply(inverse(B),inverse(C))),C))) = inverse(multiply(multiply(D,multiply(inverse(D),inverse(E))),multiply(F,multiply(inverse(F),E)))). [para(4295(a,1),1720(a,1,1,1,2,2,1)),flip(a)].
% 1.58/1.90 4524 multiply(A,multiply(inverse(A),inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),inverse(D))))) = D. [para(4295(a,1),1952(a,1))].
% 1.58/1.90 4540 multiply(A,multiply(B,multiply(inverse(B),multiply(C,multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),multiply(multiply(E,multiply(inverse(E),inverse(F))),F))))))))) = A. [para(4295(a,1),4295(a,1,2,2,2))].
% 1.58/1.90 4542 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(multiply(inverse(C),C)). [para(4486(a,1),1(a,1,1,2)),flip(a)].
% 1.58/1.90 4669 inverse(multiply(inverse(A),multiply(A,multiply(multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B))),inverse(E))))) = E. [para(4486(a,1),1280(a,1,1,2,2,2,1))].
% 1.58/1.90 4704 multiply(inverse(A),multiply(A,multiply(B,multiply(C,inverse(multiply(multiply(D,inverse(multiply(multiply(multiply(E,multiply(inverse(E),inverse(F))),F),D))),C)))))) = B. [para(4486(a,1),2304(a,1,2,2))].
% 1.58/1.90 4720 multiply(A,inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),A))) = inverse(multiply(inverse(D),multiply(D,multiply(multiply(E,multiply(inverse(E),inverse(F))),F)))). [para(4486(a,1),1709(a,1,1,2,2,1,2,2,1)),flip(a)].
% 1.58/1.90 4724 multiply(A,inverse(multiply(multiply(multiply(B,multiply(inverse(B),inverse(C))),C),A))) = inverse(multiply(multiply(D,multiply(inverse(D),inverse(E))),multiply(F,multiply(inverse(F),E)))). [para(4486(a,1),1720(a,1,1,1,2,2,1)),flip(a)].
% 1.58/1.90 4725 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(multiply(multiply(C,multiply(inverse(C),inverse(D))),D),B))),E)))),multiply(F,inverse(F)))) = E. [para(4486(a,1),1720(a,1,1,2,2))].
% 1.58/1.90 4754 multiply(A,multiply(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D))),inverse(multiply(multiply(E,multiply(inverse(E),inverse(F))),F)))) = A. [para(4295(a,1),4486(a,1,2,2,1))].
% 1.58/1.90 5292 multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))))),inverse(multiply(inverse(E),E))) = B. [para(4542(a,1),2304(a,1,2))].
% 1.58/1.90 5328 multiply(inverse(A),A) = inverse(inverse(multiply(inverse(B),B))). [para(4542(a,1),1720(a,1,1)),flip(a)].
% 1.58/1.90 5369 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))))) = inverse(multiply(inverse(E),E)). [para(4542(a,1),4295(a,1)),flip(a)].
% 1.58/1.90 5398 multiply(inverse(A),A) = c_0. [new_symbol(5328)].
% 1.58/1.90 5417 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),multiply(multiply(C,multiply(inverse(C),inverse(D))),D)))))) = inverse(c_0). [back_rewrite(5369),rewrite([5398(14)])].
% 1.58/1.90 5450 inverse(inverse(c_0)) = c_0. [back_rewrite(5328),rewrite([5398(2),5398(3)]),flip(a)].
% 1.58/1.90 5480 multiply(inverse(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,multiply(C,inverse(multiply(D,C)))),D))))),inverse(c_0)) = B. [back_rewrite(5292),rewrite([5398(12)])].
% 1.58/1.90 5687 multiply(multiply(A,multiply(inverse(A),inverse(B))),B) = inverse(c_0). [back_rewrite(4542),rewrite([5398(7)])].
% 1.58/1.90 5688 multiply(c_0,a2) != a2 # answer(prove_these_axioms_2). [back_rewrite(2),rewrite([5398(4)])].
% 1.58/1.90 5694 multiply(A,multiply(B,multiply(inverse(B),multiply(C,multiply(inverse(C),inverse(multiply(D,multiply(inverse(D),inverse(c_0))))))))) = A. [back_rewrite(4540),rewrite([5687(8)])].
% 1.58/1.90 5705 multiply(A,multiply(inverse(A),inverse(multiply(B,multiply(inverse(B),inverse(c_0)))))) = inverse(c_0). [back_rewrite(5417),rewrite([5687(7)])].
% 1.58/1.90 5782 multiply(A,inverse(c_0)) = A. [back_rewrite(4754),rewrite([5687(6),5687(10),5450(8),5687(7)])].
% 1.58/1.90 5800 inverse(multiply(multiply(A,multiply(inverse(A),inverse(multiply(multiply(B,inverse(multiply(inverse(c_0),B))),C)))),multiply(D,inverse(D)))) = C. [back_rewrite(4725),rewrite([5687(6)])].
% 1.58/1.90 5801 multiply(A,inverse(multiply(inverse(c_0),A))) = inverse(multiply(multiply(B,multiply(inverse(B),inverse(C))),multiply(D,multiply(inverse(D),C)))). [back_rewrite(4724),rewrite([5687(5)])].
% 1.58/1.90 5803 multiply(A,inverse(multiply(inverse(c_0),A))) = inverse(c_0). [back_rewrite(4720),rewrite([5687(5),5687(11),5782(9),5398(7)])].
% 1.58/1.90 5814 multiply(inverse(A),multiply(A,B)) = B. [back_rewrite(4704),rewrite([5687(6),5803(6),5803(6),5782(4)])].
% 1.58/1.90 5833 inverse(multiply(inverse(c_0),inverse(A))) = A. [back_rewrite(4669),rewrite([5687(6),5803(6),5814(7)])].
% 1.58/1.90 5930 multiply(A,multiply(inverse(A),B)) = B. [back_rewrite(4524),rewrite([5687(6),5833(6)])].
% 1.58/1.90 5936 inverse(c_0) = c_0. [back_rewrite(4515),rewrite([5930(5),5398(3),5930(4),5930(5),5930(5),5398(3)]),flip(a)].
% 1.58/1.90 5951 multiply(c_0,inverse(inverse(A))) = A. [back_rewrite(4482),rewrite([5930(5),5398(3),5930(4),5930(6)])].
% 1.58/1.90 6033 multiply(A,multiply(multiply(inverse(A),multiply(inverse(multiply(B,C)),B)),C)) = c_0. [back_rewrite(4326),rewrite([5930(6),5930(12),5398(10),5814(11),5936(9)])].
% 1.58/1.90 6034 multiply(A,c_0) = A. [back_rewrite(4295),rewrite([5930(5),5398(3),5930(4)])].
% 1.58/1.90 6037 multiply(A,inverse(multiply(B,inverse(B)))) = A. [back_rewrite(5694),rewrite([5936(5),6034(5),5930(7),5930(6)])].
% 1.58/1.90 6042 multiply(multiply(A,multiply(B,inverse(multiply(C,B)))),C) = A. [back_rewrite(4339),rewrite([5930(6),6033(7),5936(2),5936(2),5951(4)])].
% 1.58/1.90 6086 multiply(A,inverse(A)) = c_0. [back_rewrite(5705),rewrite([5936(4),6034(4),6037(5),5936(4)])].
% 1.58/1.90 6124 inverse(inverse(A)) = A. [back_rewrite(5480),rewrite([6042(6),5930(4),5936(4),6034(4)])].
% 1.58/1.90 6134 multiply(A,inverse(multiply(c_0,A))) = c_0. [back_rewrite(5801),rewrite([5936(2),5930(8),5930(8),5398(6),5936(6)])].
% 1.58/1.90 6135 multiply(c_0,A) = A. [back_rewrite(5800),rewrite([5936(3),6134(5),5930(6),6086(5),6034(5),6124(4)])].
% 1.58/1.90 6136 $F # answer(prove_these_axioms_2). [resolve(6135,a,5688,a)].
% 1.58/1.90
% 1.58/1.90 % SZS output end Refutation
% 1.58/1.90 ============================== end of proof ==========================
% 1.58/1.90
% 1.58/1.90 ============================== STATISTICS ============================
% 1.58/1.90
% 1.58/1.90 Given=44. Generated=8528. Kept=6135. proofs=1.
% 1.58/1.90 Usable=39. Sos=4682. Demods=4391. Limbo=332, Disabled=1083. Hints=0.
% 1.58/1.90 Megabytes=15.59.
% 1.58/1.90 User_CPU=0.92, System_CPU=0.01, Wall_clock=1.
% 1.58/1.90
% 1.58/1.90 ============================== end of statistics =====================
% 1.58/1.90
% 1.58/1.90 ============================== end of search =========================
% 1.58/1.90
% 1.58/1.90 THEOREM PROVED
% 1.58/1.90 % SZS status Unsatisfiable
% 1.58/1.90
% 1.58/1.90 Exiting with 1 proof.
% 1.58/1.90
% 1.58/1.90 Process 21538 exit (max_proofs) Mon Jun 13 10:48:11 2022
% 1.58/1.90 Prover9 interrupted
%------------------------------------------------------------------------------