TSTP Solution File: GRP203-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP203-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 11:18:08 EDT 2022
% Result : Unsatisfiable 4.41s 4.71s
% Output : Refutation 4.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP203-1 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n018.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Tue Jun 14 11:35:28 EDT 2022
% 0.15/0.36 % CPUTime :
% 4.41/4.71 ============================== Prover9 ===============================
% 4.41/4.71 Prover9 (32) version 2009-11A, November 2009.
% 4.41/4.71 Process 18837 was started by sandbox2 on n018.cluster.edu,
% 4.41/4.71 Tue Jun 14 11:35:29 2022
% 4.41/4.71 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18684_n018.cluster.edu".
% 4.41/4.71 ============================== end of head ===========================
% 4.41/4.71
% 4.41/4.71 ============================== INPUT =================================
% 4.41/4.71
% 4.41/4.71 % Reading from file /tmp/Prover9_18684_n018.cluster.edu
% 4.41/4.71
% 4.41/4.71 set(prolog_style_variables).
% 4.41/4.71 set(auto2).
% 4.41/4.71 % set(auto2) -> set(auto).
% 4.41/4.71 % set(auto) -> set(auto_inference).
% 4.41/4.71 % set(auto) -> set(auto_setup).
% 4.41/4.71 % set(auto_setup) -> set(predicate_elim).
% 4.41/4.71 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.41/4.71 % set(auto) -> set(auto_limits).
% 4.41/4.71 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.41/4.71 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.41/4.71 % set(auto) -> set(auto_denials).
% 4.41/4.71 % set(auto) -> set(auto_process).
% 4.41/4.71 % set(auto2) -> assign(new_constants, 1).
% 4.41/4.71 % set(auto2) -> assign(fold_denial_max, 3).
% 4.41/4.71 % set(auto2) -> assign(max_weight, "200.000").
% 4.41/4.71 % set(auto2) -> assign(max_hours, 1).
% 4.41/4.71 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.41/4.71 % set(auto2) -> assign(max_seconds, 0).
% 4.41/4.71 % set(auto2) -> assign(max_minutes, 5).
% 4.41/4.71 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.41/4.71 % set(auto2) -> set(sort_initial_sos).
% 4.41/4.71 % set(auto2) -> assign(sos_limit, -1).
% 4.41/4.71 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.41/4.71 % set(auto2) -> assign(max_megs, 400).
% 4.41/4.71 % set(auto2) -> assign(stats, some).
% 4.41/4.71 % set(auto2) -> clear(echo_input).
% 4.41/4.71 % set(auto2) -> set(quiet).
% 4.41/4.71 % set(auto2) -> clear(print_initial_clauses).
% 4.41/4.71 % set(auto2) -> clear(print_given).
% 4.41/4.71 assign(lrs_ticks,-1).
% 4.41/4.71 assign(sos_limit,10000).
% 4.41/4.71 assign(order,kbo).
% 4.41/4.71 set(lex_order_vars).
% 4.41/4.71 clear(print_given).
% 4.41/4.71
% 4.41/4.71 % formulas(sos). % not echoed (4 formulas)
% 4.41/4.71
% 4.41/4.71 ============================== end of input ==========================
% 4.41/4.71
% 4.41/4.71 % From the command line: assign(max_seconds, 300).
% 4.41/4.71
% 4.41/4.71 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.41/4.71
% 4.41/4.71 % Formulas that are not ordinary clauses:
% 4.41/4.71
% 4.41/4.71 ============================== end of process non-clausal formulas ===
% 4.41/4.71
% 4.41/4.71 ============================== PROCESS INITIAL CLAUSES ===============
% 4.41/4.71
% 4.41/4.71 ============================== PREDICATE ELIMINATION =================
% 4.41/4.71
% 4.41/4.71 ============================== end predicate elimination =============
% 4.41/4.71
% 4.41/4.71 Auto_denials:
% 4.41/4.71 % copying label prove_moufang2 to answer in negative clause
% 4.41/4.71
% 4.41/4.71 Term ordering decisions:
% 4.41/4.71
% 4.41/4.71 % Assigning unary symbol left_inverse kb_weight 0 and highest precedence (7).
% 4.41/4.71 Function symbol KB weights: identity=1. a=1. b=1. c=1. multiply=1. left_inverse=0.
% 4.41/4.71
% 4.41/4.71 ============================== end of process initial clauses ========
% 4.41/4.71
% 4.41/4.71 ============================== CLAUSES FOR SEARCH ====================
% 4.41/4.71
% 4.41/4.71 ============================== end of clauses for search =============
% 4.41/4.71
% 4.41/4.71 ============================== SEARCH ================================
% 4.41/4.71
% 4.41/4.71 % Starting search at 0.01 seconds.
% 4.41/4.71
% 4.41/4.71 ============================== PROOF =================================
% 4.41/4.71 % SZS status Unsatisfiable
% 4.41/4.71 % SZS output start Refutation
% 4.41/4.71
% 4.41/4.71 % Proof 1 at 3.66 (+ 0.03) seconds: prove_moufang2.
% 4.41/4.71 % Length of proof is 57.
% 4.41/4.71 % Level of proof is 23.
% 4.41/4.71 % Maximum clause weight is 30.000.
% 4.41/4.71 % Given clauses 158.
% 4.41/4.71
% 4.41/4.71 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 4.41/4.71 2 multiply(left_inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 4.41/4.71 3 multiply(multiply(multiply(A,B),A),C) = multiply(A,multiply(B,multiply(A,C))) # label(moufang3) # label(axiom). [assumption].
% 4.41/4.71 4 multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))) # label(prove_moufang2) # label(negated_conjecture) # answer(prove_moufang2). [assumption].
% 4.41/4.71 5 multiply(multiply(A,identity),B) = multiply(A,B). [para(1(a,1),3(a,1,1,1)),rewrite([1(6),1(6)])].
% 4.41/4.71 6 multiply(multiply(A,A),B) = multiply(A,multiply(A,B)). [para(1(a,1),3(a,2,2)),rewrite([5(3)])].
% 4.41/4.71 7 multiply(left_inverse(A),multiply(A,multiply(left_inverse(A),B))) = multiply(left_inverse(A),B). [para(2(a,1),3(a,1,1,1)),rewrite([1(3)]),flip(a)].
% 4.41/4.71 10 multiply(left_inverse(identity),A) = A. [para(2(a,1),5(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.41/4.71 12 multiply(multiply(A,multiply(B,multiply(A,identity))),C) = multiply(A,multiply(B,multiply(A,C))). [para(3(a,1),5(a,1,1)),rewrite([3(8)])].
% 4.41/4.71 13 multiply(multiply(A,left_inverse(identity)),B) = multiply(A,B). [para(10(a,1),3(a,1,1,1)),rewrite([10(9),10(8)])].
% 4.41/4.71 14 multiply(left_inverse(left_inverse(identity)),A) = A. [para(2(a,1),13(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.41/4.71 17 left_inverse(identity) = identity. [para(14(a,1),2(a,1))].
% 4.41/4.71 26 multiply(left_inverse(A),multiply(A,identity)) = identity. [para(2(a,1),7(a,1,2,2)),rewrite([2(6)])].
% 4.41/4.71 28 multiply(left_inverse(multiply(multiply(A,B),A)),multiply(A,multiply(B,multiply(A,multiply(left_inverse(multiply(multiply(A,B),A)),C))))) = multiply(left_inverse(multiply(multiply(A,B),A)),C). [para(3(a,1),7(a,1,2))].
% 4.41/4.71 32 multiply(left_inverse(multiply(multiply(A,B),A)),multiply(A,multiply(B,multiply(A,identity)))) = identity. [para(3(a,1),26(a,1,2))].
% 4.41/4.71 73 multiply(left_inverse(multiply(multiply(A,B),multiply(A,identity))),multiply(A,multiply(B,multiply(A,identity)))) = identity. [para(5(a,1),32(a,1,1,1,1)),rewrite([5(11),5(11)])].
% 4.41/4.71 76 multiply(left_inverse(multiply(multiply(A,multiply(B,B)),A)),multiply(A,multiply(B,multiply(B,multiply(A,identity))))) = identity. [para(6(a,1),32(a,1,2,2))].
% 4.41/4.71 148 multiply(A,multiply(left_inverse(multiply(A,identity)),multiply(A,B))) = multiply(A,B). [para(2(a,1),12(a,1,1,2)),rewrite([5(3)]),flip(a)].
% 4.41/4.71 153 multiply(A,multiply(left_inverse(A),multiply(A,B))) = multiply(A,B). [para(26(a,1),12(a,1,1,2)),rewrite([5(3)]),flip(a)].
% 4.41/4.71 171 multiply(left_inverse(A),multiply(left_inverse(left_inverse(A)),identity)) = identity. [para(2(a,1),153(a,1,2,2)),rewrite([2(8)])].
% 4.41/4.71 381 multiply(left_inverse(multiply(multiply(A,left_inverse(A)),multiply(A,identity))),multiply(A,identity)) = identity. [para(26(a,1),73(a,1,2,2))].
% 4.41/4.71 415 multiply(A,multiply(left_inverse(multiply(multiply(A,left_inverse(A)),multiply(A,identity))),multiply(A,B))) = multiply(A,B). [para(381(a,1),12(a,1,1,2)),rewrite([5(3)]),flip(a)].
% 4.41/4.71 745 multiply(left_inverse(A),multiply(left_inverse(multiply(multiply(left_inverse(A),left_inverse(left_inverse(A))),multiply(left_inverse(A),identity))),identity)) = identity. [para(2(a,1),415(a,1,2,2)),rewrite([2(15)])].
% 4.41/4.71 928 multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),left_inverse(A))),left_inverse(left_inverse(A)))),identity) = identity. [para(171(a,1),76(a,1,2,2,2)),rewrite([26(16)])].
% 4.41/4.71 959 multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),left_inverse(A))),left_inverse(left_inverse(A)))),B) = B. [para(928(a,1),5(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.41/4.71 982 multiply(multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),left_inverse(A))),left_inverse(left_inverse(A))) = identity. [para(959(a,1),2(a,1))].
% 4.41/4.71 983 multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),multiply(left_inverse(A),multiply(left_inverse(left_inverse(A)),B)))) = B. [para(959(a,1),28(a,1,2,2,2,2)),rewrite([982(9),17(2),6(10),1(12),982(19),17(12),1(12)])].
% 4.41/4.71 988 multiply(multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),left_inverse(A))),multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),left_inverse(A))),identity)),identity)) = identity. [para(982(a,1),148(a,1,2,2)),rewrite([982(27)])].
% 4.41/4.71 993 multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),multiply(left_inverse(A),identity))) = left_inverse(A). [para(2(a,1),983(a,1,2,2,2))].
% 4.41/4.71 995 multiply(left_inverse(left_inverse(A)),multiply(left_inverse(A),B)) = B. [para(983(a,1),7(a,1,2,2)),rewrite([983(15)])].
% 4.41/4.71 1021 multiply(left_inverse(multiply(multiply(left_inverse(left_inverse(A)),left_inverse(left_inverse(left_inverse(A)))),multiply(left_inverse(left_inverse(A)),identity))),identity) = multiply(left_inverse(A),identity). [para(745(a,1),983(a,1,2,2,2)),rewrite([995(8)]),flip(a)].
% 4.41/4.71 1023 multiply(left_inverse(A),identity) = left_inverse(A). [back_rewrite(993),rewrite([995(8)])].
% 4.41/4.72 1026 multiply(left_inverse(A),left_inverse(left_inverse(A))) = identity. [back_rewrite(988),rewrite([995(6),995(7),1023(4),1023(5)])].
% 4.41/4.72 1029 left_inverse(left_inverse(left_inverse(A))) = left_inverse(A). [back_rewrite(1021),rewrite([1026(6),1023(5),1(4),1023(5),1023(6)])].
% 4.41/4.72 1063 left_inverse(left_inverse(A)) = A. [para(2(a,1),995(a,1,2)),rewrite([1023(4)])].
% 4.41/4.72 1064 multiply(A,multiply(multiply(left_inverse(A),B),multiply(A,C))) = multiply(multiply(B,A),C). [para(995(a,1),3(a,1,1,1)),rewrite([1063(2),1063(4),1063(6)]),flip(a)].
% 4.41/4.72 1066 multiply(A,multiply(left_inverse(A),B)) = B. [para(995(a,1),5(a,2)),rewrite([1063(2),5(5)])].
% 4.41/4.72 1068 multiply(A,left_inverse(A)) = identity. [para(995(a,1),32(a,1,2,2)),rewrite([1063(3),2(2),1(3),1063(2),1023(3)])].
% 4.41/4.72 1081 multiply(left_inverse(A),multiply(A,B)) = B. [para(1029(a,1),995(a,1,1)),rewrite([1063(3)])].
% 4.41/4.72 1082 multiply(A,identity) = A. [para(1026(a,1),995(a,1,2)),rewrite([1063(2),1063(4)])].
% 4.41/4.72 1293 multiply(multiply(A,multiply(B,A)),C) = multiply(A,multiply(B,multiply(A,C))). [back_rewrite(12),rewrite([1082(2)])].
% 4.41/4.72 1330 multiply(multiply(A,B),A) = multiply(A,multiply(B,A)). [para(1082(a,1),3(a,1)),rewrite([1082(4)])].
% 4.41/4.72 1441 multiply(A,multiply(multiply(left_inverse(A),B),A)) = multiply(B,A). [para(1066(a,1),1330(a,1,1)),flip(a)].
% 4.41/4.72 1483 multiply(multiply(A,B),left_inverse(A)) = multiply(A,multiply(B,left_inverse(A))). [para(1441(a,1),1066(a,1,2)),rewrite([1063(5)]),flip(a)].
% 4.41/4.72 1484 multiply(multiply(left_inverse(A),B),A) = multiply(left_inverse(A),multiply(B,A)). [para(1441(a,1),1081(a,1,2)),flip(a)].
% 4.41/4.72 1694 multiply(A,multiply(multiply(B,A),left_inverse(A))) = multiply(A,B). [para(1068(a,1),1293(a,2,2,2)),rewrite([1483(4),1082(6)])].
% 4.41/4.72 1751 multiply(multiply(A,left_inverse(B)),B) = A. [para(1694(a,1),1066(a,1,2)),rewrite([1066(3),1063(4)]),flip(a)].
% 4.41/4.72 1753 multiply(multiply(A,B),left_inverse(B)) = A. [para(1066(a,1),1694(a,2)),rewrite([1484(3),1330(5),1066(6)])].
% 4.41/4.72 1796 multiply(multiply(A,multiply(B,multiply(A,left_inverse(C)))),C) = multiply(A,multiply(B,A)). [para(1293(a,1),1751(a,1,1))].
% 4.41/4.72 1802 multiply(left_inverse(multiply(A,B)),A) = left_inverse(B). [para(1753(a,1),1081(a,1,2))].
% 4.41/4.72 1901 left_inverse(multiply(A,B)) = multiply(left_inverse(B),left_inverse(A)). [para(1081(a,1),1802(a,1,1,1)),flip(a)].
% 4.41/4.72 3374 multiply(multiply(A,B),multiply(left_inverse(A),C)) = multiply(A,multiply(multiply(B,left_inverse(A)),C)). [para(1064(a,1),1066(a,1,2)),rewrite([1063(6)]),flip(a)].
% 4.41/4.72 3378 multiply(multiply(A,left_inverse(B)),multiply(B,C)) = multiply(left_inverse(B),multiply(multiply(B,A),C)). [para(1081(a,1),1064(a,1,2,2)),rewrite([1063(3)]),flip(a)].
% 4.41/4.72 4590 multiply(A,multiply(multiply(B,multiply(C,left_inverse(A))),A)) = multiply(multiply(A,B),C). [para(1751(a,1),1796(a,1,1,2)),rewrite([1901(5),1063(4)]),flip(a)].
% 4.41/4.72 5702 multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)). [para(1751(a,1),4590(a,1,2,1,2)),rewrite([1063(6)]),flip(a)].
% 4.41/4.72 6200 multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))). [para(1081(a,1),5702(a,1,2)),rewrite([3378(8),3374(9),5702(8),1081(6)])].
% 4.41/4.72 6201 $F # answer(prove_moufang2). [resolve(6200,a,4,a)].
% 4.41/4.72
% 4.41/4.72 % SZS output end Refutation
% 4.41/4.72 ============================== end of proof ==========================
% 4.41/4.72
% 4.41/4.72 ============================== STATISTICS ============================
% 4.41/4.72
% 4.41/4.72 Given=158. Generated=31256. Kept=6200. proofs=1.
% 4.41/4.72 Usable=54. Sos=2789. Demods=2848. Limbo=8, Disabled=3352. Hints=0.
% 4.41/4.72 Megabytes=16.39.
% 4.41/4.72 User_CPU=3.66, System_CPU=0.03, Wall_clock=4.
% 4.41/4.72
% 4.41/4.72 ============================== end of statistics =====================
% 4.41/4.72
% 4.41/4.72 ============================== end of search =========================
% 4.41/4.72
% 4.41/4.72 THEOREM PROVED
% 4.41/4.72 % SZS status Unsatisfiable
% 4.41/4.72
% 4.41/4.72 Exiting with 1 proof.
% 4.41/4.72
% 4.41/4.72 Process 18837 exit (max_proofs) Tue Jun 14 11:35:33 2022
% 4.41/4.72 Prover9 interrupted
%------------------------------------------------------------------------------