TSTP Solution File: GRP200-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 0.82s 1.10s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP200-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 07:11:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.82/1.10 ============================== Prover9 ===============================
% 0.82/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.10 Process 23898 was started by sandbox on n026.cluster.edu,
% 0.82/1.10 Tue Jun 14 07:11:07 2022
% 0.82/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23745_n026.cluster.edu".
% 0.82/1.10 ============================== end of head ===========================
% 0.82/1.10
% 0.82/1.10 ============================== INPUT =================================
% 0.82/1.10
% 0.82/1.10 % Reading from file /tmp/Prover9_23745_n026.cluster.edu
% 0.82/1.10
% 0.82/1.10 set(prolog_style_variables).
% 0.82/1.10 set(auto2).
% 0.82/1.10 % set(auto2) -> set(auto).
% 0.82/1.10 % set(auto) -> set(auto_inference).
% 0.82/1.10 % set(auto) -> set(auto_setup).
% 0.82/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.10 % set(auto) -> set(auto_limits).
% 0.82/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.10 % set(auto) -> set(auto_denials).
% 0.82/1.10 % set(auto) -> set(auto_process).
% 0.82/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.10 % set(auto2) -> assign(stats, some).
% 0.82/1.10 % set(auto2) -> clear(echo_input).
% 0.82/1.10 % set(auto2) -> set(quiet).
% 0.82/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.10 % set(auto2) -> clear(print_given).
% 0.82/1.10 assign(lrs_ticks,-1).
% 0.82/1.10 assign(sos_limit,10000).
% 0.82/1.10 assign(order,kbo).
% 0.82/1.10 set(lex_order_vars).
% 0.82/1.10 clear(print_given).
% 0.82/1.10
% 0.82/1.10 % formulas(sos). % not echoed (10 formulas)
% 0.82/1.10
% 0.82/1.10 ============================== end of input ==========================
% 0.82/1.10
% 0.82/1.10 % From the command line: assign(max_seconds, 300).
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.10
% 0.82/1.10 % Formulas that are not ordinary clauses:
% 0.82/1.10
% 0.82/1.10 ============================== end of process non-clausal formulas ===
% 0.82/1.10
% 0.82/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.10
% 0.82/1.10 ============================== PREDICATE ELIMINATION =================
% 0.82/1.10
% 0.82/1.10 ============================== end predicate elimination =============
% 0.82/1.10
% 0.82/1.10 Auto_denials:
% 0.82/1.10 % copying label prove_moufang2 to answer in negative clause
% 0.82/1.10
% 0.82/1.10 Term ordering decisions:
% 0.82/1.10 Function symbol KB weights: identity=1. a=1. b=1. c=1. multiply=1. left_division=1. right_division=1. left_inverse=1. right_inverse=1.
% 0.82/1.10
% 0.82/1.10 ============================== end of process initial clauses ========
% 0.82/1.10
% 0.82/1.10 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.10
% 0.82/1.10 ============================== end of clauses for search =============
% 0.82/1.10
% 0.82/1.10 ============================== SEARCH ================================
% 0.82/1.10
% 0.82/1.10 % Starting search at 0.01 seconds.
% 0.82/1.10
% 0.82/1.10 ============================== PROOF =================================
% 0.82/1.10 % SZS status Unsatisfiable
% 0.82/1.10 % SZS output start Refutation
% 0.82/1.10
% 0.82/1.10 % Proof 1 at 0.11 (+ 0.01) seconds: prove_moufang2.
% 0.82/1.10 % Length of proof is 39.
% 0.82/1.10 % Level of proof is 10.
% 0.82/1.10 % Maximum clause weight is 19.000.
% 0.82/1.10 % Given clauses 81.
% 0.82/1.10
% 0.82/1.10 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.82/1.10 2 multiply(A,identity) = A # label(right_identity) # label(axiom). [assumption].
% 0.82/1.10 3 multiply(A,right_inverse(A)) = identity # label(right_inverse) # label(axiom). [assumption].
% 0.82/1.10 4 multiply(left_inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.82/1.10 5 multiply(A,left_division(A,B)) = B # label(multiply_left_division) # label(axiom). [assumption].
% 0.82/1.10 6 left_division(A,multiply(A,B)) = B # label(left_division_multiply) # label(axiom). [assumption].
% 0.82/1.10 7 multiply(right_division(A,B),B) = A # label(multiply_right_division) # label(axiom). [assumption].
% 0.82/1.10 8 right_division(multiply(A,B),B) = A # label(right_division_multiply) # label(axiom). [assumption].
% 0.82/1.10 9 multiply(multiply(A,multiply(B,C)),A) = multiply(multiply(A,B),multiply(C,A)) # label(moufang1) # label(axiom). [assumption].
% 0.82/1.10 10 multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))) # label(prove_moufang2) # label(negated_conjecture) # answer(prove_moufang2). [assumption].
% 0.82/1.10 14 left_division(A,A) = identity. [para(2(a,1),6(a,1,2))].
% 0.82/1.10 15 left_division(A,identity) = right_inverse(A). [para(3(a,1),6(a,1,2))].
% 0.82/1.10 18 left_division(right_division(A,B),A) = B. [para(7(a,1),6(a,1,2))].
% 0.82/1.10 21 right_division(identity,A) = left_inverse(A). [para(4(a,1),8(a,1,1))].
% 0.82/1.10 24 multiply(multiply(A,B),A) = multiply(A,multiply(B,A)). [para(1(a,1),9(a,1,1,2)),rewrite([2(4)])].
% 0.82/1.10 30 multiply(left_inverse(A),multiply(multiply(A,B),left_inverse(A))) = multiply(B,left_inverse(A)). [para(4(a,1),9(a,2,1)),rewrite([24(5),1(9)])].
% 0.82/1.10 31 multiply(A,multiply(multiply(B,left_inverse(A)),A)) = multiply(A,B). [para(4(a,1),9(a,2,2)),rewrite([24(4),2(7)])].
% 0.82/1.10 33 multiply(A,multiply(multiply(left_division(A,B),C),A)) = multiply(B,multiply(C,A)). [para(5(a,1),9(a,2,1)),rewrite([24(4)])].
% 0.82/1.10 34 multiply(left_division(A,B),multiply(multiply(C,A),left_division(A,B))) = multiply(multiply(left_division(A,B),C),B). [para(5(a,1),9(a,2,2)),rewrite([24(5)])].
% 0.82/1.10 45 multiply(multiply(A,B),multiply(C,A)) = multiply(A,multiply(multiply(B,C),A)). [back_rewrite(9),rewrite([24(3)]),flip(a)].
% 0.82/1.10 53 multiply(A,multiply(right_inverse(A),A)) = A. [para(3(a,1),24(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.82/1.10 60 multiply(right_inverse(A),A) = identity. [para(53(a,1),6(a,1,2)),rewrite([14(1)]),flip(a)].
% 0.82/1.10 61 right_inverse(right_inverse(A)) = A. [para(60(a,1),6(a,1,2)),rewrite([15(3)])].
% 0.82/1.10 62 right_inverse(A) = left_inverse(A). [para(60(a,1),8(a,1,1)),rewrite([21(2)]),flip(a)].
% 0.82/1.10 64 left_inverse(left_inverse(A)) = A. [back_rewrite(61),rewrite([62(1),62(2)])].
% 0.82/1.10 68 multiply(left_inverse(A),multiply(B,left_inverse(A))) = multiply(left_division(A,B),left_inverse(A)). [para(5(a,1),30(a,1,2,1))].
% 0.82/1.10 74 multiply(multiply(A,left_inverse(B)),B) = A. [para(31(a,1),6(a,1,2)),rewrite([6(2)]),flip(a)].
% 0.82/1.10 78 right_division(A,left_inverse(B)) = multiply(A,B). [para(7(a,1),74(a,1,1)),flip(a)].
% 0.82/1.10 79 multiply(A,left_inverse(B)) = right_division(A,B). [para(74(a,1),8(a,1,1)),flip(a)].
% 0.82/1.10 80 multiply(multiply(left_inverse(A),right_division(B,A)),A) = multiply(left_inverse(A),B). [para(24(a,1),74(a,1,1)),rewrite([79(3)])].
% 0.82/1.10 85 multiply(left_inverse(A),right_division(B,A)) = right_division(left_division(A,B),A). [back_rewrite(68),rewrite([79(3),79(6)])].
% 0.82/1.10 86 multiply(left_inverse(A),B) = left_division(A,B). [back_rewrite(80),rewrite([85(3),7(3)]),flip(a)].
% 0.82/1.10 89 left_division(multiply(A,B),A) = left_inverse(B). [para(78(a,1),18(a,1,1))].
% 0.82/1.10 95 left_division(left_inverse(A),B) = multiply(A,B). [para(64(a,1),86(a,1,1)),flip(a)].
% 0.82/1.10 109 multiply(multiply(A,B),multiply(left_division(B,C),multiply(A,B))) = multiply(A,multiply(C,multiply(A,B))). [para(89(a,1),33(a,1,2,1,1)),rewrite([86(3)])].
% 0.82/1.10 126 multiply(multiply(A,B),multiply(right_division(C,A),multiply(A,B))) = multiply(multiply(multiply(A,B),C),B). [para(79(a,1),34(a,1,2,1)),rewrite([95(2),95(4),95(7)])].
% 0.82/1.10 751 multiply(multiply(A,B),multiply(C,multiply(A,B))) = multiply(A,multiply(B,multiply(multiply(C,A),B))). [para(6(a,1),109(a,1,2,1)),rewrite([45(7)])].
% 0.82/1.10 862 multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))). [back_rewrite(126),rewrite([751(5),7(2)]),flip(a)].
% 0.82/1.10 863 $F # answer(prove_moufang2). [resolve(862,a,10,a)].
% 0.82/1.10
% 0.82/1.10 % SZS output end Refutation
% 0.82/1.10 ============================== end of proof ==========================
% 0.82/1.10
% 0.82/1.10 ============================== STATISTICS ============================
% 0.82/1.10
% 0.82/1.10 Given=81. Generated=3182. Kept=862. proofs=1.
% 0.82/1.10 Usable=64. Sos=397. Demods=570. Limbo=111, Disabled=299. Hints=0.
% 0.82/1.10 Megabytes=0.96.
% 0.82/1.10 User_CPU=0.12, System_CPU=0.01, Wall_clock=0.
% 0.82/1.10
% 0.82/1.10 ============================== end of statistics =====================
% 0.82/1.10
% 0.82/1.10 ============================== end of search =========================
% 0.82/1.10
% 0.82/1.10 THEOREM PROVED
% 0.82/1.10 % SZS status Unsatisfiable
% 0.82/1.10
% 0.82/1.10 Exiting with 1 proof.
% 0.82/1.10
% 0.82/1.10 Process 23898 exit (max_proofs) Tue Jun 14 07:11:07 2022
% 0.82/1.10 Prover9 interrupted
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