TSTP Solution File: GRP201-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP201-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 3.78s 4.08s
% Output : Refutation 3.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP201-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 06:24:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 3.78/4.08 ============================== Prover9 ===============================
% 3.78/4.08 Prover9 (32) version 2009-11A, November 2009.
% 3.78/4.08 Process 31470 was started by sandbox2 on n015.cluster.edu,
% 3.78/4.08 Mon Jun 13 06:24:23 2022
% 3.78/4.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31317_n015.cluster.edu".
% 3.78/4.08 ============================== end of head ===========================
% 3.78/4.08
% 3.78/4.08 ============================== INPUT =================================
% 3.78/4.08
% 3.78/4.08 % Reading from file /tmp/Prover9_31317_n015.cluster.edu
% 3.78/4.08
% 3.78/4.08 set(prolog_style_variables).
% 3.78/4.08 set(auto2).
% 3.78/4.08 % set(auto2) -> set(auto).
% 3.78/4.08 % set(auto) -> set(auto_inference).
% 3.78/4.08 % set(auto) -> set(auto_setup).
% 3.78/4.08 % set(auto_setup) -> set(predicate_elim).
% 3.78/4.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.78/4.08 % set(auto) -> set(auto_limits).
% 3.78/4.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.78/4.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.78/4.08 % set(auto) -> set(auto_denials).
% 3.78/4.08 % set(auto) -> set(auto_process).
% 3.78/4.08 % set(auto2) -> assign(new_constants, 1).
% 3.78/4.08 % set(auto2) -> assign(fold_denial_max, 3).
% 3.78/4.08 % set(auto2) -> assign(max_weight, "200.000").
% 3.78/4.08 % set(auto2) -> assign(max_hours, 1).
% 3.78/4.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.78/4.08 % set(auto2) -> assign(max_seconds, 0).
% 3.78/4.08 % set(auto2) -> assign(max_minutes, 5).
% 3.78/4.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.78/4.08 % set(auto2) -> set(sort_initial_sos).
% 3.78/4.08 % set(auto2) -> assign(sos_limit, -1).
% 3.78/4.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.78/4.08 % set(auto2) -> assign(max_megs, 400).
% 3.78/4.08 % set(auto2) -> assign(stats, some).
% 3.78/4.08 % set(auto2) -> clear(echo_input).
% 3.78/4.08 % set(auto2) -> set(quiet).
% 3.78/4.08 % set(auto2) -> clear(print_initial_clauses).
% 3.78/4.08 % set(auto2) -> clear(print_given).
% 3.78/4.08 assign(lrs_ticks,-1).
% 3.78/4.08 assign(sos_limit,10000).
% 3.78/4.08 assign(order,kbo).
% 3.78/4.08 set(lex_order_vars).
% 3.78/4.08 clear(print_given).
% 3.78/4.08
% 3.78/4.08 % formulas(sos). % not echoed (10 formulas)
% 3.78/4.08
% 3.78/4.08 ============================== end of input ==========================
% 3.78/4.08
% 3.78/4.08 % From the command line: assign(max_seconds, 300).
% 3.78/4.08
% 3.78/4.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.78/4.08
% 3.78/4.08 % Formulas that are not ordinary clauses:
% 3.78/4.08
% 3.78/4.08 ============================== end of process non-clausal formulas ===
% 3.78/4.08
% 3.78/4.08 ============================== PROCESS INITIAL CLAUSES ===============
% 3.78/4.08
% 3.78/4.08 ============================== PREDICATE ELIMINATION =================
% 3.78/4.08
% 3.78/4.08 ============================== end predicate elimination =============
% 3.78/4.08
% 3.78/4.08 Auto_denials:
% 3.78/4.08 % copying label prove_moufang3 to answer in negative clause
% 3.78/4.08
% 3.78/4.08 Term ordering decisions:
% 3.78/4.08 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.
% 3.78/4.08
% 3.78/4.08 ============================== end of process initial clauses ========
% 3.78/4.08
% 3.78/4.08 ============================== CLAUSES FOR SEARCH ====================
% 3.78/4.08
% 3.78/4.08 ============================== end of clauses for search =============
% 3.78/4.08
% 3.78/4.08 ============================== SEARCH ================================
% 3.78/4.08
% 3.78/4.08 % Starting search at 0.01 seconds.
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=71.000, iters=3383
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=67.000, iters=3406
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=63.000, iters=3371
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=59.000, iters=3343
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=55.000, iters=3428
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=51.000, iters=3376
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=47.000, iters=3356
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=43.000, iters=3336
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=39.000, iters=3338
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=35.000, iters=3345
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=31.000, iters=3336
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=29.000, iters=3352
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=28.000, iters=3366
% 3.78/4.08
% 3.78/4.08 Low Water (keep): wt=27.000, iters=3337
% 3.78/4.08
% 3.78/4.08 ============================== PROOF =================================
% 3.78/4.08 % SZS status Unsatisfiable
% 3.78/4.08 % SZS output start Refutation
% 3.78/4.08
% 3.78/4.08 % Proof 1 at 3.04 (+ 0.05) seconds: prove_moufang3.
% 3.78/4.08 % Length of proof is 64.
% 3.78/4.08 % Level of proof is 15.
% 3.78/4.08 % Maximum clause weight is 27.000.
% 3.78/4.08 % Given clauses 300.
% 3.78/4.08
% 3.78/4.08 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.78/4.08 2 multiply(A,identity) = A # label(right_identity) # label(axiom). [assumption].
% 3.78/4.08 3 multiply(A,right_inverse(A)) = identity # label(right_inverse) # label(axiom). [assumption].
% 3.78/4.08 4 multiply(left_inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.78/4.08 5 multiply(A,left_division(A,B)) = B # label(multiply_left_division) # label(axiom). [assumption].
% 3.78/4.08 6 left_division(A,multiply(A,B)) = B # label(left_division_multiply) # label(axiom). [assumption].
% 3.78/4.08 7 multiply(right_division(A,B),B) = A # label(multiply_right_division) # label(axiom). [assumption].
% 3.78/4.08 8 right_division(multiply(A,B),B) = A # label(right_division_multiply) # label(axiom). [assumption].
% 3.78/4.08 9 multiply(multiply(multiply(A,B),C),B) = multiply(A,multiply(B,multiply(C,B))) # label(moufang2) # label(axiom). [assumption].
% 3.78/4.08 10 multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))) # label(prove_moufang3) # label(negated_conjecture) # answer(prove_moufang3). [assumption].
% 3.78/4.08 14 left_division(A,A) = identity. [para(2(a,1),6(a,1,2))].
% 3.78/4.08 15 left_division(A,identity) = right_inverse(A). [para(3(a,1),6(a,1,2))].
% 3.78/4.08 16 right_inverse(left_inverse(A)) = A. [para(4(a,1),6(a,1,2)),rewrite([15(3)])].
% 3.78/4.08 24 multiply(multiply(A,B),A) = multiply(A,multiply(B,A)). [para(1(a,1),9(a,1,1,1)),rewrite([1(6)])].
% 3.78/4.08 28 multiply(left_inverse(A),multiply(A,multiply(B,A))) = multiply(B,A). [para(4(a,1),9(a,1,1,1)),rewrite([1(2)]),flip(a)].
% 3.78/4.08 30 multiply(A,multiply(B,multiply(left_division(multiply(A,B),C),B))) = multiply(C,B). [para(5(a,1),9(a,1,1)),flip(a)].
% 3.78/4.08 32 multiply(right_division(A,B),multiply(B,multiply(C,B))) = multiply(multiply(A,C),B). [para(7(a,1),9(a,1,1,1)),flip(a)].
% 3.78/4.08 37 multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))) # answer(prove_moufang3). [back_rewrite(10),rewrite([24(5)])].
% 3.78/4.08 38 multiply(A,multiply(right_inverse(A),A)) = A. [para(3(a,1),24(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.78/4.08 40 multiply(A,multiply(left_division(A,B),A)) = multiply(B,A). [para(5(a,1),24(a,1,1)),flip(a)].
% 3.78/4.08 43 right_division(multiply(A,multiply(B,A)),A) = multiply(A,B). [para(24(a,1),8(a,1,1))].
% 3.78/4.08 44 multiply(multiply(multiply(A,multiply(B,A)),C),A) = multiply(multiply(A,B),multiply(A,multiply(C,A))). [para(24(a,1),9(a,1,1,1))].
% 3.78/4.08 46 multiply(multiply(A,multiply(B,A)),multiply(C,multiply(A,multiply(B,A)))) = multiply(A,multiply(multiply(B,multiply(multiply(A,multiply(C,A)),B)),A)). [para(24(a,1),9(a,2)),rewrite([44(4),9(5),24(6)]),flip(a)].
% 3.78/4.08 49 multiply(right_inverse(A),A) = identity. [para(38(a,1),6(a,1,2)),rewrite([14(1)]),flip(a)].
% 3.78/4.08 52 multiply(A,left_inverse(A)) = identity. [para(16(a,1),49(a,1,1))].
% 3.78/4.08 72 multiply(left_inverse(A),multiply(A,B)) = B. [para(7(a,1),28(a,1,2,2)),rewrite([7(5)])].
% 3.78/4.08 74 multiply(multiply(A,multiply(multiply(B,multiply(C,B)),A)),B) = multiply(multiply(multiply(A,B),C),multiply(B,multiply(A,B))). [para(28(a,1),9(a,1,1,1)),rewrite([46(12),72(13)]),flip(a)].
% 3.78/4.08 78 multiply(multiply(A,multiply(B,A)),multiply(C,multiply(A,multiply(B,A)))) = multiply(A,multiply(multiply(multiply(B,A),C),multiply(A,multiply(B,A)))). [back_rewrite(46),rewrite([74(11)])].
% 3.78/4.08 79 multiply(left_inverse(A),B) = left_division(A,B). [para(5(a,1),72(a,1,2))].
% 3.78/4.08 80 left_division(left_inverse(A),B) = multiply(A,B). [para(72(a,1),6(a,1,2))].
% 3.78/4.08 81 right_division(A,multiply(B,A)) = left_inverse(B). [para(72(a,1),8(a,1,1))].
% 3.78/4.08 87 left_division(A,multiply(B,multiply(C,B))) = multiply(multiply(left_division(A,B),C),B). [para(79(a,1),9(a,1,1,1)),rewrite([79(7)]),flip(a)].
% 3.78/4.08 115 left_division(A,multiply(B,A)) = multiply(left_division(A,B),A). [para(40(a,1),6(a,1,2))].
% 3.78/4.08 124 multiply(A,multiply(left_division(multiply(B,A),C),A)) = left_division(B,multiply(C,A)). [para(30(a,1),6(a,1,2)),flip(a)].
% 3.78/4.08 131 right_division(multiply(A,B),A) = multiply(A,right_division(B,A)). [para(7(a,1),43(a,1,1,2))].
% 3.78/4.08 221 multiply(multiply(A,B),left_inverse(B)) = A. [para(52(a,1),32(a,1,2,2)),rewrite([2(5),7(4)]),flip(a)].
% 3.78/4.08 230 multiply(multiply(A,left_division(B,C)),B) = multiply(right_division(A,B),multiply(C,B)). [para(40(a,1),32(a,1,2)),flip(a)].
% 3.78/4.08 246 left_division(multiply(A,B),A) = left_inverse(B). [para(221(a,1),6(a,1,2))].
% 3.78/4.08 247 multiply(A,left_inverse(B)) = right_division(A,B). [para(7(a,1),221(a,1,1))].
% 3.78/4.08 248 right_division(A,left_inverse(B)) = multiply(A,B). [para(221(a,1),8(a,1,1))].
% 3.78/4.08 253 left_inverse(multiply(A,B)) = right_division(left_inverse(B),A). [para(221(a,1),81(a,1,2)),flip(a)].
% 3.78/4.08 259 right_division(multiply(A,multiply(B,C)),C) = multiply(multiply(A,C),left_division(C,B)). [para(221(a,1),32(a,1,2,2)),rewrite([248(2),79(3),247(7)]),flip(a)].
% 3.78/4.08 282 left_inverse(left_division(A,B)) = left_division(B,A). [para(5(a,1),246(a,1,1)),flip(a)].
% 3.78/4.08 284 left_division(multiply(A,multiply(B,A)),multiply(A,B)) = left_inverse(A). [para(24(a,1),246(a,1,1))].
% 3.78/4.08 296 right_division(left_inverse(A),B) = left_division(A,left_inverse(B)). [para(247(a,1),79(a,1))].
% 3.78/4.08 306 left_inverse(multiply(A,B)) = left_division(B,left_inverse(A)). [back_rewrite(253),rewrite([296(4)])].
% 3.78/4.08 323 left_division(left_division(A,B),C) = multiply(left_division(B,A),C). [para(282(a,1),79(a,1,1)),flip(a)].
% 3.78/4.08 383 multiply(left_division(A,right_division(B,A)),A) = left_division(A,B). [para(7(a,1),115(a,1,2)),flip(a)].
% 3.78/4.08 384 left_division(A,multiply(B,multiply(A,multiply(C,A)))) = multiply(left_division(A,multiply(multiply(B,A),C)),A). [para(9(a,1),115(a,1,2))].
% 3.78/4.08 838 multiply(left_division(A,B),multiply(left_division(B,A),C)) = C. [para(323(a,1),5(a,1,2))].
% 3.78/4.08 2578 multiply(multiply(A,B),multiply(C,multiply(A,B))) = multiply(A,multiply(multiply(B,C),multiply(A,B))). [para(7(a,1),78(a,1,1,2)),rewrite([7(3),7(6),7(7)])].
% 3.78/4.08 2625 multiply(multiply(A,multiply(A,multiply(B,A))),left_division(multiply(A,multiply(B,A)),multiply(multiply(B,A),C))) = multiply(multiply(A,multiply(B,A)),C). [para(78(a,1),131(a,1,1)),rewrite([259(9),8(17)])].
% 3.78/4.08 3189 left_division(multiply(A,multiply(B,A)),C) = left_division(A,left_division(B,left_division(A,C))). [para(87(a,1),282(a,1,1)),rewrite([306(4),306(3),282(2)]),flip(a)].
% 3.78/4.08 3217 left_division(A,left_division(B,multiply(multiply(B,C),multiply(A,B)))) = multiply(left_division(A,C),multiply(A,B)). [para(284(a,1),87(a,2,1,1)),rewrite([2578(6),3189(7),6(5),79(7)])].
% 3.78/4.08 3271 multiply(multiply(A,multiply(A,multiply(B,A))),left_division(A,left_division(B,left_division(A,multiply(multiply(B,A),C))))) = multiply(multiply(A,multiply(B,A)),C). [back_rewrite(2625),rewrite([3189(8)])].
% 3.78/4.08 3431 multiply(A,multiply(multiply(left_division(A,B),C),A)) = multiply(B,multiply(C,A)). [para(79(a,1),124(a,1,2,1,1)),rewrite([323(2),80(7)])].
% 3.78/4.08 4482 multiply(left_division(A,multiply(multiply(B,A),C)),A) = multiply(multiply(left_division(A,B),multiply(A,C)),A). [para(230(a,1),74(a,2)),rewrite([3189(3),40(5),3431(5),81(8),79(9),384(8)]),flip(a)].
% 3.78/4.08 4839 left_division(A,multiply(B,multiply(C,A))) = multiply(multiply(left_division(A,B),C),A). [para(259(a,1),383(a,1,1,2)),rewrite([4482(5),5(3)]),flip(a)].
% 3.78/4.08 4937 left_division(A,multiply(multiply(B,A),C)) = multiply(left_division(A,B),multiply(A,C)). [back_rewrite(3217),rewrite([4839(4),6(2)])].
% 3.78/4.08 4945 multiply(multiply(A,multiply(A,multiply(B,A))),left_division(A,left_division(B,multiply(left_division(A,B),multiply(A,C))))) = multiply(multiply(A,multiply(B,A)),C). [back_rewrite(3271),rewrite([4937(6)])].
% 3.78/4.08 13842 multiply(multiply(A,B),left_division(B,C)) = multiply(B,multiply(left_division(B,A),C)). [para(3431(a,1),131(a,1,1)),rewrite([259(3),8(7)])].
% 3.78/4.08 15440 multiply(multiply(A,B),left_division(A,C)) = multiply(A,multiply(right_division(B,A),C)). [para(79(a,1),4937(a,2,2)),rewrite([247(3),80(4),80(5)]),flip(a)].
% 3.78/4.08 15482 multiply(multiply(A,multiply(B,A)),C) = multiply(A,multiply(B,multiply(A,C))). [back_rewrite(4945),rewrite([15440(9),131(3),8(2),13842(6),838(5)]),flip(a)].
% 3.78/4.08 15483 $F # answer(prove_moufang3). [resolve(15482,a,37,a)].
% 3.78/4.08
% 3.78/4.08 % SZS output end Refutation
% 3.78/4.08 ============================== end of proof ==========================
% 3.78/4.08
% 3.78/4.08 ============================== STATISTICS ============================
% 3.78/4.08
% 3.78/4.08 Given=300. Generated=77355. Kept=15482. proofs=1.
% 3.78/4.08 Usable=205. Sos=7801. Demods=8047. Limbo=42, Disabled=7443. Hints=0.
% 3.78/4.08 Megabytes=18.88.
% 3.78/4.08 User_CPU=3.04, System_CPU=0.05, Wall_clock=3.
% 3.78/4.08
% 3.78/4.08 ============================== end of statistics =====================
% 3.78/4.08
% 3.78/4.08 ============================== end of search =========================
% 3.78/4.08
% 3.78/4.08 THEOREM PROVED
% 3.78/4.08 % SZS status Unsatisfiable
% 3.78/4.08
% 3.78/4.08 Exiting with 1 proof.
% 3.78/4.08
% 3.78/4.08 Process 31470 exit (max_proofs) Mon Jun 13 06:24:26 2022
% 3.78/4.08 Prover9 interrupted
%------------------------------------------------------------------------------