TSTP Solution File: GRP707-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP707-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 11:20:43 EDT 2022
% Result : Unsatisfiable 0.82s 1.13s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP707-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.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 07:43:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.82/1.13 ============================== Prover9 ===============================
% 0.82/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.13 Process 18658 was started by sandbox2 on n004.cluster.edu,
% 0.82/1.13 Tue Jun 14 07:43:39 2022
% 0.82/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_18502_n004.cluster.edu".
% 0.82/1.13 ============================== end of head ===========================
% 0.82/1.13
% 0.82/1.13 ============================== INPUT =================================
% 0.82/1.13
% 0.82/1.13 % Reading from file /tmp/Prover9_18502_n004.cluster.edu
% 0.82/1.13
% 0.82/1.13 set(prolog_style_variables).
% 0.82/1.13 set(auto2).
% 0.82/1.13 % set(auto2) -> set(auto).
% 0.82/1.13 % set(auto) -> set(auto_inference).
% 0.82/1.13 % set(auto) -> set(auto_setup).
% 0.82/1.13 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.13 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.13 % set(auto) -> set(auto_limits).
% 0.82/1.13 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.13 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.13 % set(auto) -> set(auto_denials).
% 0.82/1.13 % set(auto) -> set(auto_process).
% 0.82/1.13 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.13 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.13 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.13 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.13 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.13 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.13 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.13 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.13 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.13 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.13 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.13 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.13 % set(auto2) -> assign(stats, some).
% 0.82/1.13 % set(auto2) -> clear(echo_input).
% 0.82/1.13 % set(auto2) -> set(quiet).
% 0.82/1.13 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.13 % set(auto2) -> clear(print_given).
% 0.82/1.13 assign(lrs_ticks,-1).
% 0.82/1.13 assign(sos_limit,10000).
% 0.82/1.13 assign(order,kbo).
% 0.82/1.13 set(lex_order_vars).
% 0.82/1.13 clear(print_given).
% 0.82/1.13
% 0.82/1.13 % formulas(sos). % not echoed (10 formulas)
% 0.82/1.13
% 0.82/1.13 ============================== end of input ==========================
% 0.82/1.13
% 0.82/1.13 % From the command line: assign(max_seconds, 300).
% 0.82/1.13
% 0.82/1.13 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.13
% 0.82/1.13 % Formulas that are not ordinary clauses:
% 0.82/1.13
% 0.82/1.13 ============================== end of process non-clausal formulas ===
% 0.82/1.13
% 0.82/1.13 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.13
% 0.82/1.13 ============================== PREDICATE ELIMINATION =================
% 0.82/1.13
% 0.82/1.13 ============================== end predicate elimination =============
% 0.82/1.13
% 0.82/1.13 Auto_denials:
% 0.82/1.13 % copying label goals to answer in negative clause
% 0.82/1.13
% 0.82/1.13 Term ordering decisions:
% 0.82/1.13 Function symbol KB weights: unit=1. a=1. b=1. mult=1. ld=1. rd=1.
% 0.82/1.13
% 0.82/1.13 ============================== end of process initial clauses ========
% 0.82/1.13
% 0.82/1.13 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.13
% 0.82/1.13 ============================== end of clauses for search =============
% 0.82/1.13
% 0.82/1.13 ============================== SEARCH ================================
% 0.82/1.13
% 0.82/1.13 % Starting search at 0.01 seconds.
% 0.82/1.13
% 0.82/1.13 ============================== PROOF =================================
% 0.82/1.13 % SZS status Unsatisfiable
% 0.82/1.13 % SZS output start Refutation
% 0.82/1.13
% 0.82/1.13 % Proof 1 at 0.15 (+ 0.01) seconds: goals.
% 0.82/1.13 % Length of proof is 72.
% 0.82/1.13 % Level of proof is 16.
% 0.82/1.13 % Maximum clause weight is 19.000.
% 0.82/1.13 % Given clauses 88.
% 0.82/1.13
% 0.82/1.13 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 0.82/1.13 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 0.82/1.13 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 0.82/1.13 4 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 0.82/1.13 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 0.82/1.13 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 0.82/1.13 7 mult(A,mult(A,mult(A,A))) = unit # label(c08) # label(axiom). [assumption].
% 0.82/1.13 8 mult(mult(A,A),B) = mult(B,mult(A,A)) # label(c09) # label(axiom). [assumption].
% 0.82/1.13 9 mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) # label(c07) # label(axiom). [assumption].
% 0.82/1.13 10 mult(mult(mult(A,B),B),C) = mult(A,mult(B,mult(B,C))). [copy(9),flip(a)].
% 0.82/1.13 11 mult(mult(a,b),a) != mult(a,mult(b,a)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 0.82/1.13 15 ld(rd(A,B),A) = B. [para(5(a,1),4(a,1,2))].
% 0.82/1.13 17 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 0.82/1.13 18 mult(A,mult(A,A)) = ld(A,unit). [para(7(a,1),4(a,1,2)),flip(a)].
% 0.82/1.13 21 rd(mult(A,mult(B,B)),A) = mult(B,B). [para(8(a,1),6(a,1,1))].
% 0.82/1.13 22 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(10(a,1),1(a,1)),rewrite([1(2)]),flip(a)].
% 0.82/1.13 23 mult(A,mult(B,B)) = mult(B,mult(B,A)). [para(2(a,1),10(a,1,1,1)),rewrite([8(2),2(6)])].
% 0.82/1.13 25 mult(A,mult(B,mult(ld(A,C),ld(A,C)))) = mult(mult(C,ld(A,C)),B). [para(3(a,1),10(a,1,1,1)),rewrite([23(7,R)]),flip(a)].
% 0.82/1.13 28 mult(rd(A,B),mult(B,mult(B,C))) = mult(mult(A,B),C). [para(5(a,1),10(a,1,1,1)),flip(a)].
% 0.82/1.13 36 mult(A,mult(A,mult(A,B))) = mult(ld(A,unit),B). [para(8(a,1),10(a,1,1)),rewrite([18(2)]),flip(a)].
% 0.82/1.13 42 mult(A,mult(B,mult(B,mult(C,C)))) = mult(C,mult(C,mult(A,mult(B,B)))). [para(8(a,2),10(a,2,2,2)),rewrite([22(2),23(4),8(6)]),flip(a)].
% 0.82/1.13 45 mult(mult(A,B),mult(B,mult(B,C))) = mult(mult(A,ld(B,unit)),C). [para(10(a,1),10(a,1,1)),rewrite([18(2)]),flip(a)].
% 0.82/1.13 49 mult(mult(A,mult(B,B)),C) = mult(A,mult(B,mult(B,C))). [back_rewrite(10),rewrite([22(2)])].
% 0.82/1.13 62 rd(ld(A,unit),A) = mult(A,A). [para(18(a,1),21(a,1,1))].
% 0.82/1.13 63 mult(A,mult(ld(A,B),ld(A,B))) = mult(B,ld(A,B)). [para(3(a,1),22(a,1,1)),flip(a)].
% 0.82/1.13 68 mult(A,mult(A,mult(B,A))) = mult(B,ld(A,unit)). [para(22(a,1),22(a,1,1)),rewrite([49(3),18(2),23(6)]),flip(a)].
% 0.82/1.13 69 mult(mult(A,ld(B,unit)),B) = A. [para(22(a,1),22(a,2)),rewrite([49(3),18(2),23(7),18(6),3(7),1(6)])].
% 0.82/1.13 74 rd(A,ld(B,unit)) = mult(A,B). [para(5(a,1),69(a,1,1)),flip(a)].
% 0.82/1.13 75 mult(A,ld(B,unit)) = rd(A,B). [para(69(a,1),6(a,1,1)),flip(a)].
% 0.82/1.13 77 mult(A,mult(A,mult(B,A))) = rd(B,A). [back_rewrite(68),rewrite([75(6)])].
% 0.82/1.13 78 mult(mult(A,B),mult(B,mult(B,C))) = mult(rd(A,B),C). [back_rewrite(45),rewrite([75(7)])].
% 0.82/1.13 88 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(23(a,1),21(a,1,1))].
% 0.82/1.13 89 mult(A,mult(ld(A,unit),B)) = B. [para(23(a,1),22(a,1,1)),rewrite([23(4),36(3),23(7),18(6),3(7),1(6)])].
% 0.82/1.13 91 mult(A,mult(mult(A,B),mult(A,B))) = mult(B,mult(A,mult(B,mult(A,A)))). [para(23(a,2),22(a,1,1)),rewrite([49(4),23(2,R)]),flip(a)].
% 0.82/1.13 92 mult(A,mult(mult(B,A),mult(B,A))) = mult(rd(B,A),B). [para(22(a,1),23(a,2,2)),rewrite([23(7),78(8)])].
% 0.82/1.13 95 ld(mult(A,B),A) = ld(B,unit). [para(74(a,1),15(a,1,1))].
% 0.82/1.13 99 rd(rd(A,B),B) = mult(A,mult(B,B)). [para(75(a,1),22(a,1,1)),rewrite([75(4),75(7),62(5)])].
% 0.82/1.13 108 ld(ld(A,unit),B) = mult(A,B). [para(3(a,1),89(a,1,2)),flip(a)].
% 0.82/1.13 109 mult(ld(A,unit),B) = ld(A,B). [para(89(a,1),4(a,1,2)),flip(a)].
% 0.82/1.13 110 mult(A,mult(B,rd(B,A))) = mult(B,B). [para(23(a,1),89(a,1,2)),rewrite([75(3)])].
% 0.82/1.13 113 mult(A,mult(A,mult(A,B))) = ld(A,B). [back_rewrite(36),rewrite([109(6)])].
% 0.82/1.13 114 ld(ld(A,B),unit) = ld(B,A). [para(3(a,1),95(a,1,1)),flip(a)].
% 0.82/1.13 126 mult(mult(A,ld(B,A)),B) = mult(B,mult(A,ld(B,A))). [para(25(a,1),23(a,2)),rewrite([23(5),63(4)]),flip(a)].
% 0.82/1.13 133 rd(A,mult(B,A)) = ld(B,unit). [para(108(a,1),17(a,1,2))].
% 0.82/1.13 136 rd(ld(A,B),B) = ld(A,unit). [para(109(a,1),6(a,1,1))].
% 0.82/1.13 138 mult(ld(A,B),B) = mult(B,rd(B,A)). [para(109(a,1),22(a,1,1)),rewrite([23(6),75(5)])].
% 0.82/1.13 139 ld(A,mult(B,B)) = mult(B,rd(B,A)). [para(109(a,1),22(a,2)),rewrite([109(3),138(2)]),flip(a)].
% 0.82/1.13 145 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(114(a,1),74(a,1,2))].
% 0.82/1.13 164 ld(rd(A,B),unit) = rd(B,A). [para(5(a,1),133(a,1,2)),flip(a)].
% 0.82/1.13 170 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(164(a,1),75(a,1,2)),flip(a)].
% 0.82/1.13 172 ld(rd(A,B),C) = mult(rd(B,A),C). [para(164(a,1),109(a,1,1)),flip(a)].
% 0.82/1.13 173 mult(rd(A,B),mult(B,C)) = mult(mult(A,B),ld(B,C)). [para(3(a,1),28(a,1,2,2))].
% 0.82/1.13 246 mult(ld(A,B),mult(B,rd(B,A))) = mult(A,ld(B,A)). [para(3(a,1),77(a,1,2,2)),rewrite([138(3),145(6)])].
% 0.82/1.13 247 ld(A,rd(B,A)) = mult(A,mult(B,A)). [para(77(a,1),4(a,1,2))].
% 0.82/1.13 287 rd(mult(rd(A,B),A),B) = mult(rd(A,B),rd(A,B)). [para(5(a,1),88(a,1,1,2))].
% 0.82/1.13 368 mult(mult(A,B),mult(A,B)) = mult(B,mult(mult(A,B),A)). [para(6(a,1),110(a,1,2,2)),flip(a)].
% 0.82/1.13 371 mult(ld(A,B),ld(A,B)) = mult(B,rd(ld(A,B),A)). [para(136(a,1),110(a,1,2,2)),rewrite([75(4)]),flip(a)].
% 0.82/1.13 376 mult(rd(A,B),rd(A,B)) = mult(B,mult(mult(A,B),A)). [para(99(a,1),110(a,1,2,2)),rewrite([23(3),173(4),4(3)]),flip(a)].
% 0.82/1.13 394 mult(A,mult(A,mult(mult(B,A),B))) = mult(rd(B,A),B). [back_rewrite(92),rewrite([368(3)])].
% 0.82/1.13 395 mult(A,mult(B,mult(mult(A,B),A))) = mult(B,ld(A,B)). [back_rewrite(91),rewrite([368(3),23(6),113(7)])].
% 0.82/1.13 421 rd(mult(rd(A,B),A),B) = mult(B,mult(mult(A,B),A)). [back_rewrite(287),rewrite([376(6)])].
% 0.82/1.13 428 mult(rd(A,B),A) = mult(A,ld(B,A)). [para(5(a,1),113(a,1,2,2)),rewrite([23(4,R),376(3),395(4),172(4)]),flip(a)].
% 0.82/1.13 443 rd(mult(A,ld(B,A)),B) = mult(B,mult(mult(A,B),A)). [back_rewrite(421),rewrite([428(2)])].
% 0.82/1.13 445 mult(A,mult(A,mult(mult(B,A),B))) = mult(B,ld(A,B)). [back_rewrite(394),rewrite([428(6)])].
% 0.82/1.13 537 mult(A,rd(ld(B,A),B)) = mult(A,mult(mult(B,A),B)). [para(138(a,1),88(a,1,1,2)),rewrite([246(4),443(3),371(6)]),flip(a)].
% 0.82/1.13 571 mult(ld(A,B),ld(A,B)) = mult(B,mult(mult(A,B),A)). [back_rewrite(371),rewrite([537(6)])].
% 0.82/1.13 574 rd(ld(A,B),A) = mult(mult(A,B),A). [para(136(a,1),139(a,2,2)),rewrite([571(3),4(4),75(6)]),flip(a)].
% 0.82/1.13 655 mult(A,mult(A,mult(B,ld(A,B)))) = mult(mult(B,A),B). [para(78(a,1),42(a,2,2)),rewrite([368(3),445(4),5(7)])].
% 0.82/1.13 682 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(145(a,1),170(a,1,2))].
% 0.82/1.13 930 mult(A,mult(mult(B,C),B)) = mult(A,mult(B,mult(C,B))). [para(247(a,1),145(a,2,2)),rewrite([172(2),428(2),682(3),574(2)])].
% 0.82/1.13 938 mult(mult(A,B),A) = mult(A,mult(B,A)). [para(126(a,1),247(a,2,2)),rewrite([443(3),930(3),4(4),655(6)]),flip(a)].
% 0.82/1.13 939 $F # answer(goals). [resolve(938,a,11,a)].
% 0.82/1.13
% 0.82/1.13 % SZS output end Refutation
% 0.82/1.13 ============================== end of proof ==========================
% 0.82/1.13
% 0.82/1.13 ============================== STATISTICS ============================
% 0.82/1.13
% 0.82/1.13 Given=88. Generated=4060. Kept=937. proofs=1.
% 0.82/1.13 Usable=57. Sos=428. Demods=464. Limbo=18, Disabled=443. Hints=0.
% 0.82/1.13 Megabytes=0.89.
% 0.82/1.13 User_CPU=0.15, System_CPU=0.01, Wall_clock=0.
% 0.82/1.13
% 0.82/1.13 ============================== end of statistics =====================
% 0.82/1.13
% 0.82/1.13 ============================== end of search =========================
% 0.82/1.13
% 0.82/1.13 THEOREM PROVED
% 0.82/1.13 % SZS status Unsatisfiable
% 0.82/1.13
% 0.82/1.13 Exiting with 1 proof.
% 0.82/1.13
% 0.82/1.13 Process 18658 exit (max_proofs) Tue Jun 14 07:43:39 2022
% 0.82/1.13 Prover9 interrupted
%------------------------------------------------------------------------------