TSTP Solution File: GRP683-10 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP683-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 11:20:34 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
% 0.03/0.13 % Problem : GRP683-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jun 13 15:12:24 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.82/1.13 ============================== Prover9 ===============================
% 0.82/1.13 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.13 Process 24760 was started by sandbox2 on n025.cluster.edu,
% 0.82/1.13 Mon Jun 13 15:12:24 2022
% 0.82/1.13 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24604_n025.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_24604_n025.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 (8 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 goal to answer in negative clause
% 0.82/1.13
% 0.82/1.13 Term ordering decisions:
% 0.82/1.13 Function symbol KB weights: x3=1. x4=1. x5=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 0.08 (+ 0.01) seconds: goal.
% 0.82/1.13 % Length of proof is 67.
% 0.82/1.13 % Level of proof is 18.
% 0.82/1.13 % Maximum clause weight is 35.000.
% 0.82/1.13 % Given clauses 62.
% 0.82/1.13
% 0.82/1.13 1 ld(A,mult(A,A)) = A # label(f01) # label(axiom). [assumption].
% 0.82/1.13 2 rd(mult(A,A),A) = A # label(f02) # label(axiom). [assumption].
% 0.82/1.13 3 mult(A,ld(A,B)) = ld(A,mult(A,B)) # label(f03) # label(axiom). [assumption].
% 0.82/1.13 4 ld(A,mult(A,B)) = mult(A,ld(A,B)). [copy(3),flip(a)].
% 0.82/1.13 5 mult(rd(A,B),B) = rd(mult(A,B),B) # label(f04) # label(axiom). [assumption].
% 0.82/1.13 6 rd(mult(A,B),B) = mult(rd(A,B),B). [copy(5),flip(a)].
% 0.82/1.13 7 ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) # label(f07) # label(axiom). [assumption].
% 0.82/1.13 8 mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))). [copy(7),rewrite([4(3),6(6)]),flip(a)].
% 0.82/1.13 9 ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) # label(f05) # label(axiom). [assumption].
% 0.82/1.13 10 mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D). [copy(9),rewrite([4(5),4(7)])].
% 0.82/1.13 11 rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) # label(f06) # label(axiom). [assumption].
% 0.82/1.13 12 mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)). [copy(11),rewrite([6(5),6(7)])].
% 0.82/1.13 13 mult(x3,ld(x4,mult(x4,x5))) != mult(x3,x5) # label(goal) # label(negated_conjecture) # answer(goal). [assumption].
% 0.82/1.13 14 mult(x3,mult(x4,ld(x4,x5))) != mult(x3,x5) # answer(goal). [copy(13),rewrite([4(6)])].
% 0.82/1.13 15 mult(A,ld(A,A)) = A. [back_rewrite(1),rewrite([4(2)])].
% 0.82/1.13 16 mult(rd(A,A),A) = A. [back_rewrite(2),rewrite([6(2)])].
% 0.82/1.13 19 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),mult(C,D)))) = ld(ld(A,B),mult(mult(A,ld(A,C)),D)). [para(10(a,1),4(a,1,2)),flip(a)].
% 0.82/1.13 20 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D). [para(4(a,1),10(a,1,1)),rewrite([4(4)])].
% 0.82/1.13 27 mult(rd(mult(A,B),mult(rd(C,D),D)),mult(rd(C,D),D)) = mult(A,mult(rd(B,D),D)). [para(6(a,1),12(a,1,1,2)),rewrite([6(6)])].
% 0.82/1.13 33 mult(A,ld(A,ld(A,A))) = ld(A,A). [para(15(a,1),4(a,1,2)),flip(a)].
% 0.82/1.13 34 mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)). [para(15(a,1),6(a,1,1)),flip(a)].
% 0.82/1.13 36 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)). [para(15(a,1),12(a,1,1,1))].
% 0.82/1.13 38 rd(A,A) = ld(A,A). [para(16(a,1),6(a,1,1)),rewrite([8(4),33(4)])].
% 0.82/1.13 39 mult(ld(A,A),A) = A. [para(16(a,1),6(a,2)),rewrite([6(2),38(1)])].
% 0.82/1.13 40 mult(A,ld(A,ld(ld(A,A),ld(A,A)))) = ld(A,A). [para(16(a,1),8(a,1)),rewrite([38(1),38(2),38(3)]),flip(a)].
% 0.82/1.13 41 mult(ld(A,B),ld(ld(A,B),C)) = mult(mult(A,ld(A,ld(C,C))),C). [para(16(a,1),10(a,1,2,2)),rewrite([38(5)])].
% 0.82/1.13 48 mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))). [back_rewrite(8),rewrite([38(1)])].
% 0.82/1.13 49 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))). [back_rewrite(36),rewrite([48(7)])].
% 0.82/1.13 51 mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D)))) = ld(mult(A,ld(A,B)),mult(mult(A,ld(A,C)),D)). [para(4(a,1),19(a,1,1)),rewrite([4(4),4(6),4(12)])].
% 0.82/1.13 59 ld(ld(A,B),mult(mult(A,ld(A,ld(C,C))),C)) = mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))). [para(39(a,1),19(a,1,2,2,2)),flip(a)].
% 0.82/1.13 76 mult(mult(A,ld(A,B)),C) = mult(A,ld(A,mult(B,C))). [para(15(a,1),20(a,1,1)),rewrite([15(2)]),flip(a)].
% 0.82/1.13 77 mult(A,ld(A,mult(B,ld(mult(A,ld(A,B)),C)))) = mult(A,ld(A,C)). [para(15(a,1),20(a,1,2,2)),rewrite([76(6),76(10),15(8)])].
% 0.82/1.13 78 mult(A,mult(A,ld(A,B))) = mult(A,B). [para(15(a,1),20(a,2,1)),rewrite([76(7),77(7),4(2)])].
% 0.82/1.13 80 mult(A,ld(A,mult(ld(A,A),B))) = mult(ld(A,A),B). [para(33(a,1),20(a,2,1)),rewrite([76(8),77(8)])].
% 0.82/1.13 90 mult(ld(A,B),ld(ld(A,B),ld(ld(A,B),C))) = ld(ld(A,B),mult(A,ld(A,C))). [back_rewrite(59),rewrite([76(5),39(3)]),flip(a)].
% 0.82/1.13 95 ld(mult(A,ld(A,B)),mult(A,ld(A,mult(C,D)))) = mult(A,ld(A,ld(mult(A,ld(A,B)),mult(C,D)))). [back_rewrite(51),rewrite([76(10),77(10),76(11)]),flip(a)].
% 0.82/1.13 97 mult(ld(A,B),ld(ld(A,B),C)) = mult(A,ld(A,C)). [back_rewrite(41),rewrite([76(8),39(6)])].
% 0.82/1.13 102 mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)). [back_rewrite(49),rewrite([78(8)])].
% 0.82/1.13 103 ld(ld(A,B),mult(A,ld(A,C))) = mult(A,ld(A,ld(ld(A,B),C))). [back_rewrite(90),rewrite([97(6)]),flip(a)].
% 0.82/1.13 111 mult(mult(A,B),ld(C,C)) = mult(A,mult(rd(B,C),C)). [back_rewrite(12),rewrite([102(5)])].
% 0.82/1.13 132 mult(A,ld(A,ld(mult(A,ld(A,B)),mult(B,C)))) = mult(A,ld(A,C)). [para(76(a,1),4(a,1,2)),rewrite([95(6),76(12),77(12)])].
% 0.82/1.13 133 mult(A,ld(A,mult(mult(A,B),C))) = mult(mult(A,B),C). [para(4(a,1),76(a,1,1,2)),rewrite([78(3)]),flip(a)].
% 0.82/1.13 145 ld(ld(A,A),ld(A,A)) = ld(A,A). [para(33(a,1),80(a,1,2,2)),rewrite([40(5),33(8)]),flip(a)].
% 0.82/1.13 155 mult(A,mult(rd(B,ld(C,C)),ld(C,C))) = mult(A,mult(rd(B,C),C)). [para(34(a,1),27(a,1,1,2)),rewrite([34(8),102(7),145(4),111(3)]),flip(a)].
% 0.82/1.13 180 mult(A,ld(A,ld(A,B))) = ld(A,B). [para(97(a,1),15(a,1))].
% 0.82/1.13 188 mult(A,ld(A,ld(mult(A,ld(A,B)),C))) = ld(mult(A,ld(A,B)),C). [para(180(a,1),76(a,1)),rewrite([77(12)]),flip(a)].
% 0.82/1.13 189 mult(A,ld(A,ld(ld(A,B),C))) = ld(ld(A,B),C). [para(180(a,1),97(a,1)),flip(a)].
% 0.82/1.13 190 ld(mult(A,ld(A,B)),mult(B,C)) = mult(A,ld(A,C)). [back_rewrite(132),rewrite([188(6)])].
% 0.82/1.13 192 ld(ld(A,B),mult(A,ld(A,C))) = ld(ld(A,B),C). [back_rewrite(103),rewrite([189(8)])].
% 0.82/1.13 201 mult(rd(A,ld(B,B)),ld(B,B)) = mult(A,ld(B,B)). [para(38(a,1),102(a,1,1,2)),rewrite([38(3)])].
% 0.82/1.13 204 mult(ld(A,A),ld(B,B)) = mult(A,ld(A,ld(B,B))). [para(48(a,1),102(a,2)),rewrite([102(7),201(5),145(6)])].
% 0.82/1.13 208 mult(A,mult(rd(B,C),C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(155),rewrite([201(4)]),flip(a)].
% 0.82/1.13 210 rd(A,ld(A,A)) = A. [back_rewrite(34),rewrite([201(4),15(2)]),flip(a)].
% 0.82/1.13 249 mult(mult(A,B),ld(C,C)) = mult(A,mult(B,ld(C,C))). [back_rewrite(111),rewrite([208(6)])].
% 0.82/1.13 253 mult(rd(A,B),B) = mult(A,ld(B,B)). [para(210(a,1),102(a,1,1,2)),rewrite([210(3),145(5)])].
% 0.82/1.13 272 rd(mult(A,B),B) = mult(A,ld(B,B)). [back_rewrite(6),rewrite([253(4)])].
% 0.82/1.13 287 mult(mult(A,ld(B,B)),B) = mult(A,B). [para(272(a,1),253(a,1,1)),rewrite([249(6),15(5)])].
% 0.82/1.13 296 ld(A,mult(B,ld(mult(A,ld(A,B)),C))) = ld(A,C). [para(77(a,1),4(a,1,2)),rewrite([4(3),180(3),180(8)]),flip(a)].
% 0.82/1.13 337 ld(mult(A,ld(A,B)),B) = mult(A,ld(A,ld(B,B))). [para(15(a,1),190(a,1,2))].
% 0.82/1.13 339 mult(A,ld(A,mult(B,ld(B,C)))) = mult(A,ld(A,C)). [para(78(a,1),190(a,1,2)),rewrite([190(4)]),flip(a)].
% 0.82/1.13 360 ld(mult(A,ld(A,B)),mult(A,ld(A,C))) = ld(mult(A,ld(A,B)),C). [para(4(a,1),192(a,1,1)),rewrite([4(7)])].
% 0.82/1.13 368 mult(ld(A,A),B) = mult(A,ld(A,B)). [para(204(a,1),287(a,1,1)),rewrite([76(4),39(2)]),flip(a)].
% 0.82/1.13 369 ld(ld(A,A),B) = mult(A,ld(A,B)). [para(204(a,1),133(a,1,2,2,1)),rewrite([76(6),368(4),339(6),192(5),368(4),189(4),368(5),76(6),368(4),339(6)])].
% 0.82/1.13 384 ld(mult(A,ld(A,ld(B,B))),C) = mult(A,ld(A,C)). [para(76(a,1),369(a,2)),rewrite([360(5),337(3),296(9)])].
% 0.82/1.13 443 ld(A,mult(B,ld(B,C))) = ld(A,C). [para(368(a,1),296(a,1,2)),rewrite([384(4),339(4)])].
% 0.82/1.13 449 mult(A,mult(B,ld(B,C))) = mult(A,C). [para(443(a,1),78(a,1,2,2)),rewrite([78(3)]),flip(a)].
% 0.82/1.13 450 $F # answer(goal). [resolve(449,a,14,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=62. Generated=1985. Kept=443. proofs=1.
% 0.82/1.13 Usable=30. Sos=121. Demods=150. Limbo=0, Disabled=299. Hints=0.
% 0.82/1.13 Megabytes=0.55.
% 0.82/1.13 User_CPU=0.08, 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 24760 exit (max_proofs) Mon Jun 13 15:12:24 2022
% 0.82/1.13 Prover9 interrupted
%------------------------------------------------------------------------------