TSTP Solution File: GRP752-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP752-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 11:20:55 EDT 2022
% Result : Unsatisfiable 11.42s 11.70s
% Output : Refutation 11.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : GRP752-1 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 09:16:51 EDT 2022
% 0.12/0.33 % CPUTime :
% 11.42/11.70 ============================== Prover9 ===============================
% 11.42/11.70 Prover9 (32) version 2009-11A, November 2009.
% 11.42/11.70 Process 24986 was started by sandbox2 on n014.cluster.edu,
% 11.42/11.70 Tue Jun 14 09:16:52 2022
% 11.42/11.70 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24833_n014.cluster.edu".
% 11.42/11.70 ============================== end of head ===========================
% 11.42/11.70
% 11.42/11.70 ============================== INPUT =================================
% 11.42/11.70
% 11.42/11.70 % Reading from file /tmp/Prover9_24833_n014.cluster.edu
% 11.42/11.70
% 11.42/11.70 set(prolog_style_variables).
% 11.42/11.70 set(auto2).
% 11.42/11.70 % set(auto2) -> set(auto).
% 11.42/11.70 % set(auto) -> set(auto_inference).
% 11.42/11.70 % set(auto) -> set(auto_setup).
% 11.42/11.70 % set(auto_setup) -> set(predicate_elim).
% 11.42/11.70 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.42/11.70 % set(auto) -> set(auto_limits).
% 11.42/11.70 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.42/11.70 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.42/11.70 % set(auto) -> set(auto_denials).
% 11.42/11.70 % set(auto) -> set(auto_process).
% 11.42/11.70 % set(auto2) -> assign(new_constants, 1).
% 11.42/11.70 % set(auto2) -> assign(fold_denial_max, 3).
% 11.42/11.70 % set(auto2) -> assign(max_weight, "200.000").
% 11.42/11.70 % set(auto2) -> assign(max_hours, 1).
% 11.42/11.70 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.42/11.70 % set(auto2) -> assign(max_seconds, 0).
% 11.42/11.70 % set(auto2) -> assign(max_minutes, 5).
% 11.42/11.70 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.42/11.70 % set(auto2) -> set(sort_initial_sos).
% 11.42/11.70 % set(auto2) -> assign(sos_limit, -1).
% 11.42/11.70 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.42/11.70 % set(auto2) -> assign(max_megs, 400).
% 11.42/11.70 % set(auto2) -> assign(stats, some).
% 11.42/11.70 % set(auto2) -> clear(echo_input).
% 11.42/11.70 % set(auto2) -> set(quiet).
% 11.42/11.70 % set(auto2) -> clear(print_initial_clauses).
% 11.42/11.70 % set(auto2) -> clear(print_given).
% 11.42/11.70 assign(lrs_ticks,-1).
% 11.42/11.70 assign(sos_limit,10000).
% 11.42/11.70 assign(order,kbo).
% 11.42/11.70 set(lex_order_vars).
% 11.42/11.70 clear(print_given).
% 11.42/11.70
% 11.42/11.70 % formulas(sos). % not echoed (8 formulas)
% 11.42/11.70
% 11.42/11.70 ============================== end of input ==========================
% 11.42/11.70
% 11.42/11.70 % From the command line: assign(max_seconds, 300).
% 11.42/11.70
% 11.42/11.70 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.42/11.70
% 11.42/11.70 % Formulas that are not ordinary clauses:
% 11.42/11.70
% 11.42/11.70 ============================== end of process non-clausal formulas ===
% 11.42/11.70
% 11.42/11.70 ============================== PROCESS INITIAL CLAUSES ===============
% 11.42/11.70
% 11.42/11.70 ============================== PREDICATE ELIMINATION =================
% 11.42/11.70
% 11.42/11.70 ============================== end predicate elimination =============
% 11.42/11.70
% 11.42/11.70 Auto_denials:
% 11.42/11.70 % copying label goals to answer in negative clause
% 11.42/11.70
% 11.42/11.70 Term ordering decisions:
% 11.42/11.70 Function symbol KB weights: a=1. b=1. c=1. mult=1. ld=1. rd=1.
% 11.42/11.70
% 11.42/11.70 ============================== end of process initial clauses ========
% 11.42/11.70
% 11.42/11.70 ============================== CLAUSES FOR SEARCH ====================
% 11.42/11.70
% 11.42/11.70 ============================== end of clauses for search =============
% 11.42/11.70
% 11.42/11.70 ============================== SEARCH ================================
% 11.42/11.70
% 11.42/11.70 % Starting search at 0.01 seconds.
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=79.000, iters=3358
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=71.000, iters=3559
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=67.000, iters=3555
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=59.000, iters=3338
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=55.000, iters=3503
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=51.000, iters=3399
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=47.000, iters=3448
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=43.000, iters=3374
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=39.000, iters=3335
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=35.000, iters=3336
% 11.42/11.70
% 11.42/11.70 Low Water (displace): id=6156, wt=83.000
% 11.42/11.70
% 11.42/11.70 Low Water (displace): id=13950, wt=31.000
% 11.42/11.70
% 11.42/11.70 Low Water (displace): id=14051, wt=27.000
% 11.42/11.70
% 11.42/11.70 Low Water (displace): id=14054, wt=23.000
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=31.000, iters=3350
% 11.42/11.70
% 11.42/11.70 Low Water (displace): id=18487, wt=19.000
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=27.000, iters=3342
% 11.42/11.70
% 11.42/11.70 Low Water (keep): wt=23.000, iters=3371
% 11.42/11.70
% 11.42/11.70 ============================== PROOF =================================
% 11.42/11.70 % SZS status Unsatisfiable
% 11.42/11.70 % SZS output start Refutation
% 11.42/11.70
% 11.42/11.70 % Proof 1 at 10.56 (+ 0.18) seconds: goals.
% 11.42/11.70 % Length of proof is 77.
% 11.42/11.70 % Level of proof is 16.
% 11.42/11.70 % Maximum clause weight is 23.000.
% 11.42/11.70 % Given clauses 421.
% 11.42/11.70
% 11.42/11.70 1 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 11.42/11.70 2 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 11.42/11.70 3 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 11.42/11.70 4 rd(mult(A,B),B) = A # label(f04) # label(axiom). [assumption].
% 11.42/11.70 5 mult(mult(A,A),mult(B,C)) = mult(mult(A,B),mult(A,C)) # label(f06) # label(axiom). [assumption].
% 11.42/11.70 6 mult(mult(A,B),mult(A,C)) = mult(mult(A,A),mult(B,C)). [copy(5),flip(a)].
% 11.42/11.70 7 mult(mult(A,B),mult(C,C)) = mult(mult(A,C),mult(B,C)) # label(f07) # label(axiom). [assumption].
% 11.42/11.70 8 mult(mult(A,mult(A,A)),mult(B,C)) = mult(mult(A,B),mult(mult(A,A),C)) # label(f05) # label(axiom). [assumption].
% 11.42/11.70 9 mult(mult(a,b),c) != mult(mult(a,c),mult(b,ld(c,c))) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 11.42/11.70 10 mult(mult(a,c),mult(b,ld(c,c))) != mult(mult(a,b),c) # answer(goals). [copy(9),flip(a)].
% 11.42/11.70 11 ld(rd(A,B),A) = B. [para(3(a,1),2(a,1,2))].
% 11.42/11.70 12 rd(A,ld(B,A)) = B. [para(1(a,1),4(a,1,1))].
% 11.42/11.70 13 mult(mult(A,A),mult(ld(A,B),C)) = mult(B,mult(A,C)). [para(1(a,1),6(a,1,1)),flip(a)].
% 11.42/11.70 14 mult(mult(A,A),mult(B,ld(A,C))) = mult(mult(A,B),C). [para(1(a,1),6(a,1,2)),flip(a)].
% 11.42/11.70 15 mult(mult(A,B),mult(A,ld(B,C))) = mult(mult(A,A),C). [para(1(a,1),6(a,2,2))].
% 11.42/11.70 31 mult(mult(A,B),mult(ld(A,C),B)) = mult(C,mult(B,B)). [para(1(a,1),7(a,1,1)),flip(a)].
% 11.42/11.70 34 ld(mult(A,B),mult(mult(A,C),mult(B,C))) = mult(C,C). [para(7(a,1),2(a,1,2))].
% 11.42/11.70 36 mult(mult(rd(A,B),C),mult(B,C)) = mult(A,mult(C,C)). [para(3(a,1),7(a,1,1)),flip(a)].
% 11.42/11.70 37 mult(mult(rd(A,B),C),mult(B,B)) = mult(A,mult(C,B)). [para(3(a,1),7(a,2,1))].
% 11.42/11.70 63 ld(mult(A,mult(A,A)),mult(mult(A,B),mult(mult(A,A),C))) = mult(B,C). [para(8(a,1),2(a,1,2))].
% 11.42/11.70 98 mult(A,mult(B,ld(ld(B,A),C))) = mult(mult(B,B),C). [para(1(a,1),13(a,1,2)),flip(a)].
% 11.42/11.70 99 ld(mult(A,A),mult(B,mult(A,C))) = mult(ld(A,B),C). [para(13(a,1),2(a,1,2))].
% 11.42/11.70 100 rd(mult(A,mult(B,C)),mult(ld(B,A),C)) = mult(B,B). [para(13(a,1),4(a,1,1))].
% 11.42/11.70 115 mult(mult(A,rd(B,ld(A,C))),C) = mult(mult(A,A),B). [para(3(a,1),14(a,1,2)),flip(a)].
% 11.42/11.70 116 rd(mult(mult(A,B),C),mult(B,ld(A,C))) = mult(A,A). [para(14(a,1),4(a,1,1))].
% 11.42/11.70 205 ld(mult(A,B),mult(C,mult(B,B))) = mult(ld(A,C),B). [para(31(a,1),2(a,1,2))].
% 11.42/11.70 234 ld(mult(A,rd(B,C)),mult(mult(A,C),B)) = mult(C,C). [para(3(a,1),34(a,1,2,2))].
% 11.42/11.70 266 rd(mult(A,mult(B,B)),mult(C,B)) = mult(rd(A,C),B). [para(36(a,1),4(a,1,1))].
% 11.42/11.70 423 rd(mult(A,mult(B,C)),mult(C,C)) = mult(rd(A,C),B). [para(37(a,1),4(a,1,1))].
% 11.42/11.70 466 ld(A,mult(mult(B,B),C)) = mult(B,ld(ld(B,A),C)). [para(98(a,1),2(a,1,2))].
% 11.42/11.70 498 ld(mult(A,A),mult(B,C)) = mult(ld(A,B),ld(A,C)). [para(1(a,1),99(a,1,2,2))].
% 11.42/11.70 499 mult(ld(A,rd(B,mult(A,C))),C) = ld(mult(A,A),B). [para(3(a,1),99(a,1,2)),flip(a)].
% 11.42/11.70 688 mult(rd(mult(A,B),ld(B,mult(A,C))),C) = mult(B,B). [para(7(a,2),100(a,1,1)),rewrite([266(7)])].
% 11.42/11.70 712 rd(mult(mult(A,A),B),C) = mult(A,rd(B,ld(A,C))). [para(115(a,1),4(a,1,1))].
% 11.42/11.70 748 rd(A,mult(B,ld(C,ld(mult(C,B),A)))) = mult(C,C). [para(1(a,1),116(a,1,1))].
% 11.42/11.70 781 ld(A,mult(B,mult(C,C))) = mult(ld(rd(A,C),B),C). [para(3(a,1),205(a,1,1))].
% 11.42/11.70 1081 mult(A,ld(rd(mult(A,B),C),mult(C,B))) = mult(C,C). [para(6(a,1),234(a,1,2)),rewrite([466(7),2(4)])].
% 11.42/11.70 1391 rd(mult(A,B),mult(C,C)) = mult(rd(A,C),rd(B,C)). [para(3(a,1),423(a,1,1,2))].
% 11.42/11.70 1393 mult(rd(mult(A,B),C),A) = mult(rd(mult(A,A),C),B). [para(6(a,1),423(a,1,1)),rewrite([1391(5),4(4)]),flip(a)].
% 11.42/11.70 1396 mult(rd(mult(A,A),B),ld(A,C)) = mult(rd(C,B),A). [para(13(a,1),423(a,1,1)),rewrite([1391(4),4(3)]),flip(a)].
% 11.42/11.70 1416 ld(A,mult(mult(B,C),mult(B,D))) = mult(B,ld(ld(B,A),mult(C,D))). [para(6(a,2),466(a,1,2))].
% 11.42/11.70 1443 mult(ld(A,B),ld(A,ld(B,C))) = ld(mult(A,A),C). [para(1(a,1),498(a,1,2)),flip(a)].
% 11.42/11.70 1477 ld(mult(rd(A,B),rd(A,B)),C) = mult(ld(rd(A,B),rd(C,A)),B). [para(3(a,1),499(a,1,1,2,2)),flip(a)].
% 11.42/11.70 1478 rd(ld(mult(A,A),B),C) = ld(A,rd(B,mult(A,C))). [para(499(a,1),4(a,1,1))].
% 11.42/11.70 1816 mult(rd(A,ld(B,mult(rd(A,B),C))),C) = mult(B,B). [para(3(a,1),688(a,1,1,1))].
% 11.42/11.70 1818 rd(mult(A,B),ld(B,mult(A,C))) = rd(mult(B,B),C). [para(688(a,1),4(a,1,1)),flip(a)].
% 11.42/11.70 1883 rd(mult(mult(A,B),mult(A,C)),D) = mult(A,rd(mult(B,C),ld(A,D))). [para(6(a,2),712(a,1,1))].
% 11.42/11.70 1925 rd(A,mult(B,ld(rd(C,B),ld(C,A)))) = mult(rd(C,B),rd(C,B)). [para(3(a,1),748(a,1,2,2,2,1))].
% 11.42/11.70 2340 ld(rd(mult(A,B),C),mult(C,B)) = ld(A,mult(C,C)). [para(1081(a,1),2(a,1,2)),flip(a)].
% 11.42/11.70 3024 mult(rd(mult(rd(A,B),rd(A,B)),C),B) = mult(rd(A,C),rd(A,B)). [para(3(a,1),1393(a,1,1,1)),flip(a)].
% 11.42/11.70 3025 rd(mult(rd(mult(A,A),B),C),A) = rd(mult(A,C),B). [para(1393(a,1),4(a,1,1))].
% 11.42/11.70 3026 rd(mult(rd(mult(A,B),C),A),B) = rd(mult(A,A),C). [para(1393(a,2),4(a,1,1))].
% 11.42/11.70 3359 mult(ld(rd(A,B),rd(C,A)),B) = mult(B,ld(rd(A,B),ld(A,C))). [para(11(a,1),1443(a,1,1)),rewrite([1477(8)]),flip(a)].
% 11.42/11.70 3688 mult(mult(rd(A,B),rd(A,C)),mult(B,C)) = mult(A,A). [para(1816(a,1),36(a,2)),rewrite([781(4),3359(4),1925(5),3024(5)])].
% 11.42/11.70 4096 ld(rd(mult(A,A),B),mult(C,A)) = ld(A,mult(C,B)). [para(1818(a,1),11(a,1,1))].
% 11.42/11.70 7072 rd(mult(A,ld(B,C)),ld(B,D)) = ld(B,rd(mult(mult(B,A),C),D)). [para(3025(a,1),1478(a,2,2)),rewrite([1883(5),498(7),2(5),3025(6)])].
% 11.42/11.70 7103 rd(mult(A,A),ld(B,mult(A,C))) = rd(mult(B,A),C). [para(12(a,1),3026(a,1,1,1)),flip(a)].
% 11.42/11.70 7134 ld(rd(mult(A,B),C),mult(B,B)) = ld(A,mult(B,C)). [para(3026(a,1),2340(a,1,1)),rewrite([4096(4)]),flip(a)].
% 11.42/11.70 8937 rd(mult(A,A),mult(B,C)) = mult(rd(A,B),rd(A,C)). [para(3688(a,1),4(a,1,1))].
% 11.42/11.70 11346 mult(rd(mult(A,B),ld(rd(C,B),mult(A,D))),A) = rd(mult(C,mult(A,B)),mult(D,B)). [para(7(a,2),7103(a,1,2,2)),rewrite([781(7),8937(8),4(7)])].
% 11.42/11.70 11376 mult(rd(A,ld(B,mult(C,D))),C) = mult(rd(mult(B,C),D),ld(C,A)). [para(7103(a,1),1396(a,1,1)),flip(a)].
% 11.42/11.70 11427 rd(mult(A,mult(B,C)),mult(D,C)) = mult(rd(mult(rd(A,C),B),D),C). [back_rewrite(11346),rewrite([11376(6),2(5)]),flip(a)].
% 11.42/11.70 11458 ld(mult(A,B),mult(mult(A,C),D)) = mult(A,ld(B,mult(C,ld(A,D)))). [para(6(a,1),7134(a,1,1,1)),rewrite([712(4),1416(8),2(5),7134(5)]),flip(a)].
% 11.42/11.70 11547 mult(A,mult(ld(A,B),ld(ld(A,A),C))) = mult(B,C). [back_rewrite(63),rewrite([11458(7),466(4),498(6),2(5)])].
% 11.42/11.70 13209 mult(ld(A,B),ld(ld(A,A),C)) = ld(A,mult(B,C)). [para(11547(a,1),2(a,1,2)),flip(a)].
% 11.42/11.70 13210 mult(A,mult(B,ld(ld(A,A),C))) = mult(mult(A,B),C). [para(2(a,1),11547(a,1,2,1))].
% 11.42/11.70 13211 mult(A,mult(ld(B,B),C)) = mult(B,mult(ld(B,A),C)). [para(2(a,1),11547(a,1,2,2)),flip(a)].
% 11.42/11.70 14136 ld(A,mult(B,mult(ld(A,A),C))) = mult(ld(A,B),C). [para(2(a,1),13209(a,1,2)),flip(a)].
% 11.42/11.70 14239 mult(mult(A,B),mult(ld(A,A),C)) = mult(A,mult(B,C)). [para(2(a,1),13210(a,1,2,2)),flip(a)].
% 11.42/11.70 14367 mult(ld(A,rd(mult(mult(A,rd(A,B)),C),A)),B) = C. [para(13211(a,1),4(a,1,1)),rewrite([11427(6),7072(5)])].
% 11.42/11.70 16204 ld(mult(A,B),mult(A,mult(B,C))) = mult(ld(A,A),C). [para(14239(a,1),2(a,1,2))].
% 11.42/11.70 16483 mult(rd(A,ld(B,B)),C) = mult(B,ld(rd(B,C),A)). [para(15(a,1),14367(a,1,1,2,1)),rewrite([712(3),2(4)])].
% 11.42/11.70 20653 ld(mult(A,B),mult(A,C)) = mult(ld(A,A),ld(B,C)). [para(1(a,1),16204(a,1,2,2))].
% 11.42/11.70 20797 mult(A,ld(rd(A,B),mult(C,ld(A,A)))) = mult(C,B). [para(4(a,1),16483(a,1,1)),flip(a)].
% 11.42/11.70 27101 mult(mult(A,B),mult(ld(A,C),ld(B,B))) = mult(C,B). [para(4(a,1),20797(a,1,2,1)),rewrite([20653(4),14136(6)])].
% 11.42/11.70 31477 mult(mult(A,B),mult(C,ld(B,B))) = mult(mult(A,C),B). [para(2(a,1),27101(a,1,2,1))].
% 11.42/11.70 31478 $F # answer(goals). [resolve(31477,a,10,a)].
% 11.42/11.70
% 11.42/11.70 % SZS output end Refutation
% 11.42/11.70 ============================== end of proof ==========================
% 11.42/11.70
% 11.42/11.70 ============================== STATISTICS ============================
% 11.42/11.70
% 11.42/11.70 Given=421. Generated=290232. Kept=31475. proofs=1.
% 11.42/11.70 Usable=325. Sos=9910. Demods=8402. Limbo=0, Disabled=21247. Hints=0.
% 11.42/11.70 Megabytes=30.20.
% 11.42/11.70 User_CPU=10.57, System_CPU=0.18, Wall_clock=11.
% 11.42/11.70
% 11.42/11.70 ============================== end of statistics =====================
% 11.42/11.70
% 11.42/11.70 ============================== end of search =========================
% 11.42/11.70
% 11.42/11.70 THEOREM PROVED
% 11.42/11.70 % SZS status Unsatisfiable
% 11.42/11.70
% 11.42/11.70 Exiting with 1 proof.
% 11.42/11.70
% 11.42/11.70 Process 24986 exit (max_proofs) Tue Jun 14 09:17:03 2022
% 11.42/11.70 Prover9 interrupted
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