TSTP Solution File: GRP748-2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP748-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 11:20:53 EDT 2022
% Result : Unsatisfiable 6.66s 6.98s
% Output : Refutation 6.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP748-2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n016.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 : Mon Jun 13 13:06:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.00/4.29 ============================== Prover9 ===============================
% 4.00/4.29 Prover9 (32) version 2009-11A, November 2009.
% 4.00/4.29 Process 10105 was started by sandbox2 on n016.cluster.edu,
% 4.00/4.29 Mon Jun 13 13:06:15 2022
% 4.00/4.29 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_9952_n016.cluster.edu".
% 4.00/4.29 ============================== end of head ===========================
% 4.00/4.29
% 4.00/4.29 ============================== INPUT =================================
% 4.00/4.29
% 4.00/4.29 % Reading from file /tmp/Prover9_9952_n016.cluster.edu
% 4.00/4.29
% 4.00/4.29 set(prolog_style_variables).
% 4.00/4.29 set(auto2).
% 4.00/4.29 % set(auto2) -> set(auto).
% 4.00/4.29 % set(auto) -> set(auto_inference).
% 4.00/4.29 % set(auto) -> set(auto_setup).
% 4.00/4.29 % set(auto_setup) -> set(predicate_elim).
% 4.00/4.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.00/4.29 % set(auto) -> set(auto_limits).
% 4.00/4.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.00/4.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.00/4.29 % set(auto) -> set(auto_denials).
% 4.00/4.29 % set(auto) -> set(auto_process).
% 4.00/4.29 % set(auto2) -> assign(new_constants, 1).
% 4.00/4.29 % set(auto2) -> assign(fold_denial_max, 3).
% 4.00/4.29 % set(auto2) -> assign(max_weight, "200.000").
% 4.00/4.29 % set(auto2) -> assign(max_hours, 1).
% 4.00/4.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.00/4.29 % set(auto2) -> assign(max_seconds, 0).
% 4.00/4.29 % set(auto2) -> assign(max_minutes, 5).
% 4.00/4.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.00/4.29 % set(auto2) -> set(sort_initial_sos).
% 4.00/4.29 % set(auto2) -> assign(sos_limit, -1).
% 4.00/4.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.00/4.29 % set(auto2) -> assign(max_megs, 400).
% 4.00/4.29 % set(auto2) -> assign(stats, some).
% 4.00/4.29 % set(auto2) -> clear(echo_input).
% 4.00/4.29 % set(auto2) -> set(quiet).
% 4.00/4.29 % set(auto2) -> clear(print_initial_clauses).
% 4.00/4.29 % set(auto2) -> clear(print_given).
% 4.00/4.29 assign(lrs_ticks,-1).
% 4.00/4.29 assign(sos_limit,10000).
% 4.00/4.29 assign(order,kbo).
% 4.00/4.29 set(lex_order_vars).
% 4.00/4.29 clear(print_given).
% 4.00/4.29
% 4.00/4.29 % formulas(sos). % not echoed (12 formulas)
% 4.00/4.29
% 4.00/4.29 ============================== end of input ==========================
% 4.00/4.29
% 4.00/4.29 % From the command line: assign(max_seconds, 300).
% 4.00/4.29
% 4.00/4.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.00/4.29
% 4.00/4.29 % Formulas that are not ordinary clauses:
% 4.00/4.29
% 4.00/4.29 ============================== end of process non-clausal formulas ===
% 4.00/4.29
% 4.00/4.29 ============================== PROCESS INITIAL CLAUSES ===============
% 4.00/4.29
% 4.00/4.29 ============================== PREDICATE ELIMINATION =================
% 4.00/4.29
% 4.00/4.29 ============================== end predicate elimination =============
% 4.00/4.29
% 4.00/4.29 Auto_denials: (non-Horn, no changes).
% 4.00/4.29
% 4.00/4.29 Term ordering decisions:
% 4.00/4.29
% 4.00/4.29 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 4.00/4.29 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 4.00/4.29
% 4.00/4.29 ============================== end of process initial clauses ========
% 4.00/4.29
% 4.00/4.29 ============================== CLAUSES FOR SEARCH ====================
% 4.00/4.29
% 4.00/4.29 ============================== end of clauses for search =============
% 4.00/4.29
% 4.00/4.29 ============================== SEARCH ================================
% 4.00/4.29
% 4.00/4.29 % Starting search at 0.01 seconds.
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=59.000, iters=3405
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=55.000, iters=3366
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=53.000, iters=3338
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=50.000, iters=3388
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=48.000, iters=3421
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=45.000, iters=3356
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=44.000, iters=3366
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=43.000, iters=3378
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=42.000, iters=3404
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=40.000, iters=3385
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=39.000, iters=3375
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=38.000, iters=3360
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=37.000, iters=3408
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=36.000, iters=3336
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=35.000, iters=3430
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=34.000, iters=3381
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=33.000, iters=3341
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=32.000, iters=3358
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=31.000, iters=3352
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=30.000, iters=3398
% 4.00/4.29
% 4.00/4.29 Low Water (keep): wt=29.000, iters=3342
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=2371, wt=109.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=2369, wt=101.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=2370, wt=97.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=2303, wt=95.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=5603, wt=93.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=6127, wt=89.000
% 4.00/4.29
% 4.00/4.29 Low Water (displace): id=5079, wt=87.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=6123, wt=85.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=5132, wt=83.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=4414, wt=81.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=11625, wt=28.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=11679, wt=25.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=11888, wt=24.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=11896, wt=23.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=12061, wt=22.000
% 6.66/6.98
% 6.66/6.98 Low Water (displace): id=12063, wt=21.000
% 6.66/6.98
% 6.66/6.98 Low Water (keep): wt=28.000, iters=3341
% 6.66/6.98
% 6.66/6.98 Low Water (keep): wt=26.000, iters=3506
% 6.66/6.98
% 6.66/6.98 ============================== PROOF =================================
% 6.66/6.98 % SZS status Unsatisfiable
% 6.66/6.98 % SZS output start Refutation
% 6.66/6.98
% 6.66/6.98 % Proof 1 at 5.98 (+ 0.04) seconds.
% 6.66/6.98 % Length of proof is 53.
% 6.66/6.98 % Level of proof is 14.
% 6.66/6.98 % Maximum clause weight is 24.000.
% 6.66/6.98 % Given clauses 271.
% 6.66/6.98
% 6.66/6.98 2 mult(unit,A) = A # label(f06) # label(axiom). [assumption].
% 6.66/6.98 3 mult(A,i(A)) = unit # label(f09) # label(axiom). [assumption].
% 6.66/6.98 4 mult(i(A),A) = unit # label(f10) # label(axiom). [assumption].
% 6.66/6.98 5 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [assumption].
% 6.66/6.98 6 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [assumption].
% 6.66/6.98 7 mult(rd(A,B),B) = A # label(f03) # label(axiom). [assumption].
% 6.66/6.98 9 mult(mult(A,B),i(B)) = A # label(f08) # label(axiom). [assumption].
% 6.66/6.98 10 mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) # label(f07) # label(axiom). [assumption].
% 6.66/6.98 11 mult(A,B) = mult(B,A) | mult(i(A),mult(A,B)) = B # label(f11) # label(axiom). [assumption].
% 6.66/6.98 12 mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c) # label(goals) # label(negated_conjecture). [assumption].
% 6.66/6.98 13 mult(mult(mult(a,b),a),c) != mult(a,mult(b,mult(a,c))). [copy(12),flip(a)].
% 6.66/6.98 17 ld(A,unit) = i(A). [para(3(a,1),6(a,1,2))].
% 6.66/6.98 18 i(i(A)) = A. [para(4(a,1),6(a,1,2)),rewrite([17(3)])].
% 6.66/6.98 25 mult(A,i(ld(B,A))) = B. [para(5(a,1),9(a,1,1))].
% 6.66/6.98 27 rd(A,B) = mult(A,i(B)). [para(7(a,1),9(a,1,1)),flip(a)].
% 6.66/6.98 28 mult(mult(A,i(B)),B) = A. [back_rewrite(7),rewrite([27(1)])].
% 6.66/6.98 30 mult(A,mult(mult(i(A),B),i(A))) = mult(B,i(A)). [para(3(a,1),10(a,1,1,1)),rewrite([2(2)]),flip(a)].
% 6.66/6.98 31 mult(A,mult(mult(B,i(mult(A,B))),B)) = B. [para(3(a,1),10(a,1,1)),rewrite([2(2)]),flip(a)].
% 6.66/6.98 32 mult(i(A),mult(mult(A,B),A)) = mult(B,A). [para(4(a,1),10(a,1,1,1)),rewrite([2(2)]),flip(a)].
% 6.66/6.98 34 mult(A,mult(mult(B,ld(mult(A,B),C)),B)) = mult(C,B). [para(5(a,1),10(a,1,1)),flip(a)].
% 6.66/6.98 36 mult(mult(A,mult(mult(B,C),B)),i(B)) = mult(mult(A,B),C). [para(10(a,1),9(a,1,1))].
% 6.66/6.98 41 mult(ld(A,B),A) = B | ld(A,B) = mult(i(A),B). [para(5(a,1),11(b,1,2)),rewrite([5(2)]),flip(a),flip(b)].
% 6.66/6.98 49 i(ld(A,B)) = ld(B,A). [para(25(a,1),6(a,1,2)),flip(a)].
% 6.66/6.98 116 mult(mult(A,i(mult(B,A))),A) = ld(B,A). [para(31(a,1),6(a,1,2)),flip(a)].
% 6.66/6.98 121 mult(ld(A,B),A) = mult(i(A),mult(B,A)). [para(5(a,1),32(a,1,2,1)),flip(a)].
% 6.66/6.98 123 ld(i(A),mult(B,A)) = mult(mult(A,B),A). [para(32(a,1),6(a,1,2))].
% 6.66/6.98 137 mult(i(A),mult(B,A)) = B | ld(A,B) = mult(i(A),B). [back_rewrite(41),rewrite([121(2)])].
% 6.66/6.98 198 mult(ld(A,i(B)),B) = mult(i(B),i(mult(A,i(B)))). [para(116(a,1),28(a,1,1))].
% 6.66/6.98 282 mult(mult(A,ld(mult(B,A),C)),A) = ld(B,mult(C,A)). [para(34(a,1),6(a,1,2)),flip(a)].
% 6.66/6.98 432 mult(mult(A,mult(B,C)),i(C)) = mult(mult(A,C),ld(C,B)). [para(5(a,1),36(a,1,1,2,1))].
% 6.66/6.98 1938 mult(ld(A,mult(B,C)),i(C)) = mult(C,ld(mult(A,C),B)). [para(282(a,1),9(a,1,1))].
% 6.66/6.98 1960 mult(ld(mult(A,B),C),B) = mult(i(B),ld(A,mult(C,B))). [para(282(a,1),32(a,1,2)),flip(a)].
% 6.66/6.98 3535 ld(A,B) = mult(i(A),B) | mult(A,mult(B,i(A))) = B. [para(137(a,1),30(a,1,2,1)),rewrite([9(10)])].
% 6.66/6.98 3547 ld(A,B) = mult(i(A),B) | ld(A,B) = mult(B,i(A)). [para(137(a,1),123(a,2,1)),rewrite([18(6),9(7)])].
% 6.66/6.98 7476 mult(ld(mult(i(A),i(mult(B,i(A)))),C),A) = mult(i(A),ld(ld(B,i(A)),mult(C,A))). [para(198(a,1),1960(a,1,1,1))].
% 6.66/6.98 9491 mult(mult(A,B),i(A)) = B | mult(i(A),mult(A,B)) = B. [para(3547(a,1),6(a,1)),rewrite([6(2)]),flip(a)].
% 6.66/6.98 9697 ld(i(A),B) = mult(A,B) | ld(A,mult(B,A)) = B. [para(3535(b,1),3547(a,2)),rewrite([18(4),18(6),18(9),18(11),9(12)]),merge(c)].
% 6.66/6.98 11551 mult(i(A),mult(A,B)) = B | ld(i(A),B) = mult(A,B). [para(9491(a,1),9697(b,1,2)),rewrite([18(6),6(6)]),flip(b),merge(b)].
% 6.66/6.98 12412 ld(i(A),B) = mult(A,B). [para(11551(a,1),6(a,1,2)),merge(b)].
% 6.66/6.98 13337 mult(mult(A,B),A) = mult(A,mult(B,A)). [back_rewrite(123),rewrite([12412(3)]),flip(a)].
% 6.66/6.98 14535 mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))). [back_rewrite(13),rewrite([13337(5)])].
% 6.66/6.98 14536 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [back_rewrite(10),rewrite([13337(5)])].
% 6.66/6.98 14787 mult(i(A),mult(A,B)) = B. [para(12412(a,1),5(a,1,2))].
% 6.66/6.98 14788 mult(A,mult(i(A),B)) = B. [para(12412(a,1),6(a,1))].
% 6.66/6.98 14789 ld(A,B) = mult(i(A),B). [para(18(a,1),12412(a,1,1))].
% 6.66/6.98 14790 i(mult(A,B)) = mult(i(B),i(A)). [para(12412(a,1),49(a,1,1)),rewrite([14789(4)])].
% 6.66/6.98 14797 mult(mult(i(A),B),A) = mult(i(A),mult(B,A)). [para(121(a,1),12412(a,2)),rewrite([14789(1),14790(3),18(3),14789(3),14790(3),18(3)])].
% 6.66/6.98 14821 mult(mult(A,B),mult(i(B),C)) = mult(B,mult(mult(i(B),A),C)). [para(12412(a,1),1938(a,1,1)),rewrite([432(4),14789(2),14789(7),14790(7),18(7)])].
% 6.66/6.98 15787 mult(i(A),mult(mult(A,B),mult(C,A))) = mult(mult(B,C),A). [back_rewrite(7476),rewrite([14790(4),18(3),14787(4),14789(2),18(2),14789(5),14789(8),14790(7),18(5),18(5)]),flip(a)].
% 6.66/6.98 18019 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(15787(a,1),14787(a,1,2)),rewrite([18(2)]),flip(a)].
% 6.66/6.98 18332 mult(mult(A,B),mult(mult(i(B),C),mult(A,B))) = mult(A,mult(C,mult(A,B))). [para(9(a,1),18019(a,1,1)),flip(a)].
% 6.66/6.98 18777 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [para(14821(a,1),13337(a,1,1)),rewrite([18019(6),14536(4),14797(5),14788(6),18332(9)])].
% 6.66/6.98 18778 $F. [resolve(18777,a,14535,a)].
% 6.66/6.98
% 6.66/6.98 % SZS output end Refutation
% 6.66/6.98 ============================== end of proof ==========================
% 6.66/6.98
% 6.66/6.98 ============================== STATISTICS ============================
% 6.66/6.98
% 6.66/6.98 Given=271. Generated=59646. Kept=18776. proofs=1.
% 6.66/6.98 Usable=50. Sos=2041. Demods=1962. Limbo=7, Disabled=16689. Hints=0.
% 6.66/6.98 Megabytes=18.57.
% 6.66/6.98 User_CPU=5.98, System_CPU=0.04, Wall_clock=6.
% 6.66/6.98
% 6.66/6.98 ============================== end of statistics =====================
% 6.66/6.98
% 6.66/6.98 ============================== end of search =========================
% 6.66/6.98
% 6.66/6.98 THEOREM PROVED
% 6.66/6.98 % SZS status Unsatisfiable
% 6.66/6.98
% 6.66/6.98 Exiting with 1 proof.
% 6.66/6.98
% 6.66/6.98 Process 10105 exit (max_proofs) Mon Jun 13 13:06:21 2022
% 6.66/6.98 Prover9 interrupted
%------------------------------------------------------------------------------