TSTP Solution File: GRP718-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP718-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 11:20:47 EDT 2022
% Result : Unsatisfiable 34.70s 34.97s
% Output : Refutation 34.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP718-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 11:42:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 11.93/12.20 ============================== Prover9 ===============================
% 11.93/12.20 Prover9 (32) version 2009-11A, November 2009.
% 11.93/12.20 Process 14084 was started by sandbox on n012.cluster.edu,
% 11.93/12.20 Tue Jun 14 11:42:26 2022
% 11.93/12.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13930_n012.cluster.edu".
% 11.93/12.20 ============================== end of head ===========================
% 11.93/12.20
% 11.93/12.20 ============================== INPUT =================================
% 11.93/12.20
% 11.93/12.20 % Reading from file /tmp/Prover9_13930_n012.cluster.edu
% 11.93/12.20
% 11.93/12.20 set(prolog_style_variables).
% 11.93/12.20 set(auto2).
% 11.93/12.20 % set(auto2) -> set(auto).
% 11.93/12.20 % set(auto) -> set(auto_inference).
% 11.93/12.20 % set(auto) -> set(auto_setup).
% 11.93/12.20 % set(auto_setup) -> set(predicate_elim).
% 11.93/12.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 11.93/12.20 % set(auto) -> set(auto_limits).
% 11.93/12.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 11.93/12.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 11.93/12.20 % set(auto) -> set(auto_denials).
% 11.93/12.20 % set(auto) -> set(auto_process).
% 11.93/12.20 % set(auto2) -> assign(new_constants, 1).
% 11.93/12.20 % set(auto2) -> assign(fold_denial_max, 3).
% 11.93/12.20 % set(auto2) -> assign(max_weight, "200.000").
% 11.93/12.20 % set(auto2) -> assign(max_hours, 1).
% 11.93/12.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 11.93/12.20 % set(auto2) -> assign(max_seconds, 0).
% 11.93/12.20 % set(auto2) -> assign(max_minutes, 5).
% 11.93/12.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 11.93/12.20 % set(auto2) -> set(sort_initial_sos).
% 11.93/12.20 % set(auto2) -> assign(sos_limit, -1).
% 11.93/12.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 11.93/12.20 % set(auto2) -> assign(max_megs, 400).
% 11.93/12.20 % set(auto2) -> assign(stats, some).
% 11.93/12.20 % set(auto2) -> clear(echo_input).
% 11.93/12.20 % set(auto2) -> set(quiet).
% 11.93/12.20 % set(auto2) -> clear(print_initial_clauses).
% 11.93/12.20 % set(auto2) -> clear(print_given).
% 11.93/12.20 assign(lrs_ticks,-1).
% 11.93/12.20 assign(sos_limit,10000).
% 11.93/12.20 assign(order,kbo).
% 11.93/12.20 set(lex_order_vars).
% 11.93/12.20 clear(print_given).
% 11.93/12.20
% 11.93/12.20 % formulas(sos). % not echoed (11 formulas)
% 11.93/12.20
% 11.93/12.20 ============================== end of input ==========================
% 11.93/12.20
% 11.93/12.20 % From the command line: assign(max_seconds, 300).
% 11.93/12.20
% 11.93/12.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 11.93/12.20
% 11.93/12.20 % Formulas that are not ordinary clauses:
% 11.93/12.20
% 11.93/12.20 ============================== end of process non-clausal formulas ===
% 11.93/12.20
% 11.93/12.20 ============================== PROCESS INITIAL CLAUSES ===============
% 11.93/12.20
% 11.93/12.20 ============================== PREDICATE ELIMINATION =================
% 11.93/12.20
% 11.93/12.20 ============================== end predicate elimination =============
% 11.93/12.20
% 11.93/12.20 Auto_denials:
% 11.93/12.20 % copying label goals to answer in negative clause
% 11.93/12.20
% 11.93/12.20 Term ordering decisions:
% 11.93/12.20
% 11.93/12.20 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 11.93/12.20 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 11.93/12.20
% 11.93/12.20 ============================== end of process initial clauses ========
% 11.93/12.20
% 11.93/12.20 ============================== CLAUSES FOR SEARCH ====================
% 11.93/12.20
% 11.93/12.20 ============================== end of clauses for search =============
% 11.93/12.20
% 11.93/12.20 ============================== SEARCH ================================
% 11.93/12.20
% 11.93/12.20 % Starting search at 0.01 seconds.
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=103.000, iters=3368
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=94.000, iters=3371
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=91.000, iters=3363
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=89.000, iters=3335
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=83.000, iters=3381
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=80.000, iters=3345
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=75.000, iters=3370
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=67.000, iters=3339
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=66.000, iters=3354
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=64.000, iters=3335
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=63.000, iters=3358
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=59.000, iters=3475
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=58.000, iters=3447
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=57.000, iters=3415
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=55.000, iters=3378
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=53.000, iters=3377
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=50.000, iters=3336
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=49.000, iters=3415
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=48.000, iters=3340
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=47.000, iters=3371
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=46.000, iters=3341
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=45.000, iters=3350
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=44.000, iters=3373
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=43.000, iters=3342
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=42.000, iters=3346
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=41.000, iters=3397
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=39.000, iters=3333
% 11.93/12.20
% 11.93/12.20 Low Water (keep): wt=38.000, iters=3369
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=37.000, iters=3336
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=36.000, iters=3333
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=35.000, iters=3341
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=34.000, iters=3338
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=33.000, iters=3390
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=7984, wt=187.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8029, wt=147.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8137, wt=139.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8136, wt=135.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8125, wt=131.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8206, wt=126.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=7819, wt=123.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=7960, wt=119.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=7957, wt=115.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=7959, wt=111.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=8305, wt=107.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=20554, wt=31.000
% 34.70/34.97
% 34.70/34.97 Low Water (keep): wt=32.000, iters=3333
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=20712, wt=30.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=20769, wt=29.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=20889, wt=28.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=20926, wt=26.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=21183, wt=25.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=21191, wt=24.000
% 34.70/34.97
% 34.70/34.97 Low Water (displace): id=21419, wt=21.000
% 34.70/34.97
% 34.70/34.97 ============================== PROOF =================================
% 34.70/34.97 % SZS status Unsatisfiable
% 34.70/34.97 % SZS output start Refutation
% 34.70/34.97
% 34.70/34.97 % Proof 1 at 33.82 (+ 0.18) seconds: goals.
% 34.70/34.97 % Length of proof is 135.
% 34.70/34.97 % Level of proof is 21.
% 34.70/34.97 % Maximum clause weight is 49.000.
% 34.70/34.97 % Given clauses 363.
% 34.70/34.97
% 34.70/34.97 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 34.70/34.97 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 34.70/34.97 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 34.70/34.97 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 34.70/34.97 7 mult(A,B) = mult(B,A) # label(c10) # label(axiom). [assumption].
% 34.70/34.97 8 mult(i(A),mult(A,B)) = B # label(c07) # label(axiom). [assumption].
% 34.70/34.97 10 mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) # label(c09) # label(axiom). [assumption].
% 34.70/34.97 11 mult(mult(A,B),mult(C,mult(A,B))) = mult(B,mult(A,mult(A,mult(B,C)))). [copy(10),rewrite([7(7),7(8)])].
% 34.70/34.97 12 mult(mult(a,a),mult(mult(b,c),mult(a,a))) != mult(mult(mult(a,a),b),mult(c,mult(a,a))) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 34.70/34.97 13 mult(mult(b,mult(a,a)),mult(c,mult(a,a))) != mult(mult(a,a),mult(mult(a,a),mult(b,c))) # answer(goals). [copy(12),rewrite([7(10),7(16)]),flip(a)].
% 34.70/34.97 14 mult(A,rd(B,A)) = B. [back_rewrite(5),rewrite([7(2)])].
% 34.70/34.97 17 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 34.70/34.97 19 mult(A,i(A)) = unit. [para(1(a,1),8(a,1,2)),rewrite([7(2)])].
% 34.70/34.97 20 ld(A,B) = mult(B,i(A)). [para(3(a,1),8(a,1,2)),rewrite([7(2)]),flip(a)].
% 34.70/34.97 22 rd(A,mult(A,B)) = i(B). [para(8(a,1),6(a,1,1)),rewrite([7(1)])].
% 34.70/34.97 23 mult(i(A),mult(B,A)) = B. [para(8(a,1),7(a,1)),rewrite([7(1),7(3)]),flip(a)].
% 34.70/34.97 24 i(i(A)) = A. [back_rewrite(17),rewrite([20(1),22(3)])].
% 34.70/34.97 25 mult(A,mult(B,i(A))) = B. [back_rewrite(3),rewrite([20(1)])].
% 34.70/34.97 26 mult(unit,mult(A,mult(A,B))) = mult(A,mult(A,B)). [para(1(a,1),11(a,1,1)),rewrite([1(2),7(1),7(5),1(5)]),flip(a)].
% 34.70/34.97 28 mult(A,mult(B,mult(B,mult(A,C)))) = mult(B,mult(A,mult(A,mult(B,C)))). [para(11(a,1),7(a,1)),rewrite([7(5),7(7),7(8),11(8)])].
% 34.70/34.97 30 mult(mult(A,B),mult(i(B),mult(i(B),mult(C,mult(A,B))))) = mult(A,mult(A,C)). [para(8(a,1),11(a,1,1)),rewrite([7(2),23(3),7(1),7(3),7(6),7(7)]),flip(a)].
% 34.70/34.97 31 mult(mult(A,B),mult(i(A),mult(i(A),mult(C,mult(A,B))))) = mult(B,mult(B,C)). [para(8(a,1),11(a,1,2,2)),rewrite([8(3),7(1),7(7)]),flip(a)].
% 34.70/34.97 32 mult(mult(A,mult(B,mult(B,mult(A,C)))),mult(D,mult(B,mult(A,mult(A,mult(B,C)))))) = mult(mult(C,mult(A,B)),mult(mult(A,B),mult(mult(A,B),mult(D,mult(C,mult(A,B)))))). [para(11(a,1),11(a,1,1)),rewrite([7(5),7(6),11(8),7(11),7(13),7(14),7(15),7(17)])].
% 34.70/34.97 38 rd(A,B) = mult(A,i(B)). [para(14(a,1),8(a,1,2)),rewrite([7(2)]),flip(a)].
% 34.70/34.97 39 mult(mult(A,i(B)),mult(B,mult(B,mult(C,mult(A,i(B)))))) = mult(A,mult(A,C)). [para(14(a,1),11(a,1,1)),rewrite([38(1),25(3),7(1),38(3),38(5),7(7)]),flip(a)].
% 34.70/34.97 42 mult(A,i(mult(A,B))) = i(B). [back_rewrite(22),rewrite([38(2)])].
% 34.70/34.97 44 mult(A,mult(B,B)) = mult(B,mult(B,A)). [para(19(a,1),11(a,2,2,2,2)),rewrite([23(4),7(2),1(4)]),flip(a)].
% 34.70/34.97 45 mult(mult(a,mult(a,b)),mult(a,mult(a,c))) != mult(mult(a,a),mult(mult(a,a),mult(b,c))) # answer(goals). [back_rewrite(13),rewrite([44(5),44(10)])].
% 34.70/34.97 48 mult(i(mult(A,mult(B,C))),mult(C,mult(B,mult(B,mult(A,C))))) = mult(B,C). [para(11(a,1),23(a,1,2)),rewrite([7(4)])].
% 34.70/34.97 49 i(mult(A,B)) = mult(i(A),i(B)). [para(42(a,1),8(a,1,2)),flip(a)].
% 34.70/34.97 52 mult(mult(A,B),mult(i(B),mult(i(A),mult(i(A),mult(i(B),i(C)))))) = mult(i(C),mult(i(A),i(B))). [para(11(a,1),42(a,1,2,1)),rewrite([49(6),49(6),49(6),49(6),49(14),49(14)])].
% 34.70/34.97 53 mult(A,mult(i(A),i(B))) = i(B). [para(42(a,1),20(a,2)),rewrite([20(2),49(2)])].
% 34.70/34.97 54 mult(mult(i(A),mult(i(B),i(C))),mult(C,mult(B,mult(B,mult(A,C))))) = mult(B,C). [back_rewrite(48),rewrite([49(3),49(3)])].
% 34.70/34.97 58 mult(mult(i(A),i(B)),mult(C,mult(A,B))) = C. [para(49(a,1),8(a,1,1)),rewrite([7(5)])].
% 34.70/34.97 61 mult(mult(A,B),mult(C,mult(i(A),i(B)))) = C. [para(49(a,1),25(a,1,2,2))].
% 34.70/34.97 69 mult(unit,mult(A,B)) = mult(A,B). [para(25(a,1),26(a,1,2,2)),rewrite([25(6)])].
% 34.70/34.97 71 mult(mult(A,B),mult(A,B)) = mult(B,mult(A,mult(A,B))). [para(69(a,1),11(a,1,2)),rewrite([1(5)])].
% 34.70/34.97 73 mult(mult(A,B),mult(mult(i(A),i(B)),i(C))) = i(C). [para(49(a,1),53(a,1,2,1))].
% 34.70/34.97 75 mult(A,mult(B,B)) = mult(B,mult(A,B)). [para(44(a,2),7(a,1)),rewrite([7(3),7(4)])].
% 34.70/34.97 78 mult(mult(A,A),mult(A,mult(A,B))) = mult(A,mult(A,mult(A,mult(A,B)))). [para(44(a,1),11(a,1,2))].
% 34.70/34.97 84 mult(A,mult(B,mult(B,mult(B,A)))) = mult(B,mult(A,mult(B,mult(B,A)))). [para(44(a,2),11(a,1,2)),rewrite([44(3),75(4,R),71(3),7(5)]),flip(a)].
% 34.70/34.97 85 mult(A,mult(B,mult(C,mult(C,B)))) = mult(B,mult(C,mult(C,mult(B,A)))). [para(44(a,2),11(a,2,2)),rewrite([75(4,R),71(3),44(7)])].
% 34.70/34.97 88 mult(mult(i(A),i(A)),mult(A,mult(A,B))) = B. [para(44(a,1),23(a,1,2)),rewrite([49(2)])].
% 34.70/34.97 92 mult(i(A),mult(B,mult(A,mult(A,mult(B,C))))) = mult(B,mult(B,mult(A,C))). [para(28(a,1),8(a,1,2))].
% 34.70/34.97 93 mult(A,mult(i(B),mult(i(B),mult(A,mult(B,C))))) = mult(i(B),mult(A,mult(A,C))). [para(8(a,1),28(a,1,2,2,2)),flip(a)].
% 34.70/34.97 95 mult(A,mult(B,mult(B,mult(A,mult(C,i(B)))))) = mult(B,mult(A,mult(A,C))). [para(25(a,1),28(a,1,2,2,2)),flip(a)].
% 34.70/34.97 99 mult(A,mult(B,mult(B,mult(C,A)))) = mult(B,mult(A,mult(A,mult(B,C)))). [para(44(a,2),28(a,1,2)),rewrite([44(3),7(5)]),flip(a)].
% 34.70/34.97 107 mult(i(A),mult(B,mult(A,mult(A,B)))) = mult(A,mult(B,B)). [para(8(a,1),75(a,2,2)),rewrite([71(4),7(7),75(7,R)])].
% 34.70/34.97 108 mult(mult(i(A),i(B)),mult(A,mult(B,B))) = B. [para(75(a,2),23(a,1,2)),rewrite([49(2)])].
% 34.70/34.97 110 mult(A,mult(i(B),mult(i(A),mult(i(A),i(B))))) = mult(i(A),mult(i(B),i(B))). [para(53(a,1),75(a,2,2)),rewrite([71(7),7(13),75(13,R)])].
% 34.70/34.97 116 mult(mult(A,i(B)),mult(C,mult(B,i(A)))) = C. [para(24(a,1),58(a,1,1,1)),rewrite([7(4)])].
% 34.70/34.97 123 mult(mult(A,B),mult(A,i(B))) = mult(A,A). [para(1(a,1),30(a,2,2)),rewrite([69(6),23(5),7(3)])].
% 34.70/34.97 124 mult(i(A),mult(i(A),mult(B,mult(C,A)))) = mult(mult(i(C),i(A)),mult(C,mult(C,B))). [para(30(a,1),8(a,1,2)),rewrite([49(2)]),flip(a)].
% 34.70/34.97 132 mult(A,mult(i(A),mult(B,C))) = mult(B,C). [para(69(a,1),30(a,2,2)),rewrite([7(2),1(2),7(5),1(5),7(4),8(5),69(7)])].
% 34.70/34.97 133 mult(i(A),mult(mult(A,B),mult(mult(A,B),mult(C,i(A))))) = mult(B,mult(B,C)). [para(53(a,1),30(a,1,1)),rewrite([7(4),49(5),24(3),24(3),7(5),49(6),24(4),24(4),7(6),25(7)])].
% 34.70/34.97 150 mult(mult(A,mult(A,B)),mult(mult(C,mult(C,mult(i(B),mult(i(A),i(C))))),mult(mult(C,mult(C,mult(i(B),mult(i(A),i(C))))),mult(D,mult(A,mult(A,B)))))) = mult(D,mult(C,mult(A,mult(A,C)))). [para(30(a,1),30(a,1,1)),rewrite([49(9),24(4),49(7),24(4),49(5),49(5),49(16),24(11),49(14),24(11),49(12),49(12),30(24),7(25),75(26,R),71(25)])].
% 34.70/34.97 153 mult(A,mult(B,mult(B,i(A)))) = mult(B,B). [para(25(a,1),123(a,1,1)),rewrite([49(3),24(3),7(2)])].
% 34.70/34.97 165 mult(mult(A,B),mult(mult(i(A),i(B)),mult(C,D))) = mult(C,D). [para(49(a,1),132(a,1,2,1))].
% 34.70/34.97 166 mult(A,mult(B,mult(i(A),i(A)))) = mult(B,i(A)). [para(44(a,2),132(a,1,2)),rewrite([7(7)])].
% 34.70/34.97 187 mult(i(A),mult(i(A),mult(B,mult(A,C)))) = mult(mult(i(A),i(C)),mult(C,mult(C,B))). [para(31(a,1),8(a,1,2)),rewrite([49(2)]),flip(a)].
% 34.70/34.97 188 mult(A,mult(B,mult(C,mult(C,B)))) = mult(C,mult(B,mult(B,mult(C,A)))). [para(8(a,1),31(a,1,1)),rewrite([24(2),24(2),7(2),23(3),7(1),7(5),7(6),7(7),75(8,R),71(7)]),flip(a)].
% 34.70/34.97 194 mult(mult(A,mult(A,B)),mult(i(B),mult(i(B),mult(C,mult(A,mult(A,B)))))) = mult(A,mult(A,mult(A,mult(A,C)))). [para(44(a,1),31(a,1,1)),rewrite([44(6),7(13),44(13),78(14)])].
% 34.70/34.97 203 mult(mult(A,mult(A,B)),mult(mult(C,mult(C,mult(i(B),mult(i(C),i(A))))),mult(mult(C,mult(C,mult(i(B),mult(i(C),i(A))))),mult(D,mult(A,mult(A,B)))))) = mult(D,mult(A,mult(C,mult(C,A)))). [para(31(a,1),30(a,1,2,2,2,2)),rewrite([31(8),49(9),24(4),49(7),24(4),49(5),49(5),49(16),24(11),49(14),24(11),49(12),49(12),7(25),75(26,R),71(25)])].
% 34.70/34.97 215 mult(mult(A,B),mult(i(A),mult(i(B),i(B)))) = i(B). [para(75(a,2),61(a,1,2))].
% 34.70/34.97 219 mult(mult(A,A),mult(B,i(A))) = mult(A,B). [para(8(a,1),88(a,1,2,2)),rewrite([24(2),24(2),7(3)])].
% 34.70/34.97 220 mult(mult(i(A),i(A)),mult(A,B)) = mult(B,i(A)). [para(25(a,1),88(a,1,2,2))].
% 34.70/34.97 232 mult(mult(A,A),i(B)) = mult(A,mult(A,i(B))). [para(153(a,1),88(a,1,2,2)),rewrite([220(6)])].
% 34.70/34.97 249 mult(mult(A,A),mult(A,B)) = mult(A,mult(A,mult(A,B))). [para(219(a,1),30(a,2,2)),rewrite([7(2),44(2),7(8),44(8),194(12),25(3)]),flip(a)].
% 34.70/34.97 277 mult(mult(A,mult(B,C)),mult(mult(B,C),mult(mult(B,C),mult(mult(A,mult(B,C)),mult(i(B),mult(i(B),mult(i(C),i(A)))))))) = mult(C,mult(B,mult(C,mult(C,mult(B,A))))). [para(23(a,1),32(a,1,2)),rewrite([7(5),49(13),49(13),49(13),7(19)]),flip(a)].
% 34.70/34.97 578 mult(i(A),mult(B,mult(B,A))) = mult(B,B). [para(108(a,1),71(a,1,1)),rewrite([7(3),44(5),58(6),44(3),7(6),7(9),44(11),58(12),7(7),53(7),7(5)]),flip(a)].
% 34.70/34.97 615 mult(mult(A,i(B)),mult(mult(B,i(A)),i(C))) = i(C). [para(24(a,1),73(a,1,2,1,1)),rewrite([7(2)])].
% 34.70/34.97 623 mult(mult(mult(i(A),i(B)),i(C)),mult(mult(A,B),mult(mult(A,B),i(C)))) = mult(i(C),mult(i(C),mult(A,B))). [para(73(a,1),31(a,1,2,2,2)),rewrite([49(9),24(7),24(7),49(10),24(8),24(8)])].
% 34.70/34.97 632 mult(mult(mult(A,B),i(C)),mult(mult(i(A),i(B)),i(C))) = mult(i(C),i(C)). [para(73(a,1),71(a,1,1)),rewrite([73(8),73(16),7(12)]),flip(a)].
% 34.70/34.97 1139 mult(i(A),mult(B,mult(A,A))) = mult(B,A). [para(215(a,1),23(a,1,2)),rewrite([49(6),24(2),49(4),24(2),24(2),7(4)])].
% 34.70/34.97 1175 mult(mult(i(A),i(B)),mult(C,mult(B,mult(A,mult(A,B))))) = mult(C,mult(A,B)). [para(49(a,1),1139(a,1,1)),rewrite([71(6)])].
% 34.70/34.97 1207 mult(mult(A,i(B)),mult(B,mult(B,C))) = mult(A,mult(A,mult(C,mult(B,i(A))))). [para(39(a,1),8(a,1,2)),rewrite([49(3),24(3),7(2)])].
% 34.70/34.97 1269 mult(mult(A,A),mult(B,C)) = mult(A,mult(A,mult(B,C))). [para(132(a,1),249(a,1,2)),rewrite([132(7)])].
% 34.70/34.97 1363 mult(mult(a,mult(a,b)),mult(a,mult(a,c))) != mult(a,mult(a,mult(a,mult(a,mult(b,c))))) # answer(goals). [back_rewrite(45),rewrite([1269(21),1269(22)])].
% 34.70/34.97 1421 mult(mult(i(A),i(B)),mult(mult(A,B),i(C))) = i(C). [para(24(a,1),615(a,1,2,1,2)),rewrite([7(4)])].
% 34.70/34.97 1544 mult(mult(A,mult(A,mult(B,B))),mult(C,D)) = mult(mult(A,B),mult(mult(A,B),mult(C,D))). [para(71(a,1),1269(a,1,1)),rewrite([7(1),75(2,R),7(6),7(7)])].
% 34.70/34.97 1688 mult(A,mult(B,mult(C,mult(C,B)))) = mult(B,mult(C,mult(C,mult(A,B)))). [para(54(a,1),8(a,1,2)),rewrite([49(6),24(2),49(4),24(2),24(2),7(4),75(4,R),71(3)])].
% 34.70/34.97 1754 mult(i(A),mult(B,mult(C,mult(C,mult(A,B))))) = mult(B,mult(C,mult(C,B))). [para(54(a,1),71(a,1,2)),rewrite([54(10),71(3),54(22),7(14),61(14),7(9)]),flip(a)].
% 34.70/34.97 3781 mult(mult(A,B),mult(i(C),mult(A,B))) = mult(B,mult(A,mult(A,mult(B,i(C))))). [para(52(a,1),165(a,1,2)),rewrite([24(4),24(4),24(7),24(7),24(7),24(7)])].
% 34.70/34.97 3920 mult(i(A),mult(i(A),mult(B,C))) = mult(mult(B,C),mult(i(A),i(A))). [para(73(a,1),84(a,1,2,2,2)),rewrite([623(11),73(19),7(15),632(15)])].
% 34.70/34.97 4242 mult(i(A),mult(B,mult(A,mult(A,mult(C,C))))) = mult(C,mult(C,mult(A,B))). [para(85(a,2),8(a,1,2)),rewrite([7(2),75(3,R)])].
% 34.70/34.97 4462 mult(mult(i(A),mult(i(B),mult(i(C),mult(i(C),mult(i(D),i(D)))))),mult(mult(C,D),mult(mult(C,D),mult(B,mult(B,mult(A,mult(C,mult(C,mult(D,D))))))))) = mult(C,mult(D,mult(D,mult(B,C)))). [para(85(a,1),54(a,2)),rewrite([7(3),75(4,R),49(6),49(6),49(6),7(12),75(13,R),7(15),75(16,R),1544(21),7(23)])].
% 34.70/34.97 6487 mult(i(A),mult(B,mult(A,mult(A,C)))) = mult(B,mult(B,mult(A,mult(C,i(B))))). [para(25(a,1),92(a,1,2,2,2,2))].
% 34.70/34.97 6504 mult(A,mult(A,mult(B,mult(C,mult(C,i(A)))))) = mult(C,mult(C,mult(B,A))). [para(153(a,1),92(a,1,2,2,2,2)),rewrite([4242(6)]),flip(a)].
% 34.70/34.97 6630 mult(i(A),mult(B,mult(C,mult(A,mult(A,C))))) = mult(C,mult(C,mult(A,B))). [para(85(a,2),92(a,1,2))].
% 34.70/34.97 7706 mult(mult(A,i(B)),mult(C,mult(B,mult(B,C)))) = mult(B,mult(A,mult(C,C))). [para(95(a,1),85(a,2)),rewrite([7(7),75(8,R)])].
% 34.70/34.97 8941 mult(A,mult(mult(B,C),mult(mult(B,C),mult(A,i(C))))) = mult(mult(B,C),mult(B,mult(A,A))). [para(23(a,1),99(a,1,2,2,2)),rewrite([7(2),75(3,R)]),flip(a)].
% 34.70/34.97 9507 mult(A,mult(B,mult(B,mult(C,A)))) = mult(B,mult(A,mult(A,mult(C,B)))). [para(188(a,1),54(a,2)),rewrite([7(3),75(4,R),49(6),49(6),49(6),7(12),75(13,R),7(15),75(16,R),1544(21),4462(22),7(5)])].
% 34.70/34.97 12184 mult(i(A),mult(mult(A,B),mult(C,mult(C,mult(A,B))))) = mult(mult(A,B),mult(B,mult(C,C))). [para(8(a,1),1688(a,2,2,2,2)),rewrite([7(9),75(10,R)])].
% 34.70/34.97 12974 mult(mult(A,B),mult(mult(A,B),i(C))) = mult(B,mult(A,mult(A,mult(B,i(C))))). [para(3920(a,1),31(a,1,2,2,2)),rewrite([24(5),24(5),166(9),25(7),7(5),3781(5)]),flip(a)].
% 34.70/34.97 13668 mult(mult(A,i(B)),mult(mult(A,i(B)),mult(B,C))) = mult(i(B),mult(A,mult(A,C))). [para(25(a,1),124(a,1,2,2,2)),rewrite([49(3),24(3),7(2),49(5),24(5),7(4),7(5),49(11),24(11),7(10),8(11)])].
% 34.70/34.97 13673 mult(mult(A,B),mult(mult(A,B),mult(C,i(B)))) = mult(B,mult(A,mult(A,C))). [para(53(a,1),124(a,1,2,2,2)),rewrite([49(4),24(2),24(2),49(5),24(3),24(3),49(11),24(9),24(9),8(9)])].
% 34.70/34.97 13999 mult(mult(A,B),mult(C,mult(C,A))) = mult(C,mult(B,mult(C,mult(A,A)))). [back_rewrite(8941),rewrite([13673(6),7(1),75(2,R),44(7)]),flip(a)].
% 34.70/34.97 14063 mult(mult(A,B),mult(A,mult(C,C))) = mult(C,mult(B,mult(A,mult(A,C)))). [para(23(a,1),9507(a,1,2,2,2)),rewrite([7(2),75(3,R),7(8),13673(10)])].
% 34.70/34.97 14219 mult(mult(A,mult(A,B)),mult(C,B)) = mult(A,mult(C,mult(A,mult(B,B)))). [para(13999(a,1),7(a,1)),rewrite([7(7)]),flip(a)].
% 34.70/34.97 14220 mult(mult(A,mult(A,B)),mult(B,C)) = mult(A,mult(C,mult(A,mult(B,B)))). [para(13999(a,1),7(a,2))].
% 34.70/34.97 14222 mult(mult(A,B),mult(B,mult(C,C))) = mult(C,mult(A,mult(B,mult(B,C)))). [para(7(a,1),13999(a,1,1)),rewrite([7(2),75(3,R),44(6)])].
% 34.70/34.97 14223 mult(mult(i(A),i(B)),mult(C,mult(B,mult(A,mult(A,C))))) = mult(A,mult(C,C)). [para(13999(a,1),8(a,1,2)),rewrite([49(2),44(5),7(9),75(10,R)])].
% 34.70/34.97 14226 mult(mult(A,i(B)),mult(C,mult(B,A))) = mult(i(B),mult(C,mult(B,mult(A,A)))). [para(8(a,1),13999(a,1,2,2)),rewrite([7(2),7(4),7(5),71(10),107(11)])].
% 34.70/34.97 14712 mult(mult(A,mult(B,B)),mult(A,C)) = mult(B,mult(C,mult(A,mult(A,B)))). [para(14063(a,1),7(a,2))].
% 34.70/34.97 14717 mult(mult(A,B),mult(C,mult(C,i(A)))) = mult(i(A),mult(B,mult(A,mult(C,C)))). [para(25(a,1),14063(a,2,2,2,2)),rewrite([71(6),132(7),14226(10)])].
% 34.70/34.97 14811 mult(mult(A,B),mult(i(A),mult(i(A),mult(C,mult(B,mult(A,mult(A,C))))))) = mult(mult(A,B),mult(B,mult(C,C))). [para(14063(a,1),93(a,1,2,2,2)),rewrite([44(15),12184(17)])].
% 34.70/34.97 14919 mult(mult(A,B),mult(C,mult(B,i(A)))) = mult(A,mult(C,mult(B,mult(B,i(A))))). [para(25(a,1),14219(a,1,1,2)),rewrite([71(10),132(11)])].
% 34.70/34.97 14959 mult(mult(i(A),i(B)),mult(C,mult(A,mult(mult(B,C),mult(A,mult(B,B)))))) = mult(C,mult(A,mult(B,mult(B,C)))). [para(14219(a,1),1139(a,2)),rewrite([49(2),7(4),75(5,R),71(8),14712(9),14220(8),44(12)])].
% 34.70/34.97 15131 mult(mult(A,B),mult(B,mult(C,C))) = mult(B,mult(B,mult(A,mult(C,C)))). [para(14220(a,1),31(a,1,2,2,2)),rewrite([44(5),14811(10),7(5),75(6,R)])].
% 34.70/34.97 15238 mult(A,mult(B,mult(C,mult(C,A)))) = mult(C,mult(C,mult(B,mult(A,A)))). [back_rewrite(14222),rewrite([15131(4)]),flip(a)].
% 34.70/34.97 15893 mult(i(A),mult(B,mult(B,mult(A,C)))) = mult(A,mult(C,mult(B,mult(B,i(A))))). [para(8(a,1),15238(a,1,2,2,2)),rewrite([7(3),14919(5),71(10),6630(12)]),flip(a)].
% 34.70/34.97 15920 mult(A,mult(B,mult(C,mult(B,mult(i(A),i(A)))))) = mult(i(A),mult(B,mult(B,C))). [para(15238(a,2),132(a,1,2)),rewrite([7(3),75(4,R),44(10)])].
% 34.70/34.97 16501 mult(mult(A,B),mult(mult(A,B),mult(C,i(A)))) = mult(A,mult(B,mult(B,C))). [para(133(a,1),8(a,1,2)),rewrite([24(2)]),flip(a)].
% 34.70/34.97 17660 mult(mult(A,B),mult(C,mult(C,mult(A,B)))) = mult(A,mult(B,mult(B,mult(A,mult(C,C))))). [para(8(a,1),1754(a,1,2,2,2,2)),rewrite([24(2),7(2),75(3,R),15131(4)]),flip(a)].
% 34.70/34.97 18055 mult(i(A),mult(B,mult(A,mult(C,C)))) = mult(A,mult(C,mult(C,mult(B,i(A))))). [para(6504(a,1),132(a,1,2)),rewrite([24(8),7(7),75(8,R)]),flip(a)].
% 34.70/34.97 18119 mult(mult(A,B),mult(C,mult(C,i(A)))) = mult(A,mult(C,mult(C,mult(B,i(A))))). [back_rewrite(14717),rewrite([18055(10)])].
% 34.70/34.97 18748 mult(mult(A,i(B)),mult(A,mult(C,mult(C,B)))) = mult(C,mult(A,mult(A,C))). [para(13673(a,1),123(a,1,1)),rewrite([7(4),7(5),49(9),49(6),49(10),24(10),7(9),165(11),7(6),7(7),7(8),71(9)])].
% 34.70/34.97 19180 mult(A,mult(B,mult(i(A),mult(C,mult(D,mult(D,mult(C,i(A)))))))) = mult(mult(D,C),mult(mult(D,C),mult(B,i(A)))). [para(1421(a,1),187(a,1,2,2,2)),rewrite([49(4),24(2),24(2),49(5),24(3),24(3),49(10),24(8),24(8),49(11),49(9),24(12),7(11),61(12),7(13),75(14,R),71(13),12974(12)]),flip(a)].
% 34.70/34.97 19822 mult(mult(A,i(B)),mult(B,mult(C,mult(C,B)))) = mult(B,mult(C,mult(C,A))). [para(7706(a,1),203(a,2)),rewrite([7(6),7(13),150(24),44(8)])].
% 34.70/34.97 19878 mult(mult(A,mult(B,C)),mult(A,mult(C,i(B)))) = mult(C,mult(A,mult(A,C))). [para(25(a,1),18748(a,1,2,2,2)),rewrite([49(3),24(3),7(2),7(4),7(6)])].
% 34.70/34.97 20326 mult(mult(A,i(B)),mult(C,mult(C,mult(B,B)))) = mult(B,mult(C,mult(C,A))). [para(95(a,1),19822(a,2)),rewrite([7(5),8(5),7(3),75(4,R)])].
% 34.70/34.97 20355 mult(mult(A,B),mult(A,mult(B,mult(C,C)))) = mult(B,mult(C,mult(C,mult(A,mult(A,B))))). [para(8(a,1),19878(a,1,1,2)),rewrite([7(2),24(4),7(3),75(3,R),7(6),7(7),17660(10),44(7)])].
% 34.70/34.97 20379 mult(mult(A,mult(A,B)),mult(A,mult(B,mult(C,mult(C,i(A)))))) = mult(C,mult(B,mult(B,mult(A,mult(A,C))))). [para(7706(a,1),19878(a,1,1)),rewrite([7(9),578(9),44(7),25(6),7(5),20355(5),13668(15),15893(12)]),flip(a)].
% 34.70/34.97 20493 mult(mult(A,B),mult(A,mult(C,mult(C,B)))) = mult(B,mult(C,mult(C,mult(A,mult(A,B))))). [para(20326(a,1),19878(a,1,1)),rewrite([44(7),7(9),578(9),44(7),25(6),7(5),44(7),44(13),13668(15),15893(12),20379(13)])].
% 34.70/34.97 20637 mult(mult(A,mult(B,B)),mult(C,A)) = mult(B,mult(C,mult(A,mult(A,B)))). [para(14220(a,1),1175(a,1,2)),rewrite([44(7),14220(8),14959(10),7(5),75(6,R)]),flip(a)].
% 34.70/34.97 20676 mult(mult(A,mult(A,i(B))),mult(A,mult(A,C))) = mult(A,mult(A,mult(A,mult(A,mult(C,i(B)))))). [para(20637(a,1),95(a,1,2,2,2)),rewrite([44(3),7(6),75(7,R),15920(10),132(8),44(9),44(12),7(13),75(14,R),71(13),20493(13),19180(15),1269(11),1269(12)])].
% 34.70/34.97 20692 mult(A,mult(A,mult(mult(B,i(C)),mult(C,i(A))))) = mult(mult(A,i(C)),mult(C,B)). [para(25(a,1),1207(a,1,2,2)),flip(a)].
% 34.70/34.97 20696 mult(A,mult(A,mult(mult(i(B),i(C)),mult(B,i(A))))) = mult(mult(A,i(B)),mult(B,i(C))). [para(53(a,1),1207(a,1,2,2)),flip(a)].
% 34.70/34.97 20884 mult(mult(A,B),mult(B,mult(B,mult(mult(A,B),mult(C,mult(i(A),mult(i(B),i(B)))))))) = mult(C,mult(A,mult(B,B))). [para(1207(a,1),277(a,2,2)),rewrite([7(3),25(3),7(4),25(4),7(4),25(4),7(4),25(4),49(5),24(5),7(4),49(7),24(7),7(6),7(9),16501(11),7(6),75(7,R),7(15),7(18),116(18),7(13),75(14,R)])].
% 34.70/34.97 22624 mult(mult(A,B),mult(C,mult(i(A),mult(i(B),i(B))))) = mult(mult(C,i(A)),mult(A,i(B))). [para(14223(a,1),6487(a,1,2,2)),rewrite([49(4),24(2),24(2),71(8),110(9),53(15),25(14),20696(16)])].
% 34.70/34.97 22628 mult(mult(A,B),mult(mult(B,i(A)),mult(A,C))) = mult(C,mult(A,mult(B,B))). [back_rewrite(20884),rewrite([22624(9),20692(8)])].
% 34.70/34.97 22661 mult(mult(A,i(B)),mult(mult(B,A),mult(B,C))) = mult(B,mult(A,mult(A,C))). [para(1139(a,1),22628(a,1,2,2)),rewrite([7(2),24(4),7(3),7(4),44(8),44(11),18119(12),7(9),8(9)])].
% 34.70/34.97 22901 mult(mult(A,i(B)),mult(A,mult(B,mult(B,C)))) = mult(mult(B,A),mult(A,C)). [para(22661(a,1),8(a,1,2)),rewrite([49(3),24(3),7(2),7(7)])].
% 34.70/34.97 23072 mult(mult(A,mult(A,B)),mult(A,mult(A,C))) = mult(A,mult(A,mult(A,mult(A,mult(B,C))))). [para(44(a,1),22901(a,2,1)),rewrite([232(3),1269(7),20676(8),7(4),8(4),7(9),44(9)]),flip(a)].
% 34.70/34.97 23073 $F # answer(goals). [resolve(23072,a,1363,a)].
% 34.70/34.97
% 34.70/34.97 % SZS output end Refutation
% 34.70/34.97 ============================== end of proof ==========================
% 34.70/34.97
% 34.70/34.97 ============================== STATISTICS ============================
% 34.70/34.97
% 34.70/34.97 Given=363. Generated=285190. Kept=23069. proofs=1.
% 34.70/34.97 Usable=275. Sos=9999. Demods=7564. Limbo=8, Disabled=12797. Hints=0.
% 34.70/34.97 Megabytes=28.43.
% 34.70/34.97 User_CPU=33.82, System_CPU=0.18, Wall_clock=34.
% 34.70/34.97
% 34.70/34.97 ============================== end of statistics =====================
% 34.70/34.97
% 34.70/34.97 ============================== end of search =========================
% 34.70/34.98
% 34.70/34.98 THEOREM PROVED
% 34.70/34.98 % SZS status Unsatisfiable
% 34.70/34.98
% 34.70/34.98 Exiting with 1 proof.
% 34.70/34.98
% 34.70/34.98 Process 14084 exit (max_proofs) Tue Jun 14 11:43:00 2022
% 34.70/34.98 Prover9 interrupted
%------------------------------------------------------------------------------