TSTP Solution File: GRP681-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP681-1 : 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 11:20:33 EDT 2022
% Result : Unsatisfiable 38.65s 38.92s
% Output : Refutation 38.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP681-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n014.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 : Mon Jun 13 20:30:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 34.20/34.50 ============================== Prover9 ===============================
% 34.20/34.50 Prover9 (32) version 2009-11A, November 2009.
% 34.20/34.50 Process 25911 was started by sandbox on n014.cluster.edu,
% 34.20/34.50 Mon Jun 13 20:30:52 2022
% 34.20/34.50 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25758_n014.cluster.edu".
% 34.20/34.50 ============================== end of head ===========================
% 34.20/34.50
% 34.20/34.50 ============================== INPUT =================================
% 34.20/34.50
% 34.20/34.50 % Reading from file /tmp/Prover9_25758_n014.cluster.edu
% 34.20/34.50
% 34.20/34.50 set(prolog_style_variables).
% 34.20/34.50 set(auto2).
% 34.20/34.50 % set(auto2) -> set(auto).
% 34.20/34.50 % set(auto) -> set(auto_inference).
% 34.20/34.50 % set(auto) -> set(auto_setup).
% 34.20/34.50 % set(auto_setup) -> set(predicate_elim).
% 34.20/34.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 34.20/34.50 % set(auto) -> set(auto_limits).
% 34.20/34.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 34.20/34.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 34.20/34.50 % set(auto) -> set(auto_denials).
% 34.20/34.50 % set(auto) -> set(auto_process).
% 34.20/34.50 % set(auto2) -> assign(new_constants, 1).
% 34.20/34.50 % set(auto2) -> assign(fold_denial_max, 3).
% 34.20/34.50 % set(auto2) -> assign(max_weight, "200.000").
% 34.20/34.50 % set(auto2) -> assign(max_hours, 1).
% 34.20/34.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 34.20/34.50 % set(auto2) -> assign(max_seconds, 0).
% 34.20/34.50 % set(auto2) -> assign(max_minutes, 5).
% 34.20/34.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 34.20/34.50 % set(auto2) -> set(sort_initial_sos).
% 34.20/34.50 % set(auto2) -> assign(sos_limit, -1).
% 34.20/34.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 34.20/34.50 % set(auto2) -> assign(max_megs, 400).
% 34.20/34.50 % set(auto2) -> assign(stats, some).
% 34.20/34.50 % set(auto2) -> clear(echo_input).
% 34.20/34.50 % set(auto2) -> set(quiet).
% 34.20/34.50 % set(auto2) -> clear(print_initial_clauses).
% 34.20/34.50 % set(auto2) -> clear(print_given).
% 34.20/34.50 assign(lrs_ticks,-1).
% 34.20/34.50 assign(sos_limit,10000).
% 34.20/34.50 assign(order,kbo).
% 34.20/34.50 set(lex_order_vars).
% 34.20/34.50 clear(print_given).
% 34.20/34.50
% 34.20/34.50 % formulas(sos). % not echoed (10 formulas)
% 34.20/34.50
% 34.20/34.50 ============================== end of input ==========================
% 34.20/34.50
% 34.20/34.50 % From the command line: assign(max_seconds, 300).
% 34.20/34.50
% 34.20/34.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 34.20/34.50
% 34.20/34.50 % Formulas that are not ordinary clauses:
% 34.20/34.50
% 34.20/34.50 ============================== end of process non-clausal formulas ===
% 34.20/34.50
% 34.20/34.50 ============================== PROCESS INITIAL CLAUSES ===============
% 34.20/34.50
% 34.20/34.50 ============================== PREDICATE ELIMINATION =================
% 34.20/34.50
% 34.20/34.50 ============================== end predicate elimination =============
% 34.20/34.50
% 34.20/34.50 Auto_denials:
% 34.20/34.50 % copying label goals to answer in negative clause
% 34.20/34.50
% 34.20/34.50 Term ordering decisions:
% 34.20/34.50 Function symbol KB weights: op_c=1. op_d=1. unit=1. a=1. mult=1. ld=1. rd=1.
% 34.20/34.50
% 34.20/34.50 ============================== end of process initial clauses ========
% 34.20/34.50
% 34.20/34.50 ============================== CLAUSES FOR SEARCH ====================
% 34.20/34.50
% 34.20/34.50 ============================== end of clauses for search =============
% 34.20/34.50
% 34.20/34.50 ============================== SEARCH ================================
% 34.20/34.50
% 34.20/34.50 % Starting search at 0.01 seconds.
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=91.000, iters=3395
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=87.000, iters=3376
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=79.000, iters=3341
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=63.000, iters=3372
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=59.000, iters=3341
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=55.000, iters=3348
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=51.000, iters=3338
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=47.000, iters=3355
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=45.000, iters=3357
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=43.000, iters=3335
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=39.000, iters=3351
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=37.000, iters=3342
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=35.000, iters=3366
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=33.000, iters=3340
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=31.000, iters=3335
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=29.000, iters=3348
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=27.000, iters=3353
% 34.20/34.50
% 34.20/34.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 3.60 sec).
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=4811, wt=119.000
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=2654, wt=115.000
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=15873, wt=23.000
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=25.000, iters=3339
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=15977, wt=21.000
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=16123, wt=19.000
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=23.000, iters=3341
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=17908, wt=17.000
% 34.20/34.50
% 34.20/34.50 Low Water (displace): id=18450, wt=15.000
% 34.20/34.50
% 34.20/34.50 Low Water (keep): wt=21.000, iters=3336
% 38.65/38.92
% 38.65/38.92 ============================== PROOF =================================
% 38.65/38.92 % SZS status Unsatisfiable
% 38.65/38.92 % SZS output start Refutation
% 38.65/38.92
% 38.65/38.92 % Proof 1 at 37.43 (+ 0.56) seconds: goals.
% 38.65/38.92 % Length of proof is 95.
% 38.65/38.92 % Level of proof is 25.
% 38.65/38.92 % Maximum clause weight is 27.000.
% 38.65/38.92 % Given clauses 1489.
% 38.65/38.92
% 38.65/38.92 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 38.65/38.92 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 38.65/38.92 3 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 38.65/38.92 4 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 38.65/38.92 5 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 38.65/38.92 6 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 38.65/38.92 7 mult(op_c,A) = mult(A,op_c) # label(c08) # label(axiom). [assumption].
% 38.65/38.92 8 mult(op_d,A) = mult(A,op_d) # label(c09) # label(axiom). [assumption].
% 38.65/38.92 9 mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) # label(c07) # label(axiom). [assumption].
% 38.65/38.92 10 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [copy(9),flip(a)].
% 38.65/38.92 11 mult(mult(mult(op_c,op_c),op_d),a) != mult(a,mult(mult(op_c,op_c),op_d)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 38.65/38.92 12 mult(mult(op_d,mult(op_c,op_c)),a) != mult(a,mult(op_d,mult(op_c,op_c))) # answer(goals). [copy(11),rewrite([8(5,R),8(13,R)])].
% 38.65/38.92 14 ld(A,A) = unit. [para(1(a,1),4(a,1,2))].
% 38.65/38.92 16 ld(rd(A,B),A) = B. [para(5(a,1),4(a,1,2))].
% 38.65/38.92 17 rd(A,A) = unit. [para(2(a,1),6(a,1,1))].
% 38.65/38.92 18 rd(A,ld(B,A)) = B. [para(3(a,1),6(a,1,1))].
% 38.65/38.92 19 ld(op_c,mult(A,op_c)) = A. [para(7(a,1),4(a,1,2))].
% 38.65/38.92 24 rd(mult(A,op_d),A) = op_d. [para(8(a,1),6(a,1,1))].
% 38.65/38.92 25 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(2(a,1),10(a,1,1,2)),rewrite([2(5)])].
% 38.65/38.92 27 mult(ld(A,B),mult(A,mult(ld(A,B),C))) = mult(mult(ld(A,B),B),C). [para(3(a,1),10(a,1,1,2)),flip(a)].
% 38.65/38.92 28 ld(mult(A,mult(B,A)),mult(A,mult(B,mult(A,C)))) = C. [para(10(a,1),4(a,1,2))].
% 38.65/38.92 29 mult(A,mult(rd(B,A),mult(A,C))) = mult(mult(A,B),C). [para(5(a,1),10(a,1,1,2)),flip(a)].
% 38.65/38.92 30 rd(mult(A,mult(B,mult(A,C))),C) = mult(A,mult(B,A)). [para(10(a,1),6(a,1,1))].
% 38.65/38.92 31 mult(op_c,mult(A,mult(B,A))) = mult(A,mult(B,mult(A,op_c))). [para(10(a,1),7(a,2))].
% 38.65/38.92 32 mult(mult(A,mult(A,op_c)),B) = mult(A,mult(op_c,mult(A,B))). [para(7(a,1),10(a,1,1,2))].
% 38.65/38.92 34 mult(mult(A,mult(A,op_d)),B) = mult(A,mult(op_d,mult(A,B))). [para(8(a,1),10(a,1,1,2))].
% 38.65/38.92 35 mult(mult(A,mult(B,mult(C,mult(B,A)))),D) = mult(A,mult(B,mult(C,mult(B,mult(A,D))))). [para(10(a,1),10(a,1,1,2)),rewrite([10(9)])].
% 38.65/38.92 37 rd(A,op_c) = ld(op_c,A). [para(5(a,1),19(a,1,2)),flip(a)].
% 38.65/38.92 38 ld(op_c,mult(A,mult(B,mult(A,op_c)))) = mult(A,mult(B,A)). [para(10(a,1),19(a,1,2))].
% 38.65/38.92 43 mult(A,mult(A,ld(mult(A,A),B))) = B. [para(25(a,1),3(a,1))].
% 38.65/38.92 45 rd(mult(A,mult(A,B)),B) = mult(A,A). [para(25(a,1),6(a,1,1))].
% 38.65/38.92 46 mult(op_c,mult(A,A)) = mult(A,mult(A,op_c)). [para(25(a,1),7(a,2))].
% 38.65/38.92 47 mult(op_d,mult(A,A)) = mult(A,mult(A,op_d)). [para(25(a,1),8(a,2))].
% 38.65/38.92 54 mult(a,mult(op_c,mult(op_c,op_d))) != mult(op_c,mult(op_d,mult(op_c,a))) # answer(goals). [back_rewrite(12),rewrite([47(5),34(7),47(13)]),flip(a)].
% 38.65/38.92 55 ld(ld(op_c,A),A) = op_c. [para(37(a,1),16(a,1,1))].
% 38.65/38.92 63 mult(A,ld(mult(A,A),B)) = ld(A,B). [para(43(a,1),4(a,1,2)),flip(a)].
% 38.65/38.92 68 rd(mult(A,B),ld(A,B)) = mult(A,A). [para(3(a,1),45(a,1,1,2))].
% 38.65/38.92 70 rd(mult(op_c,mult(A,op_c)),A) = mult(op_c,op_c). [para(7(a,1),45(a,1,1,2))].
% 38.65/38.92 90 mult(op_c,mult(ld(op_c,A),mult(B,op_c))) = mult(mult(A,op_c),B). [para(55(a,1),27(a,1,1)),rewrite([55(6),7(5),55(10),7(9)])].
% 38.65/38.92 121 ld(mult(A,mult(A,op_c)),mult(A,mult(op_c,mult(A,B)))) = B. [para(7(a,1),28(a,1,1,2))].
% 38.65/38.92 137 ld(mult(A,A),B) = ld(A,ld(A,B)). [para(63(a,1),4(a,1,2)),flip(a)].
% 38.65/38.92 142 rd(A,ld(A,unit)) = mult(A,A). [para(1(a,1),68(a,1,1))].
% 38.65/38.92 153 mult(ld(op_c,unit),ld(op_c,unit)) = ld(op_c,ld(op_c,unit)). [para(55(a,1),142(a,1,2)),rewrite([37(5)]),flip(a)].
% 38.65/38.92 155 mult(mult(A,B),ld(A,C)) = mult(A,mult(rd(B,A),C)). [para(3(a,1),29(a,1,2,2)),flip(a)].
% 38.65/38.92 156 ld(A,mult(mult(A,B),C)) = mult(rd(B,A),mult(A,C)). [para(29(a,1),4(a,1,2))].
% 38.65/38.92 191 mult(A,mult(rd(B,mult(A,C)),A)) = rd(mult(A,B),C). [para(5(a,1),30(a,1,1,2)),flip(a)].
% 38.65/38.92 283 mult(ld(op_c,unit),mult(ld(op_c,unit),A)) = mult(ld(op_c,ld(op_c,unit)),A). [para(153(a,1),25(a,1,1)),flip(a)].
% 38.65/38.92 287 mult(ld(op_c,unit),mult(rd(A,ld(op_c,unit)),ld(op_c,ld(op_c,unit)))) = mult(mult(ld(op_c,unit),A),ld(op_c,unit)). [para(153(a,1),29(a,1,2,2))].
% 38.65/38.92 293 mult(op_d,mult(A,mult(A,op_c))) = mult(A,mult(op_c,mult(A,op_d))). [para(32(a,1),8(a,2))].
% 38.65/38.92 513 mult(op_c,mult(A,op_c)) = mult(A,mult(op_c,op_c)). [para(38(a,1),4(a,1))].
% 38.65/38.92 542 rd(mult(A,mult(op_c,op_c)),A) = mult(op_c,op_c). [back_rewrite(70),rewrite([513(4)])].
% 38.65/38.92 574 rd(A,rd(A,mult(op_c,op_c))) = mult(op_c,op_c). [para(5(a,1),542(a,1,1))].
% 38.65/38.92 610 rd(A,mult(op_c,op_c)) = ld(op_c,ld(op_c,A)). [para(574(a,1),16(a,1,1)),rewrite([137(4)]),flip(a)].
% 38.65/38.92 625 ld(ld(op_c,ld(op_c,A)),A) = mult(op_c,op_c). [para(610(a,1),16(a,1,1))].
% 38.65/38.92 671 ld(ld(op_c,unit),op_c) = mult(op_c,op_c). [para(14(a,1),625(a,1,1,2))].
% 38.65/38.92 958 mult(mult(A,op_c),ld(op_c,B)) = mult(op_c,mult(ld(op_c,A),B)). [para(5(a,1),90(a,1,2,2)),rewrite([37(9)]),flip(a)].
% 38.65/38.92 1434 mult(A,mult(rd(unit,A),B)) = B. [para(1(a,1),155(a,1,1)),rewrite([3(2)]),flip(a)].
% 38.65/38.92 1460 mult(ld(op_c,ld(op_c,unit)),ld(ld(op_c,unit),A)) = mult(ld(op_c,unit),A). [para(153(a,1),155(a,1,1)),rewrite([17(20),2(15)])].
% 38.65/38.92 1477 mult(ld(op_c,unit),mult(op_c,rd(A,ld(op_c,unit)))) = mult(op_c,mult(op_c,mult(ld(op_c,unit),A))). [para(671(a,1),155(a,1,2)),rewrite([513(8,R),7(7,R),7(17,R)]),flip(a)].
% 38.65/38.92 1521 mult(A,rd(unit,A)) = unit. [para(1(a,1),1434(a,1,2))].
% 38.65/38.92 1522 ld(rd(unit,A),B) = mult(A,B). [para(3(a,1),1434(a,1,2)),flip(a)].
% 38.65/38.92 1523 mult(rd(unit,A),B) = ld(A,B). [para(1434(a,1),4(a,1,2)),flip(a)].
% 38.65/38.92 1524 mult(op_c,mult(ld(op_c,unit),A)) = A. [para(1434(a,1),7(a,1)),rewrite([37(3),7(6,R)]),flip(a)].
% 38.65/38.92 1528 mult(ld(A,unit),mult(A,B)) = B. [para(18(a,1),1434(a,1,2,1))].
% 38.65/38.92 1534 mult(ld(op_c,unit),A) = mult(A,ld(op_c,unit)). [para(1434(a,1),31(a,1)),rewrite([37(3),37(7),37(10),7(12,R),3(12),1(9)]),flip(a)].
% 38.65/38.92 1538 mult(mult(A,ld(B,A)),C) = mult(A,ld(B,mult(A,C))). [para(1434(a,1),35(a,1,1,2,2)),rewrite([1523(3),1523(9),3(8),1523(7)])].
% 38.65/38.92 1572 mult(op_c,mult(op_c,mult(A,ld(op_c,unit)))) = rd(A,ld(op_c,unit)). [back_rewrite(1477),rewrite([1528(10),1534(10)]),flip(a)].
% 38.65/38.92 1574 mult(op_c,mult(A,ld(op_c,unit))) = A. [back_rewrite(1524),rewrite([1534(5)])].
% 38.65/38.92 1575 mult(ld(op_c,ld(op_c,unit)),ld(ld(op_c,unit),A)) = mult(A,ld(op_c,unit)). [back_rewrite(1460),rewrite([1534(14)])].
% 38.65/38.92 1576 mult(ld(op_c,unit),mult(rd(A,ld(op_c,unit)),ld(op_c,ld(op_c,unit)))) = mult(ld(op_c,unit),mult(A,ld(op_c,unit))). [back_rewrite(287),rewrite([1534(18),1534(22,R)])].
% 38.65/38.92 1577 mult(ld(op_c,unit),mult(A,ld(op_c,unit))) = mult(ld(op_c,ld(op_c,unit)),A). [back_rewrite(283),rewrite([1534(7)])].
% 38.65/38.92 1603 rd(A,ld(op_c,unit)) = mult(A,op_c). [back_rewrite(1572),rewrite([1574(7),7(2)]),flip(a)].
% 38.65/38.92 1604 mult(ld(op_c,ld(op_c,unit)),A) = mult(ld(op_c,unit),ld(op_c,A)). [back_rewrite(1576),rewrite([1603(7),958(11),1574(11),1577(14)]),flip(a)].
% 38.65/38.92 1617 mult(ld(op_c,unit),ld(op_c,ld(ld(op_c,unit),A))) = mult(A,ld(op_c,unit)). [back_rewrite(1575),rewrite([1604(10)])].
% 38.65/38.92 1637 rd(unit,A) = ld(A,unit). [para(1521(a,1),4(a,1,2)),flip(a)].
% 38.65/38.92 1677 mult(ld(A,unit),B) = ld(A,B). [back_rewrite(1523),rewrite([1637(2)])].
% 38.65/38.92 1678 ld(ld(A,unit),B) = mult(A,B). [back_rewrite(1522),rewrite([1637(2)])].
% 38.65/38.92 1684 mult(A,ld(op_c,unit)) = ld(op_c,A). [back_rewrite(1617),rewrite([1678(8),7(6),19(7),1677(4)]),flip(a)].
% 38.65/38.92 2021 ld(op_c,mult(A,A)) = mult(A,ld(op_c,A)). [para(1684(a,1),25(a,1)),rewrite([1684(7)])].
% 38.65/38.92 2025 mult(A,mult(rd(B,A),ld(op_c,A))) = ld(op_c,mult(A,B)). [para(1684(a,1),29(a,1,2,2)),rewrite([1684(10)])].
% 38.65/38.92 2035 ld(mult(A,mult(A,op_c)),mult(A,A)) = ld(op_c,unit). [para(1684(a,1),121(a,1,2,2,2)),rewrite([3(7)])].
% 38.65/38.92 4178 ld(op_c,mult(A,mult(op_c,mult(A,B)))) = mult(A,ld(op_c,mult(A,mult(B,op_c)))). [para(46(a,1),156(a,1,2,1)),rewrite([32(5),37(9),2021(9),7(11),1538(12)])].
% 38.65/38.92 4236 ld(A,ld(op_c,mult(A,B))) = mult(rd(B,A),ld(op_c,A)). [para(1684(a,1),156(a,1,2)),rewrite([1684(9)])].
% 38.65/38.92 7300 mult(A,mult(op_c,mult(A,mult(rd(B,mult(A,mult(A,op_c))),mult(A,A))))) = mult(A,ld(op_c,mult(A,mult(B,op_c)))). [para(2035(a,1),155(a,1,2)),rewrite([32(4),1684(8),4178(6),32(16)]),flip(a)].
% 38.65/38.92 8239 ld(A,rd(mult(A,B),C)) = mult(rd(B,mult(A,C)),A). [para(191(a,1),4(a,1,2))].
% 38.65/38.92 8244 mult(A,mult(rd(B,mult(A,C)),mult(A,D))) = mult(rd(mult(A,B),C),D). [para(191(a,1),10(a,1,1)),flip(a)].
% 38.65/38.92 8292 mult(rd(mult(A,B),C),ld(A,D)) = mult(A,mult(rd(B,mult(A,C)),D)). [para(191(a,1),155(a,1,1)),rewrite([6(8)])].
% 38.65/38.92 8418 mult(A,mult(op_c,mult(rd(mult(A,B),mult(A,op_c)),A))) = mult(A,ld(op_c,mult(A,mult(B,op_c)))). [back_rewrite(7300),rewrite([8244(8)])].
% 38.65/38.92 14577 ld(op_c,mult(op_d,mult(A,mult(A,op_c)))) = mult(A,ld(op_c,mult(A,mult(op_c,op_d)))). [para(293(a,2),2025(a,2,2)),rewrite([8292(8),7(5),8418(9),7(4,R)]),flip(a)].
% 38.65/38.92 16180 mult(op_c,mult(rd(mult(A,op_d),mult(A,op_c)),A)) = ld(op_c,mult(A,mult(op_c,op_d))). [para(293(a,2),4236(a,1,2,2)),rewrite([14577(7),4(8),8292(14),7(11)]),flip(a)].
% 38.65/38.92 17690 mult(rd(A,mult(B,op_c)),B) = mult(rd(A,B),ld(op_c,B)). [para(7(a,2),8239(a,2,1,2)),rewrite([37(3),4236(4),7(6)]),flip(a)].
% 38.65/38.92 17787 ld(op_c,mult(A,mult(op_c,op_d))) = mult(op_c,mult(op_d,ld(op_c,A))). [back_rewrite(16180),rewrite([17690(7),24(4)]),flip(a)].
% 38.65/38.92 22977 mult(ld(op_c,A),mult(op_c,mult(op_c,op_d))) = mult(op_c,mult(A,op_d)). [para(17787(a,1),156(a,1)),rewrite([7(5),19(6),8(3),37(6)]),flip(a)].
% 38.65/38.92 28004 mult(op_c,mult(op_d,mult(A,op_c))) = mult(A,mult(op_c,mult(op_c,op_d))). [para(4(a,1),22977(a,1,1)),rewrite([7(9),8(11,R)]),flip(a)].
% 38.65/38.92 30325 $F # answer(goals). [para(28004(a,2),54(a,1)),rewrite([7(5,R)]),xx(a)].
% 38.65/38.92
% 38.65/38.92 % SZS output end Refutation
% 38.65/38.92 ============================== end of proof ==========================
% 38.65/38.92
% 38.65/38.92 ============================== STATISTICS ============================
% 38.65/38.92
% 38.65/38.92 Given=1489. Generated=949342. Kept=30322. proofs=1.
% 38.65/38.92 Usable=1285. Sos=9999. Demods=10521. Limbo=1, Disabled=19047. Hints=0.
% 38.65/38.92 Megabytes=30.81.
% 38.65/38.92 User_CPU=37.43, System_CPU=0.56, Wall_clock=38.
% 38.65/38.92
% 38.65/38.92 ============================== end of statistics =====================
% 38.65/38.92
% 38.65/38.92 ============================== end of search =========================
% 38.65/38.92
% 38.65/38.92 THEOREM PROVED
% 38.65/38.92 % SZS status Unsatisfiable
% 38.65/38.92
% 38.65/38.92 Exiting with 1 proof.
% 38.65/38.92
% 38.65/38.92 Process 25911 exit (max_proofs) Mon Jun 13 20:31:30 2022
% 38.65/38.92 Prover9 interrupted
%------------------------------------------------------------------------------