TSTP Solution File: GRP696-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP696-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 11:20:39 EDT 2022
% Result : Unsatisfiable 1.96s 2.30s
% Output : Refutation 1.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP696-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n009.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 14:58:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.96/2.30 ============================== Prover9 ===============================
% 1.96/2.30 Prover9 (32) version 2009-11A, November 2009.
% 1.96/2.30 Process 30731 was started by sandbox on n009.cluster.edu,
% 1.96/2.30 Mon Jun 13 14:58:53 2022
% 1.96/2.30 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30575_n009.cluster.edu".
% 1.96/2.30 ============================== end of head ===========================
% 1.96/2.30
% 1.96/2.30 ============================== INPUT =================================
% 1.96/2.30
% 1.96/2.30 % Reading from file /tmp/Prover9_30575_n009.cluster.edu
% 1.96/2.30
% 1.96/2.30 set(prolog_style_variables).
% 1.96/2.30 set(auto2).
% 1.96/2.30 % set(auto2) -> set(auto).
% 1.96/2.30 % set(auto) -> set(auto_inference).
% 1.96/2.30 % set(auto) -> set(auto_setup).
% 1.96/2.30 % set(auto_setup) -> set(predicate_elim).
% 1.96/2.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.96/2.30 % set(auto) -> set(auto_limits).
% 1.96/2.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.96/2.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.96/2.30 % set(auto) -> set(auto_denials).
% 1.96/2.30 % set(auto) -> set(auto_process).
% 1.96/2.30 % set(auto2) -> assign(new_constants, 1).
% 1.96/2.30 % set(auto2) -> assign(fold_denial_max, 3).
% 1.96/2.30 % set(auto2) -> assign(max_weight, "200.000").
% 1.96/2.30 % set(auto2) -> assign(max_hours, 1).
% 1.96/2.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.96/2.30 % set(auto2) -> assign(max_seconds, 0).
% 1.96/2.30 % set(auto2) -> assign(max_minutes, 5).
% 1.96/2.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.96/2.30 % set(auto2) -> set(sort_initial_sos).
% 1.96/2.30 % set(auto2) -> assign(sos_limit, -1).
% 1.96/2.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.96/2.30 % set(auto2) -> assign(max_megs, 400).
% 1.96/2.30 % set(auto2) -> assign(stats, some).
% 1.96/2.30 % set(auto2) -> clear(echo_input).
% 1.96/2.30 % set(auto2) -> set(quiet).
% 1.96/2.30 % set(auto2) -> clear(print_initial_clauses).
% 1.96/2.30 % set(auto2) -> clear(print_given).
% 1.96/2.30 assign(lrs_ticks,-1).
% 1.96/2.30 assign(sos_limit,10000).
% 1.96/2.30 assign(order,kbo).
% 1.96/2.30 set(lex_order_vars).
% 1.96/2.30 clear(print_given).
% 1.96/2.30
% 1.96/2.30 % formulas(sos). % not echoed (12 formulas)
% 1.96/2.30
% 1.96/2.30 ============================== end of input ==========================
% 1.96/2.30
% 1.96/2.30 % From the command line: assign(max_seconds, 300).
% 1.96/2.30
% 1.96/2.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.96/2.30
% 1.96/2.30 % Formulas that are not ordinary clauses:
% 1.96/2.30
% 1.96/2.30 ============================== end of process non-clausal formulas ===
% 1.96/2.30
% 1.96/2.30 ============================== PROCESS INITIAL CLAUSES ===============
% 1.96/2.30
% 1.96/2.30 ============================== PREDICATE ELIMINATION =================
% 1.96/2.30
% 1.96/2.30 ============================== end predicate elimination =============
% 1.96/2.30
% 1.96/2.30 Auto_denials:
% 1.96/2.30 % copying label goals to answer in negative clause
% 1.96/2.30
% 1.96/2.30 Term ordering decisions:
% 1.96/2.30
% 1.96/2.30 % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 1.96/2.30 Function symbol KB weights: unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 1.96/2.30
% 1.96/2.30 ============================== end of process initial clauses ========
% 1.96/2.30
% 1.96/2.30 ============================== CLAUSES FOR SEARCH ====================
% 1.96/2.30
% 1.96/2.30 ============================== end of clauses for search =============
% 1.96/2.30
% 1.96/2.30 ============================== SEARCH ================================
% 1.96/2.30
% 1.96/2.30 % Starting search at 0.01 seconds.
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=59.000, iters=3390
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=54.000, iters=3360
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=49.000, iters=3400
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=47.000, iters=3434
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=46.000, iters=3401
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=44.000, iters=3413
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=42.000, iters=3355
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=40.000, iters=3355
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=38.000, iters=3339
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=37.000, iters=3338
% 1.96/2.30
% 1.96/2.30 Low Water (keep): wt=36.000, iters=3356
% 1.96/2.30
% 1.96/2.30 ============================== PROOF =================================
% 1.96/2.30 % SZS status Unsatisfiable
% 1.96/2.30 % SZS output start Refutation
% 1.96/2.30
% 1.96/2.30 % Proof 1 at 1.30 (+ 0.04) seconds: goals.
% 1.96/2.30 % Length of proof is 109.
% 1.96/2.30 % Level of proof is 25.
% 1.96/2.30 % Maximum clause weight is 22.000.
% 1.96/2.30 % Given clauses 254.
% 1.96/2.30
% 1.96/2.30 1 mult(A,unit) = A # label(c05) # label(axiom). [assumption].
% 1.96/2.30 2 mult(unit,A) = A # label(c06) # label(axiom). [assumption].
% 1.96/2.30 3 mult(i(A),A) = unit # label(c10) # label(axiom). [assumption].
% 1.96/2.30 4 mult(A,i(A)) = unit # label(c11) # label(axiom). [assumption].
% 1.96/2.30 5 mult(A,ld(A,B)) = B # label(c01) # label(axiom). [assumption].
% 1.96/2.30 6 ld(A,mult(A,B)) = B # label(c02) # label(axiom). [assumption].
% 1.96/2.30 7 mult(rd(A,B),B) = A # label(c03) # label(axiom). [assumption].
% 1.96/2.30 8 rd(mult(A,B),B) = A # label(c04) # label(axiom). [assumption].
% 1.96/2.30 9 mult(A,i(mult(B,A))) = i(B) # label(c07) # label(axiom). [assumption].
% 1.96/2.30 10 mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)) # label(c08) # label(axiom). [assumption].
% 1.96/2.30 11 mult(rd(mult(A,B),A),mult(A,C)) = mult(A,mult(B,C)). [copy(10),flip(a)].
% 1.96/2.30 12 mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))) # label(c09) # label(axiom). [assumption].
% 1.96/2.30 13 mult(mult(A,B),ld(B,mult(C,B))) = mult(mult(A,C),B). [copy(12),flip(a)].
% 1.96/2.30 14 mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)) # label(goals) # label(negated_conjecture) # answer(goals). [assumption].
% 1.96/2.30 18 ld(i(A),unit) = A. [para(3(a,1),6(a,1,2))].
% 1.96/2.30 19 ld(A,unit) = i(A). [para(4(a,1),6(a,1,2))].
% 1.96/2.30 20 i(i(A)) = A. [back_rewrite(18),rewrite([19(3)])].
% 1.96/2.30 24 rd(unit,A) = i(A). [para(3(a,1),8(a,1,1))].
% 1.96/2.30 26 mult(ld(A,B),i(B)) = i(A). [para(5(a,1),9(a,1,2,1))].
% 1.96/2.30 27 i(mult(A,B)) = ld(B,i(A)). [para(9(a,1),6(a,1,2)),flip(a)].
% 1.96/2.30 28 i(rd(A,B)) = mult(B,i(A)). [para(7(a,1),9(a,1,2,1)),flip(a)].
% 1.96/2.30 29 mult(ld(A,i(B)),B) = i(A). [para(9(a,1),9(a,1,2,1)),rewrite([27(2),20(4)])].
% 1.96/2.30 30 mult(i(A),mult(A,B)) = mult(A,mult(i(A),B)). [para(3(a,1),11(a,1,1,1)),rewrite([24(3),20(2)]),flip(a)].
% 1.96/2.30 33 rd(mult(A,B),A) = mult(A,mult(B,i(A))). [para(4(a,1),11(a,1,2)),rewrite([1(4)])].
% 1.96/2.30 36 mult(mult(A,mult(B,i(A))),C) = mult(A,mult(B,ld(A,C))). [para(5(a,1),11(a,1,2)),rewrite([33(2)])].
% 1.96/2.30 45 ld(A,mult(B,A)) = mult(mult(i(A),B),A). [para(3(a,1),13(a,1,1)),rewrite([2(4)])].
% 1.96/2.30 46 mult(mult(A,i(B)),B) = mult(mult(A,B),i(B)). [para(3(a,1),13(a,1,2,2)),rewrite([19(3)]),flip(a)].
% 1.96/2.30 51 mult(mult(A,ld(B,C)),ld(ld(B,C),C)) = mult(mult(A,B),ld(B,C)). [para(5(a,1),13(a,1,2,2))].
% 1.96/2.30 54 ld(mult(A,B),mult(mult(A,C),B)) = mult(mult(i(B),C),B). [para(13(a,1),6(a,1,2)),rewrite([45(6)])].
% 1.96/2.30 56 mult(mult(A,rd(B,C)),C) = mult(mult(A,C),ld(C,B)). [para(7(a,1),13(a,1,2,2)),flip(a)].
% 1.96/2.30 63 mult(mult(A,B),mult(mult(i(B),C),B)) = mult(mult(A,C),B). [back_rewrite(13),rewrite([45(3)])].
% 1.96/2.30 66 ld(ld(A,B),i(A)) = i(B). [para(26(a,1),6(a,1,2))].
% 1.96/2.30 73 rd(A,B) = ld(i(A),i(B)). [para(28(a,1),20(a,1,1)),rewrite([27(3)]),flip(a)].
% 1.96/2.30 76 mult(mult(A,ld(i(B),i(C))),C) = mult(mult(A,C),ld(C,B)). [back_rewrite(56),rewrite([73(1)])].
% 1.96/2.30 85 ld(ld(A,i(B)),i(B)) = mult(B,mult(A,i(B))). [back_rewrite(33),rewrite([73(2),27(2)])].
% 1.96/2.30 88 ld(ld(i(A),B),A) = i(B). [para(20(a,1),66(a,1,2))].
% 1.96/2.30 89 i(ld(A,B)) = mult(i(B),A). [para(66(a,1),26(a,1,1)),rewrite([20(3)]),flip(a)].
% 1.96/2.30 92 mult(A,mult(i(A),i(A))) = i(A). [para(4(a,1),30(a,1,2)),rewrite([1(3)]),flip(a)].
% 1.96/2.30 96 ld(mult(i(A),B),i(A)) = ld(mult(A,B),A). [para(30(a,1),27(a,1,1)),rewrite([27(4),20(7)])].
% 1.96/2.30 98 ld(ld(ld(A,i(B)),C),mult(B,A)) = i(C). [para(27(a,1),88(a,1,1,1))].
% 1.96/2.30 99 mult(mult(i(A),B),ld(B,A)) = unit. [para(89(a,1),3(a,1,1))].
% 1.96/2.30 112 mult(mult(i(A),mult(B,A)),C) = mult(i(A),mult(B,ld(i(A),C))). [para(20(a,1),36(a,1,1,2,2))].
% 1.96/2.30 135 mult(A,ld(mult(A,A),A)) = unit. [para(92(a,1),99(a,1,1)),rewrite([20(2),20(2),20(2)])].
% 1.96/2.30 136 ld(mult(A,A),A) = i(A). [para(135(a,1),6(a,1,2)),rewrite([19(2)]),flip(a)].
% 1.96/2.30 156 mult(mult(A,A),i(A)) = A. [para(136(a,1),5(a,1,2))].
% 1.96/2.30 157 ld(i(A),A) = mult(A,A). [para(136(a,1),29(a,1,1)),rewrite([20(2),27(5),20(4)]),flip(a)].
% 1.96/2.30 163 mult(A,mult(mult(A,A),ld(A,B))) = mult(mult(A,A),B). [para(156(a,1),36(a,1,1,2)),flip(a)].
% 1.96/2.30 171 mult(A,mult(mult(i(A),B),A)) = mult(B,A). [para(45(a,1),5(a,1,2))].
% 1.96/2.30 179 ld(A,ld(B,A)) = mult(ld(A,i(B)),A). [para(45(a,1),89(a,1,1)),rewrite([27(4),27(3),20(2),27(4)])].
% 1.96/2.30 221 mult(ld(i(A),B),A) = mult(A,mult(B,A)). [para(5(a,1),171(a,1,2,1)),flip(a)].
% 1.96/2.30 224 mult(A,mult(i(A),mult(mult(i(A),B),A))) = mult(i(A),mult(B,A)). [para(171(a,1),30(a,1,2)),flip(a)].
% 1.96/2.30 225 mult(A,mult(mult(A,mult(i(A),B)),A)) = mult(mult(A,B),A). [para(30(a,1),171(a,1,2,1))].
% 1.96/2.30 228 mult(A,mult(i(A),mult(B,mult(A,A)))) = mult(mult(B,A),A). [para(36(a,1),171(a,1,2)),rewrite([157(3),20(7)])].
% 1.96/2.30 248 mult(A,mult(ld(A,i(B)),A)) = ld(B,A). [para(179(a,1),5(a,1,2))].
% 1.96/2.30 259 mult(mult(A,A),ld(A,B)) = mult(B,ld(ld(A,B),B)). [para(5(a,1),51(a,1,1)),flip(a)].
% 1.96/2.30 262 mult(mult(A,ld(B,C)),i(C)) = mult(mult(A,i(C)),ld(i(C),i(B))). [para(66(a,1),51(a,1,1,2)),rewrite([66(5),66(11)]),flip(a)].
% 1.96/2.30 277 ld(ld(i(A),B),mult(A,mult(B,A))) = A. [para(221(a,1),6(a,1,2))].
% 1.96/2.30 278 mult(ld(A,B),i(A)) = mult(i(A),mult(B,i(A))). [para(20(a,1),221(a,1,1,1))].
% 1.96/2.30 280 ld(mult(A,B),i(B)) = ld(B,mult(i(A),i(B))). [para(221(a,1),27(a,1,1)),rewrite([27(3),89(6)])].
% 1.96/2.30 287 mult(mult(A,mult(i(A),mult(B,i(A)))),C) = mult(A,mult(ld(A,B),ld(A,C))). [para(221(a,1),36(a,1,1,2)),rewrite([20(8)])].
% 1.96/2.30 297 mult(A,mult(ld(A,B),A)) = ld(i(B),A). [para(20(a,1),248(a,1,2,1,2))].
% 1.96/2.30 319 mult(mult(A,ld(i(B),C)),B) = mult(mult(A,B),mult(C,B)). [para(277(a,1),51(a,1,1,2)),rewrite([277(6),6(4),277(11)]),flip(a)].
% 1.96/2.30 322 ld(ld(A,i(B)),B) = mult(B,mult(A,B)). [para(6(a,1),297(a,1,2,1)),rewrite([27(4)]),flip(a)].
% 1.96/2.30 332 mult(mult(A,mult(B,A)),i(A)) = mult(A,B). [para(297(a,1),171(a,1,2,1)),rewrite([29(4),20(2),46(6),221(4)]),flip(a)].
% 1.96/2.30 333 mult(A,mult(mult(ld(A,i(B)),A),A)) = ld(mult(i(A),B),A). [para(179(a,1),297(a,1,2,1)),rewrite([89(7)])].
% 1.96/2.30 341 ld(mult(A,B),B) = mult(mult(i(B),i(A)),B). [para(4(a,1),54(a,1,2,1)),rewrite([2(3)])].
% 1.96/2.30 355 ld(A,mult(mult(mult(A,A),B),i(A))) = mult(mult(A,B),i(A)). [para(156(a,1),54(a,1,1)),rewrite([20(7)])].
% 1.96/2.30 410 ld(A,mult(i(B),i(A))) = mult(i(A),ld(B,i(A))). [para(322(a,1),89(a,1,1)),rewrite([27(3),280(3)])].
% 1.96/2.30 421 ld(ld(mult(A,B),A),A) = mult(B,A). [para(171(a,1),322(a,2)),rewrite([96(4)])].
% 1.96/2.30 431 ld(mult(A,B),i(B)) = mult(i(B),ld(A,i(B))). [back_rewrite(280),rewrite([410(7)])].
% 1.96/2.30 434 mult(ld(mult(A,B),A),mult(B,A)) = A. [para(421(a,1),5(a,1,2))].
% 1.96/2.30 435 ld(ld(A,B),B) = mult(ld(B,A),B). [para(5(a,1),421(a,1,1,1))].
% 1.96/2.30 436 mult(mult(A,B),i(B)) = mult(B,mult(i(B),A)). [para(421(a,1),26(a,1,1)),rewrite([89(6),30(6)])].
% 1.96/2.30 453 mult(mult(ld(A,B),A),A) = mult(i(A),mult(B,mult(A,A))). [para(297(a,1),421(a,1,1,1)),rewrite([435(3),341(4),89(4),20(3),112(4),157(3)]),flip(a)].
% 1.96/2.30 470 mult(mult(A,A),ld(A,B)) = ld(i(A),B). [back_rewrite(259),rewrite([435(5),297(6)])].
% 1.96/2.30 472 mult(ld(i(A),B),i(A)) = mult(A,mult(B,i(A))). [back_rewrite(85),rewrite([435(4)])].
% 1.96/2.30 483 ld(mult(i(A),B),A) = mult(mult(i(B),A),A). [back_rewrite(333),rewrite([453(4),228(6)]),flip(a)].
% 1.96/2.30 484 mult(mult(A,A),B) = mult(A,ld(i(A),B)). [back_rewrite(163),rewrite([470(3)]),flip(a)].
% 1.96/2.30 490 ld(A,mult(mult(A,ld(i(A),B)),i(A))) = mult(mult(A,B),i(A)). [back_rewrite(355),rewrite([484(2)])].
% 1.96/2.30 517 mult(A,mult(i(A),mult(B,i(A)))) = ld(i(B),i(A)). [para(66(a,1),435(a,1,1)),rewrite([472(8),278(6)]),flip(a)].
% 1.96/2.30 519 mult(mult(i(A),i(B)),A) = mult(i(A),ld(B,A)). [para(435(a,1),89(a,1,1)),rewrite([27(3),89(2),45(3)])].
% 1.96/2.30 527 mult(A,mult(ld(A,B),ld(A,C))) = mult(ld(i(B),i(A)),C). [back_rewrite(287),rewrite([517(5)]),flip(a)].
% 1.96/2.30 534 ld(mult(A,B),B) = mult(i(B),ld(A,B)). [back_rewrite(341),rewrite([519(6)])].
% 1.96/2.30 605 mult(A,mult(i(A),mult(B,A))) = ld(i(B),A). [para(297(a,1),332(a,2)),rewrite([453(3),228(5),436(4)])].
% 1.96/2.30 610 mult(mult(mult(A,mult(B,A)),C),i(A)) = mult(mult(A,B),mult(mult(A,C),i(A))). [para(332(a,1),63(a,1,1)),rewrite([20(3)]),flip(a)].
% 1.96/2.30 614 mult(mult(A,mult(i(A),B)),A) = ld(i(B),A). [para(332(a,1),332(a,1,1,2)),rewrite([30(3),20(5),30(8),605(8)])].
% 1.96/2.30 635 mult(ld(A,B),A) = mult(i(A),mult(B,A)). [back_rewrite(224),rewrite([605(6),27(3),20(2),435(2)])].
% 1.96/2.30 640 mult(mult(A,B),A) = mult(A,ld(i(B),A)). [back_rewrite(225),rewrite([614(4)]),flip(a)].
% 1.96/2.30 688 ld(ld(A,B),B) = mult(i(B),mult(A,B)). [back_rewrite(435),rewrite([635(4)])].
% 1.96/2.30 712 mult(mult(a,ld(i(b),a)),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)) # answer(goals). [back_rewrite(14),rewrite([640(5)])].
% 1.96/2.30 843 mult(mult(A,ld(B,A)),ld(A,B)) = A. [para(3(a,1),76(a,1,1)),rewrite([2(2),89(4),20(2),640(3),20(2)]),flip(a)].
% 1.96/2.30 846 mult(mult(A,ld(B,i(C))),C) = mult(mult(A,C),ld(C,i(B))). [para(20(a,1),76(a,1,1,2,1))].
% 1.96/2.30 886 ld(mult(A,ld(B,A)),A) = ld(A,B). [para(843(a,1),6(a,1,2))].
% 1.96/2.30 893 mult(mult(A,B),ld(B,A)) = mult(A,A). [para(843(a,1),36(a,2,2)),rewrite([262(4),4(2),2(5),846(5),20(3)])].
% 1.96/2.30 926 mult(ld(A,B),mult(ld(B,A),A)) = A. [para(886(a,1),434(a,1,1))].
% 1.96/2.30 1028 ld(mult(A,B),mult(A,A)) = ld(B,A). [para(893(a,1),6(a,1,2))].
% 1.96/2.30 1094 ld(ld(A,B),A) = mult(ld(B,A),A). [para(926(a,1),6(a,1,2))].
% 1.96/2.30 1157 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(5(a,1),1028(a,1,1)),rewrite([1094(4)])].
% 1.96/2.30 1168 ld(mult(A,ld(i(A),B)),mult(A,mult(A,mult(A,A)))) = mult(ld(B,A),A). [para(484(a,1),1028(a,1,1)),rewrite([484(6),1157(6),157(5),484(5),157(5),1157(9)])].
% 1.96/2.30 1186 mult(ld(mult(A,B),A),A) = ld(B,A). [back_rewrite(1028),rewrite([1157(3)])].
% 1.96/2.30 1294 ld(A,mult(B,mult(B,mult(B,B)))) = mult(mult(ld(A,B),B),mult(B,B)). [para(484(a,1),1157(a,1,2)),rewrite([1157(3),157(2),484(2),157(2),1157(6)])].
% 1.96/2.30 1304 mult(ld(A,B),B) = mult(i(A),mult(B,B)). [back_rewrite(1168),rewrite([1294(7),1186(5),88(3)]),flip(a)].
% 1.96/2.30 1363 ld(ld(A,B),A) = mult(i(B),mult(A,A)). [back_rewrite(1094),rewrite([1304(4)])].
% 1.96/2.30 1529 ld(mult(i(A),mult(B,B)),B) = mult(i(B),mult(i(B),mult(A,B))). [para(688(a,1),534(a,2,2)),rewrite([1304(2)])].
% 1.96/2.30 2032 ld(A,mult(B,i(A))) = mult(i(A),ld(i(B),i(A))). [para(277(a,1),98(a,1,1)),rewrite([27(7),431(7)])].
% 1.96/2.30 2052 mult(mult(A,B),i(A)) = mult(A,ld(i(B),i(A))). [back_rewrite(490),rewrite([2032(6),27(5),1363(5),1529(8),20(3),20(3),30(6),30(5),517(5)]),flip(a)].
% 1.96/2.30 2063 mult(mult(mult(A,mult(B,A)),C),i(A)) = mult(mult(A,B),mult(A,ld(i(C),i(A)))). [back_rewrite(610),rewrite([2052(9)])].
% 1.96/2.30 9680 mult(mult(A,B),mult(A,C)) = mult(A,mult(ld(i(B),A),C)). [para(527(a,1),436(a,2,2)),rewrite([319(6),221(3),2063(6),27(3),66(5),20(3),20(6)])].
% 1.96/2.30 10256 $F # answer(goals). [back_rewrite(712),rewrite([9680(10),89(6),483(8),20(4)]),xx(a)].
% 1.96/2.30
% 1.96/2.30 % SZS output end Refutation
% 1.96/2.30 ============================== end of proof ==========================
% 1.96/2.30
% 1.96/2.30 ============================== STATISTICS ============================
% 1.96/2.30
% 1.96/2.30 Given=254. Generated=35111. Kept=10253. proofs=1.
% 1.96/2.30 Usable=178. Sos=5784. Demods=6460. Limbo=576, Disabled=3727. Hints=0.
% 1.96/2.30 Megabytes=12.89.
% 1.96/2.30 User_CPU=1.30, System_CPU=0.04, Wall_clock=2.
% 1.96/2.30
% 1.96/2.30 ============================== end of statistics =====================
% 1.96/2.30
% 1.96/2.30 ============================== end of search =========================
% 1.96/2.30
% 1.96/2.30 THEOREM PROVED
% 1.96/2.30 % SZS status Unsatisfiable
% 1.96/2.30
% 1.96/2.30 Exiting with 1 proof.
% 1.96/2.30
% 1.96/2.30 Process 30731 exit (max_proofs) Mon Jun 13 14:58:55 2022
% 1.96/2.30 Prover9 interrupted
%------------------------------------------------------------------------------