TSTP Solution File: GRP667+6 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP667+6 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 11:20:30 EDT 2022
% Result : Theorem 6.40s 6.68s
% Output : Refutation 30.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP667+6 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue Jun 14 10:53:43 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 5410 was started by sandbox2 on n021.cluster.edu,
% 0.45/1.01 Tue Jun 14 10:53:43 2022
% 0.45/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5256_n021.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_5256_n021.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (10 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 10 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.01
% 0.45/1.01 ============================== end of process non-clausal formulas ===
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.01
% 0.45/1.01 ============================== PREDICATE ELIMINATION =================
% 0.45/1.01
% 0.45/1.01 ============================== end predicate elimination =============
% 0.45/1.01
% 0.45/1.01 Auto_denials:
% 0.45/1.01 % copying label goals to answer in negative clause
% 0.45/1.01 % copying label goals to answer in negative clause
% 0.45/1.01 % copying label goals to answer in negative clause
% 0.45/1.01 % copying label goals to answer in negative clause
% 0.45/1.01 % assign(max_proofs, 4). % (Horn set with more than one neg. clause)
% 6.40/6.68
% 6.40/6.68 Term ordering decisions:
% 6.40/6.68
% 6.40/6.68 % Assigning unary symbol f kb_weight 0 and highest precedence (18).
% 6.40/6.68 Function symbol KB weights: unit=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. c11=1. c12=1. mult=1. ld=1. rd=1. f=0.
% 6.40/6.68
% 6.40/6.68 ============================== end of process initial clauses ========
% 6.40/6.68
% 6.40/6.68 ============================== CLAUSES FOR SEARCH ====================
% 6.40/6.68
% 6.40/6.68 ============================== end of clauses for search =============
% 6.40/6.68
% 6.40/6.68 ============================== SEARCH ================================
% 6.40/6.68
% 6.40/6.68 % Starting search at 0.01 seconds.
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=107.000, iters=3376
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=103.000, iters=3356
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=99.000, iters=3342
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=91.000, iters=3538
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=71.000, iters=3341
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=67.000, iters=3456
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=63.000, iters=3361
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=59.000, iters=3352
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=55.000, iters=3354
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=51.000, iters=3365
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=49.000, iters=3356
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=47.000, iters=3361
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=45.000, iters=3335
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=43.000, iters=3345
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=41.000, iters=3349
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=39.000, iters=3341
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=37.000, iters=3347
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=35.000, iters=3351
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=33.000, iters=3348
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=31.000, iters=3351
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=29.000, iters=3350
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=27.000, iters=3359
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=25.000, iters=3341
% 6.40/6.68
% 6.40/6.68 Low Water (displace): id=8774, wt=191.000
% 6.40/6.68
% 6.40/6.68 Low Water (displace): id=8765, wt=187.000
% 6.40/6.68
% 6.40/6.68 Low Water (displace): id=16635, wt=22.000
% 6.40/6.68
% 6.40/6.68 Low Water (displace): id=16638, wt=19.000
% 6.40/6.68
% 6.40/6.68 Low Water (displace): id=17464, wt=17.000
% 6.40/6.68
% 6.40/6.68 Low Water (keep): wt=23.000, iters=3337
% 6.40/6.68
% 6.40/6.68 ============================== PROOF =================================
% 6.40/6.68 % SZS status Theorem
% 6.40/6.68 % SZS output start Refutation
% 6.40/6.68
% 6.40/6.68 % Proof 1 at 5.57 (+ 0.11) seconds: goals.
% 6.40/6.68 % Length of proof is 97.
% 6.40/6.68 % Level of proof is 20.
% 6.40/6.68 % Maximum clause weight is 43.000.
% 6.40/6.68 % Given clauses 499.
% 6.40/6.68
% 6.40/6.68 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 6.40/6.68 10 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 6.40/6.68 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 6.40/6.68 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 6.40/6.68 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 6.40/6.68 14 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 6.40/6.68 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 6.40/6.68 16 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 6.40/6.68 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(9)].
% 6.40/6.68 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(8)].
% 6.40/6.68 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(7)].
% 6.40/6.68 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])].
% 6.40/6.68 23 mult(mult(mult(c4,c6),c5),c6) != mult(c4,mult(c6,mult(c5,c6))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)].
% 6.40/6.68 28 ld(A,A) = unit. [para(11(a,1),14(a,1,2))].
% 6.40/6.68 30 ld(rd(A,B),A) = B. [para(15(a,1),14(a,1,2))].
% 6.40/6.68 33 ld(f(A),A) = f(A). [para(17(a,1),14(a,1,2))].
% 6.40/6.68 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)].
% 6.40/6.68 36 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),14(a,1,2))].
% 6.40/6.68 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)].
% 6.40/6.68 38 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),16(a,1,1))].
% 6.40/6.68 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)].
% 6.40/6.68 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])].
% 6.40/6.68 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])].
% 6.40/6.68 44 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(13(a,1),20(a,2,2,2)),rewrite([35(3)])].
% 6.40/6.68 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])].
% 6.40/6.68 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)].
% 6.40/6.68 49 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),16(a,1,1))].
% 6.40/6.68 50 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(17(a,1),20(a,1,1,2,2)),rewrite([39(2),17(11),39(9)])].
% 6.40/6.68 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)].
% 6.40/6.68 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),14(a,1,2))].
% 6.40/6.68 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)].
% 6.40/6.68 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),36(a,1,1)),rewrite([60(6)])].
% 6.40/6.68 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),38(a,1,1,2))].
% 6.40/6.68 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),38(a,2)),rewrite([41(3),66(4)])].
% 6.40/6.68 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)].
% 6.40/6.68 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([28(1)]),flip(a)].
% 6.40/6.68 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)].
% 6.40/6.68 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)].
% 6.40/6.68 155 ld(ld(A,unit),unit) = A. [para(145(a,1),14(a,1,2))].
% 6.40/6.68 156 rd(unit,A) = ld(A,unit). [para(145(a,1),16(a,1,1))].
% 6.40/6.68 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)].
% 6.40/6.68 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(39(a,1),42(a,1,1,2)),rewrite([50(5),60(9)])].
% 6.40/6.68 191 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),14(a,1,2))].
% 6.40/6.68 193 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),158(a,1,2))].
% 6.40/6.68 203 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(30(a,1),191(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)].
% 6.40/6.68 204 mult(mult(A,A),ld(A,unit)) = A. [para(191(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)].
% 6.40/6.68 230 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(193(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)].
% 6.40/6.68 231 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(193(a,1),20(a,1,1,2,2)),rewrite([230(16),11(10)])].
% 6.40/6.68 232 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(193(a,1),20(a,2,2,2)),rewrite([230(8),11(2)]),flip(a)].
% 6.40/6.68 237 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(193(a,1),42(a,1,1,2)),rewrite([230(14),11(8)])].
% 6.40/6.68 241 mult(A,ld(f(A),unit)) = f(A). [para(17(a,1),204(a,1,1))].
% 6.40/6.68 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(241(a,1),41(a,1,1)),rewrite([13(5),203(8)]),flip(a)].
% 6.40/6.68 422 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))].
% 6.40/6.68 465 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)].
% 6.40/6.68 466 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(17(a,1),84(a,1,1,2))].
% 6.40/6.68 479 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(17(a,1),47(a,1,1,1,2,2)),rewrite([39(2),17(9),39(7)])].
% 30.94/31.22 508 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),204(11),145(8),11(7)])].
% 30.94/31.22 527 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),14(a,1,2))].
% 30.94/31.22 645 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(237(a,1),16(a,1,1))].
% 30.94/31.22 648 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(237(a,1),41(a,1,1)),rewrite([241(4),203(10)]),flip(a)].
% 30.94/31.22 708 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),49(a,1,1,1)),rewrite([12(4),81(3),16(2)]),flip(a)].
% 30.94/31.22 775 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),14(a,1,2)),flip(a)].
% 30.94/31.22 781 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(648),rewrite([775(7)])].
% 30.94/31.22 791 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(50(a,1),41(a,1,1)),rewrite([50(7),41(4),17(3),17(10)]),flip(a)].
% 30.94/31.22 810 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(50(a,1),84(a,2)),rewrite([17(6),791(4)])].
% 30.94/31.22 878 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(465(a,1),14(a,1,2))].
% 30.94/31.22 880 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),465(a,1,1,2))].
% 30.94/31.22 912 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(465(a,1),50(a,1,1)),rewrite([171(10)]),flip(a)].
% 30.94/31.22 1026 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),466(a,1,1)),rewrite([156(3)]),flip(a)].
% 30.94/31.22 1068 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(241(a,1),527(a,1,2)),rewrite([645(4),203(11),775(9)])].
% 30.94/31.22 1089 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1068(4)])].
% 30.94/31.22 1622 mult(A,ld(B,unit)) = rd(A,B). [para(781(a,1),47(a,1,2,2)),rewrite([1089(7),41(4),17(3),1026(9),231(9),465(3)]),flip(a)].
% 30.94/31.22 1673 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(508),rewrite([1622(8)])].
% 30.94/31.22 1677 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(232),rewrite([1622(4)])].
% 30.94/31.22 1678 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(231),rewrite([1622(7)])].
% 30.94/31.22 1696 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(810),rewrite([1678(6),41(2)]),flip(a)].
% 30.94/31.22 1720 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(912),rewrite([1696(8),1673(5)]),flip(a)].
% 30.94/31.22 1755 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(479),rewrite([1720(5)])].
% 30.94/31.22 2227 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),878(a,1,1,2))].
% 30.94/31.22 3420 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),708(a,1,2,2)),rewrite([13(4),147(6)])].
% 30.94/31.22 4035 rd(ld(A,B),B) = ld(A,unit). [para(3420(a,1),16(a,1,1))].
% 30.94/31.22 4352 rd(A,mult(B,A)) = ld(B,unit). [para(14(a,1),4035(a,1,1))].
% 30.94/31.22 4353 ld(rd(A,B),unit) = rd(B,A). [para(30(a,1),4035(a,1,1)),flip(a)].
% 30.94/31.22 4367 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2227(a,1),4035(a,1,1)),rewrite([4353(7)])].
% 30.94/31.22 4692 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4353(a,1),1622(a,1,2)),flip(a)].
% 30.94/31.22 4700 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4367),rewrite([4692(4)])].
% 30.94/31.22 20288 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1755(a,1),422(a,1,2,2)),rewrite([880(3),33(4),39(4),1677(5),33(4),4352(6),1622(5),1755(7),33(8),33(9),1755(12),4352(11),1622(10),46(9),4700(8)])].
% 30.94/31.22 20315 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))). [back_rewrite(49),rewrite([20288(5),16(4)])].
% 30.94/31.22 20316 $F # answer(goals). [resolve(20315,a,23,a)].
% 30.94/31.22
% 30.94/31.22 % SZS output end Refutation
% 30.94/31.22 ============================== end of proof ==========================
% 30.94/31.22 % Redundant proof: 20324 $F # answer(goals). [back_rewrite(23),rewrite([20315(7)]),xx(a)].
% 30.94/31.22
% 30.94/31.22 % Disable descendants (x means already disabled):
% 30.94/31.22 23x
% 30.94/31.22
% 30.94/31.22 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 5.65 sec).
% 30.94/31.22
% 30.94/31.22 Low Water (keep): wt=22.000, iters=3343
% 30.94/31.22
% 30.94/31.22 Low Water (keep): wt=21.000, iters=3343
% 30.94/31.22
% 30.94/31.22 Low Water (displace): id=23033, wt=15.000
% 30.94/31.22
% 30.94/31.22 ============================== PROOF =================================
% 30.94/31.22 % SZS status Theorem
% 30.94/31.22 % SZS output start Refutation
% 30.94/31.22
% 30.94/31.22 % Proof 2 at 29.74 (+ 0.48) seconds: goals.
% 30.94/31.22 % Length of proof is 123.
% 30.94/31.22 % Level of proof is 25.
% 30.94/31.22 % Maximum clause weight is 29.000.
% 30.94/31.22 % Given clauses 1005.
% 30.94/31.22
% 30.94/31.22 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 10 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 30.94/31.22 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 30.94/31.22 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 30.94/31.22 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 30.94/31.22 14 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 30.94/31.22 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 30.94/31.22 16 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 30.94/31.22 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(9)].
% 30.94/31.22 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(8)].
% 30.94/31.22 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(7)].
% 30.94/31.22 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])].
% 30.94/31.22 26 mult(mult(c12,c10),mult(c11,c12)) != mult(c12,mult(mult(c10,c11),c12)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)].
% 30.94/31.22 28 ld(A,A) = unit. [para(11(a,1),14(a,1,2))].
% 30.94/31.22 30 ld(rd(A,B),A) = B. [para(15(a,1),14(a,1,2))].
% 30.94/31.22 32 rd(A,ld(B,A)) = B. [para(13(a,1),16(a,1,1))].
% 30.94/31.22 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)].
% 30.94/31.22 36 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),14(a,1,2))].
% 30.94/31.22 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)].
% 30.94/31.22 38 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),16(a,1,1))].
% 30.94/31.22 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)].
% 30.94/31.22 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))].
% 30.94/31.22 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])].
% 30.94/31.22 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])].
% 30.94/31.22 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])].
% 30.94/31.22 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)].
% 30.94/31.22 49 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),16(a,1,1))].
% 30.94/31.22 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))].
% 30.94/31.22 59 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),16(a,1,1))].
% 30.94/31.22 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)].
% 30.94/31.22 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),14(a,1,2))].
% 30.94/31.22 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)].
% 30.94/31.22 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),36(a,1,1)),rewrite([60(6)])].
% 30.94/31.22 78 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),36(a,1,1)),rewrite([41(4),66(5)])].
% 30.94/31.22 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),38(a,1,1,2))].
% 30.94/31.22 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),38(a,2)),rewrite([41(3),66(4)])].
% 30.94/31.22 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])].
% 30.94/31.22 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),14(a,1,2)),flip(a)].
% 30.94/31.22 94 mult(ld(A,f(A)),A) = f(A). [para(86(a,1),15(a,1,1))].
% 30.94/31.22 96 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(86(a,1),37(a,1,1)),rewrite([86(4),13(5),86(7)])].
% 30.94/31.22 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)].
% 30.94/31.22 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([28(1)]),flip(a)].
% 30.94/31.22 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)].
% 30.94/31.22 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)].
% 30.94/31.22 155 ld(ld(A,unit),unit) = A. [para(145(a,1),14(a,1,2))].
% 30.94/31.22 156 rd(unit,A) = ld(A,unit). [para(145(a,1),16(a,1,1))].
% 30.94/31.22 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)].
% 30.94/31.22 191 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),14(a,1,2))].
% 30.94/31.22 192 rd(A,mult(A,A)) = ld(A,unit). [para(158(a,1),16(a,1,1))].
% 30.94/31.22 193 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),158(a,1,2))].
% 30.94/31.22 203 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(30(a,1),191(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)].
% 30.94/31.22 204 mult(mult(A,A),ld(A,unit)) = A. [para(191(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)].
% 30.94/31.22 205 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),192(a,1,2)),rewrite([86(2)]),flip(a)].
% 30.94/31.22 230 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(193(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)].
% 30.94/31.22 231 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(193(a,1),20(a,1,1,2,2)),rewrite([230(16),11(10)])].
% 30.94/31.22 237 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(193(a,1),42(a,1,1,2)),rewrite([230(14),11(8)])].
% 30.94/31.22 241 mult(A,ld(f(A),unit)) = f(A). [para(17(a,1),204(a,1,1))].
% 30.94/31.22 245 mult(f(A),ld(A,f(A))) = unit. [para(205(a,1),13(a,1,2))].
% 30.94/31.22 252 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(96),rewrite([245(8)])].
% 30.94/31.22 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(241(a,1),41(a,1,1)),rewrite([13(5),203(8)]),flip(a)].
% 30.94/31.22 432 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),78(a,1,2,2))].
% 30.94/31.22 465 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)].
% 30.94/31.22 466 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(17(a,1),84(a,1,1,2))].
% 30.94/31.22 476 ld(mult(rd(A,mult(B,mult(C,B))),B),mult(A,C)) = mult(C,mult(B,C)). [para(47(a,1),14(a,1,2))].
% 30.94/31.22 494 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(94(a,1),47(a,1,1,1,2,2)),rewrite([13(9),252(8),11(6)])].
% 30.94/31.22 511 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(193(a,1),47(a,1,1,1,2,2)),rewrite([494(4),241(10),145(8),11(5)]),flip(a)].
% 30.94/31.22 527 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),14(a,1,2))].
% 30.94/31.22 645 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(237(a,1),16(a,1,1))].
% 30.94/31.22 648 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(237(a,1),41(a,1,1)),rewrite([241(4),203(10)]),flip(a)].
% 30.94/31.22 708 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),49(a,1,1,1)),rewrite([12(4),81(3),16(2)]),flip(a)].
% 30.94/31.22 775 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),14(a,1,2)),flip(a)].
% 30.94/31.22 781 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(648),rewrite([775(7)])].
% 30.94/31.22 1026 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),466(a,1,1)),rewrite([156(3)]),flip(a)].
% 30.94/31.22 1068 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(241(a,1),527(a,1,2)),rewrite([645(4),203(11),775(9)])].
% 30.94/31.22 1089 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1068(4)])].
% 30.94/31.22 1622 mult(A,ld(B,unit)) = rd(A,B). [para(781(a,1),47(a,1,2,2)),rewrite([1089(7),41(4),17(3),1026(9),231(9),465(3)]),flip(a)].
% 30.94/31.22 1672 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(511),rewrite([1622(4)]),flip(a)].
% 30.94/31.22 1778 ld(A,rd(A,B)) = ld(B,unit). [para(1622(a,1),14(a,1,2))].
% 30.94/31.22 1863 ld(mult(A,B),A) = ld(B,unit). [para(16(a,1),1778(a,1,2))].
% 30.94/31.22 1864 ld(ld(A,B),unit) = ld(B,A). [para(32(a,1),1778(a,1,2)),flip(a)].
% 30.94/31.22 2068 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1864(a,1),1622(a,1,2)),flip(a)].
% 30.94/31.22 2638 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1672(a,1),43(a,1,1,2)),flip(a)].
% 30.94/31.22 3399 mult(ld(A,unit),mult(A,B)) = B. [para(15(a,1),708(a,1,2,2)),rewrite([15(6)])].
% 30.94/31.22 3406 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),708(a,1,2))].
% 30.94/31.22 3408 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(708(a,1),40(a,1,2)),rewrite([1622(7),81(5),16(4),3399(4),3399(7),3399(10),3406(7)]),flip(a)].
% 30.94/31.22 3420 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),708(a,1,2,2)),rewrite([13(4),147(6)])].
% 30.94/31.22 3432 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(708(a,1),53(a,1,2)),rewrite([1622(9),81(7),16(6),3420(6),14(4),3420(3),1622(7),3420(10),14(8),3420(13),14(11),3420(10),64(8),3408(9)])].
% 30.94/31.22 3682 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2638),rewrite([3432(8)])].
% 30.94/31.22 4035 rd(ld(A,B),B) = ld(A,unit). [para(3420(a,1),16(a,1,1))].
% 30.94/31.22 4041 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3420(a,1),41(a,1,1)),rewrite([3420(6)]),flip(a)].
% 30.94/31.22 4045 mult(ld(A,f(A)),B) = ld(f(A),B). [para(205(a,1),3420(a,1,1))].
% 30.94/31.22 4057 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3420(a,1),432(a,1,1)),rewrite([3420(5)])].
% 30.94/31.22 4071 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3420(a,1),1622(a,1)),flip(a)].
% 30.94/31.22 4076 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1864(a,1),3420(a,1,1)),flip(a)].
% 30.94/31.22 4107 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3682),rewrite([4045(6),4045(6)]),flip(a)].
% 30.94/31.22 4168 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4057),rewrite([4076(4)])].
% 30.94/31.22 4352 rd(A,mult(B,A)) = ld(B,unit). [para(14(a,1),4035(a,1,1))].
% 30.94/31.22 4353 ld(rd(A,B),unit) = rd(B,A). [para(30(a,1),4035(a,1,1)),flip(a)].
% 30.94/31.22 4364 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1863(a,1),4035(a,1,1)),rewrite([4071(3)]),flip(a)].
% 30.94/31.22 4692 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4353(a,1),1622(a,1,2)),flip(a)].
% 30.94/31.22 4696 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4353(a,1),3420(a,1,1)),flip(a)].
% 30.94/31.22 5046 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1672(a,1),4041(a,1,2)),rewrite([4035(4),1672(9)]),flip(a)].
% 30.94/31.22 5402 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4107),rewrite([5046(5)]),flip(a)].
% 30.94/31.22 5868 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4168(a,1),1863(a,1,1)),rewrite([4076(7),11(7)])].
% 30.94/31.22 5886 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5402),rewrite([5868(5)]),flip(a)].
% 30.94/31.22 6083 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4364(a,1),1622(a,1,2))].
% 30.94/31.22 6092 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5886),rewrite([6083(4)])].
% 30.94/31.22 6314 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(2068(a,1),4692(a,1,2))].
% 30.94/31.22 6530 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(4696(a,1),4076(a,1,1))].
% 30.94/31.22 6619 mult(ld(A,rd(mult(A,mult(B,A)),C)),mult(C,B)) = mult(B,mult(A,B)). [back_rewrite(476),rewrite([6530(6)])].
% 30.94/31.22 20011 mult(A,mult(ld(A,B),rd(A,C))) = rd(mult(B,A),C). [para(6092(a,1),4352(a,1,2)),rewrite([6314(4),4692(3),4696(8),11(8)])].
% 30.94/31.22 24338 rd(mult(A,mult(B,A)),C) = mult(A,mult(B,rd(A,C))). [para(14(a,1),20011(a,1,2,1)),rewrite([18(5)]),flip(a)].
% 30.94/31.22 24388 mult(mult(A,rd(B,C)),mult(C,A)) = mult(A,mult(B,A)). [back_rewrite(6619),rewrite([24338(3),14(4)])].
% 30.94/31.22 25808 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),24388(a,1,1,2))].
% 30.94/31.22 25809 $F # answer(goals). [resolve(25808,a,26,a)].
% 30.94/31.22
% 30.94/31.22 % SZS output end Refutation
% 30.94/31.22 ============================== end of proof ==========================
% 30.94/31.22
% 30.94/31.22 ============================== PROOF =================================
% 30.94/31.22 % SZS status Theorem
% 30.94/31.22 % SZS output start Refutation
% 30.94/31.22
% 30.94/31.22 % Proof 3 at 29.74 (+ 0.48) seconds: goals.
% 30.94/31.22 % Length of proof is 124.
% 30.94/31.22 % Level of proof is 25.
% 30.94/31.22 % Maximum clause weight is 29.000.
% 30.94/31.22 % Given clauses 1005.
% 30.94/31.22
% 30.94/31.22 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 30.94/31.22 10 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 30.94/31.22 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 30.94/31.22 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 30.94/31.22 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 30.94/31.22 14 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 30.94/31.22 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 30.94/31.22 16 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 30.94/31.22 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(9)].
% 30.94/31.22 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(8)].
% 30.94/31.22 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(7)].
% 30.94/31.22 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])].
% 30.94/31.22 24 mult(mult(c9,mult(c7,c8)),c9) != mult(mult(c9,c7),mult(c8,c9)) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)].
% 30.94/31.22 25 mult(mult(c9,c7),mult(c8,c9)) != mult(c9,mult(mult(c7,c8),c9)) # answer(goals). [copy(24),rewrite([18(7)]),flip(a)].
% 30.94/31.22 28 ld(A,A) = unit. [para(11(a,1),14(a,1,2))].
% 30.94/31.22 30 ld(rd(A,B),A) = B. [para(15(a,1),14(a,1,2))].
% 30.94/31.22 32 rd(A,ld(B,A)) = B. [para(13(a,1),16(a,1,1))].
% 30.94/31.22 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)].
% 30.94/31.22 36 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),14(a,1,2))].
% 30.94/31.22 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)].
% 30.94/31.22 38 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),16(a,1,1))].
% 30.94/31.22 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)].
% 30.94/31.22 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))].
% 30.94/31.22 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])].
% 30.94/31.22 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])].
% 30.94/31.22 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])].
% 30.94/31.22 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)].
% 30.94/31.22 49 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),16(a,1,1))].
% 30.94/31.22 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))].
% 30.94/31.22 59 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),16(a,1,1))].
% 30.94/31.22 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)].
% 30.94/31.22 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),14(a,1,2))].
% 30.94/31.22 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)].
% 30.94/31.22 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),36(a,1,1)),rewrite([60(6)])].
% 30.94/31.22 78 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),36(a,1,1)),rewrite([41(4),66(5)])].
% 30.94/31.22 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),38(a,1,1,2))].
% 30.94/31.22 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),38(a,2)),rewrite([41(3),66(4)])].
% 30.94/31.22 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])].
% 30.94/31.22 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),14(a,1,2)),flip(a)].
% 30.94/31.22 94 mult(ld(A,f(A)),A) = f(A). [para(86(a,1),15(a,1,1))].
% 30.94/31.22 96 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(86(a,1),37(a,1,1)),rewrite([86(4),13(5),86(7)])].
% 30.94/31.22 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)].
% 30.94/31.22 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([28(1)]),flip(a)].
% 30.94/31.22 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)].
% 30.94/31.22 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)].
% 30.94/31.22 155 ld(ld(A,unit),unit) = A. [para(145(a,1),14(a,1,2))].
% 30.94/31.22 156 rd(unit,A) = ld(A,unit). [para(145(a,1),16(a,1,1))].
% 30.94/31.22 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)].
% 30.94/31.22 191 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),14(a,1,2))].
% 30.94/31.22 192 rd(A,mult(A,A)) = ld(A,unit). [para(158(a,1),16(a,1,1))].
% 30.94/31.22 193 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),158(a,1,2))].
% 30.94/31.22 203 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(30(a,1),191(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)].
% 30.94/31.22 204 mult(mult(A,A),ld(A,unit)) = A. [para(191(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)].
% 30.94/31.22 205 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),192(a,1,2)),rewrite([86(2)]),flip(a)].
% 30.94/31.22 230 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(193(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)].
% 30.94/31.22 231 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(193(a,1),20(a,1,1,2,2)),rewrite([230(16),11(10)])].
% 30.94/31.22 237 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(193(a,1),42(a,1,1,2)),rewrite([230(14),11(8)])].
% 30.94/31.22 241 mult(A,ld(f(A),unit)) = f(A). [para(17(a,1),204(a,1,1))].
% 30.94/31.22 245 mult(f(A),ld(A,f(A))) = unit. [para(205(a,1),13(a,1,2))].
% 30.94/31.22 252 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(96),rewrite([245(8)])].
% 30.94/31.22 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(241(a,1),41(a,1,1)),rewrite([13(5),203(8)]),flip(a)].
% 30.94/31.22 432 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),78(a,1,2,2))].
% 30.94/31.22 465 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)].
% 30.94/31.22 466 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(17(a,1),84(a,1,1,2))].
% 30.94/31.22 476 ld(mult(rd(A,mult(B,mult(C,B))),B),mult(A,C)) = mult(C,mult(B,C)). [para(47(a,1),14(a,1,2))].
% 30.94/31.22 494 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(94(a,1),47(a,1,1,1,2,2)),rewrite([13(9),252(8),11(6)])].
% 30.94/31.22 511 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(193(a,1),47(a,1,1,1,2,2)),rewrite([494(4),241(10),145(8),11(5)]),flip(a)].
% 30.94/31.22 527 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),14(a,1,2))].
% 30.94/31.22 645 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(237(a,1),16(a,1,1))].
% 30.94/31.22 648 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(237(a,1),41(a,1,1)),rewrite([241(4),203(10)]),flip(a)].
% 30.94/31.22 708 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),49(a,1,1,1)),rewrite([12(4),81(3),16(2)]),flip(a)].
% 30.94/31.22 775 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),14(a,1,2)),flip(a)].
% 30.94/31.22 781 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(648),rewrite([775(7)])].
% 30.94/31.22 1026 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),466(a,1,1)),rewrite([156(3)]),flip(a)].
% 30.94/31.22 1068 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(241(a,1),527(a,1,2)),rewrite([645(4),203(11),775(9)])].
% 30.94/31.22 1089 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1068(4)])].
% 30.94/31.22 1622 mult(A,ld(B,unit)) = rd(A,B). [para(781(a,1),47(a,1,2,2)),rewrite([1089(7),41(4),17(3),1026(9),231(9),465(3)]),flip(a)].
% 30.94/31.22 1672 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(511),rewrite([1622(4)]),flip(a)].
% 30.94/31.22 1778 ld(A,rd(A,B)) = ld(B,unit). [para(1622(a,1),14(a,1,2))].
% 30.94/31.22 1863 ld(mult(A,B),A) = ld(B,unit). [para(16(a,1),1778(a,1,2))].
% 30.94/31.22 1864 ld(ld(A,B),unit) = ld(B,A). [para(32(a,1),1778(a,1,2)),flip(a)].
% 30.94/31.22 2068 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1864(a,1),1622(a,1,2)),flip(a)].
% 30.94/31.22 2638 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1672(a,1),43(a,1,1,2)),flip(a)].
% 30.94/31.22 3399 mult(ld(A,unit),mult(A,B)) = B. [para(15(a,1),708(a,1,2,2)),rewrite([15(6)])].
% 30.94/31.22 3406 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),708(a,1,2))].
% 30.94/31.22 3408 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(708(a,1),40(a,1,2)),rewrite([1622(7),81(5),16(4),3399(4),3399(7),3399(10),3406(7)]),flip(a)].
% 32.29/32.61 3420 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),708(a,1,2,2)),rewrite([13(4),147(6)])].
% 32.29/32.61 3432 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(708(a,1),53(a,1,2)),rewrite([1622(9),81(7),16(6),3420(6),14(4),3420(3),1622(7),3420(10),14(8),3420(13),14(11),3420(10),64(8),3408(9)])].
% 32.29/32.61 3682 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2638),rewrite([3432(8)])].
% 32.29/32.61 4035 rd(ld(A,B),B) = ld(A,unit). [para(3420(a,1),16(a,1,1))].
% 32.29/32.61 4041 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3420(a,1),41(a,1,1)),rewrite([3420(6)]),flip(a)].
% 32.29/32.61 4045 mult(ld(A,f(A)),B) = ld(f(A),B). [para(205(a,1),3420(a,1,1))].
% 32.29/32.61 4057 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3420(a,1),432(a,1,1)),rewrite([3420(5)])].
% 32.29/32.61 4071 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3420(a,1),1622(a,1)),flip(a)].
% 32.29/32.61 4076 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1864(a,1),3420(a,1,1)),flip(a)].
% 32.29/32.61 4107 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3682),rewrite([4045(6),4045(6)]),flip(a)].
% 32.29/32.61 4168 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4057),rewrite([4076(4)])].
% 32.29/32.61 4352 rd(A,mult(B,A)) = ld(B,unit). [para(14(a,1),4035(a,1,1))].
% 32.29/32.61 4353 ld(rd(A,B),unit) = rd(B,A). [para(30(a,1),4035(a,1,1)),flip(a)].
% 32.29/32.61 4364 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1863(a,1),4035(a,1,1)),rewrite([4071(3)]),flip(a)].
% 32.29/32.61 4692 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4353(a,1),1622(a,1,2)),flip(a)].
% 32.29/32.61 4696 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4353(a,1),3420(a,1,1)),flip(a)].
% 32.29/32.61 5046 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1672(a,1),4041(a,1,2)),rewrite([4035(4),1672(9)]),flip(a)].
% 32.29/32.61 5402 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4107),rewrite([5046(5)]),flip(a)].
% 32.29/32.61 5868 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4168(a,1),1863(a,1,1)),rewrite([4076(7),11(7)])].
% 32.29/32.61 5886 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5402),rewrite([5868(5)]),flip(a)].
% 32.29/32.61 6083 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4364(a,1),1622(a,1,2))].
% 32.29/32.61 6092 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5886),rewrite([6083(4)])].
% 32.29/32.61 6314 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(2068(a,1),4692(a,1,2))].
% 32.29/32.61 6530 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(4696(a,1),4076(a,1,1))].
% 32.29/32.61 6619 mult(ld(A,rd(mult(A,mult(B,A)),C)),mult(C,B)) = mult(B,mult(A,B)). [back_rewrite(476),rewrite([6530(6)])].
% 32.29/32.61 20011 mult(A,mult(ld(A,B),rd(A,C))) = rd(mult(B,A),C). [para(6092(a,1),4352(a,1,2)),rewrite([6314(4),4692(3),4696(8),11(8)])].
% 32.29/32.61 24338 rd(mult(A,mult(B,A)),C) = mult(A,mult(B,rd(A,C))). [para(14(a,1),20011(a,1,2,1)),rewrite([18(5)]),flip(a)].
% 32.29/32.61 24388 mult(mult(A,rd(B,C)),mult(C,A)) = mult(A,mult(B,A)). [back_rewrite(6619),rewrite([24338(3),14(4)])].
% 32.29/32.61 25808 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),24388(a,1,1,2))].
% 32.29/32.61 25810 $F # answer(goals). [resolve(25808,a,25,a)].
% 32.29/32.61
% 32.29/32.61 % SZS output end Refutation
% 32.29/32.61 ============================== end of proof ==========================
% 32.29/32.61 % Redundant proof: 25827 $F # answer(goals). [back_rewrite(26),rewrite([25808(7)]),xx(a)].
% 32.29/32.61 % Redundant proof: 25828 $F # answer(goals). [back_rewrite(25),rewrite([25808(7)]),xx(a)].
% 32.29/32.61
% 32.29/32.61 % Disable descendants (x means already disabled):
% 32.29/32.61 24x 25x 26x
% 32.29/32.61
% 32.29/32.61 ============================== PROOF =================================
% 32.29/32.61 % SZS status Theorem
% 32.29/32.61 % SZS output start Refutation
% 32.29/32.61
% 32.29/32.61 % Proof 4 at 31.10 (+ 0.51) seconds: goals.
% 32.29/32.61 % Length of proof is 174.
% 32.29/32.61 % Level of proof is 27.
% 32.29/32.61 % Maximum clause weight is 43.000.
% 32.29/32.61 % Given clauses 1052.
% 32.29/32.61
% 32.29/32.61 1 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 2 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 3 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 4 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 5 (all A mult(A,unit) = A) # label(f05) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 6 (all A mult(unit,A) = A) # label(f06) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 7 (all C all B all A mult(mult(A,B),mult(mult(C,B),C)) = mult(mult(A,mult(mult(B,C),B)),C)) # label(f07) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 8 (all B all A mult(mult(A,B),A) = mult(A,mult(B,A))) # label(f08) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 9 (all A mult(f(A),f(A)) = A) # label(f09) # label(axiom) # label(non_clause). [assumption].
% 32.29/32.61 10 -((all X0 all X1 all X2 mult(X2,mult(X0,mult(X2,X1))) = mult(mult(mult(X2,X0),X2),X1)) | (all X3 all X4 all X5 mult(X3,mult(X5,mult(X4,X5))) = mult(mult(mult(X3,X5),X4),X5)) | (all X6 all X7 all X8 mult(mult(X8,X6),mult(X7,X8)) = mult(mult(X8,mult(X6,X7)),X8)) | (all X9 all X10 all X11 mult(mult(X11,X9),mult(X10,X11)) = mult(X11,mult(mult(X9,X10),X11)))) # label(goals) # label(negated_conjecture) # label(non_clause). [assumption].
% 32.29/32.61 11 mult(A,unit) = A # label(f05) # label(axiom). [clausify(5)].
% 32.29/32.61 12 mult(unit,A) = A # label(f06) # label(axiom). [clausify(6)].
% 32.29/32.61 13 mult(A,ld(A,B)) = B # label(f01) # label(axiom). [clausify(1)].
% 32.29/32.61 14 ld(A,mult(A,B)) = B # label(f02) # label(axiom). [clausify(2)].
% 32.29/32.61 15 mult(rd(A,B),B) = A # label(f03) # label(axiom). [clausify(3)].
% 32.29/32.61 16 rd(mult(A,B),B) = A # label(f04) # label(axiom). [clausify(4)].
% 32.29/32.61 17 mult(f(A),f(A)) = A # label(f09) # label(axiom). [clausify(9)].
% 32.29/32.61 18 mult(mult(A,B),A) = mult(A,mult(B,A)) # label(f08) # label(axiom). [clausify(8)].
% 32.29/32.61 19 mult(mult(A,mult(mult(B,C),B)),C) = mult(mult(A,B),mult(mult(C,B),C)) # label(f07) # label(axiom). [clausify(7)].
% 32.29/32.61 20 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))). [copy(19),rewrite([18(2),18(7)])].
% 32.29/32.61 21 mult(mult(mult(c3,c1),c3),c2) != mult(c3,mult(c1,mult(c3,c2))) # label(goals) # label(negated_conjecture) # answer(goals). [clausify(10)].
% 32.29/32.61 22 mult(mult(c3,mult(c1,c3)),c2) != mult(c3,mult(c1,mult(c3,c2))) # answer(goals). [copy(21),rewrite([18(5)])].
% 32.29/32.61 28 ld(A,A) = unit. [para(11(a,1),14(a,1,2))].
% 32.29/32.61 30 ld(rd(A,B),A) = B. [para(15(a,1),14(a,1,2))].
% 32.29/32.61 32 rd(A,ld(B,A)) = B. [para(13(a,1),16(a,1,1))].
% 32.29/32.61 33 ld(f(A),A) = f(A). [para(17(a,1),14(a,1,2))].
% 32.29/32.61 35 mult(A,mult(ld(A,B),A)) = mult(B,A). [para(13(a,1),18(a,1,1)),flip(a)].
% 32.29/32.61 36 ld(mult(A,B),mult(A,mult(B,A))) = A. [para(18(a,1),14(a,1,2))].
% 32.29/32.61 37 mult(rd(A,B),mult(B,rd(A,B))) = mult(A,rd(A,B)). [para(15(a,1),18(a,1,1)),flip(a)].
% 32.29/32.61 38 rd(mult(A,mult(B,A)),A) = mult(A,B). [para(18(a,1),16(a,1,1))].
% 32.29/32.61 39 mult(f(A),A) = mult(A,f(A)). [para(17(a,1),18(a,1,1)),rewrite([17(6)]),flip(a)].
% 32.29/32.61 40 mult(mult(A,mult(B,A)),mult(A,B)) = mult(mult(A,B),mult(A,mult(A,B))). [para(18(a,1),18(a,1,1))].
% 32.29/32.61 41 mult(mult(A,B),B) = mult(A,mult(B,B)). [para(20(a,1),11(a,1)),rewrite([11(4),12(3),12(4)])].
% 32.29/32.61 42 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))). [para(12(a,1),20(a,1,1)),rewrite([12(5)])].
% 32.29/32.61 43 mult(mult(A,mult(ld(B,C),C)),B) = mult(mult(A,ld(B,C)),mult(C,B)). [para(13(a,1),20(a,1,1,2,2)),rewrite([35(9)])].
% 32.29/32.61 44 mult(mult(A,mult(B,C)),ld(C,B)) = mult(mult(A,C),mult(ld(C,B),B)). [para(13(a,1),20(a,2,2,2)),rewrite([35(3)])].
% 32.29/32.61 46 mult(mult(A,mult(B,C)),rd(C,B)) = mult(mult(A,B),mult(C,rd(C,B))). [para(15(a,1),20(a,1,1,2,2)),rewrite([37(9)])].
% 32.29/32.61 47 mult(mult(rd(A,mult(B,mult(C,B))),B),mult(C,mult(B,C))) = mult(A,C). [para(15(a,1),20(a,1,1)),flip(a)].
% 32.29/32.61 49 rd(mult(mult(A,B),mult(C,mult(B,C))),C) = mult(A,mult(B,mult(C,B))). [para(20(a,1),16(a,1,1))].
% 32.29/32.61 50 mult(mult(A,mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(17(a,1),20(a,1,1,2,2)),rewrite([39(2),17(11),39(9)])].
% 32.29/32.61 53 mult(mult(A,mult(B,mult(B,mult(C,B)))),mult(B,C)) = mult(mult(A,B),mult(mult(B,C),mult(B,mult(B,C)))). [para(18(a,1),20(a,1,1,2,2))].
% 32.29/32.61 59 rd(mult(A,f(A)),A) = f(A). [para(39(a,1),16(a,1,1))].
% 32.29/32.61 60 mult(f(A),mult(A,f(A))) = mult(A,A). [para(39(a,1),18(a,1,1)),rewrite([41(4),17(3)]),flip(a)].
% 32.29/32.61 64 ld(A,mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),14(a,1,2))].
% 32.29/32.61 66 mult(A,mult(ld(A,B),mult(A,A))) = mult(B,mult(A,A)). [para(35(a,1),18(a,1,1)),rewrite([41(2),41(5)]),flip(a)].
% 32.29/32.61 72 ld(mult(A,mult(B,A)),mult(mult(A,B),mult(A,mult(A,B)))) = mult(A,B). [para(18(a,1),36(a,1,1))].
% 32.29/32.61 76 ld(mult(A,f(A)),mult(A,A)) = f(A). [para(39(a,1),36(a,1,1)),rewrite([60(6)])].
% 32.29/32.61 78 ld(mult(A,B),mult(A,mult(B,B))) = B. [para(35(a,1),36(a,1,1)),rewrite([41(4),66(5)])].
% 32.29/32.61 81 rd(mult(A,B),A) = mult(A,rd(B,A)). [para(15(a,1),38(a,1,1,2))].
% 32.29/32.61 84 rd(mult(A,mult(B,B)),B) = mult(A,B). [para(35(a,1),38(a,2)),rewrite([41(3),66(4)])].
% 32.29/32.61 85 mult(A,rd(f(A),A)) = f(A). [back_rewrite(59),rewrite([81(3)])].
% 32.29/32.61 86 rd(f(A),A) = ld(A,f(A)). [para(85(a,1),14(a,1,2)),flip(a)].
% 32.29/32.61 94 mult(ld(A,f(A)),A) = f(A). [para(86(a,1),15(a,1,1))].
% 32.29/32.61 96 mult(ld(A,f(A)),f(A)) = mult(f(A),ld(A,f(A))). [para(86(a,1),37(a,1,1)),rewrite([86(4),13(5),86(7)])].
% 32.29/32.61 101 mult(rd(A,B),mult(B,B)) = mult(A,B). [para(15(a,1),41(a,1,1)),flip(a)].
% 32.29/32.61 145 mult(ld(A,unit),A) = unit. [para(12(a,1),64(a,1,2)),rewrite([28(1)]),flip(a)].
% 32.29/32.61 147 mult(ld(A,rd(B,A)),A) = ld(A,B). [para(15(a,1),64(a,1,2)),flip(a)].
% 32.29/32.61 154 mult(ld(mult(A,f(A)),f(A)),mult(A,f(A))) = f(A). [para(60(a,1),64(a,1,2)),rewrite([76(4)]),flip(a)].
% 32.29/32.61 155 ld(ld(A,unit),unit) = A. [para(145(a,1),14(a,1,2))].
% 32.29/32.61 156 rd(unit,A) = ld(A,unit). [para(145(a,1),16(a,1,1))].
% 32.29/32.61 158 mult(ld(A,unit),mult(A,A)) = A. [para(145(a,1),41(a,1,1)),rewrite([12(2)]),flip(a)].
% 32.29/32.61 160 mult(mult(ld(A,B),B),A) = mult(ld(A,B),mult(B,A)). [para(13(a,1),42(a,1,1,2)),rewrite([35(7)])].
% 32.29/32.61 171 mult(mult(A,f(A)),mult(A,f(A))) = mult(A,mult(A,A)). [para(39(a,1),42(a,1,1,2)),rewrite([50(5),60(9)])].
% 32.29/32.61 191 ld(ld(A,unit),A) = mult(A,A). [para(158(a,1),14(a,1,2))].
% 32.29/32.61 192 rd(A,mult(A,A)) = ld(A,unit). [para(158(a,1),16(a,1,1))].
% 32.29/32.61 193 mult(ld(f(A),unit),A) = f(A). [para(17(a,1),158(a,1,2))].
% 32.29/32.61 203 mult(ld(A,unit),ld(A,unit)) = ld(A,ld(A,unit)). [para(30(a,1),191(a,1,1)),rewrite([156(2),156(5),156(7)]),flip(a)].
% 32.29/32.61 204 mult(mult(A,A),ld(A,unit)) = A. [para(191(a,1),64(a,2,1)),rewrite([13(5),155(4)]),flip(a)].
% 32.29/32.61 205 ld(f(A),unit) = ld(A,f(A)). [para(17(a,1),192(a,1,2)),rewrite([86(2)]),flip(a)].
% 32.29/32.61 207 mult(A,mult(ld(A,B),mult(B,A))) = mult(B,mult(B,A)). [para(13(a,1),43(a,2,1)),rewrite([18(4),160(3)])].
% 32.29/32.61 230 mult(ld(f(A),unit),mult(A,ld(f(A),unit))) = unit. [para(193(a,1),18(a,1,1)),rewrite([13(5)]),flip(a)].
% 32.29/32.61 231 mult(mult(A,mult(B,f(B))),ld(f(B),unit)) = mult(A,B). [para(193(a,1),20(a,1,1,2,2)),rewrite([230(16),11(10)])].
% 32.29/32.61 232 mult(mult(A,ld(f(B),unit)),mult(B,f(B))) = mult(A,B). [para(193(a,1),20(a,2,2,2)),rewrite([230(8),11(2)]),flip(a)].
% 32.29/32.61 237 mult(mult(A,f(A)),ld(f(A),unit)) = A. [para(193(a,1),42(a,1,1,2)),rewrite([230(14),11(8)])].
% 32.29/32.61 241 mult(A,ld(f(A),unit)) = f(A). [para(17(a,1),204(a,1,1))].
% 32.29/32.61 245 mult(f(A),ld(A,f(A))) = unit. [para(205(a,1),13(a,1,2))].
% 32.29/32.61 252 mult(ld(A,f(A)),f(A)) = unit. [back_rewrite(96),rewrite([245(8)])].
% 32.29/32.61 294 mult(A,ld(f(A),ld(f(A),unit))) = unit. [para(241(a,1),41(a,1,1)),rewrite([13(5),203(8)]),flip(a)].
% 32.29/32.61 422 mult(mult(A,mult(mult(B,C),mult(ld(C,D),D))),rd(ld(C,D),mult(B,mult(D,C)))) = mult(mult(A,mult(B,mult(D,C))),mult(ld(C,D),rd(ld(C,D),mult(B,mult(D,C))))). [para(44(a,1),46(a,1,1,2))].
% 32.29/32.61 432 ld(mult(A,f(B)),mult(A,B)) = f(B). [para(17(a,1),78(a,1,2,2))].
% 32.29/32.61 465 mult(rd(A,mult(B,B)),B) = rd(A,B). [para(15(a,1),84(a,1,1)),flip(a)].
% 32.29/32.61 466 rd(mult(A,B),f(B)) = mult(A,f(B)). [para(17(a,1),84(a,1,1,2))].
% 32.29/32.61 476 ld(mult(rd(A,mult(B,mult(C,B))),B),mult(A,C)) = mult(C,mult(B,C)). [para(47(a,1),14(a,1,2))].
% 32.29/32.61 479 mult(mult(rd(A,mult(B,f(B))),f(B)),mult(B,f(B))) = mult(A,f(B)). [para(17(a,1),47(a,1,1,1,2,2)),rewrite([39(2),17(9),39(7)])].
% 32.29/32.61 494 mult(rd(A,mult(B,f(B))),B) = mult(A,ld(B,f(B))). [para(94(a,1),47(a,1,1,1,2,2)),rewrite([13(9),252(8),11(6)])].
% 32.29/32.61 508 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = mult(A,ld(B,unit)). [para(158(a,1),47(a,1,1,1,2,2)),rewrite([18(2),204(11),145(8),11(7)])].
% 32.29/32.61 511 mult(A,ld(f(B),unit)) = mult(A,ld(B,f(B))). [para(193(a,1),47(a,1,1,1,2,2)),rewrite([494(4),241(10),145(8),11(5)]),flip(a)].
% 32.29/32.61 527 ld(rd(A,B),mult(A,B)) = mult(B,B). [para(101(a,1),14(a,1,2))].
% 32.29/32.61 529 mult(rd(A,f(B)),B) = mult(A,f(B)). [para(17(a,1),101(a,1,2))].
% 32.29/32.61 645 rd(A,ld(f(A),unit)) = mult(A,f(A)). [para(237(a,1),16(a,1,1))].
% 32.29/32.61 648 mult(mult(A,f(A)),ld(f(A),ld(f(A),unit))) = f(A). [para(237(a,1),41(a,1,1)),rewrite([241(4),203(10)]),flip(a)].
% 32.29/32.61 708 mult(ld(A,unit),mult(A,mult(B,A))) = mult(B,A). [para(145(a,1),49(a,1,1,1)),rewrite([12(4),81(3),16(2)]),flip(a)].
% 32.29/32.61 775 ld(f(A),ld(f(A),unit)) = ld(A,unit). [para(294(a,1),14(a,1,2)),flip(a)].
% 32.29/32.61 781 mult(mult(A,f(A)),ld(A,unit)) = f(A). [back_rewrite(648),rewrite([775(7)])].
% 32.29/32.61 791 mult(mult(A,mult(B,f(B))),B) = mult(mult(A,B),mult(B,f(B))). [para(50(a,1),41(a,1,1)),rewrite([50(7),41(4),17(3),17(10)]),flip(a)].
% 32.29/32.61 810 rd(mult(mult(A,B),mult(B,f(B))),f(B)) = mult(mult(A,f(B)),mult(B,f(B))). [para(50(a,1),84(a,2)),rewrite([17(6),791(4)])].
% 32.29/32.61 878 ld(rd(A,mult(B,B)),rd(A,B)) = B. [para(465(a,1),14(a,1,2))].
% 32.29/32.61 880 mult(rd(A,B),f(B)) = rd(A,f(B)). [para(17(a,1),465(a,1,1,2))].
% 32.29/32.61 912 mult(mult(rd(A,mult(B,mult(B,B))),f(B)),mult(B,f(B))) = mult(rd(A,mult(B,f(B))),f(B)). [para(465(a,1),50(a,1,1)),rewrite([171(10)]),flip(a)].
% 32.29/32.61 1026 mult(ld(A,unit),f(A)) = ld(f(A),unit). [para(145(a,1),466(a,1,1)),rewrite([156(3)]),flip(a)].
% 32.29/32.61 1068 ld(mult(A,f(A)),f(A)) = ld(A,unit). [para(241(a,1),527(a,1,2)),rewrite([645(4),203(11),775(9)])].
% 32.29/32.61 1089 mult(ld(A,unit),mult(A,f(A))) = f(A). [back_rewrite(154),rewrite([1068(4)])].
% 32.29/32.61 1622 mult(A,ld(B,unit)) = rd(A,B). [para(781(a,1),47(a,1,2,2)),rewrite([1089(7),41(4),17(3),1026(9),231(9),465(3)]),flip(a)].
% 32.29/32.61 1672 mult(A,ld(B,f(B))) = rd(A,f(B)). [back_rewrite(511),rewrite([1622(4)]),flip(a)].
% 32.29/32.61 1673 mult(rd(A,mult(B,mult(B,B))),mult(B,B)) = rd(A,B). [back_rewrite(508),rewrite([1622(8)])].
% 32.29/32.61 1677 mult(rd(A,f(B)),mult(B,f(B))) = mult(A,B). [back_rewrite(232),rewrite([1622(4)])].
% 32.29/32.61 1678 rd(mult(A,mult(B,f(B))),f(B)) = mult(A,B). [back_rewrite(231),rewrite([1622(7)])].
% 32.29/32.61 1696 mult(mult(A,f(B)),mult(B,f(B))) = mult(A,mult(B,B)). [back_rewrite(810),rewrite([1678(6),41(2)]),flip(a)].
% 32.29/32.61 1720 mult(rd(A,mult(B,f(B))),f(B)) = rd(A,B). [back_rewrite(912),rewrite([1696(8),1673(5)]),flip(a)].
% 32.29/32.61 1755 mult(rd(A,B),mult(B,f(B))) = mult(A,f(B)). [back_rewrite(479),rewrite([1720(5)])].
% 32.29/32.61 1778 ld(A,rd(A,B)) = ld(B,unit). [para(1622(a,1),14(a,1,2))].
% 32.29/32.61 1863 ld(mult(A,B),A) = ld(B,unit). [para(16(a,1),1778(a,1,2))].
% 32.29/32.61 1864 ld(ld(A,B),unit) = ld(B,A). [para(32(a,1),1778(a,1,2)),flip(a)].
% 32.29/32.61 2038 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(mult(A,B),unit). [para(40(a,1),1863(a,1,1))].
% 32.29/32.61 2068 rd(A,ld(B,C)) = mult(A,ld(C,B)). [para(1864(a,1),1622(a,1,2)),flip(a)].
% 32.29/32.61 2227 ld(rd(A,B),rd(A,f(B))) = f(B). [para(17(a,1),878(a,1,1,2))].
% 32.29/32.61 2638 mult(mult(A,ld(B,ld(C,f(C)))),mult(ld(C,f(C)),B)) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [para(1672(a,1),43(a,1,1,2)),flip(a)].
% 32.29/32.61 3399 mult(ld(A,unit),mult(A,B)) = B. [para(15(a,1),708(a,1,2,2)),rewrite([15(6)])].
% 32.29/32.61 3406 mult(ld(A,unit),mult(B,A)) = mult(ld(A,B),A). [para(35(a,1),708(a,1,2))].
% 32.29/32.61 3408 mult(mult(A,B),mult(ld(B,A),B)) = mult(A,mult(A,B)). [para(708(a,1),40(a,1,2)),rewrite([1622(7),81(5),16(4),3399(4),3399(7),3399(10),3406(7)]),flip(a)].
% 32.29/32.61 3420 mult(ld(A,unit),B) = ld(A,B). [para(147(a,1),708(a,1,2,2)),rewrite([13(4),147(6)])].
% 32.29/32.61 3432 mult(mult(A,ld(B,C)),mult(C,B)) = mult(rd(A,B),mult(C,mult(C,B))). [para(708(a,1),53(a,1,2)),rewrite([1622(9),81(7),16(6),3420(6),14(4),3420(3),1622(7),3420(10),14(8),3420(13),14(11),3420(10),64(8),3408(9)])].
% 32.29/32.61 3682 mult(rd(A,B),mult(ld(C,f(C)),mult(ld(C,f(C)),B))) = mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B). [back_rewrite(2638),rewrite([3432(8)])].
% 32.29/32.61 4035 rd(ld(A,B),B) = ld(A,unit). [para(3420(a,1),16(a,1,1))].
% 32.29/32.61 4041 ld(A,mult(B,B)) = mult(ld(A,B),B). [para(3420(a,1),41(a,1,1)),rewrite([3420(6)]),flip(a)].
% 32.29/32.61 4045 mult(ld(A,f(A)),B) = ld(f(A),B). [para(205(a,1),3420(a,1,1))].
% 32.29/32.61 4054 rd(mult(ld(A,B),mult(C,mult(B,C))),C) = ld(A,mult(B,mult(C,B))). [para(3420(a,1),49(a,1,1,1)),rewrite([3420(10)])].
% 32.29/32.61 4057 ld(ld(A,f(B)),ld(A,B)) = f(B). [para(3420(a,1),432(a,1,1)),rewrite([3420(5)])].
% 32.29/32.61 4071 rd(ld(A,unit),B) = ld(A,ld(B,unit)). [para(3420(a,1),1622(a,1)),flip(a)].
% 32.29/32.61 4076 ld(ld(A,B),C) = mult(ld(B,A),C). [para(1864(a,1),3420(a,1,1)),flip(a)].
% 32.29/32.61 4107 mult(mult(A,rd(ld(B,ld(C,f(C))),f(C))),B) = mult(rd(A,B),ld(f(C),ld(f(C),B))). [back_rewrite(3682),rewrite([4045(6),4045(6)]),flip(a)].
% 32.29/32.61 4168 mult(ld(f(A),B),ld(B,A)) = f(A). [back_rewrite(4057),rewrite([4076(4)])].
% 32.29/32.61 4352 rd(A,mult(B,A)) = ld(B,unit). [para(14(a,1),4035(a,1,1))].
% 32.29/32.61 4353 ld(rd(A,B),unit) = rd(B,A). [para(30(a,1),4035(a,1,1)),flip(a)].
% 32.29/32.61 4363 mult(ld(A,f(B)),f(B)) = ld(A,B). [para(4035(a,1),529(a,1,1)),rewrite([3420(3)]),flip(a)].
% 32.29/32.61 4364 ld(mult(A,B),unit) = ld(B,ld(A,unit)). [para(1863(a,1),4035(a,1,1)),rewrite([4071(3)]),flip(a)].
% 32.29/32.61 4367 rd(f(A),rd(B,f(A))) = rd(A,B). [para(2227(a,1),4035(a,1,1)),rewrite([4353(7)])].
% 32.29/32.61 4393 ld(mult(mult(A,B),mult(A,mult(A,B))),mult(A,mult(B,A))) = ld(B,ld(A,unit)). [back_rewrite(2038),rewrite([4364(10)])].
% 32.29/32.61 4692 rd(A,rd(B,C)) = mult(A,rd(C,B)). [para(4353(a,1),1622(a,1,2)),flip(a)].
% 32.29/32.61 4696 ld(rd(A,B),C) = mult(rd(B,A),C). [para(4353(a,1),3420(a,1,1)),flip(a)].
% 32.29/32.61 4700 mult(f(A),rd(f(A),B)) = rd(A,B). [back_rewrite(4367),rewrite([4692(4)])].
% 32.29/32.61 5032 mult(mult(A,A),B) = mult(A,mult(A,B)). [para(4041(a,1),35(a,1,2,1)),rewrite([160(3),207(4)]),flip(a)].
% 32.29/32.61 5046 rd(ld(A,ld(B,f(B))),f(B)) = ld(A,ld(B,unit)). [para(1672(a,1),4041(a,1,2)),rewrite([4035(4),1672(9)]),flip(a)].
% 32.29/32.61 5402 mult(rd(A,B),ld(f(C),ld(f(C),B))) = mult(mult(A,ld(B,ld(C,unit))),B). [back_rewrite(4107),rewrite([5046(5)]),flip(a)].
% 32.29/32.61 5481 mult(ld(A,ld(B,unit)),C) = ld(mult(B,A),C). [para(72(a,1),4076(a,1,1)),rewrite([4393(9)]),flip(a)].
% 32.29/32.61 5868 ld(f(A),ld(f(A),B)) = ld(A,B). [para(4168(a,1),1863(a,1,1)),rewrite([4076(7),11(7)])].
% 32.29/32.61 5886 mult(mult(A,ld(B,ld(C,unit))),B) = mult(rd(A,B),ld(C,B)). [back_rewrite(5402),rewrite([5868(5)]),flip(a)].
% 32.29/32.61 6083 mult(A,ld(B,ld(C,unit))) = rd(A,mult(C,B)). [para(4364(a,1),1622(a,1,2))].
% 32.29/32.61 6092 mult(rd(A,mult(B,C)),C) = mult(rd(A,C),ld(B,C)). [back_rewrite(5886),rewrite([6083(4)])].
% 32.29/32.61 6314 rd(A,mult(B,ld(C,D))) = mult(A,rd(ld(D,C),B)). [para(2068(a,1),4692(a,1,2))].
% 32.29/32.61 6530 ld(mult(rd(A,B),C),D) = mult(ld(C,rd(B,A)),D). [para(4696(a,1),4076(a,1,1))].
% 32.29/32.61 6619 mult(ld(A,rd(mult(A,mult(B,A)),C)),mult(C,B)) = mult(B,mult(A,B)). [back_rewrite(476),rewrite([6530(6)])].
% 32.29/32.61 7140 mult(f(A),mult(f(A),B)) = mult(A,B). [para(17(a,1),5032(a,1,1)),flip(a)].
% 32.29/32.61 8215 rd(mult(A,mult(B,C)),C) = mult(mult(A,C),ld(C,B)). [para(7140(a,1),44(a,1,1,2)),rewrite([1863(6),1622(5),1863(10),3420(10),44(9),4363(8)])].
% 32.29/32.61 13374 mult(ld(A,ld(B,ld(C,unit))),D) = ld(mult(mult(C,B),A),D). [para(4364(a,1),5481(a,1,1,2))].
% 32.29/32.61 19985 mult(rd(mult(A,B),C),mult(rd(C,B),ld(A,B))) = B. [para(6092(a,1),14(a,1,2)),rewrite([4696(6)])].
% 32.29/32.61 20011 mult(A,mult(ld(A,B),rd(A,C))) = rd(mult(B,A),C). [para(6092(a,1),4352(a,1,2)),rewrite([6314(4),4692(3),4696(8),11(8)])].
% 32.29/32.61 20012 ld(mult(mult(A,B),C),B) = ld(mult(B,C),ld(A,B)). [para(4071(a,1),6092(a,1,1)),rewrite([4364(3),13374(5),4071(6),5481(8)])].
% 32.29/32.61 20288 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)). [para(1755(a,1),422(a,1,2,2)),rewrite([880(3),33(4),39(4),1677(5),33(4),4352(6),1622(5),1755(7),33(8),33(9),1755(12),4352(11),1622(10),46(9),4700(8)])].
% 32.29/32.61 20305 ld(A,mult(B,mult(C,B))) = mult(mult(ld(A,B),C),B). [back_rewrite(4054),rewrite([20288(5),16(4)]),flip(a)].
% 32.29/32.61 22004 mult(ld(A,mult(mult(B,A),ld(A,C))),A) = ld(A,mult(B,mult(C,A))). [para(8215(a,1),147(a,1,1,2))].
% 32.29/32.61 24250 mult(mult(mult(A,B),ld(B,C)),ld(C,ld(A,B))) = B. [para(4035(a,1),19985(a,1,2,1)),rewrite([2068(3),3420(7)])].
% 32.29/32.61 24338 rd(mult(A,mult(B,A)),C) = mult(A,mult(B,rd(A,C))). [para(14(a,1),20011(a,1,2,1)),rewrite([18(5)]),flip(a)].
% 32.29/32.61 24388 mult(mult(A,rd(B,C)),mult(C,A)) = mult(A,mult(B,A)). [back_rewrite(6619),rewrite([24338(3),14(4)])].
% 32.29/32.61 24447 mult(ld(A,mult(mult(B,A),C)),D) = mult(mult(ld(A,B),mult(A,C)),D). [para(20012(a,1),4076(a,1,1)),rewrite([4076(4),4076(3)]),flip(a)].
% 32.29/32.61 24477 ld(A,mult(B,mult(C,A))) = mult(mult(ld(A,B),C),A). [back_rewrite(22004),rewrite([24447(5),13(3)]),flip(a)].
% 32.29/32.61 24580 mult(A,mult(mult(ld(A,B),C),B)) = mult(B,mult(C,B)). [para(20305(a,1),13(a,1,2))].
% 32.29/32.61 24584 mult(A,mult(mult(mult(ld(A,B),C),B),A)) = mult(mult(B,mult(C,B)),A). [para(20305(a,1),35(a,1,2,1))].
% 32.29/32.61 25493 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)). [para(24250(a,1),16(a,1,1)),rewrite([2068(3),4076(2)]),flip(a)].
% 32.29/32.61 25808 mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)). [para(16(a,1),24388(a,1,1,2))].
% 32.29/32.61 25888 mult(A,mult(mult(ld(A,B),C),A)) = mult(B,mult(C,A)). [para(24477(a,1),13(a,1,2))].
% 32.29/32.61 26050 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))). [para(14(a,1),24580(a,1,2,1,1)),rewrite([25808(3)]),flip(a)].
% 32.29/32.61 26456 mult(mult(A,mult(B,A)),C) = mult(A,mult(B,mult(A,C))). [para(25493(a,1),18(a,1,1)),rewrite([25808(5),24584(5),26050(8),25888(7)])].
% 32.29/32.61 26457 $F # answer(goals). [resolve(26456,a,22,a)].
% 32.29/32.61
% 32.29/32.61 % SZS output end Refutation
% 32.29/32.61 ============================== end of proof ==========================
% 32.29/32.61
% 32.29/32.61 ============================== STATISTICS ============================
% 32.29/32.61
% 32.29/32.61 Given=1052. Generated=909438. Kept=26437. proofs=4.
% 32.29/32.61 Usable=634. Sos=8849. Demods=8956. Limbo=1, Disabled=16965. Hints=0.
% 32.29/32.61 Megabytes=27.75.
% 32.29/32.61 User_CPU=31.11, System_CPU=0.51, Wall_clock=32.
% 32.29/32.61
% 32.29/32.61 ============================== end of statistics =====================
% 32.29/32.61
% 32.29/32.61 ============================== end of search =========================
% 32.29/32.61
% 32.29/32.61 THEOREM PROVED
% 32.29/32.61 % SZS status Theorem
% 32.29/32.61
% 32.29/32.61 Exiting with 4 proofs.
% 32.29/32.61
% 32.29/32.61 Process 5410 exit (max_proofs) Tue Jun 14 10:54:15 2022
% 32.29/32.61 Prover9 interrupted
%------------------------------------------------------------------------------