0.03/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.13/0.33	% Computer : n002.cluster.edu
0.13/0.33	% Model    : x86_64 x86_64
0.13/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory   : 8042.1875MB
0.13/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 1440
0.13/0.34	% WCLimit  : 180
0.13/0.34	% DateTime : Mon Jul  3 07:56:37 EDT 2023
0.13/0.34	% CPUTime  : 
3.09/3.39	============================== Prover9 ===============================
3.09/3.39	Prover9 (32) version 2009-11A, November 2009.
3.09/3.39	Process 28402 was started by sandbox on n002.cluster.edu,
3.09/3.39	Mon Jul  3 07:56:37 2023
3.09/3.39	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_28249_n002.cluster.edu".
3.09/3.39	============================== end of head ===========================
3.09/3.39	
3.09/3.39	============================== INPUT =================================
3.09/3.39	
3.09/3.39	% Reading from file /tmp/Prover9_28249_n002.cluster.edu
3.09/3.39	
3.09/3.39	set(prolog_style_variables).
3.09/3.39	set(auto2).
3.09/3.39	    % set(auto2) -> set(auto).
3.09/3.39	    % set(auto) -> set(auto_inference).
3.09/3.39	    % set(auto) -> set(auto_setup).
3.09/3.39	    % set(auto_setup) -> set(predicate_elim).
3.09/3.39	    % set(auto_setup) -> assign(eq_defs, unfold).
3.09/3.39	    % set(auto) -> set(auto_limits).
3.09/3.39	    % set(auto_limits) -> assign(max_weight, "100.000").
3.09/3.39	    % set(auto_limits) -> assign(sos_limit, 20000).
3.09/3.39	    % set(auto) -> set(auto_denials).
3.09/3.39	    % set(auto) -> set(auto_process).
3.09/3.39	    % set(auto2) -> assign(new_constants, 1).
3.09/3.39	    % set(auto2) -> assign(fold_denial_max, 3).
3.09/3.39	    % set(auto2) -> assign(max_weight, "200.000").
3.09/3.39	    % set(auto2) -> assign(max_hours, 1).
3.09/3.39	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
3.09/3.39	    % set(auto2) -> assign(max_seconds, 0).
3.09/3.39	    % set(auto2) -> assign(max_minutes, 5).
3.09/3.39	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
3.09/3.39	    % set(auto2) -> set(sort_initial_sos).
3.09/3.39	    % set(auto2) -> assign(sos_limit, -1).
3.09/3.39	    % set(auto2) -> assign(lrs_ticks, 3000).
3.09/3.39	    % set(auto2) -> assign(max_megs, 400).
3.09/3.39	    % set(auto2) -> assign(stats, some).
3.09/3.39	    % set(auto2) -> clear(echo_input).
3.09/3.39	    % set(auto2) -> set(quiet).
3.09/3.39	    % set(auto2) -> clear(print_initial_clauses).
3.09/3.39	    % set(auto2) -> clear(print_given).
3.09/3.39	assign(lrs_ticks,-1).
3.09/3.39	assign(sos_limit,10000).
3.09/3.39	assign(order,kbo).
3.09/3.39	set(lex_order_vars).
3.09/3.39	clear(print_given).
3.09/3.39	
3.09/3.39	% formulas(sos).  % not echoed (6 formulas)
3.09/3.39	
3.09/3.39	============================== end of input ==========================
3.09/3.39	
3.09/3.39	% From the command line: assign(max_seconds, 1440).
3.09/3.39	
3.09/3.39	============================== PROCESS NON-CLAUSAL FORMULAS ==========
3.09/3.39	
3.09/3.39	% Formulas that are not ordinary clauses:
3.09/3.39	1 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause).  [assumption].
3.09/3.39	2 (all C all B all A mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C)))) # label(f05) # label(axiom) # label(non_clause).  [assumption].
3.09/3.39	3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause).  [assumption].
3.09/3.39	4 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause).  [assumption].
3.09/3.39	5 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause).  [assumption].
3.09/3.39	6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & X0 = mult(rd(X1,X1),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
3.09/3.39	
3.09/3.39	============================== end of process non-clausal formulas ===
3.09/3.39	
3.09/3.39	============================== PROCESS INITIAL CLAUSES ===============
3.09/3.39	
3.09/3.39	============================== PREDICATE ELIMINATION =================
3.09/3.39	
3.09/3.39	============================== end predicate elimination =============
3.09/3.39	
3.09/3.39	Auto_denials:
3.09/3.39	  % copying label goals to answer in negative clause
3.09/3.39	
3.09/3.39	Term ordering decisions:
3.09/3.39	Function symbol KB weights:  c1=1. c2=1. mult=1. ld=1. rd=1.
3.09/3.39	
3.09/3.39	============================== end of process initial clauses ========
3.09/3.39	
3.09/3.39	============================== CLAUSES FOR SEARCH ====================
3.09/3.39	
3.09/3.39	============================== end of clauses for search =============
3.09/3.39	
3.09/3.39	============================== SEARCH ================================
3.09/3.39	
3.09/3.39	% Starting search at 0.01 seconds.
3.09/3.39	
3.09/3.39	Low Water (keep): wt=155.000, iters=3344
3.09/3.39	
3.09/3.39	Low Water (keep): wt=139.000, iters=3362
3.09/3.39	
3.09/3.39	Low Water (keep): wt=131.000, iters=3333
3.09/3.39	
3.09/3.39	Low Water (keep): wt=83.000, iters=3335
3.09/3.39	
3.09/3.39	Low Water (keep): wt=71.000, iters=3367
3.09/3.39	
3.09/3.39	Low Water (keep): wt=67.000, iters=3339
3.09/3.39	
3.09/3.39	Low Water (keep): wt=63.000, iters=3340
3.09/3.39	
3.09/3.39	Low Water (keep): wt=59.000, iters=3377
3.09/3.39	
3.09/3.39	Low Water (keep): wt=55.000, iters=3374
3.09/3.39	
3.09/3.39	Low Water (keep): wt=51.000, iters=3466
3.09/3.39	
3.09/3.39	Low Water (keep): wt=47.000, iters=3337
3.09/3.39	
3.09/3.39	Low Water (keep): wt=43.000, iters=3336
3.09/3.39	
3.09/3.39	Low Water (keep): wt=39.000, iters=3354
143.90/144.29	
143.90/144.29	Low Water (keep): wt=35.000, iters=3368
143.90/144.29	
143.90/144.29	Low Water (keep): wt=31.000, iters=3346
143.90/144.29	
143.90/144.29	Low Water (displace): id=7089, wt=199.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=6981, wt=195.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7048, wt=187.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7028, wt=183.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7127, wt=179.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7080, wt=175.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7145, wt=171.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=6710, wt=167.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7107, wt=163.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7112, wt=159.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7041, wt=155.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=5013, wt=151.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7114, wt=147.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7105, wt=143.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7313, wt=139.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7098, wt=135.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7151, wt=131.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7418, wt=127.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7314, wt=123.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=7432, wt=119.000
143.90/144.29	
143.90/144.29	Low Water (displace): id=13164, wt=23.000
143.90/144.29	
143.90/144.29	Low Water (keep): wt=27.000, iters=3383
143.90/144.29	
143.90/144.29	Low Water (displace): id=13902, wt=19.000
143.90/144.29	
143.90/144.29	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 50 (0.00 of 10.13 sec).
143.90/144.29	
143.90/144.29	Low Water (keep): wt=23.000, iters=3336
143.90/144.29	
143.90/144.29	============================== PROOF =================================
143.90/144.29	% SZS status Theorem
143.90/144.29	% SZS output start Refutation
143.90/144.29	
143.90/144.29	% Proof 1 at 140.06 (+ 3.13) seconds: goals.
143.90/144.29	% Length of proof is 291.
143.90/144.29	% Level of proof is 32.
143.90/144.29	% Maximum clause weight is 35.000.
143.90/144.29	% Given clauses 1615.
143.90/144.29	
143.90/144.29	1 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause).  [assumption].
143.90/144.29	2 (all C all B all A mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C)))) # label(f05) # label(axiom) # label(non_clause).  [assumption].
143.90/144.29	3 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause).  [assumption].
143.90/144.29	4 (all B all A B = mult(A,ld(A,B))) # label(f01) # label(axiom) # label(non_clause).  [assumption].
143.90/144.29	5 (all B all A ld(A,mult(A,B)) = B) # label(f02) # label(axiom) # label(non_clause).  [assumption].
143.90/144.29	6 -(all X0 all X1 (mult(X0,rd(X1,X1)) = X0 & X0 = mult(rd(X1,X1),X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
143.90/144.29	7 mult(rd(A,B),B) = A # label(f03) # label(axiom).  [clausify(1)].
143.90/144.29	8 rd(mult(A,B),B) = A # label(f04) # label(axiom).  [clausify(3)].
143.90/144.29	9 mult(A,ld(A,B)) = B # label(f01) # label(axiom).  [clausify(4)].
143.90/144.29	10 ld(A,mult(A,B)) = B # label(f02) # label(axiom).  [clausify(5)].
143.90/144.29	11 mult(mult(mult(A,B),A),C) = mult(A,mult(B,mult(A,C))) # label(f05) # label(axiom).  [clausify(2)].
143.90/144.29	12 mult(c1,rd(c2,c2)) != c1 | mult(rd(c2,c2),c1) != c1 # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(6)].
143.90/144.29	13 rd(A,ld(B,A)) = B.  [para(9(a,1),8(a,1,1))].
143.90/144.29	14 ld(rd(A,B),A) = B.  [para(7(a,1),10(a,1,2))].
143.90/144.29	15 mult(rd(A,B),mult(B,mult(rd(A,B),C))) = mult(mult(A,rd(A,B)),C).  [para(7(a,1),11(a,1,1,1)),flip(a)].
143.90/144.29	16 rd(mult(A,mult(B,mult(A,C))),C) = mult(mult(A,B),A).  [para(11(a,1),8(a,1,1))].
143.90/144.29	17 mult(A,mult(B,mult(A,ld(mult(mult(A,B),A),C)))) = C.  [para(11(a,1),9(a,1))].
143.90/144.29	18 mult(A,mult(ld(A,B),mult(A,C))) = mult(mult(B,A),C).  [para(9(a,1),11(a,1,1,1)),flip(a)].
143.90/144.29	21 mult(mult(A,mult(B,mult(A,mult(A,B)))),C) = mult(mult(A,B),mult(A,mult(mult(A,B),C))).  [para(11(a,1),11(a,1,1))].
143.90/144.29	22 rd(mult(rd(A,B),mult(C,A)),B) = mult(mult(rd(A,B),C),rd(A,B)).  [para(7(a,1),16(a,1,1,2,2))].
143.90/144.29	23 mult(mult(A,rd(B,mult(A,C))),A) = rd(mult(A,B),C).  [para(7(a,1),16(a,1,1,2)),flip(a)].
143.90/144.29	25 rd(mult(A,mult(B,mult(A,mult(C,mult(A,mult(B,mult(A,D))))))),D) = mult(mult(A,mult(B,mult(A,C))),mult(mult(A,B),A)).  [para(11(a,1),16(a,1,1,2,2)),rewrite([11(7),11(11)])].
143.90/144.29	28 mult(A,mult(B,ld(mult(mult(B,A),B),C))) = ld(B,C).  [para(17(a,1),10(a,1,2)),flip(a)].
143.90/144.29	34 rd(mult(mult(A,B),C),mult(ld(B,A),mult(B,C))) = B.  [para(18(a,1),8(a,1,1))].
143.90/144.29	35 mult(mult(A,B),ld(B,C)) = mult(B,mult(ld(B,A),C)).  [para(9(a,1),18(a,1,2,2)),flip(a)].
143.90/144.29	36 ld(A,mult(mult(B,A),C)) = mult(ld(A,B),mult(A,C)).  [para(18(a,1),10(a,1,2))].
143.90/144.29	37 mult(A,mult(mult(ld(A,B),mult(A,C)),mult(A,D))) = mult(mult(mult(mult(B,A),C),A),D).  [para(18(a,1),11(a,1,1,1)),flip(a)].
143.90/144.29	42 mult(mult(A,B),mult(ld(B,C),mult(B,D))) = mult(B,mult(ld(B,A),mult(mult(C,B),D))).  [para(18(a,1),18(a,1,2,2)),flip(a)].
143.90/144.29	43 mult(mult(A,rd(A,B)),B) = mult(rd(A,B),mult(B,A)).  [para(7(a,1),15(a,1,2,2)),flip(a)].
143.90/144.29	44 rd(mult(mult(A,rd(A,B)),C),mult(B,mult(rd(A,B),C))) = rd(A,B).  [para(15(a,1),8(a,1,1))].
143.90/144.29	45 mult(rd(A,B),mult(mult(B,mult(rd(A,B),C)),mult(rd(A,B),D))) = mult(mult(mult(mult(A,rd(A,B)),C),rd(A,B)),D).  [para(15(a,1),11(a,1,1,1)),flip(a)].
143.90/144.29	47 rd(mult(rd(A,B),mult(C,mult(mult(A,rd(A,B)),D))),mult(B,mult(rd(A,B),D))) = mult(mult(rd(A,B),C),rd(A,B)).  [para(15(a,1),16(a,1,1,2,2))].
143.90/144.29	50 mult(mult(A,rd(A,B)),mult(B,mult(rd(A,B),C))) = mult(rd(A,B),mult(B,mult(mult(A,rd(A,B)),C))).  [para(15(a,1),15(a,1,2,2)),flip(a)].
143.90/144.29	58 mult(mult(rd(A,B),rd(C,A)),rd(A,B)) = rd(mult(rd(A,B),C),B).  [para(7(a,1),23(a,1,1,2,2))].
143.90/144.29	59 rd(rd(mult(A,B),C),A) = mult(A,rd(B,mult(A,C))).  [para(23(a,1),8(a,1,1))].
143.90/144.29	60 rd(mult(A,B),ld(A,C)) = mult(mult(A,rd(B,C)),A).  [para(9(a,1),23(a,1,1,2,2)),flip(a)].
143.90/144.29	73 mult(ld(A,B),mult(A,ld(mult(B,A),C))) = ld(A,C).  [para(9(a,1),28(a,1,2,2,1,1))].
143.90/144.29	74 mult(A,ld(mult(mult(A,B),A),C)) = ld(B,ld(A,C)).  [para(28(a,1),10(a,1,2)),flip(a)].
143.90/144.29	82 rd(mult(mult(A,rd(B,C)),C),mult(ld(rd(B,C),A),B)) = rd(B,C).  [para(7(a,1),34(a,1,2,2))].
143.90/144.29	116 mult(A,mult(ld(A,rd(B,A)),C)) = mult(B,ld(A,C)).  [para(7(a,1),35(a,1,1)),flip(a)].
143.90/144.29	118 ld(mult(A,B),mult(B,mult(ld(B,A),C))) = ld(B,C).  [para(35(a,1),10(a,1,2))].
143.90/144.29	131 mult(ld(A,rd(B,A)),mult(A,C)) = ld(A,mult(B,C)).  [para(7(a,1),36(a,1,2,1)),flip(a)].
143.90/144.29	186 mult(A,rd(B,mult(A,B))) = rd(A,A).  [para(8(a,1),59(a,1,1)),flip(a)].
143.90/144.29	189 mult(A,rd(B,mult(A,ld(C,mult(A,B))))) = rd(C,A).  [para(13(a,1),59(a,1,1)),flip(a)].
143.90/144.29	197 rd(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)).  [para(7(a,1),186(a,1,2,2)),flip(a)].
143.90/144.29	199 mult(A,rd(ld(A,B),B)) = rd(A,A).  [para(9(a,1),186(a,1,2,2))].
143.90/144.29	200 ld(A,rd(A,A)) = rd(B,mult(A,B)).  [para(186(a,1),10(a,1,2))].
143.90/144.29	206 mult(ld(A,rd(A,A)),mult(mult(A,A),mult(ld(A,rd(A,A)),B))) = mult(rd(A,A),B).  [para(186(a,1),15(a,2,1)),rewrite([200(2,R),200(5,R)])].
143.90/144.29	230 ld(A,rd(A,A)) = rd(ld(A,B),B).  [para(199(a,1),10(a,1,2))].
143.90/144.29	247 mult(mult(rd(A,mult(B,A)),B),rd(A,mult(B,A))) = rd(A,mult(B,A)).  [para(7(a,1),22(a,1,1)),flip(a)].
143.90/144.29	256 mult(mult(rd(A,B),mult(rd(A,B),rd(B,A))),rd(A,B)) = mult(mult(rd(A,B),rd(B,A)),mult(rd(A,B),rd(A,B))).  [para(43(a,1),22(a,2)),rewrite([197(4),22(7),197(10)])].
143.90/144.29	261 ld(ld(A,rd(A,A)),B) = mult(A,B).  [para(200(a,2),14(a,1,1))].
143.90/144.29	268 mult(A,mult(rd(B,mult(A,B)),C)) = C.  [para(200(a,1),35(a,2,2,1)),rewrite([7(2),9(2)]),flip(a)].
143.90/144.29	277 rd(rd(ld(A,B),B),rd(A,A)) = ld(A,rd(A,A)).  [para(199(a,1),200(a,2,2)),flip(a)].
143.90/144.29	279 mult(mult(ld(A,rd(A,A)),B),rd(C,mult(A,C))) = mult(mult(rd(C,mult(A,C)),B),rd(C,mult(A,C))).  [para(200(a,2),22(a,2,1,1)),rewrite([22(6)]),flip(a)].
143.90/144.29	281 rd(A,mult(B,A)) = rd(C,mult(B,C)).  [para(200(a,1),200(a,1))].
143.90/144.29	283 mult(ld(A,rd(A,A)),B) = ld(A,B).  [para(230(a,2),7(a,1,1))].
143.90/144.29	289 mult(A,mult(rd(ld(A,B),B),C)) = C.  [para(230(a,1),35(a,2,2,1)),rewrite([7(2),9(2)]),flip(a)].
143.90/144.29	293 mult(mult(rd(ld(A,B),B),C),rd(ld(A,B),B)) = rd(ld(A,mult(C,ld(A,B))),B).  [para(230(a,2),22(a,1,1,1)),rewrite([283(5)]),flip(a)].
143.90/144.29	294 rd(ld(A,mult(B,ld(A,C))),C) = mult(ld(A,B),rd(ld(A,C),C)).  [para(230(a,2),22(a,2,1,1)),rewrite([22(6),293(6),283(7)])].
143.90/144.29	296 rd(ld(A,B),B) = rd(C,mult(A,C)).  [para(230(a,1),200(a,1))].
143.90/144.29	297 rd(ld(A,B),B) = rd(ld(A,C),C).  [para(230(a,1),230(a,1))].
143.90/144.29	298 mult(mult(rd(A,mult(B,A)),C),rd(A,mult(B,A))) = mult(ld(B,C),rd(A,mult(B,A))).  [back_rewrite(279),rewrite([283(3)]),flip(a)].
143.90/144.29	304 mult(rd(A,A),B) = mult(ld(A,A),B).  [back_rewrite(206),rewrite([283(6),35(5),283(6),10(4)]),flip(a)].
143.90/144.29	308 mult(ld(A,A),rd(B,mult(A,B))) = rd(B,mult(A,B)).  [back_rewrite(247),rewrite([298(6)])].
143.90/144.29	316 mult(c1,rd(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # answer(goals).  [back_rewrite(12),rewrite([304(12)])].
143.90/144.29	317 ld(A,mult(mult(A,B),ld(A,C))) = mult(mult(B,ld(A,rd(A,A))),C).  [para(261(a,1),18(a,1,2,1)),rewrite([283(6),283(6)])].
143.90/144.29	323 ld(rd(A,mult(B,A)),C) = mult(B,C).  [para(200(a,1),261(a,1,1))].
143.90/144.29	352 mult(rd(A,B),mult(rd(B,A),C)) = C.  [para(7(a,1),268(a,1,2,1,2))].
143.90/144.29	354 mult(rd(A,mult(B,A)),C) = ld(B,C).  [para(268(a,1),10(a,1,2)),flip(a)].
143.90/144.29	357 mult(ld(A,A),A) = A.  [para(268(a,1),16(a,1,1)),rewrite([8(2),186(3),304(2)]),flip(a)].
143.90/144.29	362 mult(ld(A,A),ld(A,mult(ld(A,A),B))) = mult(ld(A,ld(A,A)),B).  [para(268(a,1),21(a,1,1,2)),rewrite([354(5),354(4),354(6),354(9),354(9)]),flip(a)].
143.90/144.29	364 mult(ld(A,B),rd(ld(A,C),C)) = mult(ld(A,B),rd(D,mult(A,D))).  [para(268(a,1),25(a,1,1,2,2,2,2,2)),rewrite([354(7),354(7),9(6),354(5),294(4),354(9),9(8),354(7),354(8),308(9)])].
143.90/144.29	367 rd(A,A) = ld(A,A).  [para(357(a,1),8(a,1,1))].
143.90/144.29	368 ld(ld(A,A),A) = A.  [para(357(a,1),10(a,1,2))].
143.90/144.29	370 mult(mult(A,ld(mult(A,B),mult(A,B))),A) = rd(mult(A,mult(A,B)),B).  [para(357(a,1),16(a,1,1,2)),flip(a)].
143.90/144.29	371 mult(ld(A,A),mult(ld(ld(A,A),B),A)) = mult(mult(B,ld(A,A)),A).  [para(357(a,1),18(a,1,2,2))].
143.90/144.29	376 mult(ld(A,A),rd(A,mult(ld(A,A),B))) = rd(rd(A,B),ld(A,A)).  [para(357(a,1),59(a,1,1,1)),flip(a)].
143.90/144.29	378 mult(mult(rd(A,B),ld(A,A)),rd(A,B)) = rd(mult(rd(A,B),A),B).  [para(357(a,1),22(a,1,1,2)),flip(a)].
143.90/144.29	393 ld(A,mult(mult(A,B),ld(A,C))) = mult(mult(B,ld(A,ld(A,A))),C).  [back_rewrite(317),rewrite([367(5)])].
143.90/144.29	394 mult(c1,ld(c2,c2)) != c1 | mult(ld(c2,c2),c1) != c1 # answer(goals).  [back_rewrite(316),rewrite([367(4)])].
143.90/144.29	399 mult(ld(A,ld(A,A)),B) = ld(A,B).  [back_rewrite(283),rewrite([367(1)])].
143.90/144.29	400 rd(rd(ld(A,B),B),ld(A,A)) = ld(A,ld(A,A)).  [back_rewrite(277),rewrite([367(3),367(5)])].
143.90/144.29	420 ld(A,ld(A,A)) = rd(ld(A,B),B).  [back_rewrite(230),rewrite([367(1)])].
143.90/144.29	436 ld(A,ld(A,A)) = rd(B,mult(A,B)).  [back_rewrite(200),rewrite([367(1)])].
143.90/144.29	437 mult(A,rd(ld(A,B),B)) = ld(A,A).  [back_rewrite(199),rewrite([367(4)])].
143.90/144.29	439 ld(rd(A,B),rd(A,B)) = mult(rd(A,B),rd(B,A)).  [back_rewrite(197),rewrite([367(3)])].
143.90/144.29	441 mult(ld(A,A),ld(A,mult(ld(A,A),B))) = ld(A,B).  [back_rewrite(362),rewrite([399(8)])].
143.90/144.29	443 rd(ld(mult(A,B),mult(A,B)),A) = mult(A,rd(B,mult(A,mult(A,B)))).  [para(367(a,1),59(a,1,1))].
143.90/144.29	444 rd(mult(A,B),mult(A,mult(ld(A,A),B))) = ld(A,A).  [para(368(a,1),34(a,1,2,1)),rewrite([9(2)])].
143.90/144.29	445 mult(ld(A,A),mult(A,B)) = mult(A,ld(ld(A,A),B)).  [para(368(a,1),35(a,2,2,1)),rewrite([9(2)]),flip(a)].
143.90/144.29	463 rd(A,mult(rd(B,C),A)) = rd(C,B).  [para(7(a,1),281(a,1,2)),flip(a)].
143.90/144.29	465 mult(mult(A,ld(B,ld(B,B))),C) = mult(mult(A,rd(D,mult(B,D))),C).  [para(281(a,1),15(a,2,1,2)),rewrite([354(6),354(6),393(4)])].
143.90/144.29	472 rd(A,mult(ld(B,B),A)) = ld(B,B).  [para(357(a,1),281(a,1,2)),rewrite([367(1)]),flip(a)].
143.90/144.29	473 mult(rd(ld(A,B),B),C) = ld(A,C).  [para(289(a,1),10(a,1,2)),flip(a)].
143.90/144.29	477 mult(ld(A,A),mult(ld(A,A),B)) = B.  [para(368(a,1),289(a,1,2,1,1)),rewrite([367(2)])].
143.90/144.29	485 rd(ld(mult(mult(A,B),A),C),C) = rd(D,mult(A,mult(B,mult(A,D)))).  [para(11(a,1),296(a,2,2))].
143.90/144.29	498 mult(mult(A,rd(ld(B,C),C)),A) = rd(mult(A,ld(B,mult(A,D))),D).  [para(297(a,1),23(a,1,1,2))].
143.90/144.29	523 ld(rd(A,B),C) = mult(rd(B,A),C).  [para(7(a,1),323(a,1,1,2))].
143.90/144.29	525 ld(ld(A,A),B) = mult(ld(A,A),B).  [para(357(a,1),323(a,1,1,2)),rewrite([367(1)])].
143.90/144.29	544 mult(rd(A,B),rd(B,A)) = mult(rd(B,A),rd(A,B)).  [back_rewrite(439),rewrite([523(3)])].
143.90/144.29	551 rd(mult(mult(A,rd(B,C)),C),mult(mult(rd(C,B),A),B)) = rd(B,C).  [back_rewrite(82),rewrite([523(5)])].
143.90/144.29	556 mult(ld(A,A),mult(A,B)) = mult(A,mult(ld(A,A),B)).  [back_rewrite(445),rewrite([525(5)])].
143.90/144.29	558 mult(ld(A,A),mult(mult(ld(A,A),B),A)) = mult(mult(B,ld(A,A)),A).  [back_rewrite(371),rewrite([525(3)])].
143.90/144.29	562 mult(mult(A,rd(B,C)),mult(rd(C,B),D)) = mult(rd(B,C),mult(mult(rd(C,B),A),D)).  [para(352(a,1),18(a,1,2,2)),rewrite([523(3)]),flip(a)].
143.90/144.29	565 rd(mult(rd(A,B),C),mult(rd(B,A),D)) = mult(mult(rd(A,B),rd(C,D)),rd(A,B)).  [para(352(a,1),23(a,1,1,2,2)),flip(a)].
143.90/144.29	572 mult(rd(A,B),mult(mult(rd(B,A),rd(C,D)),rd(B,A))) = rd(rd(C,D),rd(A,B)).  [para(352(a,1),59(a,1,1,1)),rewrite([565(9)]),flip(a)].
143.90/144.29	580 mult(mult(rd(A,B),mult(rd(A,B),rd(B,A))),rd(A,B)) = rd(rd(A,B),rd(B,A)).  [back_rewrite(256),rewrite([562(14),572(14)])].
143.90/144.29	591 mult(rd(A,mult(rd(B,A),mult(A,B))),C) = ld(mult(B,rd(B,A)),C).  [para(43(a,1),354(a,1,1,2))].
143.90/144.29	653 mult(rd(A,B),mult(rd(A,B),rd(B,A))) = rd(A,B).  [para(7(a,1),436(a,2,2)),rewrite([523(4),523(5)])].
143.90/144.29	655 rd(rd(A,B),rd(B,A)) = mult(rd(A,B),rd(A,B)).  [back_rewrite(580),rewrite([653(5)]),flip(a)].
143.90/144.29	706 rd(A,mult(rd(B,C),mult(D,mult(rd(B,C),A)))) = rd(C,mult(rd(B,C),mult(D,B))).  [para(22(a,1),463(a,1,2,1)),rewrite([11(5)])].
143.90/144.29	772 mult(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),mult(mult(B,ld(A,A)),C)).  [para(18(a,1),477(a,1,2)),rewrite([525(7)]),flip(a)].
143.90/144.29	773 rd(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(mult(ld(A,A),rd(B,C)),ld(A,A)).  [para(477(a,1),23(a,1,1,2,2)),flip(a)].
143.90/144.29	783 ld(mult(mult(rd(A,B),C),rd(A,B)),D) = mult(rd(B,mult(rd(A,B),mult(C,A))),D).  [para(22(a,1),523(a,1,1))].
143.90/144.29	799 mult(mult(A,rd(A,B)),rd(C,mult(rd(A,B),mult(B,mult(mult(A,rd(A,B)),C))))) = ld(A,ld(A,A)).  [para(44(a,1),59(a,1,1)),rewrite([436(4,R),50(10)]),flip(a)].
143.90/144.29	819 mult(mult(A,rd(ld(A,B),C)),A) = rd(B,ld(A,C)).  [para(9(a,1),60(a,1,1)),flip(a)].
143.90/144.29	830 mult(mult(ld(A,A),rd(A,B)),ld(A,A)) = rd(A,mult(ld(A,A),B)).  [para(357(a,1),60(a,1,1)),rewrite([525(2)]),flip(a)].
143.90/144.29	844 mult(ld(A,rd(B,C)),rd(ld(A,D),D)) = rd(ld(A,B),mult(A,C)).  [para(473(a,1),60(a,1,1)),rewrite([523(4),13(3),473(7)]),flip(a)].
143.90/144.29	849 ld(ld(A,B),ld(A,C)) = mult(A,ld(mult(B,A),C)).  [para(73(a,1),10(a,1,2))].
143.90/144.29	866 mult(mult(A,rd(ld(mult(B,A),C),C)),A) = rd(D,mult(ld(A,B),D)).  [para(73(a,1),281(a,1,2)),rewrite([60(5)])].
143.90/144.29	880 mult(ld(A,A),ld(A,B)) = mult(A,ld(mult(A,A),B)).  [para(73(a,1),477(a,1,2))].
143.90/144.29	888 mult(A,ld(mult(A,A),mult(ld(A,A),B))) = ld(A,B).  [back_rewrite(441),rewrite([880(5)])].
143.90/144.29	892 ld(mult(mult(A,B),A),C) = ld(A,ld(B,ld(A,C))).  [para(74(a,1),10(a,1,2)),flip(a)].
143.90/144.29	910 ld(A,ld(B,ld(B,B))) = ld(A,rd(ld(B,C),C)).  [para(420(a,1),74(a,2,2)),rewrite([892(4),9(5)])].
143.90/144.29	912 ld(A,ld(B,ld(B,B))) = ld(A,rd(C,mult(B,C))).  [para(436(a,1),74(a,2,2)),rewrite([892(4),9(5)])].
143.90/144.29	915 ld(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),ld(mult(B,ld(A,A)),C)).  [para(477(a,1),74(a,1,2,1,1)),rewrite([525(9)]),flip(a)].
143.90/144.29	920 mult(rd(A,mult(rd(B,A),mult(C,B))),D) = mult(rd(A,B),ld(C,mult(rd(A,B),D))).  [back_rewrite(783),rewrite([892(5),523(3),523(5)]),flip(a)].
143.90/144.29	926 rd(ld(A,ld(B,ld(A,C))),C) = rd(D,mult(A,mult(B,mult(A,D)))).  [back_rewrite(485),rewrite([892(3)])].
143.90/144.29	934 mult(rd(A,B),ld(A,mult(rd(A,B),C))) = ld(mult(B,rd(B,A)),C).  [back_rewrite(591),rewrite([920(5)])].
143.90/144.29	972 mult(rd(A,B),mult(mult(B,mult(rd(B,A),rd(A,B))),mult(rd(A,B),C))) = mult(mult(mult(mult(A,rd(A,B)),rd(B,A)),rd(A,B)),C).  [para(437(a,1),45(a,1,2,1,2)),rewrite([523(4),523(13),8(14)])].
143.90/144.29	979 rd(mult(A,ld(B,C)),mult(ld(B,rd(A,B)),C)) = B.  [para(116(a,1),8(a,1,1))].
143.90/144.29	981 ld(A,mult(B,ld(A,C))) = mult(ld(A,rd(B,A)),C).  [para(116(a,1),10(a,1,2))].
143.90/144.29	1013 mult(A,ld(B,ld(B,B))) = mult(A,rd(ld(B,C),C)).  [para(420(a,1),116(a,2,2)),rewrite([116(5)])].
143.90/144.29	1015 mult(A,ld(B,ld(B,B))) = mult(A,rd(C,mult(B,C))).  [para(436(a,1),116(a,2,2)),rewrite([116(5)])].
143.90/144.29	1023 mult(mult(ld(A,A),rd(B,ld(A,A))),C) = mult(ld(A,A),mult(B,mult(ld(A,A),C))).  [para(116(a,1),477(a,1,2)),rewrite([525(3),525(9)]),flip(a)].
143.90/144.29	1048 mult(ld(A,B),rd(ld(A,C),C)) = ld(A,rd(B,A)).  [back_rewrite(294),rewrite([981(3),8(4)]),flip(a)].
143.90/144.29	1052 rd(ld(A,B),mult(A,C)) = ld(A,rd(rd(B,C),A)).  [back_rewrite(844),rewrite([1048(5)]),flip(a)].
143.90/144.29	1054 mult(ld(A,B),rd(C,mult(A,C))) = ld(A,rd(B,A)).  [back_rewrite(364),rewrite([1048(4)]),flip(a)].
143.90/144.29	1065 ld(mult(A,B),mult(B,C)) = ld(B,ld(ld(B,A),C)).  [para(9(a,1),118(a,1,2,2))].
143.90/144.29	1103 ld(ld(A,rd(B,A)),C) = mult(A,ld(B,mult(A,C))).  [para(131(a,1),354(a,1,1,2)),rewrite([60(4),11(5),354(4)]),flip(a)].
143.90/144.29	1123 ld(A,mult(B,mult(ld(A,rd(C,A)),D))) = mult(ld(A,rd(B,A)),mult(C,ld(A,D))).  [para(116(a,1),131(a,1,2)),flip(a)].
143.90/144.29	1132 rd(A,mult(B,ld(C,mult(B,A)))) = ld(B,rd(C,B)).  [para(189(a,1),10(a,1,2)),flip(a)].
143.90/144.29	1140 ld(A,rd(B,ld(A,ld(C,ld(A,B))))) = rd(C,rd(D,mult(A,D))).  [para(189(a,1),354(a,1)),rewrite([354(8),354(8)]),flip(a)].
143.90/144.29	1141 ld(A,rd(B,ld(A,ld(C,ld(A,B))))) = rd(C,ld(A,ld(A,A))).  [para(189(a,1),399(a,1)),rewrite([399(8),399(8)]),flip(a)].
143.90/144.29	1148 rd(A,ld(B,ld(B,B))) = rd(A,rd(C,mult(B,C))).  [back_rewrite(1140),rewrite([1141(5)])].
143.90/144.29	1190 mult(ld(A,ld(A,ld(A,A))),B) = ld(mult(A,A),B).  [para(400(a,1),15(a,1,1)),rewrite([400(7),399(6),880(5),399(6),10(4),400(8),473(7)]),flip(a)].
143.90/144.29	1191 ld(mult(A,A),ld(A,A)) = ld(A,ld(A,ld(A,A))).  [para(400(a,1),43(a,1,1,2)),rewrite([473(5),1190(5),400(7),1048(9),367(6),399(8)])].
143.90/144.29	1219 mult(A,ld(mult(A,A),A)) = ld(A,A).  [para(437(a,1),444(a,1,1)),rewrite([1048(5),367(2),9(4),367(3),525(3),880(3)])].
143.90/144.29	1233 ld(mult(A,A),A) = ld(A,ld(A,A)).  [para(1219(a,1),10(a,1,2)),flip(a)].
143.90/144.29	1265 mult(ld(A,B),ld(A,ld(A,A))) = ld(A,rd(B,A)).  [para(420(a,2),47(a,2,2)),rewrite([1048(6),473(7),1123(5),473(8),8(8),473(5)]),flip(a)].
143.90/144.29	1271 rd(mult(A,mult(rd(B,A),C)),mult(rd(B,A),mult(D,mult(mult(B,rd(B,A)),C)))) = rd(A,mult(rd(B,A),mult(D,B))).  [para(47(a,1),463(a,1,2,1)),rewrite([11(5),706(6)]),flip(a)].
143.90/144.29	1272 mult(mult(rd(A,B),C),rd(A,B)) = mult(rd(A,B),rd(C,rd(B,A))).  [para(47(a,1),463(a,2)),rewrite([1271(10),920(5),1132(6),523(4)]),flip(a)].
143.90/144.29	1342 mult(rd(A,B),rd(ld(A,A),rd(B,A))) = rd(mult(rd(A,B),A),B).  [back_rewrite(378),rewrite([1272(5)])].
143.90/144.29	1354 mult(rd(A,B),rd(rd(C,A),rd(B,A))) = rd(mult(rd(A,B),C),B).  [back_rewrite(58),rewrite([1272(5)])].
143.90/144.29	1355 rd(mult(rd(A,B),mult(C,mult(mult(A,rd(A,B)),D))),mult(B,mult(rd(A,B),D))) = mult(rd(A,B),rd(C,rd(B,A))).  [back_rewrite(47),rewrite([1272(14)])].
143.90/144.29	1358 rd(A,ld(A,ld(A,A))) = mult(A,A).  [para(1233(a,1),13(a,1,2))].
143.90/144.29	1359 mult(mult(A,A),mult(A,mult(ld(A,A),B))) = mult(mult(A,mult(A,A)),B).  [para(1233(a,1),18(a,1,2,1)),rewrite([399(6),36(4),556(4)])].
143.90/144.29	1363 rd(ld(A,ld(A,A)),A) = rd(B,mult(mult(A,A),B)).  [para(1233(a,1),296(a,1,1))].
143.90/144.29	1364 rd(ld(mult(A,A),B),B) = rd(ld(A,ld(A,A)),A).  [para(1233(a,1),297(a,1,1)),flip(a)].
143.90/144.29	1367 rd(ld(A,ld(A,A)),A) = ld(A,ld(A,ld(A,A))).  [para(1233(a,1),420(a,2,1)),rewrite([1065(4),525(3),357(3),1191(3)]),flip(a)].
143.90/144.29	1375 ld(A,ld(A,ld(A,A))) = rd(ld(mult(A,A),B),B).  [back_rewrite(1364),rewrite([1367(6)]),flip(a)].
143.90/144.29	1376 ld(A,ld(A,ld(A,A))) = rd(B,mult(mult(A,A),B)).  [back_rewrite(1363),rewrite([1367(3)])].
143.90/144.29	1381 rd(A,rd(ld(A,B),B)) = mult(A,A).  [para(420(a,1),1358(a,1,2))].
143.90/144.29	1383 rd(rd(ld(A,B),B),A) = ld(A,rd(ld(A,B),B)).  [para(473(a,1),1358(a,2)),rewrite([523(9),13(6),437(7),523(6),13(4),9(4)])].
143.90/144.29	1384 ld(ld(A,ld(A,ld(A,A))),B) = mult(mult(A,A),B).  [para(1358(a,1),523(a,2,1)),rewrite([1367(3)])].
143.90/144.29	1390 mult(mult(A,A),rd(ld(A,B),B)) = A.  [para(1381(a,1),7(a,1,1))].
143.90/144.29	1398 mult(ld(A,rd(ld(A,B),B)),C) = ld(mult(A,A),C).  [para(1381(a,1),523(a,1,1)),rewrite([1383(5)]),flip(a)].
143.90/144.29	1469 mult(A,mult(A,mult(ld(A,A),B))) = mult(mult(A,A),B).  [para(1390(a,1),37(a,2,1,1)),rewrite([437(4),880(3),1233(2),9(3),556(3)])].
143.90/144.29	1540 mult(mult(A,mult(A,A)),B) = mult(A,mult(A,mult(A,B))).  [para(556(a,1),21(a,1,1,2)),rewrite([9(3),357(2),9(5),9(5)])].
143.90/144.29	1554 mult(mult(A,B),mult(B,mult(ld(B,B),C))) = mult(B,mult(ld(B,A),mult(mult(B,B),C))).  [para(556(a,1),42(a,1,2))].
143.90/144.29	1572 mult(A,mult(ld(A,A),mult(mult(A,A),B))) = mult(A,mult(A,mult(A,B))).  [back_rewrite(1359),rewrite([1554(5),1540(8)])].
143.90/144.29	1577 mult(rd(A,B),rd(B,rd(B,A))) = mult(A,rd(A,B)).  [para(50(a,1),8(a,1,1)),rewrite([1355(10)])].
143.90/144.29	1657 ld(mult(A,A),ld(A,ld(A,ld(A,A)))) = ld(A,rd(ld(A,ld(A,ld(A,A))),A)).  [para(1358(a,1),655(a,1,2)),rewrite([1367(3),1052(5),1367(3),1367(8),1367(11),1190(12)]),flip(a)].
143.90/144.29	1729 rd(rd(A,ld(B,C)),B) = mult(B,rd(ld(B,A),C)).  [para(819(a,1),8(a,1,1))].
143.90/144.29	1734 rd(A,ld(B,ld(C,ld(B,A)))) = mult(mult(B,C),B).  [para(13(a,1),819(a,1,1,2)),flip(a)].
143.90/144.29	1741 mult(rd(A,ld(B,C)),ld(B,D)) = mult(B,mult(rd(ld(B,A),C),D)).  [para(819(a,1),35(a,1,1)),rewrite([10(8)])].
143.90/144.29	1751 mult(mult(A,rd(ld(B,C),C)),A) = rd(D,mult(ld(A,rd(B,A)),D)).  [para(296(a,2),819(a,1,1,2)),rewrite([981(7)])].
143.90/144.29	1784 rd(A,ld(B,ld(B,B))) = ld(B,mult(mult(B,A),B)).  [back_rewrite(1141),rewrite([1734(4)]),flip(a)].
143.90/144.29	1798 ld(A,mult(mult(A,B),A)) = rd(B,rd(C,mult(A,C))).  [back_rewrite(1148),rewrite([1784(3)])].
143.90/144.29	1959 ld(mult(A,A),mult(ld(A,A),B)) = ld(A,ld(A,B)).  [para(888(a,1),10(a,1,2)),flip(a)].
143.90/144.29	2208 mult(A,ld(B,ld(C,ld(C,C)))) = mult(A,ld(B,rd(D,mult(C,D)))).  [para(912(a,1),116(a,2,2)),rewrite([116(6)])].
143.90/144.29	2548 rd(mult(A,ld(B,ld(B,B))),C) = rd(mult(A,rd(D,mult(B,D))),C).  [para(1015(a,1),23(a,2,1)),rewrite([23(6)])].
143.90/144.29	2570 mult(rd(ld(A,ld(A,A)),mult(B,rd(C,mult(A,C)))),D) = ld(B,D).  [para(1015(a,1),354(a,1,1,2))].
143.90/144.29	2767 mult(mult(ld(A,A),B),ld(A,A)) = mult(ld(A,A),rd(B,ld(A,A))).  [para(525(a,1),1048(a,1,1)),rewrite([525(4),8(5),525(8)])].
143.90/144.29	2769 mult(A,ld(B,rd(ld(B,C),C))) = rd(rd(A,B),B).  [para(1048(a,1),116(a,1,2)),rewrite([9(4)]),flip(a)].
143.90/144.29	2776 mult(mult(A,A),A) = mult(A,mult(A,A)).  [para(1381(a,1),1048(a,2,2)),rewrite([523(3),13(2),523(4),13(3),8(3),523(6),13(4)])].
143.90/144.29	2811 mult(ld(A,A),rd(rd(A,B),ld(A,A))) = rd(A,mult(ld(A,A),B)).  [back_rewrite(830),rewrite([2767(5)])].
143.90/144.29	2812 rd(mult(ld(A,A),B),mult(ld(A,A),C)) = mult(ld(A,A),rd(rd(B,C),ld(A,A))).  [back_rewrite(773),rewrite([2767(10)])].
143.90/144.29	3066 mult(A,rd(B,rd(C,mult(A,C)))) = mult(mult(A,B),A).  [para(354(a,1),1054(a,1,2,2)),rewrite([523(3),8(2),13(3),523(8),8(4)]),flip(a)].
143.90/144.29	3077 mult(A,rd(B,rd(ld(A,C),C))) = mult(mult(A,B),A).  [para(473(a,1),1054(a,1,2,2)),rewrite([523(3),13(2),13(3),523(8),13(4)]),flip(a)].
143.90/144.29	3170 rd(mult(mult(A,A),B),mult(mult(A,A),mult(ld(A,A),B))) = ld(A,A).  [para(1065(a,1),444(a,1,2,2,1)),rewrite([525(5),357(5),1065(10),525(9),357(9)])].
143.90/144.29	3176 mult(ld(A,A),mult(mult(A,A),B)) = mult(mult(A,A),mult(ld(A,A),B)).  [para(1065(a,1),556(a,1,1)),rewrite([525(2),357(2),1065(8),525(7),357(7)])].
143.90/144.29	3204 mult(A,ld(B,ld(B,ld(B,B)))) = mult(A,rd(ld(mult(B,B),C),C)).  [para(1065(a,1),1013(a,1,2,2)),rewrite([525(3),357(3),1191(3)])].
143.90/144.29	3214 mult(A,mult(mult(A,A),mult(ld(A,A),B))) = mult(A,mult(A,mult(A,B))).  [back_rewrite(1572),rewrite([3176(4)])].
143.90/144.29	3419 mult(mult(A,ld(B,ld(B,ld(B,B)))),mult(mult(B,B),C)) = ld(mult(B,B),mult(mult(mult(B,B),A),C)).  [para(1190(a,1),35(a,2)),rewrite([1384(8),1384(12)])].
143.90/144.29	3443 mult(mult(A,A),mult(ld(A,A),B)) = mult(A,mult(A,B)).  [para(1190(a,1),880(a,2,2,1)),rewrite([849(7),399(3),525(4),880(4),1191(3),9(4),9(3),1384(5),3176(4),1657(12),1103(13),1384(12),1190(12),1065(10),525(9),3176(9),556(8),1554(9),3176(8),3214(9),10(8)])].
143.90/144.29	3461 mult(ld(A,A),mult(mult(A,A),B)) = mult(A,mult(A,B)).  [back_rewrite(3176),rewrite([3443(8)])].
143.90/144.29	3462 rd(mult(mult(A,A),B),mult(A,mult(A,B))) = ld(A,A).  [back_rewrite(3170),rewrite([3443(6)])].
143.90/144.29	3732 mult(A,ld(mult(B,A),rd(B,A))) = ld(A,ld(A,A)).  [para(1265(a,1),10(a,1,2)),rewrite([849(4)])].
143.90/144.29	3760 mult(A,ld(B,ld(B,ld(B,B)))) = rd(rd(A,B),B).  [para(1265(a,1),116(a,1,2)),rewrite([9(4)]),flip(a)].
143.90/144.29	3810 ld(mult(A,A),mult(mult(mult(A,A),B),C)) = mult(rd(rd(B,A),A),mult(mult(A,A),C)).  [back_rewrite(3419),rewrite([3760(4)]),flip(a)].
143.90/144.29	3814 mult(A,rd(ld(mult(B,B),C),C)) = rd(rd(A,B),B).  [back_rewrite(3204),rewrite([3760(4)]),flip(a)].
143.90/144.29	3964 rd(A,rd(ld(mult(B,B),C),C)) = mult(mult(A,B),B).  [para(1375(a,1),819(a,2,2)),rewrite([1784(4),9(2),9(3)]),flip(a)].
143.90/144.29	3993 rd(A,rd(B,mult(mult(C,C),B))) = mult(mult(A,C),C).  [para(1376(a,1),819(a,2,2)),rewrite([1784(4),9(2),9(3)]),flip(a)].
143.90/144.29	4806 mult(mult(A,A),mult(A,B)) = mult(A,mult(mult(A,A),B)).  [para(18(a,1),1469(a,1,2)),flip(a)].
143.90/144.29	5488 rd(mult(A,rd(A,B)),rd(B,rd(B,A))) = rd(A,B).  [para(1577(a,1),8(a,1,1))].
143.90/144.29	5505 rd(rd(A,rd(A,B)),mult(B,rd(B,A))) = rd(A,B).  [para(1577(a,1),281(a,1,2)),rewrite([463(8)])].
143.90/144.29	5589 rd(mult(A,ld(mult(B,A),B)),A) = mult(A,rd(ld(A,ld(A,B)),B)).  [para(367(a,1),1729(a,1,1)),rewrite([849(3)])].
143.90/144.29	5607 rd(rd(A,mult(ld(B,B),C)),ld(B,B)) = mult(ld(B,B),rd(mult(ld(B,B),A),C)).  [para(525(a,1),1729(a,1,1,2)),rewrite([525(8)])].
143.90/144.29	5720 rd(mult(ld(A,A),B),ld(A,A)) = mult(ld(A,A),mult(B,ld(A,A))).  [para(477(a,1),1784(a,2,2,1)),rewrite([525(6),880(6),1233(5),9(6),525(5),880(5),1233(4),9(5),525(8)])].
143.90/144.29	5748 mult(rd(rd(A,B),B),mult(B,mult(B,mult(B,B)))) = rd(A,ld(B,ld(B,ld(B,B)))).  [para(1065(a,1),1784(a,1,2,2)),rewrite([525(3),357(3),1191(3),3810(10),4806(9),2776(8)]),flip(a)].
143.90/144.29	6044 mult(rd(A,rd(B,mult(C,B))),rd(ld(C,D),D)) = A.  [para(1798(a,1),1048(a,1,1)),rewrite([8(9),10(8)])].
143.90/144.29	6059 rd(A,ld(B,ld(B,ld(B,B)))) = mult(mult(A,B),B).  [para(1798(a,1),1190(a,2)),rewrite([1190(8),3810(6),4806(5),2776(4),5748(6),3993(8)])].
143.90/144.29	6512 ld(mult(A,A),ld(A,B)) = ld(A,ld(mult(A,A),B)).  [para(73(a,1),1959(a,1,2)),rewrite([10(7)])].
143.90/144.29	8237 ld(A,rd(ld(A,B),B)) = ld(C,rd(rd(C,A),A)).  [para(2769(a,1),10(a,1,2)),flip(a)].
143.90/144.29	8564 mult(mult(A,ld(mult(B,B),rd(ld(A,C),C))),A) = rd(rd(A,B),B).  [para(1375(a,2),3077(a,1,2)),rewrite([3760(4)]),flip(a)].
143.90/144.29	8821 rd(mult(mult(A,A),B),mult(ld(A,A),ld(C,mult(A,mult(A,B))))) = mult(ld(A,A),rd(C,ld(A,A))).  [para(3461(a,1),1132(a,1,2,2,2)),rewrite([525(12)])].
143.90/144.29	8856 rd(mult(mult(mult(A,A),B),ld(mult(A,mult(A,B)),C)),mult(ld(mult(A,mult(A,B)),ld(A,A)),C)) = mult(A,mult(A,B)).  [para(3462(a,1),979(a,1,2,1,2))].
143.90/144.29	8896 ld(mult(A,B),rd(A,B)) = ld(B,ld(B,ld(B,B))).  [para(3732(a,1),10(a,1,2)),flip(a)].
143.90/144.29	9497 mult(A,ld(B,rd(rd(B,C),C))) = rd(rd(A,C),C).  [para(910(a,1),3814(a,1,2,1)),rewrite([1784(7),8564(6)])].
143.90/144.29	9641 mult(mult(A,ld(B,B)),ld(B,B)) = rd(A,ld(B,B)).  [para(544(a,1),3964(a,1,2,1,1)),rewrite([367(1),367(2),880(3),1233(2),9(3),525(2),8(3),367(3),367(5)]),flip(a)].
143.90/144.29	10018 rd(mult(A,rd(B,mult(C,B))),rd(mult(C,A),C)) = rd(A,mult(C,A)).  [para(281(a,1),5488(a,1,1,2)),rewrite([8(6)])].
143.90/144.29	10707 mult(mult(A,A),mult(mult(ld(A,ld(B,ld(B,ld(B,B)))),B),B)) = A.  [para(6059(a,1),1390(a,1,2))].
143.90/144.29	12062 mult(ld(A,rd(rd(A,B),B)),C) = ld(mult(B,B),C).  [para(8237(a,1),981(a,2,1)),rewrite([880(3),10(4)]),flip(a)].
143.90/144.29	12067 ld(mult(A,A),rd(B,mult(C,B))) = ld(C,rd(rd(rd(C,A),A),C)).  [para(8237(a,2),1054(a,1,1)),rewrite([1398(6)])].
143.90/144.29	12381 rd(A,ld(mult(B,C),rd(B,C))) = mult(mult(A,C),C).  [para(8896(a,1),819(a,2,2)),rewrite([819(8),6059(8)])].
143.90/144.29	12412 ld(mult(A,B),rd(A,B)) = rd(C,mult(mult(B,B),C)).  [para(8896(a,2),1376(a,1))].
143.90/144.29	12673 mult(A,ld(ld(B,C),rd(ld(B,ld(B,B)),C))) = rd(rd(A,C),C).  [para(420(a,2),9497(a,1,2,2,1))].
143.90/144.29	12677 rd(ld(A,rd(rd(A,B),B)),rd(rd(rd(C,D),B),B)) = rd(D,C).  [para(9497(a,1),463(a,1,2))].
143.90/144.29	12809 rd(ld(mult(A,ld(B,B)),C),C) = rd(ld(B,B),rd(A,ld(B,B))).  [para(9641(a,1),296(a,2,2))].
143.90/144.29	12819 mult(ld(A,A),mult(rd(mult(ld(A,A),B),C),ld(A,A))) = mult(rd(B,mult(ld(A,A),C)),ld(A,A)).  [para(819(a,1),9641(a,1,1)),rewrite([525(2),525(8),5720(12)]),flip(a)].
143.90/144.29	13355 mult(ld(ld(A,B),rd(ld(A,ld(A,A)),B)),C) = ld(mult(B,B),C).  [para(420(a,2),12062(a,1,1,2,1))].
143.90/144.29	13773 ld(A,ld(A,A)) = mult(mult(ld(A,ld(mult(B,C),rd(B,C))),C),C).  [para(12381(a,1),420(a,2))].
143.90/144.29	15200 mult(ld(mult(A,ld(B,B)),A),ld(B,B)) = ld(A,A).  [para(352(a,1),370(a,2,1)),rewrite([367(1),367(2),367(4),915(6),477(7),367(4),367(6)])].
143.90/144.29	15210 rd(ld(mult(A,ld(B,B)),A),ld(B,B)) = mult(ld(A,A),ld(B,B)).  [para(370(a,1),9641(a,1,1)),rewrite([477(4),367(1),915(9),477(10)]),flip(a)].
143.90/144.29	15213 rd(ld(A,A),ld(B,B)) = ld(mult(A,ld(B,B)),A).  [para(15200(a,1),8(a,1,1))].
143.90/144.29	15258 rd(rd(rd(A,B),ld(A,A)),rd(A,mult(ld(A,A),B))) = ld(A,A).  [para(376(a,1),8(a,1,1))].
143.90/144.29	15643 mult(ld(A,ld(B,ld(B,B))),C) = mult(ld(A,rd(D,mult(B,D))),C).  [para(354(a,1),465(a,1,1)),rewrite([354(9)])].
143.90/144.29	15901 mult(ld(A,A),rd(rd(ld(B,C),C),ld(A,A))) = rd(mult(ld(A,A),ld(B,A)),A).  [para(357(a,1),498(a,2,1,2,2)),rewrite([2767(6)])].
143.90/144.29	16032 rd(mult(A,B),mult(C,mult(A,B))) = rd(ld(C,B),B).  [para(6044(a,1),551(a,1,1,1)),rewrite([13(3),3066(5),35(5),10(3)])].
143.90/144.29	16039 rd(mult(A,ld(B,mult(A,C))),C) = mult(mult(A,rd(C,mult(B,C))),A).  [para(131(a,1),16032(a,1,2)),rewrite([60(4),1103(7)]),flip(a)].
143.90/144.29	16093 mult(ld(A,A),mult(mult(B,ld(A,A)),A)) = mult(mult(ld(A,A),B),A).  [para(558(a,1),477(a,1,2))].
143.90/144.29	16386 rd(rd(A,mult(ld(A,A),B)),rd(rd(A,B),ld(A,A))) = ld(A,A).  [para(376(a,1),866(a,2,2)),rewrite([3814(4),367(1),420(2,R),399(3)]),flip(a)].
143.90/144.29	16472 mult(ld(A,A),rd(rd(B,mult(C,B)),ld(A,A))) = rd(A,mult(ld(A,A),mult(C,A))).  [para(357(a,1),926(a,2,2,2,2)),rewrite([525(3),525(5),16039(6),2767(6)])].
143.90/144.29	16477 rd(A,mult(ld(B,B),mult(C,mult(ld(B,B),A)))) = rd(B,mult(ld(B,B),mult(C,B))).  [para(525(a,1),926(a,1,1,2,2)),rewrite([525(5),16039(6),2767(6),16472(6)]),flip(a)].
143.90/144.29	16504 ld(mult(A,rd(A,B)),A) = mult(rd(B,A),ld(B,B)).  [para(7(a,1),934(a,1,2,2)),flip(a)].
143.90/144.29	16521 rd(ld(mult(A,rd(A,B)),A),ld(B,B)) = rd(B,A).  [para(16504(a,2),8(a,1,1))].
143.90/144.29	16522 mult(ld(mult(A,rd(A,B)),A),rd(B,A)) = rd(mult(rd(B,A),B),A).  [para(16504(a,2),16(a,2,1)),rewrite([16(7),1272(5),1342(5)]),flip(a)].
143.90/144.29	16525 rd(ld(mult(A,rd(A,B)),A),C) = rd(mult(rd(B,A),ld(B,B)),C).  [para(16504(a,2),23(a,2,1)),rewrite([23(8)]),flip(a)].
143.90/144.29	16526 rd(ld(A,A),ld(mult(B,rd(B,A)),B)) = rd(B,A).  [para(16504(a,2),281(a,1,2)),rewrite([463(8)])].
143.90/144.29	16560 ld(ld(mult(A,rd(A,B)),A),rd(rd(B,A),ld(B,B))) = ld(B,B).  [para(16504(a,2),8896(a,1,1)),rewrite([525(12),880(12),1233(11),9(12),525(11),880(11),1233(10),9(11),525(10),880(10),1233(9),9(10)])].
143.90/144.29	16599 rd(rd(ld(A,A),rd(B,A)),rd(mult(rd(A,B),A),B)) = rd(B,A).  [para(16521(a,1),5505(a,1,2,2)),rewrite([16526(6),16522(8),16526(12)])].
143.90/144.29	16615 rd(ld(A,A),ld(mult(B,rd(B,ld(A,A))),B)) = rd(B,ld(A,A)).  [para(525(a,1),16526(a,1,1)),rewrite([880(3),1233(2),9(3)])].
143.90/144.29	17036 mult(ld(mult(A,ld(B,B)),A),ld(B,C)) = mult(B,mult(rd(ld(B,ld(A,A)),B),C)).  [para(15213(a,1),1741(a,1,1))].
143.90/144.29	17109 rd(mult(ld(A,A),ld(B,A)),A) = rd(A,mult(ld(A,A),mult(B,A))).  [para(525(a,1),1751(a,2,2,1)),rewrite([2767(6),15901(6),1023(9),16477(10)])].
143.90/144.29	17167 mult(ld(A,A),rd(rd(ld(B,C),C),ld(A,A))) = rd(A,mult(ld(A,A),mult(B,A))).  [back_rewrite(15901),rewrite([17109(10)])].
143.90/144.29	17877 mult(rd(ld(A,rd(B,mult(C,B))),mult(D,ld(A,ld(C,ld(C,C))))),E) = ld(D,E).  [para(2208(a,2),354(a,1,1,2))].
143.90/144.29	17880 ld(A,ld(A,A)) = rd(ld(B,rd(C,mult(D,C))),mult(A,ld(B,ld(D,ld(D,D))))).  [para(2208(a,2),436(a,2,2))].
143.90/144.29	18542 rd(ld(A,ld(B,ld(B,B))),C) = rd(ld(A,rd(D,mult(B,D))),C).  [para(2570(a,1),2548(a,1,1)),rewrite([2570(13)])].
143.90/144.29	20020 mult(rd(A,B),mult(rd(mult(rd(B,A),C),A),D)) = mult(rd(C,B),mult(rd(B,A),D)).  [para(1354(a,1),562(a,2,2,1)),rewrite([7(5)]),flip(a)].
143.90/144.29	33245 rd(ld(mult(A,A),rd(B,mult(C,B))),rd(rd(rd(C,A),A),C)) = ld(C,ld(C,C)).  [para(12067(a,2),420(a,2,1)),flip(a)].
143.90/144.29	38024 rd(ld(ld(A,B),rd(ld(A,ld(A,A)),B)),rd(rd(rd(C,D),B),B)) = rd(D,C).  [para(420(a,2),12677(a,1,1,2,1))].
143.90/144.29	39703 rd(ld(A,A),ld(mult(B,ld(A,A)),B)) = rd(B,mult(mult(ld(B,B),ld(A,A)),B)).  [para(915(a,1),12809(a,1,1)),rewrite([2812(9),17167(9),16093(6),15213(9)]),flip(a)].
143.90/144.29	41148 ld(A,ld(A,A)) = rd(ld(ld(B,C),rd(ld(B,ld(B,B)),C)),rd(rd(A,C),C)).  [para(13355(a,1),10018(a,1,1)),rewrite([12673(10),33245(8),12673(13)])].
143.90/144.29	44192 mult(ld(A,ld(mult(B,C),rd(B,C))),C) = rd(ld(A,ld(A,A)),C).  [para(13773(a,2),8(a,1,1)),flip(a)].
143.90/144.29	46043 mult(ld(A,ld(mult(B,C),rd(B,C))),D) = mult(ld(A,ld(C,ld(C,ld(C,C)))),D).  [para(12412(a,2),15643(a,2,1,2)),rewrite([1065(4),525(3),357(3),6512(3),1233(2)]),flip(a)].
143.90/144.29	46123 mult(ld(A,A),mult(rd(A,B),mult(ld(A,A),C))) = mult(rd(A,mult(ld(A,A),B)),C).  [para(15258(a,1),972(a,1,2,1,2,1)),rewrite([16386(7),16386(12),880(7),1233(6),9(7),7(6),16386(9),16386(16),15258(18),9641(13),5607(11),357(9),16386(16),2767(11),2811(11)])].
143.90/144.29	46897 ld(mult(ld(A,A),ld(B,B)),ld(mult(A,ld(B,B)),A)) = ld(B,B).  [para(472(a,1),16560(a,1,2,1)),rewrite([8(5),2767(4),915(7),7(5),15213(6)])].
143.90/144.29	46900 mult(ld(A,A),rd(mult(ld(A,A),B),A)) = rd(rd(B,A),ld(A,A)).  [para(16599(a,1),799(a,1,1,2)),rewrite([7(5),16599(8),16599(15),7(10),20020(9),367(2),46123(7),463(6),523(15),523(16),653(16)])].
143.90/144.29	46905 mult(ld(A,A),ld(B,B)) = ld(A,A).  [para(443(a,1),16615(a,1,2,1,2)),rewrite([915(6),477(11),367(8),772(10),17036(7),7(6),9(5),880(5),1233(4),9(5),915(9),915(10),46897(9),880(4),1233(3),9(4),367(3),525(3),880(3),1233(2),9(3),915(6),5589(8),525(5),10(6),367(3)]),flip(a)].
143.90/144.29	46906 rd(ld(A,A),ld(mult(B,ld(A,A)),B)) = ld(A,A).  [para(443(a,1),16615(a,2)),rewrite([915(6),915(11),5589(13),525(10),10(11),367(8),46905(9),2767(8),15210(7),46905(5),46905(4),915(7),10(8),477(10),367(7),46905(8)])].
143.90/144.29	46910 ld(A,A) = ld(B,B).  [back_rewrite(39703),rewrite([46906(5),46905(4),357(3),367(2)])].
143.90/144.29	46913 ld(A,A) = c_0.  [new_symbol(46910)].
143.90/144.29	46920 mult(c_0,c_0) = c_0.  [back_rewrite(46905),rewrite([46913(1),46913(2),46913(4)])].
143.90/144.29	46922 mult(c_0,rd(mult(c_0,A),B)) = rd(rd(A,B),c_0).  [back_rewrite(46900),rewrite([46913(1),46913(2),46913(7)])].
143.90/144.29	47113 mult(ld(A,ld(mult(B,C),rd(B,C))),D) = mult(ld(A,ld(C,ld(C,c_0))),D).  [back_rewrite(46043),rewrite([46913(6)])].
143.90/144.29	47227 mult(ld(A,ld(B,ld(B,c_0))),B) = rd(ld(A,c_0),B).  [back_rewrite(44192),rewrite([47113(5),46913(6)])].
143.90/144.29	47244 rd(ld(ld(A,B),rd(ld(A,c_0),B)),rd(rd(C,B),B)) = ld(C,c_0).  [back_rewrite(41148),rewrite([46913(1),46913(4)]),flip(a)].
143.90/144.29	47276 mult(rd(A,B),c_0) = rd(A,B).  [back_rewrite(38024),rewrite([46913(2),47244(9),523(3)])].
143.90/144.29	47658 rd(ld(A,rd(B,mult(C,B))),D) = rd(ld(A,ld(C,c_0)),D).  [back_rewrite(18542),rewrite([46913(1)]),flip(a)].
143.90/144.30	47682 rd(ld(A,ld(B,c_0)),mult(C,ld(A,ld(B,c_0)))) = ld(C,c_0).  [back_rewrite(17880),rewrite([46913(1),46913(6),47658(10)]),flip(a)].
143.90/144.30	47685 mult(ld(A,c_0),B) = ld(A,B).  [back_rewrite(17877),rewrite([46913(4),47658(8),47682(8)])].
143.90/144.30	47801 rd(ld(mult(A,rd(A,B)),A),C) = rd(rd(B,A),C).  [back_rewrite(16525),rewrite([46913(6),47276(7)])].
143.90/144.30	47804 rd(rd(A,B),c_0) = rd(A,B).  [back_rewrite(16521),rewrite([46913(4),47801(5)])].
143.90/144.30	48000 rd(A,mult(c_0,B)) = rd(A,B).  [back_rewrite(12819),rewrite([46913(1),46913(2),46913(5),47276(6),46922(5),47804(3),46913(2),46913(5),47276(6)]),flip(a)].
143.90/144.30	48183 mult(A,c_0) = A.  [back_rewrite(10707),rewrite([46913(2),47227(6),7(5),35(4),46913(1),46920(3)])].
143.90/144.30	48254 rd(A,c_0) = A.  [back_rewrite(9641),rewrite([46913(1),48183(2),46913(1),48183(2),46913(1)]),flip(a)].
143.90/144.30	48312 mult(mult(A,A),B) = mult(A,mult(A,B)).  [back_rewrite(8856),rewrite([46913(9),47685(11),8(10)])].
143.90/144.30	48326 mult(c_0,A) = A.  [back_rewrite(8821),rewrite([48312(2),46913(3),48000(8),13(6),46913(1),46913(2),48254(3)]),flip(a)].
143.90/144.30	48577 $F # answer(goals).  [back_rewrite(394),rewrite([46913(4),48183(3),46913(6),48326(6)]),xx(a),xx(b)].
143.90/144.30	
143.90/144.30	% SZS output end Refutation
143.90/144.30	============================== end of proof ==========================
143.90/144.30	
143.90/144.30	============================== STATISTICS ============================
143.90/144.30	
143.90/144.30	Given=1615. Generated=4110809. Kept=48570. proofs=1.
143.90/144.30	Usable=959. Sos=6505. Demods=6885. Limbo=1664, Disabled=39448. Hints=0.
143.90/144.30	Megabytes=44.67.
143.90/144.30	User_CPU=140.06, System_CPU=3.13, Wall_clock=144.
143.90/144.30	
143.90/144.30	============================== end of statistics =====================
143.90/144.30	
143.90/144.30	============================== end of search =========================
143.90/144.30	
143.90/144.30	THEOREM PROVED
143.90/144.30	% SZS status Theorem
143.90/144.30	
143.90/144.30	Exiting with 1 proof.
143.90/144.30	
143.90/144.30	Process 28402 exit (max_proofs) Mon Jul  3 07:59:01 2023
143.90/144.30	Prover9 interrupted
143.90/144.30	EOF