0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n004.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% DateTime   : Tue Jul 13 14:39:39 EDT 2021
0.13/0.35	% CPUTime    : 
3.06/3.37	============================== Prover9 ===============================
3.06/3.37	Prover9 (32) version 2009-11A, November 2009.
3.06/3.37	Process 18727 was started by sandbox2 on n004.cluster.edu,
3.06/3.37	Tue Jul 13 14:39:39 2021
3.06/3.37	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_18574_n004.cluster.edu".
3.06/3.37	============================== end of head ===========================
3.06/3.37	
3.06/3.37	============================== INPUT =================================
3.06/3.37	
3.06/3.37	% Reading from file /tmp/Prover9_18574_n004.cluster.edu
3.06/3.37	
3.06/3.37	set(prolog_style_variables).
3.06/3.37	set(auto2).
3.06/3.37	    % set(auto2) -> set(auto).
3.06/3.37	    % set(auto) -> set(auto_inference).
3.06/3.37	    % set(auto) -> set(auto_setup).
3.06/3.37	    % set(auto_setup) -> set(predicate_elim).
3.06/3.37	    % set(auto_setup) -> assign(eq_defs, unfold).
3.06/3.37	    % set(auto) -> set(auto_limits).
3.06/3.37	    % set(auto_limits) -> assign(max_weight, "100.000").
3.06/3.37	    % set(auto_limits) -> assign(sos_limit, 20000).
3.06/3.37	    % set(auto) -> set(auto_denials).
3.06/3.37	    % set(auto) -> set(auto_process).
3.06/3.37	    % set(auto2) -> assign(new_constants, 1).
3.06/3.37	    % set(auto2) -> assign(fold_denial_max, 3).
3.06/3.37	    % set(auto2) -> assign(max_weight, "200.000").
3.06/3.37	    % set(auto2) -> assign(max_hours, 1).
3.06/3.37	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
3.06/3.37	    % set(auto2) -> assign(max_seconds, 0).
3.06/3.37	    % set(auto2) -> assign(max_minutes, 5).
3.06/3.37	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
3.06/3.37	    % set(auto2) -> set(sort_initial_sos).
3.06/3.37	    % set(auto2) -> assign(sos_limit, -1).
3.06/3.37	    % set(auto2) -> assign(lrs_ticks, 3000).
3.06/3.37	    % set(auto2) -> assign(max_megs, 400).
3.06/3.37	    % set(auto2) -> assign(stats, some).
3.06/3.37	    % set(auto2) -> clear(echo_input).
3.06/3.37	    % set(auto2) -> set(quiet).
3.06/3.37	    % set(auto2) -> clear(print_initial_clauses).
3.06/3.37	    % set(auto2) -> clear(print_given).
3.06/3.37	assign(lrs_ticks,-1).
3.06/3.37	assign(sos_limit,10000).
3.06/3.37	assign(order,kbo).
3.06/3.37	set(lex_order_vars).
3.06/3.37	clear(print_given).
3.06/3.37	
3.06/3.37	% formulas(sos).  % not echoed (6 formulas)
3.06/3.37	
3.06/3.37	============================== end of input ==========================
3.06/3.37	
3.06/3.37	% From the command line: assign(max_seconds, 1200).
3.06/3.37	
3.06/3.37	============================== PROCESS NON-CLAUSAL FORMULAS ==========
3.06/3.37	
3.06/3.37	% Formulas that are not ordinary clauses:
3.06/3.37	1 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B)))) # label(f05) # label(axiom) # label(non_clause).  [assumption].
3.06/3.37	2 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause).  [assumption].
3.06/3.37	3 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause).  [assumption].
3.06/3.37	4 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause).  [assumption].
3.06/3.37	5 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause).  [assumption].
3.06/3.37	6 -(all X0 all X1 (mult(ld(X1,X1),X0) = X0 & X0 = mult(X0,ld(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
3.06/3.37	
3.06/3.37	============================== end of process non-clausal formulas ===
3.06/3.37	
3.06/3.37	============================== PROCESS INITIAL CLAUSES ===============
3.06/3.37	
3.06/3.37	============================== PREDICATE ELIMINATION =================
3.06/3.37	
3.06/3.37	============================== end predicate elimination =============
3.06/3.37	
3.06/3.37	Auto_denials:
3.06/3.37	  % copying label goals to answer in negative clause
3.06/3.37	
3.06/3.37	Term ordering decisions:
3.06/3.37	Function symbol KB weights:  c1=1. c2=1. mult=1. ld=1. rd=1.
3.06/3.37	
3.06/3.37	============================== end of process initial clauses ========
3.06/3.37	
3.06/3.37	============================== CLAUSES FOR SEARCH ====================
3.06/3.37	
3.06/3.37	============================== end of clauses for search =============
3.06/3.37	
3.06/3.37	============================== SEARCH ================================
3.06/3.37	
3.06/3.37	% Starting search at 0.01 seconds.
3.06/3.37	
3.06/3.37	Low Water (keep): wt=83.000, iters=3391
3.06/3.37	
3.06/3.37	Low Water (keep): wt=71.000, iters=3434
3.06/3.37	
3.06/3.37	Low Water (keep): wt=67.000, iters=3360
3.06/3.37	
3.06/3.37	Low Water (keep): wt=63.000, iters=3341
3.06/3.37	
3.06/3.37	Low Water (keep): wt=59.000, iters=3391
3.06/3.37	
3.06/3.37	Low Water (keep): wt=55.000, iters=3405
3.06/3.37	
3.06/3.37	Low Water (keep): wt=51.000, iters=3361
3.06/3.37	
3.06/3.37	Low Water (keep): wt=47.000, iters=3353
3.06/3.37	
3.06/3.37	Low Water (keep): wt=43.000, iters=3343
3.06/3.37	
3.06/3.37	Low Water (keep): wt=39.000, iters=3372
3.06/3.37	
3.06/3.37	Low Water (keep): wt=35.000, iters=3349
3.06/3.37	
3.06/3.37	Low Water (keep): wt=31.000, iters=3381
3.06/3.37	
3.06/3.37	Low Water (displace): id=4176, wt=191.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4174, wt=179.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4167, wt=171.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=6417, wt=167.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4165, wt=151.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4130, wt=147.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4686, wt=143.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=6346, wt=139.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=4147, wt=135.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=6720, wt=127.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=6221, wt=123.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=6416, wt=119.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=12620, wt=23.000
22.48/22.78	
22.48/22.78	Low Water (displace): id=13058, wt=19.000
22.48/22.78	
22.48/22.78	Low Water (keep): wt=27.000, iters=3338
22.48/22.78	
22.48/22.78	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 7.58 sec).
22.48/22.78	
22.48/22.78	============================== PROOF =================================
22.48/22.78	% SZS status Theorem
22.48/22.78	% SZS output start Refutation
22.48/22.78	
22.48/22.78	% Proof 1 at 21.21 (+ 0.55) seconds: goals.
22.48/22.78	% Length of proof is 167.
22.48/22.78	% Level of proof is 32.
22.48/22.78	% Maximum clause weight is 31.000.
22.48/22.78	% Given clauses 831.
22.48/22.78	
22.48/22.78	1 (all C all B all A mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B)))) # label(f05) # label(axiom) # label(non_clause).  [assumption].
22.48/22.78	2 (all B all A mult(rd(A,B),B) = A) # label(f03) # label(axiom) # label(non_clause).  [assumption].
22.48/22.78	3 (all B all A B = ld(A,mult(A,B))) # label(f02) # label(axiom) # label(non_clause).  [assumption].
22.48/22.78	4 (all B all A mult(A,ld(A,B)) = B) # label(f01) # label(axiom) # label(non_clause).  [assumption].
22.48/22.78	5 (all B all A rd(mult(A,B),B) = A) # label(f04) # label(axiom) # label(non_clause).  [assumption].
22.48/22.78	6 -(all X0 all X1 (mult(ld(X1,X1),X0) = X0 & X0 = mult(X0,ld(X1,X1)))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
22.48/22.78	7 mult(rd(A,B),B) = A # label(f03) # label(axiom).  [clausify(2)].
22.48/22.78	8 ld(A,mult(A,B)) = B # label(f02) # label(axiom).  [clausify(3)].
22.48/22.78	9 mult(A,ld(A,B)) = B # label(f01) # label(axiom).  [clausify(4)].
22.48/22.78	10 rd(mult(A,B),B) = A # label(f04) # label(axiom).  [clausify(5)].
22.48/22.78	11 mult(mult(mult(A,B),C),B) = mult(A,mult(B,mult(C,B))) # label(f05) # label(axiom).  [clausify(1)].
22.48/22.78	12 mult(ld(c2,c2),c1) != c1 | mult(c1,ld(c2,c2)) != c1 # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(6)].
22.48/22.78	13 ld(rd(A,B),A) = B.  [para(7(a,1),8(a,1,2))].
22.48/22.78	14 rd(A,ld(B,A)) = B.  [para(9(a,1),10(a,1,1))].
22.48/22.78	15 mult(rd(A,B),mult(B,mult(C,B))) = mult(mult(A,C),B).  [para(7(a,1),11(a,1,1,1)),flip(a)].
22.48/22.78	16 ld(mult(mult(A,B),C),mult(A,mult(B,mult(C,B)))) = B.  [para(11(a,1),8(a,1,2))].
22.48/22.78	17 mult(A,mult(ld(A,B),mult(C,ld(A,B)))) = mult(mult(B,C),ld(A,B)).  [para(9(a,1),11(a,1,1,1)),flip(a)].
22.48/22.78	18 mult(A,mult(B,mult(ld(mult(A,B),C),B))) = mult(C,B).  [para(9(a,1),11(a,1,1)),flip(a)].
22.48/22.78	19 rd(mult(A,mult(B,mult(C,B))),B) = mult(mult(A,B),C).  [para(11(a,1),10(a,1,1))].
22.48/22.78	20 mult(mult(mult(A,mult(B,mult(C,B))),D),B) = mult(mult(mult(A,B),C),mult(B,mult(D,B))).  [para(11(a,1),11(a,1,1,1))].
22.48/22.78	21 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))).  [para(11(a,1),11(a,1,1))].
22.48/22.78	22 mult(A,mult(mult(B,mult(C,B)),mult(D,mult(B,mult(C,B))))) = mult(A,mult(B,mult(mult(C,mult(mult(B,mult(D,B)),C)),B))).  [para(11(a,1),11(a,2)),rewrite([20(5),11(6),11(7)]),flip(a)].
22.48/22.78	23 mult(mult(A,rd(B,C)),C) = mult(rd(A,C),mult(C,B)).  [para(7(a,1),15(a,1,2,2)),flip(a)].
22.48/22.78	24 ld(rd(A,B),mult(mult(A,C),B)) = mult(B,mult(C,B)).  [para(15(a,1),8(a,1,2))].
22.48/22.78	26 rd(mult(mult(A,B),C),mult(C,mult(B,C))) = rd(A,C).  [para(15(a,1),10(a,1,1))].
22.48/22.78	30 ld(mult(mult(A,B),rd(C,B)),mult(A,mult(B,C))) = B.  [para(7(a,1),16(a,1,2,2,2))].
22.48/22.78	32 ld(mult(mult(A,ld(B,C)),B),mult(A,mult(ld(B,C),C))) = ld(B,C).  [para(9(a,1),16(a,1,2,2,2))].
22.48/22.78	37 mult(A,mult(ld(mult(B,A),C),A)) = ld(B,mult(C,A)).  [para(18(a,1),8(a,1,2)),flip(a)].
22.48/22.78	39 ld(A,mult(mult(B,C),ld(A,B))) = mult(ld(A,B),mult(C,ld(A,B))).  [para(17(a,1),8(a,1,2))].
22.48/22.78	40 mult(mult(A,B),ld(B,A)) = mult(B,mult(ld(B,A),A)).  [para(9(a,1),17(a,1,2,2)),flip(a)].
22.48/22.78	45 rd(mult(A,mult(B,C)),B) = mult(mult(A,B),rd(C,B)).  [para(7(a,1),19(a,1,1,2,2))].
22.48/22.78	46 mult(mult(rd(A,mult(B,mult(C,B))),B),C) = rd(A,B).  [para(7(a,1),19(a,1,1)),flip(a)].
22.48/22.78	47 mult(rd(rd(A,rd(B,C)),C),mult(C,B)) = mult(A,C).  [para(7(a,1),23(a,1,1)),flip(a)].
22.48/22.78	60 ld(rd(A,B),mult(C,B)) = mult(B,mult(ld(A,C),B)).  [para(9(a,1),24(a,1,2,1))].
22.48/22.78	64 rd(mult(A,B),mult(B,mult(C,B))) = rd(rd(A,C),B).  [para(7(a,1),26(a,1,1,1))].
22.48/22.78	102 ld(A,ld(B,mult(C,A))) = mult(ld(mult(B,A),C),A).  [para(37(a,1),8(a,1,2))].
22.48/22.78	146 mult(mult(rd(A,mult(B,C)),B),rd(C,B)) = rd(A,B).  [para(7(a,1),45(a,1,1)),flip(a)].
22.48/22.78	147 mult(mult(A,B),rd(ld(B,C),B)) = rd(mult(A,C),B).  [para(9(a,1),45(a,1,1,2)),flip(a)].
22.48/22.78	167 ld(mult(mult(mult(A,B),mult(C,mult(B,C))),D),mult(mult(A,mult(B,mult(C,B))),mult(C,mult(D,C)))) = C.  [para(21(a,1),16(a,1,1,1))].
22.48/22.78	168 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(mult(C,mult(mult(B,mult(C,B)),C)),B)))) = mult(B,mult(C,B)).  [para(21(a,1),16(a,1,1)),rewrite([22(11)])].
22.48/22.78	188 mult(rd(A,mult(B,mult(C,B))),B) = rd(rd(A,B),C).  [para(46(a,1),10(a,1,1)),flip(a)].
22.48/22.78	204 rd(rd(A,rd(B,C)),C) = rd(mult(A,C),mult(C,B)).  [para(47(a,1),10(a,1,1)),flip(a)].
22.48/22.78	224 mult(A,mult(ld(B,rd(C,A)),A)) = ld(rd(B,A),C).  [para(7(a,1),60(a,1,2)),flip(a)].
22.48/22.78	233 ld(mult(mult(A,B),rd(C,B)),mult(D,B)) = mult(B,mult(ld(mult(A,mult(B,C)),D),B)).  [para(45(a,1),60(a,1,1))].
22.48/22.78	276 rd(rd(rd(A,B),C),B) = rd(A,mult(B,mult(C,B))).  [para(7(a,1),64(a,1,1)),flip(a)].
22.48/22.78	293 mult(ld(mult(A,B),rd(C,B)),B) = ld(B,ld(A,C)).  [para(7(a,1),102(a,1,2,2)),flip(a)].
22.48/22.78	294 mult(ld(mult(A,B),A),B) = ld(B,B).  [para(8(a,1),102(a,1,2)),flip(a)].
22.48/22.78	297 mult(ld(mult(rd(mult(A,B),C),B),A),B) = ld(B,C).  [para(13(a,1),102(a,1,2)),flip(a)].
22.48/22.78	309 mult(ld(A,rd(A,B)),B) = ld(B,B).  [para(7(a,1),294(a,1,1,1))].
22.48/22.78	310 ld(ld(mult(A,B),A),ld(B,B)) = B.  [para(294(a,1),8(a,1,2))].
22.48/22.78	311 ld(ld(A,B),ld(A,B)) = mult(ld(B,A),ld(A,B)).  [para(9(a,1),294(a,1,1,1)),flip(a)].
22.48/22.78	312 ld(mult(A,B),A) = rd(ld(B,B),B).  [para(294(a,1),10(a,1,1)),flip(a)].
22.48/22.78	326 ld(ld(mult(A,B),A),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)).  [para(294(a,1),37(a,1,2,1,1)),flip(a)].
22.48/22.78	337 mult(ld(mult(A,B),ld(mult(C,B),C)),B) = ld(B,ld(A,ld(B,B))).  [para(294(a,1),102(a,1,2,2)),flip(a)].
22.48/22.78	339 ld(ld(A,rd(A,B)),ld(B,B)) = B.  [para(309(a,1),8(a,1,2))].
22.48/22.78	340 ld(A,rd(A,B)) = rd(ld(B,B),B).  [para(309(a,1),10(a,1,1)),flip(a)].
22.48/22.78	342 mult(mult(A,ld(B,rd(B,C))),C) = A.  [para(309(a,1),15(a,1,2,2)),rewrite([9(3),7(2)]),flip(a)].
22.48/22.78	351 ld(ld(A,rd(A,B)),mult(C,B)) = mult(B,mult(ld(ld(B,B),C),B)).  [para(309(a,1),37(a,1,2,1,1)),flip(a)].
22.48/22.78	353 mult(mult(A,ld(B,rd(B,C))),rd(C,ld(B,rd(B,C)))) = rd(mult(A,ld(C,C)),ld(B,rd(B,C))).  [para(309(a,1),45(a,1,1,2)),flip(a)].
22.48/22.78	363 mult(ld(mult(A,B),ld(C,rd(C,B))),B) = ld(B,ld(A,ld(B,B))).  [para(309(a,1),102(a,1,2,2)),flip(a)].
22.48/22.78	393 rd(A,rd(ld(B,B),B)) = mult(A,B).  [para(312(a,1),14(a,1,2))].
22.48/22.78	404 mult(mult(A,B),ld(mult(C,B),C)) = A.  [para(312(a,2),45(a,2,2)),rewrite([9(2),10(2)]),flip(a)].
22.48/22.78	405 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = rd(ld(C,C),C).  [para(21(a,1),312(a,1,1))].
22.48/22.78	417 ld(mult(A,B),A) = ld(mult(C,B),C).  [para(312(a,2),312(a,2))].
22.48/22.78	421 mult(A,rd(ld(B,B),B)) = rd(A,B).  [para(340(a,1),9(a,1,2))].
22.48/22.78	439 ld(mult(A,B),A) = ld(C,rd(C,B)).  [para(340(a,2),312(a,2))].
22.48/22.78	491 rd(A,ld(B,rd(B,C))) = mult(A,C).  [para(7(a,1),342(a,1,1)),flip(a)].
22.48/22.78	492 mult(A,ld(B,rd(B,C))) = rd(A,C).  [para(342(a,1),10(a,1,1)),flip(a)].
22.48/22.78	495 mult(mult(A,ld(B,C)),ld(C,B)) = A.  [para(14(a,1),342(a,1,1,2,2))].
22.48/22.78	504 mult(mult(A,ld(B,B)),B) = mult(rd(A,B),mult(B,B)).  [back_rewrite(353),rewrite([492(3),491(4),491(8)]),flip(a)].
22.48/22.78	513 ld(rd(ld(A,A),A),rd(ld(A,A),A)) = rd(A,A).  [para(393(a,1),309(a,1,1,2)),rewrite([8(2),421(3)]),flip(a)].
22.48/22.78	515 rd(ld(A,A),A) = ld(A,rd(A,A)).  [para(393(a,1),339(a,1,1,2)),rewrite([8(2),513(5)]),flip(a)].
22.48/22.78	538 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,rd(C,C)).  [back_rewrite(405),rewrite([515(10)])].
22.48/22.78	544 mult(A,ld(mult(B,C),B)) = rd(A,C).  [para(7(a,1),404(a,1,1))].
22.48/22.78	575 ld(mult(A,ld(B,C)),A) = ld(C,B).  [para(9(a,1),417(a,1,1)),flip(a)].
22.48/22.78	576 ld(mult(mult(A,B),C),rd(A,C)) = ld(mult(D,mult(C,mult(B,C))),D).  [para(15(a,1),417(a,1,1))].
22.48/22.78	633 rd(A,ld(B,C)) = mult(A,ld(C,B)).  [para(14(a,1),491(a,1,2,2))].
22.48/22.78	634 ld(mult(rd(A,B),mult(C,B)),mult(A,mult(ld(D,rd(D,B)),C))) = ld(D,rd(D,B)).  [para(491(a,1),30(a,1,1,2)),rewrite([492(3)])].
22.48/22.78	711 mult(mult(A,mult(B,ld(C,D))),ld(D,C)) = mult(mult(A,ld(C,D)),mult(ld(D,C),B)).  [para(495(a,1),15(a,1,2,2)),rewrite([633(2)]),flip(a)].
22.48/22.78	717 ld(mult(A,ld(B,C)),mult(D,ld(C,B))) = mult(ld(C,B),mult(ld(A,D),ld(C,B))).  [para(495(a,1),37(a,1,2,1,1)),flip(a)].
22.48/22.78	727 rd(A,mult(ld(B,C),mult(D,ld(B,C)))) = mult(rd(mult(A,ld(C,B)),D),ld(C,B)).  [para(495(a,1),64(a,1,1)),rewrite([633(10)])].
22.48/22.78	729 mult(mult(ld(A,B),ld(A,B)),mult(ld(B,A),ld(C,D))) = ld(ld(B,A),ld(C,D)).  [para(495(a,1),102(a,1,2,2)),rewrite([717(8),711(10)]),flip(a)].
22.48/22.78	746 mult(rd(mult(A,ld(B,C)),D),ld(B,C)) = mult(A,ld(mult(mult(B,D),ld(C,B)),C)).  [para(17(a,1),544(a,1,2,1)),rewrite([727(10)]),flip(a)].
22.48/22.78	858 ld(mult(A,rd(B,C)),A) = mult(C,mult(ld(D,rd(D,mult(C,B))),C)).  [para(146(a,1),417(a,1,1)),rewrite([60(5)]),flip(a)].
22.48/22.78	867 rd(mult(rd(A,B),C),B) = mult(A,rd(ld(B,C),B)).  [para(7(a,1),147(a,1,1)),flip(a)].
22.48/22.78	868 ld(mult(A,B),rd(mult(A,C),B)) = rd(ld(B,C),B).  [para(147(a,1),8(a,1,2))].
22.48/22.78	1013 mult(rd(A,mult(B,ld(C,A))),ld(C,A)) = rd(C,mult(ld(A,C),B)).  [para(9(a,1),204(a,2,1)),rewrite([633(2),633(5)])].
22.48/22.78	1205 rd(rd(A,mult(B,mult(C,B))),C) = rd(rd(A,B),mult(C,mult(B,C))).  [para(276(a,1),276(a,1,1))].
22.48/22.78	1243 rd(mult(A,mult(ld(A,A),A)),A) = A.  [para(310(a,1),293(a,2)),rewrite([544(3),633(4),8(3),60(3),544(6)])].
22.48/22.78	1246 ld(A,ld(mult(B,C),B)) = ld(A,ld(mult(D,C),D)).  [para(417(a,1),293(a,2,2)),rewrite([293(5)])].
22.48/22.78	1250 ld(A,ld(mult(B,C),B)) = ld(A,ld(D,rd(D,C))).  [para(439(a,1),293(a,2,2)),rewrite([293(5)])].
22.48/22.78	1275 mult(A,mult(ld(A,A),A)) = mult(A,A).  [para(1243(a,1),7(a,1,1)),flip(a)].
22.48/22.78	1280 mult(ld(A,A),A) = A.  [para(1275(a,1),8(a,1,2)),rewrite([8(2)]),flip(a)].
22.48/22.78	1283 ld(mult(A,A),mult(A,A)) = ld(A,A).  [para(1275(a,1),30(a,1,2)),rewrite([9(2),633(2),9(2)])].
22.48/22.78	1285 mult(mult(A,ld(B,B)),mult(B,B)) = mult(mult(A,B),B).  [para(1275(a,1),21(a,2,2)),rewrite([9(3),1280(2)]),flip(a)].
22.48/22.78	1315 mult(ld(mult(A,B),A),rd(C,B)) = rd(ld(B,C),B).  [para(417(a,1),39(a,1,2,2)),rewrite([544(5),868(4),544(7)]),flip(a)].
22.48/22.78	1317 mult(ld(A,rd(A,B)),rd(C,B)) = rd(ld(B,C),B).  [para(439(a,1),39(a,2,1)),rewrite([544(5),868(4),544(7)]),flip(a)].
22.48/22.78	1337 ld(ld(A,A),A) = A.  [para(1280(a,1),8(a,1,2))].
22.48/22.78	1338 rd(A,A) = ld(A,A).  [para(1280(a,1),10(a,1,1))].
22.48/22.78	1342 mult(rd(A,B),mult(B,B)) = mult(mult(A,B),ld(B,B)).  [para(1280(a,1),23(a,2,2)),rewrite([633(2),9(2),633(5),504(6)]),flip(a)].
22.48/22.78	1344 ld(mult(A,rd(B,A)),mult(ld(A,A),mult(A,B))) = A.  [para(1280(a,1),30(a,1,1,1))].
22.48/22.78	1348 mult(mult(ld(mult(A,B),mult(A,B)),A),rd(B,A)) = rd(mult(A,B),A).  [para(1280(a,1),45(a,1,1)),flip(a)].
22.48/22.78	1353 mult(ld(A,ld(A,A)),A) = ld(A,A).  [para(1280(a,1),294(a,1,1,1))].
22.48/22.78	1354 ld(ld(A,ld(A,A)),ld(A,A)) = A.  [para(1280(a,1),310(a,1,1,1))].
22.48/22.78	1356 ld(mult(A,B),A) = ld(B,ld(B,B)).  [para(1280(a,1),417(a,1,1)),flip(a)].
22.48/22.78	1358 ld(A,ld(A,A)) = ld(B,rd(B,A)).  [para(1280(a,1),439(a,1,1))].
22.48/22.78	1362 mult(A,ld(B,ld(B,B))) = rd(A,B).  [para(1280(a,1),544(a,1,2,1))].
22.48/22.78	1385 ld(mult(mult(A,B),mult(C,mult(B,C))),mult(A,mult(B,mult(C,B)))) = ld(C,ld(C,C)).  [back_rewrite(538),rewrite([1338(9)])].
22.48/22.78	1394 rd(ld(A,A),A) = ld(A,ld(A,A)).  [back_rewrite(515),rewrite([1338(3)])].
22.48/22.78	1396 mult(mult(A,ld(B,B)),B) = mult(mult(A,B),ld(B,B)).  [back_rewrite(504),rewrite([1342(6)])].
22.48/22.78	1407 ld(rd(A,B),rd(A,B)) = mult(rd(A,mult(B,A)),B).  [para(1338(a,1),188(a,2)),rewrite([7(2)]),flip(a)].
22.48/22.78	1419 ld(A,mult(mult(A,A),A)) = mult(A,A).  [para(1283(a,1),37(a,1,2,1)),rewrite([1280(2)]),flip(a)].
22.48/22.78	1425 mult(ld(A,A),ld(A,A)) = ld(A,A).  [para(492(a,1),1283(a,1,1)),rewrite([492(8),1407(7),492(5),1338(3),633(4),1396(5),309(3),311(8),13(5),492(6),1338(4)])].
22.48/22.78	1486 mult(ld(A,ld(A,A)),mult(A,mult(B,A))) = mult(mult(ld(A,A),B),A).  [para(1353(a,1),11(a,1,1,1)),flip(a)].
22.48/22.78	1528 mult(ld(mult(A,B),A),ld(B,B)) = ld(B,ld(B,B)).  [para(1356(a,2),32(a,1,2,2,1)),rewrite([1362(3),7(2),8(6)])].
22.48/22.78	1530 ld(rd(rd(A,B),C),rd(A,mult(B,mult(C,B)))) = ld(B,ld(B,B)).  [para(188(a,1),1356(a,1,1))].
22.48/22.78	1550 ld(mult(rd(A,B),C),mult(A,rd(ld(B,C),B))) = ld(C,rd(C,B)).  [para(1358(a,2),32(a,1,1,1,2)),rewrite([1362(3),1317(6)])].
22.48/22.78	1653 mult(mult(A,mult(ld(B,ld(B,B)),C)),B) = mult(rd(A,B),mult(C,B)).  [para(1362(a,1),45(a,2,1)),rewrite([633(7),1337(6),633(9),1337(8)])].
22.48/22.78	1713 mult(mult(A,A),A) = mult(A,mult(A,A)).  [para(1419(a,1),9(a,1,2)),flip(a)].
22.48/22.78	1795 mult(ld(A,ld(B,B)),mult(ld(B,B),ld(A,ld(B,B)))) = ld(A,mult(ld(B,B),ld(A,ld(B,B)))).  [para(1425(a,1),39(a,1,2,1)),flip(a)].
22.48/22.78	1831 ld(ld(A,B),ld(B,A)) = mult(ld(B,A),ld(B,A)).  [para(1713(a,1),495(a,1,1)),rewrite([711(7),729(7)])].
22.48/22.78	1882 mult(ld(ld(A,B),C),ld(B,A)) = mult(ld(B,A),mult(C,ld(B,A))).  [para(297(a,1),495(a,1,1)),rewrite([746(9),575(10),39(8)])].
22.48/22.78	1885 ld(ld(ld(A,B),C),mult(ld(B,A),mult(C,ld(B,A)))) = ld(B,A).  [para(297(a,1),575(a,1,1)),rewrite([746(7),575(8),39(6)])].
22.48/22.78	2975 ld(mult(ld(mult(A,B),A),ld(C,D)),ld(mult(E,B),E)) = ld(D,C).  [para(1246(a,1),575(a,1))].
22.48/22.78	3019 ld(ld(mult(ld(mult(A,B),A),C),ld(D,rd(D,B))),ld(C,C)) = C.  [para(1250(a,1),310(a,1,1))].
22.48/22.78	3376 mult(ld(A,ld(A,A)),mult(A,A)) = A.  [para(294(a,1),1285(a,2,1)),rewrite([1528(4),1280(6)])].
22.48/22.78	3422 ld(ld(A,ld(A,A)),A) = mult(A,A).  [para(3376(a,1),8(a,1,2))].
22.48/22.78	3496 rd(ld(mult(A,B),A),B) = ld(B,ld(mult(A,B),A)).  [para(544(a,1),3422(a,2)),rewrite([311(7),8(4),544(5),1338(3),310(4)]),flip(a)].
22.48/22.78	3858 mult(ld(A,ld(mult(B,A),B)),mult(A,C)) = ld(A,C).  [para(1315(a,1),23(a,1,1)),rewrite([7(3),3496(4)]),flip(a)].
22.48/22.78	3895 rd(A,mult(rd(B,C),rd(ld(C,B),C))) = mult(A,rd(ld(rd(B,C),C),rd(B,C))).  [para(1315(a,1),276(a,2,2,2)),rewrite([633(5),8(4),867(5)]),flip(a)].
22.48/22.78	4360 ld(mult(A,rd(ld(mult(B,C),B),A)),mult(ld(A,A),rd(A,C))) = A.  [para(544(a,1),1344(a,1,2,2))].
22.48/22.78	6094 ld(mult(A,ld(B,C)),mult(A,ld(B,C))) = mult(rd(A,mult(ld(C,B),A)),ld(C,B)).  [para(633(a,1),1407(a,1,1)),rewrite([633(4)])].
22.48/22.78	6098 mult(A,mult(mult(rd(B,mult(A,B)),A),A)) = ld(rd(rd(B,A),A),B).  [para(1407(a,1),224(a,1,2,1))].
22.48/22.78	10909 mult(ld(A,ld(mult(B,A),B)),C) = ld(A,ld(A,C)).  [para(9(a,1),3858(a,1,2))].
22.48/22.78	13626 ld(ld(A,B),ld(ld(A,B),C)) = mult(mult(ld(B,A),ld(B,A)),C).  [para(9(a,1),10909(a,1,1,2,1)),rewrite([1831(3)]),flip(a)].
22.48/22.78	18750 rd(A,mult(ld(B,A),A)) = mult(ld(B,B),ld(A,B)).  [para(9(a,1),1013(a,1,1,2)),rewrite([1338(1)]),flip(a)].
22.48/22.78	18786 ld(rd(A,mult(ld(B,A),A)),ld(B,B)) = ld(B,A).  [para(18750(a,2),417(a,1,1)),rewrite([575(8)])].
22.48/22.78	18894 ld(rd(A,mult(ld(ld(B,B),A),A)),ld(B,B)) = ld(ld(B,B),A).  [para(1831(a,1),18786(a,1,2)),rewrite([1425(7)])].
22.48/22.78	19441 mult(A,mult(ld(B,rd(B,mult(A,B))),A)) = ld(A,rd(A,rd(B,A))).  [para(1315(a,1),1530(a,1,2,2,2)),rewrite([633(5),8(4),3895(8),1550(9),1407(7),60(8)]),flip(a)].
22.48/22.78	19678 mult(A,mult(ld(B,rd(B,mult(A,C))),A)) = ld(A,rd(A,rd(C,A))).  [para(1653(a,1),858(a,1,1)),rewrite([1407(9),60(10),19441(10),634(11)]),flip(a)].
22.48/22.78	21154 mult(A,mult(ld(mult(B,mult(A,C)),B),A)) = ld(A,rd(A,rd(C,A))).  [para(439(a,1),233(a,2,2,1)),rewrite([233(5),19678(10)])].
22.48/22.78	26248 mult(ld(A,A),rd(B,mult(ld(A,A),B))) = ld(B,B).  [para(495(a,1),6098(a,1,2)),rewrite([633(7),633(9),495(9)])].
22.48/22.78	26278 rd(A,mult(ld(B,B),A)) = ld(ld(B,B),ld(A,A)).  [para(26248(a,1),8(a,1,2)),flip(a)].
22.48/22.78	26279 mult(ld(A,ld(B,B)),ld(ld(B,B),A)) = mult(ld(B,B),rd(ld(ld(B,B),A),A)).  [para(9(a,1),26248(a,1,2,2)),rewrite([311(10)]),flip(a)].
22.48/22.78	26291 ld(ld(ld(A,A),ld(B,B)),ld(A,A)) = ld(B,B).  [para(26248(a,1),326(a,1,2)),rewrite([26278(3),575(5),26278(8),26278(11),26278(14),311(15),26279(15),633(14),26278(20),21154(22),633(16),9(16),633(13),1882(13),1885(14)])].
22.48/22.78	26293 mult(ld(A,A),mult(ld(ld(A,A),ld(B,B)),ld(B,B))) = ld(B,B).  [para(26248(a,1),337(a,1,1,1)),rewrite([26278(4),575(6),13626(5),1425(3),26278(6),40(7),26278(10),26278(14),26278(17),311(18),26279(18),633(17),8(19),8(16)])].
22.48/22.78	26295 mult(ld(ld(A,A),ld(B,B)),ld(B,B)) = ld(A,A).  [para(26248(a,1),351(a,1,2)),rewrite([26278(3),633(4),8(5),26291(5),26278(4),26278(7),26278(10),311(11),26279(11),633(10),26293(11),26278(10),26279(11),633(10),26293(11)]),flip(a)].
22.48/22.78	26296 ld(A,A) = ld(B,B).  [para(26248(a,1),363(a,1,1,1)),rewrite([26278(4),633(5),8(6),13626(5),1425(3),26278(6),40(7),26295(6),1425(3),26278(4),26278(8),26278(11),311(12),26279(12),633(11),26295(11),1425(8),311(7),1425(7),26291(6)])].
22.48/22.78	26297 ld(ld(A,A),mult(ld(B,B),ld(ld(A,A),ld(B,B)))) = ld(B,B).  [para(26248(a,1),576(a,2,1,2,2)),rewrite([26278(5),26278(9),633(10),717(11),575(6),1795(9),26278(10),26295(12),575(10)])].
22.48/22.78	26301 mult(ld(A,A),mult(ld(B,B),ld(A,A))) = ld(ld(A,A),ld(B,B)).  [para(26248(a,1),167(a,1,2,2,2)),rewrite([26278(4),26278(7),26278(15),26278(21),26295(23),717(21),1385(18),311(11),26279(11),633(10),26295(10),1425(7),26291(6),26278(8)])].
22.48/22.78	26303 ld(ld(A,A),ld(B,B)) = ld(B,B).  [para(26248(a,1),168(a,1,1,2,2)),rewrite([26278(5),26295(7),495(4),26278(4),26278(8),1882(10),26301(10),9(9),26278(8),1795(10),26297(8),26301(5),8(5),26278(7),1882(9),26301(9),9(8)])].
22.48/22.78	26305 mult(mult(A,ld(B,B)),ld(C,C)) = A.  [para(26248(a,1),1205(a,1,1,2,2)),rewrite([26278(3),26303(3),1425(3),633(2),633(4),26278(7),26303(7),633(6),26278(10),26303(10),26301(11),26303(9),633(8),495(8)])].
22.48/22.78	26312 mult(ld(A,A),ld(B,B)) = ld(A,A).  [para(26248(a,1),1348(a,2,1)),rewrite([26278(4),26303(4),26278(7),26303(7),6094(7),26278(5),26303(4),26303(3),26305(5),26278(4),26303(4),633(4),26301(5),26303(3),633(4)]),flip(a)].
22.48/22.78	26315 mult(ld(A,A),B) = B.  [para(26248(a,1),1486(a,2,1)),rewrite([26278(5),26303(5),1486(6),26312(3),1280(2)]),flip(a)].
22.48/22.78	26380 ld(ld(A,B),ld(C,C)) = ld(B,A).  [para(26248(a,1),2975(a,1,1,1,1)),rewrite([26303(3),26315(3),26315(3),1338(2),575(4)])].
22.48/22.78	26387 ld(ld(A,A),B) = B.  [para(26248(a,1),3019(a,1,1,1,1,1)),rewrite([26303(3),26315(2),26315(2),1338(1),633(2),8(3),26380(4)])].
22.48/22.78	26413 ld(mult(A,rd(ld(B,B),A)),mult(A,ld(C,C))) = A.  [para(26248(a,1),4360(a,1,1,2,1,1)),rewrite([26387(3),26315(6),1338(5),633(6),26315(7)])].
22.48/22.78	26439 ld(A,A) = c_0.  [new_symbol(26296)].
22.48/22.78	26578 rd(A,mult(ld(B,A),A)) = mult(c_0,ld(A,B)).  [back_rewrite(18750),rewrite([26439(4)])].
22.48/22.78	26956 mult(c_0,A) = A.  [back_rewrite(1280),rewrite([26439(1)])].
22.48/22.78	26961 mult(c1,c_0) != c1 # answer(goals).  [back_rewrite(12),rewrite([26439(3),26956(3),26439(7)]),xx(a)].
22.48/22.78	26971 rd(c_0,A) = ld(A,c_0).  [back_rewrite(1394),rewrite([26439(1),26439(3)])].
22.48/22.78	27008 ld(ld(A,c_0),c_0) = A.  [back_rewrite(1354),rewrite([26439(1),26439(3)])].
22.48/22.78	27072 mult(A,ld(B,c_0)) = rd(A,B).  [back_rewrite(1362),rewrite([26439(1)])].
22.48/22.78	27138 ld(c_0,A) = A.  [back_rewrite(18894),rewrite([26439(1),26578(4),27072(4),26971(2),26439(3),27008(4),26439(1)]),flip(a)].
22.48/22.78	27236 mult(A,c_0) = A.  [back_rewrite(26413),rewrite([26439(1),26971(2),9(3),26439(2),27138(4)])].
22.48/22.78	27237 $F # answer(goals).  [resolve(27236,a,26961,a)].
22.48/22.78	
22.48/22.78	% SZS output end Refutation
22.48/22.78	============================== end of proof ==========================
22.48/22.78	
22.48/22.78	============================== STATISTICS ============================
22.48/22.78	
22.48/22.78	Given=831. Generated=876764. Kept=27230. proofs=1.
22.48/22.78	Usable=689. Sos=9012. Demods=8480. Limbo=813, Disabled=16721. Hints=0.
22.48/22.78	Megabytes=30.12.
22.48/22.78	User_CPU=21.21, System_CPU=0.55, Wall_clock=22.
22.48/22.78	
22.48/22.78	============================== end of statistics =====================
22.48/22.78	
22.48/22.78	============================== end of search =========================
22.48/22.78	
22.48/22.78	THEOREM PROVED
22.48/22.78	% SZS status Theorem
22.48/22.78	
22.48/22.78	Exiting with 1 proof.
22.48/22.78	
22.48/22.78	Process 18727 exit (max_proofs) Tue Jul 13 14:40:01 2021
22.48/22.78	Prover9 interrupted
22.48/22.78	EOF