0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.03/0.24	% Computer   : n002.star.cs.uiowa.edu
0.03/0.24	% Model      : x86_64 x86_64
0.03/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.24	% Memory     : 32218.625MB
0.03/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.24	% CPULimit   : 300
0.03/0.24	% DateTime   : Sat Jul 14 04:18:40 CDT 2018
0.03/0.25	% CPUTime    : 
0.54/0.79	============================== Prover9 ===============================
0.54/0.79	Prover9 (32) version 2009-11A, November 2009.
0.54/0.79	Process 3542 was started by sandbox2 on n002.star.cs.uiowa.edu,
0.54/0.79	Sat Jul 14 04:18:40 2018
0.54/0.79	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3510_n002.star.cs.uiowa.edu".
0.54/0.79	============================== end of head ===========================
0.54/0.79	
0.54/0.79	============================== INPUT =================================
0.54/0.79	
0.54/0.79	% Reading from file /tmp/Prover9_3510_n002.star.cs.uiowa.edu
0.54/0.79	
0.54/0.79	set(prolog_style_variables).
0.54/0.79	set(auto2).
0.54/0.79	    % set(auto2) -> set(auto).
0.54/0.79	    % set(auto) -> set(auto_inference).
0.54/0.79	    % set(auto) -> set(auto_setup).
0.54/0.79	    % set(auto_setup) -> set(predicate_elim).
0.54/0.79	    % set(auto_setup) -> assign(eq_defs, unfold).
0.54/0.79	    % set(auto) -> set(auto_limits).
0.54/0.79	    % set(auto_limits) -> assign(max_weight, "100.000").
0.54/0.79	    % set(auto_limits) -> assign(sos_limit, 20000).
0.54/0.79	    % set(auto) -> set(auto_denials).
0.54/0.79	    % set(auto) -> set(auto_process).
0.54/0.79	    % set(auto2) -> assign(new_constants, 1).
0.54/0.79	    % set(auto2) -> assign(fold_denial_max, 3).
0.54/0.79	    % set(auto2) -> assign(max_weight, "200.000").
0.54/0.79	    % set(auto2) -> assign(max_hours, 1).
0.54/0.79	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.54/0.79	    % set(auto2) -> assign(max_seconds, 0).
0.54/0.79	    % set(auto2) -> assign(max_minutes, 5).
0.54/0.79	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.54/0.79	    % set(auto2) -> set(sort_initial_sos).
0.54/0.79	    % set(auto2) -> assign(sos_limit, -1).
0.54/0.79	    % set(auto2) -> assign(lrs_ticks, 3000).
0.54/0.79	    % set(auto2) -> assign(max_megs, 400).
0.54/0.79	    % set(auto2) -> assign(stats, some).
0.54/0.79	    % set(auto2) -> clear(echo_input).
0.54/0.79	    % set(auto2) -> set(quiet).
0.54/0.79	    % set(auto2) -> clear(print_initial_clauses).
0.54/0.79	    % set(auto2) -> clear(print_given).
0.54/0.79	assign(lrs_ticks,-1).
0.54/0.79	assign(sos_limit,10000).
0.54/0.79	assign(order,kbo).
0.54/0.79	set(lex_order_vars).
0.54/0.79	clear(print_given).
0.54/0.79	
0.54/0.79	% formulas(sos).  % not echoed (10 formulas)
0.54/0.79	
0.54/0.79	============================== end of input ==========================
0.54/0.79	
0.54/0.79	% From the command line: assign(max_seconds, 300).
0.54/0.79	
0.54/0.79	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.54/0.79	
0.54/0.79	% Formulas that are not ordinary clauses:
0.54/0.79	1 (all B all A B = difference(A,product(A,B))) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	2 (all D all C all B all A product(product(A,C),product(B,D)) = product(product(A,B),product(C,D))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	3 (all C all B all A product(product(A,B),product(C,A)) = bigC(A,B,C)) # label(sos08) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	4 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	5 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	6 (all B all A B = product(product(product(A,B),B),product(B,product(B,A)))) # label(sos07) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	7 (all B all A B = product(A,difference(A,B))) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	8 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	9 -(all X0 bigC(a,b,X0) = bigC(c,c,X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.54/0.79	
0.54/0.79	============================== end of process non-clausal formulas ===
0.54/0.79	
0.54/0.79	============================== PROCESS INITIAL CLAUSES ===============
0.54/0.79	
0.54/0.79	============================== PREDICATE ELIMINATION =================
0.54/0.79	
0.54/0.79	============================== end predicate elimination =============
0.54/0.79	
0.54/0.79	Auto_denials:
0.54/0.79	  % copying label goals to answer in negative clause
0.54/0.79	
0.54/0.79	Term ordering decisions:
0.54/0.79	Function symbol KB weights:  a=1. b=1. c=1. c1=1. product=1. difference=1. quotient=1. bigC=1.
0.54/0.79	
0.54/0.79	============================== end of process initial clauses ========
0.54/0.79	
0.54/0.79	============================== CLAUSES FOR SEARCH ====================
0.54/0.79	
0.54/0.79	============================== end of clauses for search =============
0.54/0.79	
0.54/0.79	============================== SEARCH ================================
0.54/0.79	
0.54/0.79	% Starting search at 0.01 seconds.
0.54/0.79	
0.54/0.79	============================== PROOF =================================
0.54/0.79	% SZS status Theorem
0.54/0.79	% SZS output start Refutation
0.54/0.79	
0.54/0.79	% Proof 1 at 0.32 (+ 0.01) seconds: goals.
0.54/0.79	% Length of proof is 115.
0.54/0.79	% Level of proof is 22.
0.54/0.79	% Maximum clause weight is 23.000.
0.54/0.79	% Given clauses 106.
0.54/0.79	
0.54/0.79	1 (all B all A B = difference(A,product(A,B))) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	2 (all D all C all B all A product(product(A,C),product(B,D)) = product(product(A,B),product(C,D))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	3 (all C all B all A product(product(A,B),product(C,A)) = bigC(A,B,C)) # label(sos08) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	4 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	5 (all A A = product(A,A)) # label(sos06) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	6 (all B all A B = product(product(product(A,B),B),product(B,product(B,A)))) # label(sos07) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	7 (all B all A B = product(A,difference(A,B))) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	8 (all B all A product(quotient(A,B),B) = A) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
0.54/0.79	9 -(all X0 bigC(a,b,X0) = bigC(c,c,X0)) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.54/0.79	10 product(A,A) = A # label(sos06) # label(axiom).  [clausify(5)].
0.54/0.79	11 difference(A,product(A,B)) = B # label(sos01) # label(axiom).  [clausify(1)].
0.54/0.79	12 quotient(product(A,B),B) = A # label(sos03) # label(axiom).  [clausify(4)].
0.54/0.79	13 product(A,difference(A,B)) = B # label(sos02) # label(axiom).  [clausify(7)].
0.54/0.79	14 product(quotient(A,B),B) = A # label(sos04) # label(axiom).  [clausify(8)].
0.54/0.79	15 product(product(a,c),product(c,b)) = product(a,b) # label(sos09) # label(axiom).  [assumption].
0.54/0.79	16 bigC(A,B,C) = product(product(A,B),product(C,A)) # label(sos08) # label(axiom).  [clausify(3)].
0.54/0.79	17 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom).  [clausify(6)].
0.54/0.79	18 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom).  [clausify(2)].
0.54/0.79	19 bigC(c,c,c1) != bigC(a,b,c1) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(9)].
0.54/0.79	20 product(product(a,b),product(c1,a)) != product(c,product(c1,c)) # answer(goals).  [copy(19),rewrite([16(4),10(3),16(9)]),flip(a)].
0.54/0.79	23 quotient(A,difference(B,A)) = B.  [para(13(a,1),12(a,1,1))].
0.54/0.79	24 difference(quotient(A,B),A) = B.  [para(14(a,1),11(a,1,2))].
0.54/0.79	25 difference(product(a,c),product(a,b)) = product(c,b).  [para(15(a,1),11(a,1,2))].
0.54/0.79	26 quotient(product(a,b),product(c,b)) = product(a,c).  [para(15(a,1),12(a,1,1))].
0.54/0.79	27 difference(product(product(A,B),B),B) = product(B,product(B,A)).  [para(17(a,1),11(a,1,2))].
0.54/0.79	28 quotient(A,product(A,product(A,B))) = product(product(B,A),A).  [para(17(a,1),12(a,1,1))].
0.54/0.79	34 product(product(product(product(c,b),product(a,c)),product(a,c)),product(product(a,c),product(a,b))) = product(a,c).  [para(15(a,1),17(a,1,2,2))].
0.54/0.79	37 product(product(A,B),product(A,C)) = product(A,product(B,C)).  [para(10(a,1),18(a,1,1)),flip(a)].
0.54/0.79	38 product(product(A,B),product(C,B)) = product(product(A,C),B).  [para(10(a,1),18(a,1,2)),flip(a)].
0.54/0.79	39 difference(product(A,B),product(product(A,C),product(B,D))) = product(C,D).  [para(18(a,1),11(a,1,2))].
0.54/0.79	40 quotient(product(product(A,B),product(C,D)),product(B,D)) = product(A,C).  [para(18(a,1),12(a,1,1))].
0.54/0.79	41 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)).  [para(13(a,1),18(a,1,1)),flip(a)].
0.54/0.79	44 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B).  [para(14(a,1),18(a,1,2)),flip(a)].
0.54/0.79	46 product(product(A,product(a,c)),product(B,product(c,b))) = product(product(A,B),product(a,b)).  [para(15(a,1),18(a,1,2)),flip(a)].
0.54/0.79	57 product(product(product(product(c,b),product(a,c)),a),product(a,b)) = product(a,c).  [back_rewrite(34),rewrite([37(18),46(17)])].
0.54/0.79	67 product(product(difference(A,B),A),A) = quotient(A,product(A,B)).  [para(13(a,1),28(a,1,2,2)),flip(a)].
0.54/0.79	74 product(product(A,B),A) = product(A,product(B,A)).  [para(10(a,1),37(a,1,2))].
0.54/0.79	79 product(A,product(B,difference(A,C))) = product(product(A,B),C).  [para(13(a,1),37(a,1,2)),flip(a)].
0.54/0.79	86 product(product(product(A,B),C),product(product(A,D),E)) = product(product(A,product(B,D)),product(C,E)).  [para(37(a,1),18(a,1,1)),flip(a)].
0.54/0.79	97 quotient(product(A,product(B,A)),A) = product(A,B).  [para(74(a,1),12(a,1,1))].
0.54/0.79	118 quotient(product(A,B),A) = product(A,quotient(B,A)).  [para(14(a,1),97(a,1,1,2))].
0.54/0.79	124 product(A,quotient(difference(A,B),A)) = quotient(B,A).  [para(13(a,1),118(a,1,1)),flip(a)].
0.54/0.79	126 product(product(a,c),quotient(product(c,b),product(a,c))) = quotient(product(a,b),product(a,c)).  [para(15(a,1),118(a,1,1)),flip(a)].
0.54/0.79	129 difference(product(A,quotient(B,A)),product(A,B)) = A.  [para(118(a,1),24(a,1,1))].
0.54/0.79	133 quotient(difference(A,B),A) = difference(A,quotient(B,A)).  [para(124(a,1),11(a,1,2)),flip(a)].
0.54/0.79	152 product(difference(A,quotient(B,A)),A) = difference(A,B).  [para(133(a,1),14(a,1,1))].
0.54/0.79	153 difference(difference(A,quotient(B,A)),difference(A,B)) = A.  [para(133(a,1),24(a,1,1))].
0.54/0.79	159 difference(A,product(B,A)) = product(difference(A,B),A).  [para(12(a,1),152(a,1,1,2)),flip(a)].
0.54/0.79	164 product(difference(product(c,b),product(a,c)),product(c,b)) = difference(product(c,b),product(a,b)).  [para(26(a,1),152(a,1,1,2))].
0.54/0.79	165 difference(product(difference(A,B),A),A) = product(A,quotient(B,A)).  [para(152(a,1),27(a,1,1,1)),rewrite([13(6)])].
0.54/0.79	172 product(difference(A,quotient(B,A)),quotient(B,A)) = product(difference(A,B),difference(A,quotient(B,A))).  [para(152(a,1),74(a,1,1)),rewrite([13(9)]),flip(a)].
0.54/0.79	183 quotient(product(A,B),product(difference(B,A),B)) = B.  [para(159(a,1),23(a,1,2))].
0.54/0.79	184 difference(product(a,c),product(a,product(b,c))) = product(product(c,b),product(a,c)).  [para(25(a,1),159(a,2,1)),rewrite([37(10)])].
0.54/0.79	185 product(difference(product(A,B),product(A,C)),product(A,B)) = difference(product(A,B),product(A,product(C,B))).  [para(37(a,1),159(a,1,2)),flip(a)].
0.54/0.79	195 product(product(A,quotient(B,C)),C) = product(product(A,C),B).  [para(14(a,1),38(a,1,2)),flip(a)].
0.54/0.79	235 difference(product(difference(A,B),A),product(B,A)) = B.  [para(183(a,1),152(a,1,1,2)),rewrite([165(3),41(5),14(2),10(1)]),flip(a)].
0.54/0.79	240 product(product(difference(A,B),A),B) = product(B,A).  [para(235(a,1),13(a,1,2))].
0.54/0.79	242 difference(difference(A,B),B) = quotient(B,A).  [para(14(a,1),235(a,1,2)),rewrite([152(3)])].
0.54/0.79	244 product(difference(A,B),A) = product(B,quotient(A,B)).  [para(235(a,1),23(a,1,2)),rewrite([118(2)]),flip(a)].
0.54/0.79	251 difference(product(difference(A,B),A),product(product(B,difference(A,B)),A)) = product(B,product(difference(A,B),A)).  [para(235(a,1),159(a,2,1)),rewrite([38(6)])].
0.54/0.79	261 quotient(product(a,b),product(a,c)) = difference(product(c,b),product(a,b)).  [back_rewrite(164),rewrite([244(11),126(11)])].
0.54/0.79	268 product(product(a,c),quotient(product(c,b),product(a,c))) = difference(product(c,b),product(a,b)).  [back_rewrite(126),rewrite([261(18)])].
0.54/0.79	270 product(difference(A,B),quotient(B,A)) = B.  [para(242(a,1),13(a,1,2))].
0.54/0.79	272 quotient(product(A,B),product(A,quotient(B,A))) = B.  [para(129(a,1),242(a,1,1)),rewrite([11(2)]),flip(a)].
0.54/0.79	278 difference(product(A,B),product(C,product(B,D))) = product(difference(A,C),D).  [para(13(a,1),39(a,1,2,1))].
0.54/0.79	287 product(A,product(B,quotient(A,B))) = product(B,A).  [para(11(a,1),270(a,1,1)),rewrite([118(2)])].
0.54/0.79	306 product(product(A,quotient(B,A)),B) = product(B,quotient(B,A)).  [para(24(a,1),240(a,1,1,1))].
0.54/0.79	316 product(difference(A,B),difference(A,quotient(B,A))) = product(quotient(B,A),difference(A,B)).  [para(153(a,1),240(a,1,1,1)),rewrite([13(3)]),flip(a)].
0.54/0.79	322 product(product(A,difference(B,A)),B) = product(A,quotient(B,product(B,A))).  [para(235(a,1),240(a,1,1,1)),rewrite([37(5),67(3),38(7)]),flip(a)].
0.54/0.79	328 product(difference(A,quotient(B,A)),quotient(B,A)) = product(quotient(B,A),difference(A,B)).  [back_rewrite(172),rewrite([316(8)])].
0.54/0.79	331 difference(product(difference(A,B),A),product(B,quotient(A,product(A,B)))) = product(B,product(difference(A,B),A)).  [back_rewrite(251),rewrite([322(5)])].
0.54/0.79	333 difference(difference(A,B),product(B,quotient(A,B))) = A.  [para(244(a,1),11(a,1,2))].
0.54/0.79	334 difference(A,product(difference(B,A),B)) = quotient(B,A).  [para(244(a,2),11(a,1,2))].
0.54/0.79	335 quotient(product(A,quotient(B,A)),B) = difference(B,A).  [para(244(a,1),12(a,1,1))].
0.54/0.79	350 difference(product(A,quotient(A,B)),A) = product(A,B).  [para(244(a,1),27(a,1,1,1)),rewrite([306(3),13(5)])].
0.54/0.79	353 product(A,product(difference(B,A),B)) = difference(product(B,A),A).  [para(244(a,2),27(a,2,2)),rewrite([14(2)]),flip(a)].
0.54/0.79	355 quotient(A,product(A,B)) = product(A,quotient(A,B)).  [para(244(a,1),28(a,2,1)),rewrite([13(2),306(5)])].
0.54/0.79	365 quotient(product(difference(A,B),A),B) = product(B,quotient(quotient(A,B),B)).  [para(244(a,2),118(a,1,1))].
0.54/0.79	385 product(quotient(A,B),quotient(B,A)) = difference(product(B,A),A).  [back_rewrite(331),rewrite([355(4),278(6),242(2),353(6)])].
0.54/0.79	406 quotient(product(product(c,a),b),product(product(c,b),product(a,c))) = product(a,b).  [para(26(a,1),272(a,1,2,2)),rewrite([38(7)])].
0.54/0.79	416 quotient(product(product(A,B),C),product(B,D)) = product(A,quotient(C,D)).  [para(14(a,1),40(a,1,1,2))].
0.54/0.79	430 difference(product(A,B),B) = product(difference(A,B),B).  [para(23(a,1),287(a,1,2,2)),rewrite([353(3)])].
0.54/0.79	434 product(A,product(B,product(C,quotient(A,C)))) = product(product(A,B),product(C,A)).  [para(287(a,1),37(a,1,2)),flip(a)].
0.54/0.79	449 product(quotient(A,B),quotient(B,A)) = product(difference(B,A),A).  [back_rewrite(385),rewrite([430(5)])].
0.54/0.79	458 product(difference(difference(A,B),A),A) = product(A,quotient(B,A)).  [back_rewrite(165),rewrite([430(3)])].
0.54/0.79	489 quotient(difference(A,B),product(B,quotient(A,B))) = difference(product(B,quotient(A,B)),B).  [para(333(a,1),334(a,1,2,1)),rewrite([13(4)]),flip(a)].
0.54/0.79	499 quotient(product(difference(A,B),A),B) = difference(B,difference(A,B)).  [para(23(a,1),335(a,1,1,2))].
0.54/0.79	513 product(A,quotient(quotient(B,A),A)) = difference(A,difference(B,A)).  [back_rewrite(365),rewrite([499(3)]),flip(a)].
0.54/0.79	540 product(A,product(B,quotient(A,C))) = product(product(C,B),A).  [para(270(a,1),41(a,1,2)),flip(a)].
0.54/0.79	565 difference(product(A,B),A) = product(A,difference(B,A)).  [para(23(a,1),350(a,1,1,2))].
0.54/0.79	574 quotient(difference(A,B),product(B,quotient(A,B))) = product(B,difference(quotient(A,B),B)).  [back_rewrite(489),rewrite([565(7)])].
0.54/0.79	606 product(difference(quotient(A,B),B),B) = difference(A,B).  [para(14(a,1),430(a,1,1)),flip(a)].
0.54/0.79	616 difference(difference(A,B),A) = difference(A,difference(B,A)).  [para(152(a,1),430(a,1,1)),rewrite([458(6),513(5)])].
0.54/0.79	710 quotient(difference(A,B),B) = difference(quotient(A,B),B).  [para(606(a,1),12(a,1,1))].
0.54/0.79	740 difference(product(A,difference(B,A)),product(A,B)) = product(difference(A,B),B).  [para(11(a,1),616(a,2,2)),rewrite([565(2),430(6)])].
0.54/0.79	771 product(product(A,quotient(B,C)),product(product(D,C),E)) = product(product(A,product(D,quotient(B,C))),product(B,E)).  [para(44(a,1),37(a,1,1)),rewrite([86(6)]),flip(a)].
0.54/0.79	911 quotient(A,product(B,quotient(A,B))) = product(quotient(A,B),difference(B,A)).  [para(333(a,1),710(a,1,1)),rewrite([574(7),740(9),328(7)])].
0.54/0.79	1555 product(product(A,product(B,quotient(C,D))),D) = product(product(A,D),product(product(B,D),C)).  [para(195(a,1),38(a,1,2)),flip(a)].
0.54/0.79	1565 product(product(A,quotient(B,C)),product(product(D,C),E)) = product(product(A,product(D,quotient(E,C))),B).  [para(195(a,1),44(a,1,2))].
0.54/0.79	1580 product(product(A,product(B,quotient(C,D))),product(C,E)) = product(product(A,product(B,quotient(E,D))),C).  [back_rewrite(771),rewrite([1565(5)]),flip(a)].
0.54/0.79	2165 product(difference(product(c,b),product(a,b)),quotient(product(a,c),product(a,b))) = product(product(c,a),b).  [para(25(a,1),449(a,2,1)),rewrite([261(7),38(22)])].
0.54/0.79	2627 product(product(product(c,b),product(a,c)),a) = quotient(product(a,c),product(a,b)).  [para(57(a,1),12(a,1,1)),flip(a)].
0.54/0.79	2809 product(difference(A,product(B,C)),A) = product(C,quotient(A,B)).  [para(540(a,1),11(a,1,2)),rewrite([159(3)])].
0.54/0.79	2822 product(A,quotient(product(B,quotient(A,C)),A)) = product(C,B).  [para(540(a,1),118(a,1,1)),rewrite([12(3)]),flip(a)].
0.54/0.79	2827 product(product(A,B),quotient(C,product(A,B))) = product(B,quotient(C,A)).  [para(540(a,1),183(a,1,1)),rewrite([244(8),2822(6),118(4)])].
0.54/0.79	2908 difference(product(A,B),product(A,product(C,B))) = product(C,product(A,quotient(B,A))).  [back_rewrite(185),rewrite([2809(5),118(2)]),flip(a)].
0.54/0.79	2964 difference(product(c,b),product(a,b)) = product(c,quotient(product(c,b),a)).  [back_rewrite(268),rewrite([2827(11)]),flip(a)].
0.54/0.79	3072 product(product(c,b),product(a,c)) = product(b,product(a,quotient(c,a))).  [back_rewrite(184),rewrite([2908(9)]),flip(a)].
0.54/0.79	3096 product(product(c,quotient(product(c,b),a)),quotient(product(a,c),product(a,b))) = product(product(c,a),b).  [back_rewrite(2165),rewrite([2964(7)])].
0.54/0.79	3160 quotient(product(a,c),product(a,b)) = product(product(b,a),product(a,c)).  [back_rewrite(2627),rewrite([3072(7),1555(9),10(6)]),flip(a)].
0.54/0.79	3166 quotient(product(product(c,a),b),product(b,product(a,quotient(c,a)))) = product(a,b).  [back_rewrite(406),rewrite([3072(12)])].
0.54/0.79	3175 product(product(c,a),b) = product(product(a,b),c).  [back_rewrite(3096),rewrite([3160(14),1565(15),118(7),434(9),3072(7),1580(11),540(7),10(3)]),flip(a)].
0.54/0.79	3182 product(c,quotient(c,a)) = product(a,b).  [back_rewrite(3166),rewrite([3175(5),416(13),911(8),79(9),306(7)])].
0.54/0.79	3223 product(product(a,b),product(A,a)) = product(c,product(A,c)).  [para(3182(a,1),44(a,1,1)),rewrite([74(10)])].
0.54/0.79	3224 $F # answer(goals).  [resolve(3223,a,20,a)].
0.54/0.79	
0.54/0.79	% SZS output end Refutation
0.54/0.79	============================== end of proof ==========================
0.54/0.79	
0.54/0.79	============================== STATISTICS ============================
0.54/0.79	
0.54/0.79	Given=106. Generated=9325. Kept=3213. proofs=1.
0.54/0.79	Usable=86. Sos=1911. Demods=1763. Limbo=18, Disabled=1207. Hints=0.
0.54/0.79	Megabytes=3.89.
0.54/0.79	User_CPU=0.32, System_CPU=0.01, Wall_clock=1.
0.54/0.79	
0.54/0.79	============================== end of statistics =====================
0.54/0.79	
0.54/0.79	============================== end of search =========================
0.54/0.79	
0.54/0.79	THEOREM PROVED
0.54/0.79	% SZS status Theorem
0.54/0.79	
0.54/0.79	Exiting with 1 proof.
0.54/0.79	
0.54/0.79	Process 3542 exit (max_proofs) Sat Jul 14 04:18:41 2018
0.54/0.79	Prover9 interrupted
0.54/0.79	EOF