0.08/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.35	% Computer   : n010.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 1200
0.13/0.35	% DateTime   : Tue Jul 13 14:58:51 EDT 2021
0.13/0.35	% CPUTime    : 
0.74/1.01	============================== Prover9 ===============================
0.74/1.01	Prover9 (32) version 2009-11A, November 2009.
0.74/1.01	Process 14780 was started by sandbox on n010.cluster.edu,
0.74/1.01	Tue Jul 13 14:58:52 2021
0.74/1.01	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_14626_n010.cluster.edu".
0.74/1.01	============================== end of head ===========================
0.74/1.01	
0.74/1.01	============================== INPUT =================================
0.74/1.01	
0.74/1.01	% Reading from file /tmp/Prover9_14626_n010.cluster.edu
0.74/1.01	
0.74/1.01	set(prolog_style_variables).
0.74/1.01	set(auto2).
0.74/1.01	    % set(auto2) -> set(auto).
0.74/1.01	    % set(auto) -> set(auto_inference).
0.74/1.01	    % set(auto) -> set(auto_setup).
0.74/1.01	    % set(auto_setup) -> set(predicate_elim).
0.74/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.74/1.01	    % set(auto) -> set(auto_limits).
0.74/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.74/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.74/1.01	    % set(auto) -> set(auto_denials).
0.74/1.01	    % set(auto) -> set(auto_process).
0.74/1.01	    % set(auto2) -> assign(new_constants, 1).
0.74/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.74/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.74/1.01	    % set(auto2) -> assign(max_hours, 1).
0.74/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.74/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.74/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.74/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.74/1.01	    % set(auto2) -> set(sort_initial_sos).
0.74/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.74/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.74/1.01	    % set(auto2) -> assign(max_megs, 400).
0.74/1.01	    % set(auto2) -> assign(stats, some).
0.74/1.01	    % set(auto2) -> clear(echo_input).
0.74/1.01	    % set(auto2) -> set(quiet).
0.74/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.74/1.01	    % set(auto2) -> clear(print_given).
0.74/1.01	assign(lrs_ticks,-1).
0.74/1.01	assign(sos_limit,10000).
0.74/1.01	assign(order,kbo).
0.74/1.01	set(lex_order_vars).
0.74/1.01	clear(print_given).
0.74/1.01	
0.74/1.01	% formulas(sos).  % not echoed (6 formulas)
0.74/1.01	
0.74/1.01	============================== end of input ==========================
0.74/1.01	
0.74/1.01	% From the command line: assign(max_seconds, 1200).
0.74/1.01	
0.74/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.74/1.01	
0.74/1.01	% Formulas that are not ordinary clauses:
0.74/1.01	1 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	2 (all X4 all X5 ((exists X6 (r(X4,X6) & l(X6,X5))) <-> d(X4,X5))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	3 (all X0 all X1 (l(X0,X1) <-> product(X1,X0) = X1 & product(X0,X1) = X0)) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	4 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	5 (all X2 all X3 (X3 = product(X2,X3) & X2 = product(X3,X2) <-> r(X2,X3))) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
0.74/1.01	6 -(all X7 all X8 (X8 = product(X8,product(X7,X8)) & X7 = product(X7,product(X8,X7)) <-> d(X7,X8))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.01	
0.74/1.01	============================== end of process non-clausal formulas ===
0.74/1.01	
0.74/1.01	============================== PROCESS INITIAL CLAUSES ===============
0.74/1.01	
0.74/1.01	============================== PREDICATE ELIMINATION =================
0.74/1.01	7 product(A,B) = B | -r(A,B) # label(sos04) # label(axiom).  [clausify(5)].
0.74/1.01	8 r(A,f1(A,B)) | -d(A,B) # label(sos05) # label(axiom).  [clausify(2)].
0.74/1.01	Derived: product(A,f1(A,B)) = f1(A,B) | -d(A,B).  [resolve(7,b,8,a)].
0.74/1.01	9 product(A,B) = B | -r(B,A) # label(sos04) # label(axiom).  [clausify(5)].
0.74/1.01	Derived: product(f1(A,B),A) = A | -d(A,B).  [resolve(9,b,8,a)].
0.74/1.01	10 -r(A,B) | -l(B,C) | d(A,C) # label(sos05) # label(axiom).  [clausify(2)].
0.74/1.01	Derived: -l(f1(A,B),C) | d(A,C) | -d(A,B).  [resolve(10,a,8,a)].
0.74/1.01	11 product(A,B) != B | product(B,A) != A | r(A,B) # label(sos04) # label(axiom).  [clausify(5)].
0.74/1.01	Derived: product(A,B) != B | product(B,A) != A | -l(B,C) | d(A,C).  [resolve(11,c,10,a)].
0.74/1.01	
0.74/1.01	============================== end predicate elimination =============
0.74/1.01	
0.74/1.01	Auto_denials:  (non-Horn, no changes).
0.74/1.01	
0.74/1.01	Term ordering decisions:
0.74/1.01	Function symbol KB weights:  c1=1. c2=1. product=1. f1=1.
0.74/1.01	
0.74/1.01	============================== end of process initial clauses ========
7.98/8.25	
7.98/8.25	============================== CLAUSES FOR SEARCH ====================
7.98/8.25	
7.98/8.25	============================== end of clauses for search =============
7.98/8.25	
7.98/8.25	============================== SEARCH ================================
7.98/8.25	
7.98/8.25	% Starting search at 0.01 seconds.
7.98/8.25	
7.98/8.25	Low Water (keep): wt=50.000, iters=3356
7.98/8.25	
7.98/8.25	Low Water (keep): wt=42.000, iters=3403
7.98/8.25	
7.98/8.25	Low Water (keep): wt=40.000, iters=3383
7.98/8.25	
7.98/8.25	Low Water (keep): wt=39.000, iters=3346
7.98/8.25	
7.98/8.25	Low Water (keep): wt=36.000, iters=3354
7.98/8.25	
7.98/8.25	Low Water (keep): wt=35.000, iters=3350
7.98/8.25	
7.98/8.25	Low Water (keep): wt=34.000, iters=3383
7.98/8.25	
7.98/8.25	Low Water (keep): wt=32.000, iters=3348
7.98/8.25	
7.98/8.25	Low Water (keep): wt=30.000, iters=3346
7.98/8.25	
7.98/8.25	Low Water (keep): wt=28.000, iters=3366
7.98/8.25	
7.98/8.25	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 39 (0.00 of 1.36 sec).
7.98/8.25	
7.98/8.25	Low Water (keep): wt=27.000, iters=3343
7.98/8.25	
7.98/8.25	Low Water (keep): wt=26.000, iters=3347
7.98/8.25	
7.98/8.25	Low Water (displace): id=2744, wt=72.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5687, wt=70.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5023, wt=69.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=4118, wt=66.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=2719, wt=65.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=2801, wt=64.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5657, wt=63.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5612, wt=62.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=4116, wt=60.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=2778, wt=59.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=3893, wt=58.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5660, wt=57.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=3868, wt=56.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5551, wt=55.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=3334, wt=54.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=5652, wt=53.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=4117, wt=52.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=11426, wt=24.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=11427, wt=22.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=11720, wt=20.000
7.98/8.25	
7.98/8.25	Low Water (displace): id=12425, wt=18.000
7.98/8.25	
7.98/8.25	Low Water (keep): wt=25.000, iters=3342
7.98/8.25	
7.98/8.25	Low Water (keep): wt=24.000, iters=3339
7.98/8.25	
7.98/8.25	Low Water (keep): wt=23.000, iters=3336
7.98/8.25	
7.98/8.25	Low Water (keep): wt=22.000, iters=3375
7.98/8.25	
7.98/8.25	============================== PROOF =================================
7.98/8.25	% SZS status Theorem
7.98/8.25	% SZS output start Refutation
7.98/8.25	
7.98/8.25	% Proof 1 at 7.13 (+ 0.12) seconds.
7.98/8.25	% Length of proof is 94.
7.98/8.25	% Level of proof is 17.
7.98/8.25	% Maximum clause weight is 28.000.
7.98/8.25	% Given clauses 2610.
7.98/8.25	
7.98/8.25	1 (all A product(A,A) = A) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
7.98/8.25	2 (all X4 all X5 ((exists X6 (r(X4,X6) & l(X6,X5))) <-> d(X4,X5))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
7.98/8.25	3 (all X0 all X1 (l(X0,X1) <-> product(X1,X0) = X1 & product(X0,X1) = X0)) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
7.98/8.25	4 (all C all B all A product(product(A,B),C) = product(A,product(B,C))) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
7.98/8.25	5 (all X2 all X3 (X3 = product(X2,X3) & X2 = product(X3,X2) <-> r(X2,X3))) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
7.98/8.25	6 -(all X7 all X8 (X8 = product(X8,product(X7,X8)) & X7 = product(X7,product(X8,X7)) <-> d(X7,X8))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
7.98/8.25	7 product(A,B) = B | -r(A,B) # label(sos04) # label(axiom).  [clausify(5)].
7.98/8.25	8 r(A,f1(A,B)) | -d(A,B) # label(sos05) # label(axiom).  [clausify(2)].
7.98/8.25	9 product(A,B) = B | -r(B,A) # label(sos04) # label(axiom).  [clausify(5)].
7.98/8.25	10 -r(A,B) | -l(B,C) | d(A,C) # label(sos05) # label(axiom).  [clausify(2)].
7.98/8.25	11 product(A,B) != B | product(B,A) != A | r(A,B) # label(sos04) # label(axiom).  [clausify(5)].
7.98/8.25	12 product(A,A) = A # label(sos02) # label(axiom).  [clausify(1)].
7.98/8.25	13 product(c2,product(c1,c2)) = c2 | d(c1,c2) # label(goals) # label(negated_conjecture).  [clausify(6)].
7.98/8.25	14 product(c1,product(c2,c1)) = c1 | d(c1,c2) # label(goals) # label(negated_conjecture).  [clausify(6)].
7.98/8.25	15 product(product(A,B),C) = product(A,product(B,C)) # label(sos01) # label(axiom).  [clausify(4)].
7.98/8.25	16 product(c2,product(c1,c2)) != c2 | product(c1,product(c2,c1)) != c1 | -d(c1,c2) # label(goals) # label(negated_conjecture).  [clausify(6)].
7.98/8.25	17 l(f1(A,B),B) | -d(A,B) # label(sos05) # label(axiom).  [clausify(2)].
7.98/8.25	18 -l(A,B) | product(B,A) = B # label(sos03) # label(axiom).  [clausify(3)].
7.98/8.25	19 -l(A,B) | product(A,B) = A # label(sos03) # label(axiom).  [clausify(3)].
7.98/8.25	20 l(A,B) | product(B,A) != B | product(A,B) != A # label(sos03) # label(axiom).  [clausify(3)].
7.98/8.25	21 product(A,f1(A,B)) = f1(A,B) | -d(A,B).  [resolve(7,b,8,a)].
7.98/8.25	22 product(f1(A,B),A) = A | -d(A,B).  [resolve(9,b,8,a)].
7.98/8.25	23 -l(f1(A,B),C) | d(A,C) | -d(A,B).  [resolve(10,a,8,a)].
7.98/8.25	24 product(A,B) != B | product(B,A) != A | -l(B,C) | d(A,C).  [resolve(11,c,10,a)].
7.98/8.25	25 l(A,A).  [factor(20,b,c),rewrite([12(2)]),xx(b)].
7.98/8.25	26 -l(A,B) | d(A,B).  [factor(24,a,b),rewrite([12(1)]),xx(a)].
7.98/8.25	27 product(A,product(B,product(A,B))) = product(A,B).  [para(15(a,1),12(a,1))].
7.98/8.25	28 product(A,product(A,B)) = product(A,B).  [para(12(a,1),15(a,1,1)),flip(a)].
7.98/8.25	29 l(f1(c1,c2),c2) | product(c1,product(c2,c1)) = c1.  [resolve(17,b,14,b)].
7.98/8.25	30 l(f1(c1,c2),c2) | product(c2,product(c1,c2)) = c2.  [resolve(17,b,13,b)].
7.98/8.25	31 l(A,product(B,C)) | product(B,product(C,A)) != product(B,C) | product(A,product(B,C)) != A.  [para(15(a,1),20(b,1))].
7.98/8.25	32 l(product(A,B),C) | product(C,product(A,B)) != C | product(A,product(B,C)) != product(A,B).  [para(15(a,1),20(c,1))].
7.98/8.25	34 product(c1,f1(c1,c2)) = f1(c1,c2) | product(c2,product(c1,c2)) = c2.  [resolve(21,b,13,b)].
7.98/8.25	35 product(f1(c1,c2),c1) = c1 | product(c1,product(c2,c1)) = c1.  [resolve(22,b,14,b)].
7.98/8.25	36 product(f1(c1,c2),c1) = c1 | product(c2,product(c1,c2)) = c2.  [resolve(22,b,13,b)].
7.98/8.25	37 product(A,B) != B | product(B,A) != A | d(A,B).  [resolve(25,a,24,c)].
7.98/8.25	40 product(A,product(B,product(A,product(B,C)))) = product(A,product(B,C)).  [para(27(a,1),15(a,1,1)),rewrite([15(2),15(5),15(4)]),flip(a)].
7.98/8.25	56 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),c2) = f1(c1,c2).  [resolve(29,a,19,a)].
7.98/8.25	57 product(c1,product(c2,c1)) = c1 | product(c2,f1(c1,c2)) = c2.  [resolve(29,a,18,a)].
7.98/8.25	60 product(c2,product(c1,c2)) = c2 | product(f1(c1,c2),c2) = f1(c1,c2).  [resolve(30,a,19,a)].
7.98/8.25	61 product(c2,product(c1,c2)) = c2 | product(c2,f1(c1,c2)) = c2.  [resolve(30,a,18,a)].
7.98/8.25	70 l(A,product(B,A)) | product(A,product(B,A)) != A.  [para(12(a,1),31(b,1,2)),xx(b)].
7.98/8.25	85 l(product(A,product(B,A)),product(B,A)).  [para(27(a,1),70(b,1,2)),rewrite([27(5),15(8),12(7)]),xx(b)].
7.98/8.25	86 d(product(A,product(B,A)),product(B,A)).  [resolve(85,a,26,a)].
7.98/8.25	90 l(product(A,B),B) | product(B,product(A,B)) != B.  [para(12(a,1),32(c,1,2)),xx(c)].
7.98/8.25	96 product(A,product(B,product(A,f1(product(A,product(B,A)),product(B,A))))) = f1(product(A,product(B,A)),product(B,A)).  [resolve(86,a,21,b),rewrite([15(7),15(6)])].
7.98/8.25	97 l(f1(product(A,product(B,A)),product(B,A)),product(B,A)).  [resolve(86,a,17,b)].
7.98/8.25	102 l(product(A,B),product(B,product(A,B))).  [para(27(a,1),90(b,1,2)),rewrite([27(3),15(8),12(7)]),xx(b)].
7.98/8.25	104 product(A,product(B,C)) != product(B,C) | product(B,product(C,A)) != A | d(A,product(C,product(B,C))).  [resolve(102,a,24,c),rewrite([15(6)])].
7.98/8.25	105 l(product(A,product(B,C)),product(C,product(A,product(B,C)))).  [para(15(a,1),102(a,1)),rewrite([15(4)])].
7.98/8.25	131 product(A,product(B,A)) != A | d(A,product(A,B)).  [resolve(37,a,28,a),rewrite([15(2)])].
7.98/8.25	141 d(product(A,B),product(A,product(B,A))).  [para(28(a,1),131(a,1,2)),rewrite([12(3),15(6)]),xx(a)].
7.98/8.25	151 product(f1(product(A,B),product(A,product(B,A))),product(A,B)) = product(A,B).  [resolve(141,a,22,b)].
7.98/8.25	153 l(f1(product(A,B),product(A,product(B,A))),product(A,product(B,A))).  [resolve(141,a,17,b)].
7.98/8.25	159 product(c1,f1(c1,c2)) = f1(c1,c2) | l(product(c1,c2),c2).  [resolve(34,b,90,b)].
7.98/8.25	191 product(A,product(B,f1(product(B,product(A,B)),product(A,B)))) = product(A,B).  [resolve(97,a,18,a),rewrite([15(6)])].
7.98/8.25	200 f1(product(A,product(B,A)),product(B,A)) = product(A,product(B,A)).  [back_rewrite(96),rewrite([191(6)]),flip(a)].
7.98/8.25	289 product(c2,product(c1,c2)) = c2 | product(f1(c1,c2),product(c1,A)) = product(c1,A).  [para(36(a,1),15(a,1,1)),flip(b)].
7.98/8.25	393 l(product(A,product(B,product(A,C))),product(B,product(A,C))).  [para(40(a,1),70(b,1,2)),rewrite([40(7),15(12),12(11)]),xx(b)].
7.98/8.25	486 product(c1,product(c2,c1)) = c1 | product(c2,product(f1(c1,c2),A)) = product(c2,A).  [para(57(b,1),15(a,1,1)),flip(b)].
7.98/8.25	539 product(c2,product(c1,c2)) = c2 | product(c2,product(f1(c1,c2),A)) = product(c2,A).  [para(61(b,1),15(a,1,1)),flip(b)].
7.98/8.25	540 product(c2,product(c1,c2)) = c2 | product(A,product(c2,f1(c1,c2))) = product(A,c2).  [para(61(b,1),15(a,2,2)),rewrite([15(13)])].
7.98/8.25	623 product(c1,f1(c1,c2)) = f1(c1,c2) | product(A,product(c1,c2)) != product(c1,c2) | product(c1,product(c2,A)) != A | d(A,c2).  [resolve(159,b,24,c),rewrite([15(21)])].
7.98/8.25	710 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),product(c2,A)) = product(f1(c1,c2),A).  [para(56(b,1),15(a,1,1)),flip(b)].
7.98/8.25	1082 product(f1(product(A,B),product(A,product(B,A))),product(A,product(B,A))) = f1(product(A,B),product(A,product(B,A))).  [resolve(153,a,19,a)].
7.98/8.25	1226 product(c2,product(c1,c2)) = c2 | f1(product(c2,product(f1(c1,c2),c2)),f1(c1,c2)) = product(c2,product(f1(c1,c2),c2)).  [para(60(b,1),200(a,1,2))].
7.98/8.25	2989 product(A,product(B,A)) != A | d(A,product(B,product(A,B))).  [resolve(104,a,28,a)].
7.98/8.25	3060 d(product(A,product(B,A)),product(B,product(A,B))).  [para(27(a,1),2989(a,1,2)),rewrite([15(4),12(3),15(10),15(9),27(10)]),xx(a)].
7.98/8.25	3924 product(f1(product(A,B),product(A,product(B,A))),product(A,product(B,C))) = product(A,product(B,C)).  [para(151(a,1),15(a,1,1)),rewrite([15(2),15(8)]),flip(a)].
7.98/8.25	4038 f1(product(A,B),product(A,product(B,A))) = product(A,product(B,A)).  [back_rewrite(1082),rewrite([3924(7)]),flip(a)].
7.98/8.25	4172 -l(product(A,product(B,A)),C) | d(product(A,B),C).  [para(4038(a,1),23(a,1)),unit_del(c,141)].
7.98/8.25	4233 -l(product(A,product(B,product(C,A))),D) | d(product(A,product(B,C)),D).  [para(15(a,1),4172(a,1,2))].
7.98/8.25	8039 d(product(A,product(B,C)),product(C,product(A,product(B,product(C,A))))).  [resolve(4233,a,105,a),rewrite([15(7),28(6)])].
7.98/8.25	11651 product(c1,product(c2,c1)) = c1 | l(product(c2,A),product(f1(c1,c2),product(c2,A))).  [para(486(b,1),393(a,1)),rewrite([28(11)])].
7.98/8.25	12274 product(c2,product(c1,c2)) = c2 | product(f1(c1,c2),product(c1,product(c2,f1(c1,c2)))) = product(c1,c2).  [para(540(b,1),289(b,2)),merge(b)].
7.98/8.25	18625 product(c1,f1(c1,c2)) = f1(c1,c2) | product(c1,product(c2,c1)) != c1 | d(c1,c2).  [resolve(623,b,28,a)].
7.98/8.25	19634 product(c1,product(c2,c1)) = c1 | product(f1(c1,c2),product(c2,c1)) = c1.  [para(35(a,1),710(b,2)),merge(b)].
7.98/8.25	20170 product(c1,product(c2,c1)) = c1 | l(product(c2,c1),c1).  [para(19634(b,1),11651(b,2)),merge(b)].
7.98/8.25	20181 product(c1,product(c2,c1)) = c1.  [resolve(20170,b,18,a),merge(b)].
7.98/8.25	20182 product(c1,f1(c1,c2)) = f1(c1,c2) | d(c1,c2).  [back_rewrite(18625),rewrite([20181(14)]),xx(b)].
7.98/8.25	20205 product(c2,product(c1,c2)) != c2 | -d(c1,c2).  [back_rewrite(16),rewrite([20181(12)]),xx(b)].
7.98/8.25	20214 product(c1,product(c2,product(c1,A))) = product(c1,A).  [para(20181(a,1),15(a,1,1)),rewrite([15(7)]),flip(a)].
7.98/8.25	20261 d(product(A,c1),product(c2,product(c1,A))).  [para(20181(a,1),8039(a,1,2)),rewrite([15(10),20214(11),15(9),27(8)])].
7.98/8.25	23534 product(c1,f1(c1,c2)) = f1(c1,c2).  [resolve(20182,b,21,b),merge(b)].
7.98/8.25	23916 d(product(f1(c1,c2),c1),product(c2,f1(c1,c2))).  [para(23534(a,1),20261(a,2,2))].
7.98/8.25	23920 product(c1,product(c2,f1(c1,c2))) = f1(c1,c2).  [para(23534(a,1),20214(a,1,2,2)),rewrite([23534(12)])].
7.98/8.25	23986 product(c2,product(c1,c2)) = c2 | f1(c1,c2) = product(c1,c2).  [back_rewrite(12274),rewrite([23920(17),12(14)])].
7.98/8.25	27544 product(c2,product(c1,c2)) = c2 | f1(product(c2,product(f1(c1,c2),c2)),f1(c1,c2)) = c2.  [para(539(b,1),1226(b,2)),rewrite([12(28)]),merge(b)].
7.98/8.25	27788 f1(c1,c2) = product(c1,c2) | d(c1,c2).  [para(23986(a,1),3060(a,2)),rewrite([20181(12)])].
7.98/8.25	27903 f1(c1,c2) = product(c1,c2) | product(c2,product(c1,c2)) != c2.  [resolve(27788,b,20205,b)].
7.98/8.25	30902 f1(c1,c2) = product(c1,c2).  [resolve(27903,b,23986,a),merge(b)].
7.98/8.25	30946 product(c2,product(c1,c2)) = c2.  [back_rewrite(27544),rewrite([30902(11),15(13),12(12),30902(15),200(16)]),merge(b)].
7.98/8.25	31010 d(c1,c2).  [back_rewrite(23916),rewrite([30902(3),15(5),20181(5),30902(5),30946(6)])].
7.98/8.25	31058 $F.  [back_rewrite(20205),rewrite([30946(5)]),xx(a),unit_del(a,31010)].
7.98/8.25	
7.98/8.25	% SZS output end Refutation
7.98/8.25	============================== end of proof ==========================
7.98/8.25	
7.98/8.25	============================== STATISTICS ============================
7.98/8.25	
7.98/8.25	Given=2610. Generated=259724. Kept=31046. proofs=1.
7.98/8.25	Usable=733. Sos=3917. Demods=349. Limbo=112, Disabled=26302. Hints=0.
7.98/8.25	Megabytes=27.70.
7.98/8.25	User_CPU=7.13, System_CPU=0.12, Wall_clock=7.
7.98/8.25	
7.98/8.25	============================== end of statistics =====================
7.98/8.25	
7.98/8.25	============================== end of search =========================
7.98/8.25	
7.98/8.25	THEOREM PROVED
7.98/8.25	% SZS status Theorem
7.98/8.25	
7.98/8.25	Exiting with 1 proof.
7.98/8.25	
7.98/8.25	Process 14780 exit (max_proofs) Tue Jul 13 14:58:59 2021
7.98/8.25	Prover9 interrupted
7.98/8.25	EOF