0.11/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer : n011.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 960
0.12/0.33	% WCLimit  : 120
0.12/0.33	% DateTime : Tue Aug  9 06:14:06 EDT 2022
0.12/0.33	% CPUTime  : 
0.75/1.02	============================== Prover9 ===============================
0.75/1.02	Prover9 (32) version 2009-11A, November 2009.
0.75/1.02	Process 17280 was started by sandbox2 on n011.cluster.edu,
0.75/1.02	Tue Aug  9 06:14:07 2022
0.75/1.02	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_17007_n011.cluster.edu".
0.75/1.02	============================== end of head ===========================
0.75/1.02	
0.75/1.02	============================== INPUT =================================
0.75/1.02	
0.75/1.02	% Reading from file /tmp/Prover9_17007_n011.cluster.edu
0.75/1.02	
0.75/1.02	set(prolog_style_variables).
0.75/1.02	set(auto2).
0.75/1.02	    % set(auto2) -> set(auto).
0.75/1.02	    % set(auto) -> set(auto_inference).
0.75/1.02	    % set(auto) -> set(auto_setup).
0.75/1.02	    % set(auto_setup) -> set(predicate_elim).
0.75/1.02	    % set(auto_setup) -> assign(eq_defs, unfold).
0.75/1.02	    % set(auto) -> set(auto_limits).
0.75/1.02	    % set(auto_limits) -> assign(max_weight, "100.000").
0.75/1.02	    % set(auto_limits) -> assign(sos_limit, 20000).
0.75/1.02	    % set(auto) -> set(auto_denials).
0.75/1.02	    % set(auto) -> set(auto_process).
0.75/1.02	    % set(auto2) -> assign(new_constants, 1).
0.75/1.02	    % set(auto2) -> assign(fold_denial_max, 3).
0.75/1.02	    % set(auto2) -> assign(max_weight, "200.000").
0.75/1.02	    % set(auto2) -> assign(max_hours, 1).
0.75/1.02	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.75/1.02	    % set(auto2) -> assign(max_seconds, 0).
0.75/1.02	    % set(auto2) -> assign(max_minutes, 5).
0.75/1.02	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.75/1.02	    % set(auto2) -> set(sort_initial_sos).
0.75/1.02	    % set(auto2) -> assign(sos_limit, -1).
0.75/1.02	    % set(auto2) -> assign(lrs_ticks, 3000).
0.75/1.02	    % set(auto2) -> assign(max_megs, 400).
0.75/1.02	    % set(auto2) -> assign(stats, some).
0.75/1.02	    % set(auto2) -> clear(echo_input).
0.75/1.02	    % set(auto2) -> set(quiet).
0.75/1.02	    % set(auto2) -> clear(print_initial_clauses).
0.75/1.02	    % set(auto2) -> clear(print_given).
0.75/1.02	assign(lrs_ticks,-1).
0.75/1.02	assign(sos_limit,10000).
0.75/1.02	assign(order,kbo).
0.75/1.02	set(lex_order_vars).
0.75/1.02	clear(print_given).
0.75/1.02	
0.75/1.02	% formulas(sos).  % not echoed (16 formulas)
0.75/1.02	
0.75/1.02	============================== end of input ==========================
0.75/1.02	
0.75/1.02	% From the command line: assign(max_seconds, 960).
0.75/1.02	
0.75/1.02	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.75/1.02	
0.75/1.02	% Formulas that are not ordinary clauses:
0.75/1.02	1 (all B all A A = product(quotient(A,B),B)) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	2 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	4 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	5 (all X3 all X4 all X5 (product(product(X3,X4),product(X4,X5)) = product(X3,X5) <-> m(X3,X4,X5))) # label(sos09) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	6 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	7 (all X0 all X1 all X2 (product(X1,X2) = product(X0,X1) <-> d(X0,X1,X2))) # label(sos08) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	8 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	9 (all B all A B = product(A,difference(A,B))) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
0.75/1.02	
0.75/1.02	============================== end of process non-clausal formulas ===
0.75/1.02	
0.75/1.02	============================== PROCESS INITIAL CLAUSES ===============
0.75/1.02	
0.75/1.02	============================== PREDICATE ELIMINATION =================
0.75/1.02	10 product(A,B) = product(C,A) | -d(C,A,B) # label(sos08) # label(axiom).  [clausify(7)].
0.75/1.02	11 d(b,bigA,c) # label(sos10) # label(axiom).  [assumption].
0.75/1.02	12 d(a1,b1,c) # label(sos15) # label(axiom).  [assumption].
0.75/1.02	13 d(bigB,a,c) # label(sos11) # label(axiom).  [assumption].
0.75/1.02	14 d(b,a,bigC) # label(sos12) # label(axiom).  [assumption].
0.75/1.02	15 d(a,b1,c1) # label(sos13) # label(axiom).  [assumption].
0.75/1.02	16 d(a1,b,c1) # label(sos14) # label(axiom).  [assumption].
0.75/1.02	17 product(A,B) != product(C,A) | d(C,A,B) # label(sos08) # label(axiom).  [clausify(7)].
0.75/1.02	Derived: product(bigA,c) = product(b,bigA).  [resolve(10,b,11,a)].
5.94/6.29	Derived: product(b1,c) = product(a1,b1).  [resolve(10,b,12,a)].
5.94/6.29	Derived: product(a,c) = product(bigB,a).  [resolve(10,b,13,a)].
5.94/6.29	Derived: product(a,bigC) = product(b,a).  [resolve(10,b,14,a)].
5.94/6.29	Derived: product(b1,c1) = product(a,b1).  [resolve(10,b,15,a)].
5.94/6.29	Derived: product(b,c1) = product(a1,b).  [resolve(10,b,16,a)].
5.94/6.29	
5.94/6.29	============================== end predicate elimination =============
5.94/6.29	
5.94/6.29	Auto_denials:
5.94/6.29	  % copying label goals to answer in negative clause
5.94/6.29	
5.94/6.29	Term ordering decisions:
5.94/6.29	Function symbol KB weights:  a=1. b=1. b1=1. c=1. a1=1. bigA=1. c1=1. bigB=1. bigC=1. product=1. difference=1. quotient=1.
5.94/6.29	
5.94/6.29	============================== end of process initial clauses ========
5.94/6.29	
5.94/6.29	============================== CLAUSES FOR SEARCH ====================
5.94/6.29	
5.94/6.29	============================== end of clauses for search =============
5.94/6.29	
5.94/6.29	============================== SEARCH ================================
5.94/6.29	
5.94/6.29	% Starting search at 0.01 seconds.
5.94/6.29	
5.94/6.29	Low Water (keep): wt=55.000, iters=3371
5.94/6.29	
5.94/6.29	Low Water (keep): wt=51.000, iters=3396
5.94/6.29	
5.94/6.29	Low Water (keep): wt=47.000, iters=3390
5.94/6.29	
5.94/6.29	Low Water (keep): wt=43.000, iters=3338
5.94/6.29	
5.94/6.29	Low Water (keep): wt=41.000, iters=3346
5.94/6.29	
5.94/6.29	Low Water (keep): wt=39.000, iters=3394
5.94/6.29	
5.94/6.29	Low Water (keep): wt=37.000, iters=3336
5.94/6.29	
5.94/6.29	Low Water (keep): wt=35.000, iters=3356
5.94/6.29	
5.94/6.29	Low Water (keep): wt=33.000, iters=3355
5.94/6.29	
5.94/6.29	Low Water (keep): wt=31.000, iters=3345
5.94/6.29	
5.94/6.29	Low Water (keep): wt=29.000, iters=3356
5.94/6.29	
5.94/6.29	Low Water (keep): wt=27.000, iters=3349
5.94/6.29	
5.94/6.29	Low Water (keep): wt=25.000, iters=3400
5.94/6.29	
5.94/6.29	Low Water (keep): wt=23.000, iters=3342
5.94/6.29	
5.94/6.29	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 135 (0.00 of 1.59 sec).
5.94/6.29	
5.94/6.29	Low Water (keep): wt=21.000, iters=3373
5.94/6.29	
5.94/6.29	Low Water (displace): id=3023, wt=67.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=3467, wt=65.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=2892, wt=63.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=3182, wt=61.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=15402, wt=17.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=15404, wt=15.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=15721, wt=13.000
5.94/6.29	
5.94/6.29	Low Water (displace): id=16869, wt=11.000
5.94/6.29	
5.94/6.29	Low Water (keep): wt=19.000, iters=3344
5.94/6.29	
5.94/6.29	Low Water (keep): wt=17.000, iters=3333
5.94/6.29	
5.94/6.29	Low Water (keep): wt=15.000, iters=4861
5.94/6.29	
5.94/6.29	============================== PROOF =================================
5.94/6.29	% SZS status Theorem
5.94/6.29	% SZS output start Refutation
5.94/6.29	
5.94/6.29	% Proof 1 at 5.15 (+ 0.13) seconds: goals.
5.94/6.29	% Length of proof is 132.
5.94/6.29	% Level of proof is 27.
5.94/6.29	% Maximum clause weight is 17.000.
5.94/6.29	% Given clauses 1418.
5.94/6.29	
5.94/6.29	1 (all B all A A = product(quotient(A,B),B)) # label(sos04) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	2 (all B all A product(product(product(A,B),B),product(B,product(B,A))) = B) # label(sos07) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	3 (all B all A quotient(product(A,B),B) = A) # label(sos03) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	4 (all D all C all B all A product(product(A,B),product(C,D)) = product(product(A,C),product(B,D))) # label(sos05) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	5 (all X3 all X4 all X5 (product(product(X3,X4),product(X4,X5)) = product(X3,X5) <-> m(X3,X4,X5))) # label(sos09) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	6 (all B all A difference(A,product(A,B)) = B) # label(sos01) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	7 (all X0 all X1 all X2 (product(X1,X2) = product(X0,X1) <-> d(X0,X1,X2))) # label(sos08) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	8 (all A product(A,A) = A) # label(sos06) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	9 (all B all A B = product(A,difference(A,B))) # label(sos02) # label(axiom) # label(non_clause).  [assumption].
5.94/6.29	10 product(A,B) = product(C,A) | -d(C,A,B) # label(sos08) # label(axiom).  [clausify(7)].
5.94/6.29	11 d(b,bigA,c) # label(sos10) # label(axiom).  [assumption].
5.94/6.29	12 d(a1,b1,c) # label(sos15) # label(axiom).  [assumption].
5.94/6.29	14 d(b,a,bigC) # label(sos12) # label(axiom).  [assumption].
5.94/6.29	15 d(a,b1,c1) # label(sos13) # label(axiom).  [assumption].
5.94/6.29	16 d(a1,b,c1) # label(sos14) # label(axiom).  [assumption].
5.94/6.29	18 product(A,A) = A # label(sos06) # label(axiom).  [clausify(8)].
5.94/6.29	19 product(quotient(A,B),B) = A # label(sos04) # label(axiom).  [clausify(1)].
5.94/6.29	20 quotient(product(A,B),B) = A # label(sos03) # label(axiom).  [clausify(3)].
5.94/6.29	21 difference(A,product(A,B)) = B # label(sos01) # label(axiom).  [clausify(6)].
5.94/6.29	22 product(A,difference(A,B)) = B # label(sos02) # label(axiom).  [clausify(9)].
5.94/6.29	23 product(product(product(A,B),B),product(B,product(B,A))) = B # label(sos07) # label(axiom).  [clausify(2)].
5.94/6.29	24 product(product(A,B),product(C,D)) = product(product(A,C),product(B,D)) # label(sos05) # label(axiom).  [clausify(4)].
5.94/6.29	25 -m(bigA,b1,bigC) # label(goals) # label(negated_conjecture) # answer(goals).  [assumption].
5.94/6.29	26 product(product(A,B),product(B,C)) != product(A,C) | m(A,B,C) # label(sos09) # label(axiom).  [clausify(5)].
5.94/6.29	28 product(bigA,c) = product(b,bigA).  [resolve(10,b,11,a)].
5.94/6.29	29 product(b1,c) = product(a1,b1).  [resolve(10,b,12,a)].
5.94/6.29	30 product(a1,b1) = product(b1,c).  [copy(29),flip(a)].
5.94/6.29	33 product(a,bigC) = product(b,a).  [resolve(10,b,14,a)].
5.94/6.29	34 product(b,a) = product(a,bigC).  [copy(33),flip(a)].
5.94/6.29	35 product(b1,c1) = product(a,b1).  [resolve(10,b,15,a)].
5.94/6.29	36 product(b,c1) = product(a1,b).  [resolve(10,b,16,a)].
5.94/6.29	37 product(a1,b) = product(b,c1).  [copy(36),flip(a)].
5.94/6.29	38 quotient(A,A) = A.  [para(18(a,1),20(a,1,1))].
5.94/6.29	39 difference(A,A) = A.  [para(18(a,1),21(a,1,2))].
5.94/6.29	40 difference(quotient(A,B),A) = B.  [para(19(a,1),21(a,1,2))].
5.94/6.29	42 product(product(A,B),product(B,product(B,quotient(A,B)))) = B.  [para(19(a,1),23(a,1,1,1))].
5.94/6.29	45 difference(product(product(A,B),B),B) = product(B,product(B,A)).  [para(23(a,1),21(a,1,2))].
5.94/6.29	50 product(product(A,B),product(A,C)) = product(A,product(B,C)).  [para(18(a,1),24(a,1,1)),flip(a)].
5.94/6.29	51 product(product(A,B),product(C,B)) = product(product(A,C),B).  [para(18(a,1),24(a,1,2)),flip(a)].
5.94/6.29	52 product(product(quotient(A,B),C),product(B,D)) = product(A,product(C,D)).  [para(19(a,1),24(a,1,1)),flip(a)].
5.94/6.29	53 product(product(A,quotient(B,C)),product(D,C)) = product(product(A,D),B).  [para(19(a,1),24(a,1,2)),flip(a)].
5.94/6.29	56 product(product(A,B),product(difference(A,C),D)) = product(C,product(B,D)).  [para(22(a,1),24(a,1,1)),flip(a)].
5.94/6.29	57 product(product(A,B),product(C,difference(B,D))) = product(product(A,C),D).  [para(22(a,1),24(a,1,2)),flip(a)].
5.94/6.29	89 product(product(A,bigA),product(B,c)) = product(product(A,B),product(b,bigA)).  [para(28(a,1),24(a,1,2)),flip(a)].
5.94/6.29	93 quotient(product(b1,c),b1) = a1.  [para(30(a,1),20(a,1,1))].
5.94/6.29	111 quotient(product(a,bigC),a) = b.  [para(34(a,1),20(a,1,1))].
5.94/6.29	123 product(product(product(c1,b1),b1),product(b1,product(a,b1))) = b1.  [para(35(a,1),23(a,1,2,2))].
5.94/6.29	129 quotient(product(b,c1),b) = a1.  [para(37(a,1),20(a,1,1))].
5.94/6.29	139 product(A,product(A,quotient(B,A))) = difference(product(B,A),A).  [para(42(a,1),21(a,1,2)),flip(a)].
5.94/6.29	176 product(product(A,B),A) = product(A,product(B,A)).  [para(18(a,1),50(a,1,2))].
5.94/6.29	183 product(A,product(B,difference(A,C))) = product(product(A,B),C).  [para(22(a,1),50(a,1,2)),flip(a)].
5.94/6.29	224 quotient(product(A,product(B,A)),A) = product(A,B).  [para(176(a,1),20(a,1,1))].
5.94/6.29	279 product(product(A,B),difference(A,C)) = product(C,product(B,difference(A,C))).  [para(22(a,1),51(a,1,1)),flip(a)].
5.94/6.29	311 product(product(A,B),product(B,product(C,B))) = product(product(A,product(B,C)),B).  [para(176(a,1),51(a,1,2))].
5.94/6.29	321 product(product(product(c1,b1),product(b1,a)),b1) = b1.  [back_rewrite(123),rewrite([311(11)])].
5.94/6.29	340 quotient(product(A,product(B,C)),product(D,C)) = product(quotient(A,D),B).  [para(52(a,1),20(a,1,1))].
5.94/6.29	342 product(A,product(difference(quotient(A,B),C),D)) = product(C,product(B,D)).  [para(22(a,1),52(a,1,1)),flip(a)].
5.94/6.29	456 quotient(product(A,B),A) = product(A,quotient(B,A)).  [para(19(a,1),224(a,1,1,2))].
5.94/6.29	469 product(b,quotient(c1,b)) = a1.  [back_rewrite(129),rewrite([456(5)])].
5.94/6.29	470 product(a,quotient(bigC,a)) = b.  [back_rewrite(111),rewrite([456(5)])].
5.94/6.29	472 product(b1,quotient(c,b1)) = a1.  [back_rewrite(93),rewrite([456(5)])].
5.94/6.29	476 product(product(b,A),c1) = product(a1,product(A,b)).  [para(469(a,1),53(a,1,1)),flip(a)].
5.94/6.29	515 quotient(bigC,a) = difference(a,b).  [para(470(a,1),21(a,1,2)),flip(a)].
5.94/6.29	523 quotient(c,b1) = difference(b1,a1).  [para(472(a,1),21(a,1,2)),flip(a)].
5.94/6.29	525 product(product(b1,A),c) = product(a1,product(A,b1)).  [para(472(a,1),53(a,1,1)),flip(a)].
5.94/6.29	571 product(difference(b1,a1),b1) = c.  [para(523(a,1),19(a,1,1))].
5.94/6.29	1086 product(product(c1,b1),product(b1,a)) = b1.  [para(321(a,1),20(a,1,1)),rewrite([38(3)]),flip(a)].
5.94/6.29	1761 product(A,quotient(difference(A,B),A)) = quotient(B,A).  [para(22(a,1),456(a,1,1)),flip(a)].
5.94/6.29	1764 product(bigA,quotient(c,bigA)) = b.  [para(28(a,1),456(a,1,1)),rewrite([20(5)]),flip(a)].
5.94/6.29	1768 product(b1,quotient(c1,b1)) = a.  [para(35(a,1),456(a,1,1)),rewrite([20(5)]),flip(a)].
5.94/6.29	1770 difference(product(A,quotient(B,A)),product(A,B)) = A.  [para(456(a,1),40(a,1,1))].
5.94/6.29	1858 product(product(bigA,A),c) = product(b,product(A,bigA)).  [para(1764(a,1),53(a,1,1)),flip(a)].
5.94/6.29	1862 quotient(c1,b1) = difference(b1,a).  [para(1768(a,1),21(a,1,2)),flip(a)].
5.94/6.29	1864 product(product(b1,A),c1) = product(a,product(A,b1)).  [para(1768(a,1),53(a,1,1)),flip(a)].
5.94/6.29	1870 product(difference(b1,a),b1) = c1.  [para(1862(a,1),19(a,1,1))].
5.94/6.29	2064 product(product(a1,c1),product(c1,b)) = c1.  [para(476(a,1),23(a,1,1)),rewrite([51(11)])].
5.94/6.29	2630 product(a1,c1) = product(a,c).  [para(1870(a,1),525(a,2,2)),rewrite([22(5)]),flip(a)].
5.94/6.29	2674 product(product(a,c),product(c1,b)) = c1.  [back_rewrite(2064),rewrite([2630(3)])].
5.94/6.29	2943 product(product(a,c1),product(c,b)) = c1.  [para(2674(a,1),24(a,1)),flip(a)].
5.94/6.29	3077 difference(product(a,c1),c1) = product(c,b).  [para(2943(a,1),21(a,1,2))].
5.94/6.29	3759 quotient(difference(A,B),A) = difference(A,quotient(B,A)).  [para(1761(a,1),21(a,1,2)),flip(a)].
5.94/6.29	4017 difference(difference(product(A,B),B),product(B,product(B,A))) = B.  [para(456(a,1),1770(a,1,1,2)),rewrite([139(3)])].
5.94/6.29	4325 quotient(product(b,product(A,bigA)),c) = product(bigA,A).  [para(1858(a,1),20(a,1,1))].
5.94/6.29	4328 product(product(b,c),product(c,bigA)) = c.  [para(1858(a,1),23(a,1,1)),rewrite([51(11)])].
5.94/6.29	4404 quotient(c,product(c,bigA)) = product(b,c).  [para(4328(a,1),20(a,1,1))].
5.94/6.29	4459 product(product(c,bigA),product(b,c)) = product(c,b).  [para(4404(a,1),456(a,2,2)),rewrite([176(5),28(4),340(9),38(3)]),flip(a)].
5.94/6.29	4583 product(product(a,c1),product(c1,b1)) = c1.  [para(1864(a,1),23(a,1,1)),rewrite([51(11)])].
5.94/6.29	4660 product(c1,b1) = product(c,b).  [para(4583(a,1),21(a,1,2)),rewrite([3077(5)]),flip(a)].
5.94/6.29	4778 product(product(c,b),product(b1,a)) = b1.  [back_rewrite(1086),rewrite([4660(3)])].
5.94/6.29	4799 product(product(A,bigA),product(B,c)) = product(product(A,b),product(B,bigA)).  [para(89(a,2),24(a,1))].
5.94/6.29	4931 product(product(c,b),product(b,bigA)) = product(c,b).  [back_rewrite(4459),rewrite([4799(7)])].
5.94/6.29	4992 product(product(c,b1),product(a,bigC)) = b1.  [para(4778(a,1),24(a,1)),rewrite([34(7)]),flip(a)].
5.94/6.29	5015 product(product(c,a),product(b1,bigC)) = b1.  [para(4992(a,1),24(a,1)),flip(a)].
5.94/6.29	5227 quotient(b1,product(b1,bigC)) = product(c,a).  [para(5015(a,1),20(a,1,1))].
5.94/6.29	5228 difference(product(c,a),b1) = product(b1,bigC).  [para(5015(a,1),21(a,1,2))].
5.94/6.29	5250 product(product(c,a),quotient(product(b1,bigC),product(c,a))) = quotient(b1,product(c,a)).  [para(5015(a,1),456(a,1,1)),flip(a)].
5.94/6.29	6844 quotient(product(b,A),c) = product(bigA,quotient(A,bigA)).  [para(19(a,1),4325(a,1,1,2))].
5.94/6.29	7430 product(c,b) = product(b,bigA).  [para(4931(a,1),21(a,1,2)),rewrite([39(7)])].
5.94/6.29	7908 difference(c,product(b,bigA)) = b.  [para(7430(a,1),21(a,1,2))].
5.94/6.29	8096 quotient(b,c) = difference(c,bigA).  [para(7908(a,1),3759(a,1,1)),rewrite([6844(9),38(8),18(7)])].
5.94/6.29	8162 product(difference(c,bigA),c) = b.  [para(8096(a,1),19(a,1,1))].
5.94/6.29	8286 product(product(c,A),b) = product(bigA,product(A,c)).  [para(8162(a,1),56(a,1,2))].
5.94/6.29	8798 difference(product(A,product(B,A)),A) = product(A,difference(product(B,A),A)).  [para(139(a,1),45(a,2,2)),rewrite([176(3),19(2),176(2)])].
5.94/6.29	8815 product(b1,quotient(a1,b1)) = difference(c,b1).  [para(571(a,1),139(a,2,1)),rewrite([3759(7),22(8)])].
5.94/6.29	8826 quotient(difference(product(A,B),B),B) = difference(A,B).  [para(139(a,1),456(a,1,1)),rewrite([456(6),139(7),19(5)])].
5.94/6.29	10196 product(difference(c,b1),c) = a1.  [para(8815(a,1),525(a,1,1)),rewrite([19(11),18(8)])].
5.94/6.29	10316 product(c,quotient(b1,c)) = difference(a1,c).  [para(10196(a,1),139(a,2,1)),rewrite([3759(7),22(8)])].
5.94/6.29	11747 difference(A,product(product(A,B),C)) = product(B,difference(A,C)).  [para(183(a,1),21(a,1,2))].
5.94/6.29	15763 m(product(A,B),B,product(B,difference(A,B))).  [hyper(26,a,279,a(flip)),rewrite([11747(4)])].
5.94/6.29	18266 quotient(product(A,B),product(C,D)) = product(quotient(A,C),quotient(B,D)).  [para(19(a,1),340(a,1,1,2))].
5.94/6.29	18428 quotient(b1,product(c,a)) = product(difference(a1,c),b).  [back_rewrite(5250),rewrite([18266(10),515(9),57(11),10316(5)]),flip(a)].
5.94/6.29	18611 difference(A,product(B,product(C,D))) = product(difference(quotient(A,C),B),D).  [para(342(a,1),21(a,1,2))].
5.94/6.29	18689 product(difference(difference(A,B),B),A) = B.  [back_rewrite(4017),rewrite([18611(5),8826(3)])].
5.94/6.29	18904 difference(difference(A,B),B) = quotient(B,A).  [para(18689(a,1),20(a,1,1)),flip(a)].
5.94/6.29	18911 product(product(difference(A,B),C),B) = product(B,product(C,A)).  [para(18689(a,1),56(a,1,2))].
5.94/6.29	19135 quotient(A,quotient(A,B)) = difference(B,A).  [para(40(a,1),18904(a,1,1)),flip(a)].
5.94/6.29	19727 quotient(b1,product(difference(a1,c),b)) = product(b1,bigC).  [para(5228(a,1),19135(a,2)),rewrite([18428(6)])].
5.94/6.29	22063 product(difference(a1,c),b) = product(bigA,b1).  [para(10316(a,1),8286(a,1,1)),rewrite([19(11)])].
5.94/6.29	22088 quotient(b1,product(bigA,b1)) = product(b1,bigC).  [back_rewrite(19727),rewrite([22063(6)])].
5.94/6.29	22139 product(product(b1,bigC),product(bigA,b1)) = b1.  [para(22088(a,1),19(a,1,1))].
5.94/6.29	22143 difference(product(bigA,b1),b1) = product(c,a).  [para(22088(a,1),19135(a,1,2)),rewrite([5227(5)]),flip(a)].
5.94/6.29	22193 product(product(b1,bigA),product(bigC,b1)) = b1.  [para(22139(a,1),24(a,1)),flip(a)].
5.94/6.29	22232 difference(product(b1,bigA),b1) = product(bigC,b1).  [para(22193(a,1),21(a,1,2))].
5.94/6.29	22609 difference(product(A,B),B) = product(difference(A,B),B).  [para(8826(a,1),19(a,1,1)),flip(a)].
5.94/6.29	22610 quotient(difference(A,B),B) = difference(quotient(A,B),B).  [para(19(a,1),8826(a,1,1,1))].
5.94/6.29	22615 difference(product(A,B),A) = product(A,difference(B,A)).  [para(176(a,1),8826(a,1,1,1)),rewrite([8798(3),22609(2),456(4),20(3)]),flip(a)].
5.94/6.29	22707 quotient(product(c,a),b1) = difference(bigA,b1).  [para(22143(a,1),8826(a,1,1))].
5.94/6.29	22708 product(difference(bigA,b1),b1) = product(c,a).  [para(22143(a,1),8826(a,2)),rewrite([22609(7),22609(5),18911(7),456(7),456(6),139(7),22609(5)])].
5.94/6.29	22710 product(b1,difference(bigA,b1)) = product(bigC,b1).  [para(22232(a,1),8826(a,2)),rewrite([176(5),22615(7),22609(6),22708(6),456(7),22707(6)])].
5.94/6.29	23242 product(b1,difference(quotient(bigA,b1),b1)) = bigC.  [para(22710(a,1),456(a,1,1)),rewrite([20(5),22610(7)]),flip(a)].
5.94/6.29	23900 m(bigA,b1,bigC).  [para(23242(a,1),15763(a,3)),rewrite([19(5)])].
5.94/6.29	23901 $F # answer(goals).  [resolve(23900,a,25,a)].
5.94/6.29	
5.94/6.29	% SZS output end Refutation
5.94/6.29	============================== end of proof ==========================
5.94/6.29	
5.94/6.29	============================== STATISTICS ============================
5.94/6.29	
5.94/6.29	Given=1418. Generated=263823. Kept=23879. proofs=1.
5.94/6.29	Usable=1052. Sos=9999. Demods=6453. Limbo=11, Disabled=12840. Hints=0.
5.94/6.29	Megabytes=20.80.
5.94/6.29	User_CPU=5.15, System_CPU=0.13, Wall_clock=5.
5.94/6.29	
5.94/6.29	============================== end of statistics =====================
5.94/6.29	
5.94/6.29	============================== end of search =========================
5.94/6.29	
5.94/6.29	THEOREM PROVED
5.94/6.29	% SZS status Theorem
5.94/6.29	
5.94/6.29	Exiting with 1 proof.
5.94/6.29	
5.94/6.29	Process 17280 exit (max_proofs) Tue Aug  9 06:14:12 2022
5.94/6.29	Prover9 interrupted
5.94/6.29	EOF