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
0.03/0.23	% Computer   : n153.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:49:24 CDT 2018
0.03/0.23	% CPUTime    : 
0.07/0.43	============================== Prover9 ===============================
0.07/0.43	Prover9 (32) version 2009-11A, November 2009.
0.07/0.43	Process 57734 was started by sandbox on n153.star.cs.uiowa.edu,
0.07/0.43	Sat Jul 14 05:49:25 2018
0.07/0.43	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_57702_n153.star.cs.uiowa.edu".
0.07/0.43	============================== end of head ===========================
0.07/0.43	
0.07/0.43	============================== INPUT =================================
0.07/0.43	
0.07/0.43	% Reading from file /tmp/Prover9_57702_n153.star.cs.uiowa.edu
0.07/0.43	
0.07/0.43	set(prolog_style_variables).
0.07/0.43	set(auto2).
0.07/0.43	    % set(auto2) -> set(auto).
0.07/0.43	    % set(auto) -> set(auto_inference).
0.07/0.43	    % set(auto) -> set(auto_setup).
0.07/0.43	    % set(auto_setup) -> set(predicate_elim).
0.07/0.43	    % set(auto_setup) -> assign(eq_defs, unfold).
0.07/0.43	    % set(auto) -> set(auto_limits).
0.07/0.43	    % set(auto_limits) -> assign(max_weight, "100.000").
0.07/0.43	    % set(auto_limits) -> assign(sos_limit, 20000).
0.07/0.43	    % set(auto) -> set(auto_denials).
0.07/0.43	    % set(auto) -> set(auto_process).
0.07/0.43	    % set(auto2) -> assign(new_constants, 1).
0.07/0.43	    % set(auto2) -> assign(fold_denial_max, 3).
0.07/0.43	    % set(auto2) -> assign(max_weight, "200.000").
0.07/0.43	    % set(auto2) -> assign(max_hours, 1).
0.07/0.43	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.07/0.43	    % set(auto2) -> assign(max_seconds, 0).
0.07/0.43	    % set(auto2) -> assign(max_minutes, 5).
0.07/0.43	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.07/0.43	    % set(auto2) -> set(sort_initial_sos).
0.07/0.43	    % set(auto2) -> assign(sos_limit, -1).
0.07/0.43	    % set(auto2) -> assign(lrs_ticks, 3000).
0.07/0.43	    % set(auto2) -> assign(max_megs, 400).
0.07/0.43	    % set(auto2) -> assign(stats, some).
0.07/0.43	    % set(auto2) -> clear(echo_input).
0.07/0.43	    % set(auto2) -> set(quiet).
0.07/0.43	    % set(auto2) -> clear(print_initial_clauses).
0.07/0.43	    % set(auto2) -> clear(print_given).
0.07/0.43	assign(lrs_ticks,-1).
0.07/0.43	assign(sos_limit,10000).
0.07/0.43	assign(order,kbo).
0.07/0.43	set(lex_order_vars).
0.07/0.43	clear(print_given).
0.07/0.43	
0.07/0.43	% formulas(sos).  % not echoed (21 formulas)
0.07/0.43	
0.07/0.43	============================== end of input ==========================
0.07/0.43	
0.07/0.43	% From the command line: assign(max_seconds, 300).
0.07/0.43	
0.07/0.43	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.07/0.43	
0.07/0.43	% Formulas that are not ordinary clauses:
0.07/0.43	1 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	2 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	9 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	10 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	11 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	13 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause).  [assumption].
0.07/0.43	14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	15 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	17 (all X0 codomain(X0) = coantidomain(coantidomain(X0))) # label(codomain4) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	21 -(all X0 all X1 domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
9.46/9.73	
9.46/9.73	============================== end of process non-clausal formulas ===
9.46/9.73	
9.46/9.73	============================== PROCESS INITIAL CLAUSES ===============
9.46/9.73	
9.46/9.73	============================== PREDICATE ELIMINATION =================
9.46/9.73	22 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(11)].
9.46/9.73	23 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(11)].
9.46/9.73	
9.46/9.73	============================== end predicate elimination =============
9.46/9.73	
9.46/9.73	Auto_denials:
9.46/9.73	  % copying label goals to answer in negative clause
9.46/9.73	
9.46/9.73	Term ordering decisions:
9.46/9.73	Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. antidomain=1. coantidomain=1. codomain=1. domain=1.
9.46/9.73	
9.46/9.73	============================== end of process initial clauses ========
9.46/9.73	
9.46/9.73	============================== CLAUSES FOR SEARCH ====================
9.46/9.73	
9.46/9.73	============================== end of clauses for search =============
9.46/9.73	
9.46/9.73	============================== SEARCH ================================
9.46/9.73	
9.46/9.73	% Starting search at 0.01 seconds.
9.46/9.73	
9.46/9.73	Low Water (keep): wt=41.000, iters=3359
9.46/9.73	
9.46/9.73	Low Water (keep): wt=36.000, iters=3336
9.46/9.73	
9.46/9.73	Low Water (keep): wt=35.000, iters=3361
9.46/9.73	
9.46/9.73	Low Water (keep): wt=33.000, iters=3433
9.46/9.73	
9.46/9.73	Low Water (keep): wt=32.000, iters=3364
9.46/9.73	
9.46/9.73	Low Water (keep): wt=31.000, iters=3441
9.46/9.73	
9.46/9.73	Low Water (keep): wt=30.000, iters=3335
9.46/9.73	
9.46/9.73	Low Water (keep): wt=29.000, iters=3354
9.46/9.73	
9.46/9.73	Low Water (keep): wt=28.000, iters=3356
9.46/9.73	
9.46/9.73	Low Water (keep): wt=27.000, iters=3343
9.46/9.73	
9.46/9.73	Low Water (keep): wt=26.000, iters=3356
9.46/9.73	
9.46/9.73	Low Water (keep): wt=25.000, iters=3339
9.46/9.73	
9.46/9.73	Low Water (keep): wt=24.000, iters=3339
9.46/9.73	
9.46/9.73	Low Water (keep): wt=23.000, iters=3377
9.46/9.73	
9.46/9.73	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 2.46 sec).
9.46/9.73	
9.46/9.73	Low Water (keep): wt=22.000, iters=3340
9.46/9.73	
9.46/9.73	Low Water (keep): wt=21.000, iters=3337
9.46/9.73	
9.46/9.73	Low Water (keep): wt=20.000, iters=3333
9.46/9.73	
9.46/9.73	Low Water (displace): id=6778, wt=49.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=5278, wt=48.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=7640, wt=47.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=8866, wt=46.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=8602, wt=45.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=7050, wt=44.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=15146, wt=19.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=15229, wt=16.000
9.46/9.73	
9.46/9.73	Low Water (displace): id=15232, wt=14.000
9.46/9.73	
9.46/9.73	Low Water (keep): wt=19.000, iters=3347
9.46/9.73	
9.46/9.73	============================== PROOF =================================
9.46/9.73	% SZS status Theorem
9.46/9.73	% SZS output start Refutation
9.46/9.73	
9.46/9.73	% Proof 1 at 9.08 (+ 0.22) seconds: goals.
9.46/9.73	% Length of proof is 121.
9.46/9.73	% Level of proof is 24.
9.46/9.73	% Maximum clause weight is 26.000.
9.46/9.73	% Given clauses 928.
9.46/9.73	
9.46/9.73	1 (all A all B all C addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C))) # label(right_distributivity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	2 (all A all B all C addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C)) # label(left_distributivity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	4 (all A A = multiplication(one,A)) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	5 (all A A = multiplication(A,one)) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	6 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	8 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	9 (all A all B all C multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C))) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	10 (all C all B all A addition(A,addition(B,C)) = addition(addition(A,B),C)) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	13 (all X0 all X1 addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) = coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))) # label(codomain2) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	14 (all X0 one = addition(coantidomain(coantidomain(X0)),coantidomain(X0))) # label(codomain3) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	15 (all X0 all X1 antidomain(multiplication(X0,antidomain(antidomain(X1)))) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))) # label(domain2) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	16 (all X0 multiplication(X0,coantidomain(X0)) = zero) # label(codomain1) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	18 (all X0 zero = multiplication(antidomain(X0),X0)) # label(domain1) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	19 (all X0 one = addition(antidomain(antidomain(X0)),antidomain(X0))) # label(domain3) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	20 (all X0 domain(X0) = antidomain(antidomain(X0))) # label(domain4) # label(axiom) # label(non_clause).  [assumption].
9.46/9.73	21 -(all X0 all X1 domain(multiplication(X0,domain(X1))) = domain(multiplication(X0,X1))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
9.46/9.73	24 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(4)].
9.46/9.73	25 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(5)].
9.46/9.73	26 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(6)].
9.46/9.73	27 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(7)].
9.46/9.73	28 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [clausify(8)].
9.46/9.73	29 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(12)].
9.46/9.73	30 multiplication(A,coantidomain(A)) = zero # label(codomain1) # label(axiom).  [clausify(16)].
9.46/9.73	32 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom).  [clausify(18)].
9.46/9.73	33 domain(A) = antidomain(antidomain(A)) # label(domain4) # label(axiom).  [clausify(20)].
9.46/9.73	34 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(3)].
9.46/9.73	35 addition(coantidomain(coantidomain(A)),coantidomain(A)) = one # label(codomain3) # label(axiom).  [clausify(14)].
9.46/9.73	36 addition(coantidomain(A),coantidomain(coantidomain(A))) = one.  [copy(35),rewrite([34(4)])].
9.46/9.73	37 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom).  [clausify(19)].
9.46/9.73	38 addition(antidomain(A),antidomain(antidomain(A))) = one.  [copy(37),rewrite([34(4)])].
9.46/9.73	39 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(9)].
9.46/9.73	40 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(10)].
9.46/9.73	41 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(40),rewrite([34(2)]),flip(a)].
9.46/9.73	42 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(1)].
9.46/9.73	43 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(2)].
9.46/9.73	44 coantidomain(multiplication(coantidomain(coantidomain(A)),B)) = addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) # label(codomain2) # label(axiom).  [clausify(13)].
9.46/9.73	45 addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B))) = coantidomain(multiplication(coantidomain(coantidomain(A)),B)).  [copy(44),flip(a)].
9.46/9.73	46 antidomain(multiplication(A,antidomain(antidomain(B)))) = addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) # label(domain2) # label(axiom).  [clausify(15)].
9.46/9.73	47 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [copy(46),flip(a)].
9.46/9.73	48 domain(multiplication(c1,domain(c2))) != domain(multiplication(c1,c2)) # label(goals) # label(negated_conjecture) # answer(goals).  [clausify(21)].
9.46/9.73	49 antidomain(antidomain(multiplication(c1,antidomain(antidomain(c2))))) != antidomain(antidomain(multiplication(c1,c2))) # answer(goals).  [copy(48),rewrite([33(3),33(6),33(11)])].
9.46/9.73	50 coantidomain(one) = zero.  [para(30(a,1),24(a,1)),flip(a)].
9.46/9.73	51 antidomain(one) = zero.  [para(32(a,1),25(a,1)),flip(a)].
9.46/9.73	54 multiplication(antidomain(A),multiplication(A,B)) = zero.  [para(32(a,1),39(a,1,1)),rewrite([26(2)]),flip(a)].
9.46/9.73	55 addition(A,addition(A,B)) = addition(A,B).  [para(41(a,1),29(a,1)),rewrite([34(1),34(2),41(2,R),29(1),34(3)])].
9.46/9.73	56 addition(A,multiplication(A,B)) = multiplication(A,addition(B,one)).  [para(25(a,1),42(a,1,1)),rewrite([34(4)])].
9.46/9.73	57 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(27(a,1),42(a,2,2)),rewrite([28(3),34(3)])].
9.46/9.73	59 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B).  [para(32(a,1),42(a,1,1)),rewrite([57(4)]),flip(a)].
9.46/9.73	61 multiplication(addition(A,B),coantidomain(B)) = multiplication(A,coantidomain(B)).  [para(30(a,1),43(a,1,1)),rewrite([57(4),34(3)]),flip(a)].
9.46/9.73	70 addition(coantidomain(zero),coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)).  [para(32(a,1),45(a,1,1,1))].
9.46/9.73	75 addition(antidomain(zero),antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))).  [para(30(a,1),47(a,1,1,1))].
9.46/9.73	78 addition(antidomain(multiplication(A,multiplication(B,C))),antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C)))))) = antidomain(multiplication(A,multiplication(B,antidomain(antidomain(C))))).  [para(39(a,1),47(a,1,1,1)),rewrite([39(7),39(13)])].
9.46/9.73	79 addition(zero,coantidomain(zero)) = one.  [para(50(a,1),36(a,1,1)),rewrite([50(3)])].
9.46/9.73	80 addition(zero,antidomain(zero)) = one.  [para(51(a,1),38(a,1,1)),rewrite([51(3)])].
9.46/9.73	83 multiplication(A,coantidomain(zero)) = A.  [para(79(a,1),42(a,2,2)),rewrite([28(2),57(5),25(5)])].
9.46/9.73	87 multiplication(A,antidomain(zero)) = A.  [para(80(a,1),42(a,2,2)),rewrite([28(2),57(5),25(5)])].
9.46/9.73	96 coantidomain(zero) = one.  [para(83(a,1),24(a,1)),flip(a)].
9.46/9.73	99 addition(one,coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A))) = coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)).  [back_rewrite(70),rewrite([96(2)])].
9.46/9.73	102 antidomain(zero) = one.  [para(87(a,1),24(a,1)),flip(a)].
9.46/9.73	106 addition(one,antidomain(multiplication(A,antidomain(antidomain(coantidomain(A)))))) = antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))).  [back_rewrite(75),rewrite([102(2)])].
9.46/9.73	112 multiplication(antidomain(multiplication(A,B)),multiplication(A,multiplication(B,C))) = zero.  [para(39(a,1),54(a,1,2))].
9.46/9.73	116 addition(one,antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))).  [para(54(a,1),47(a,1,1,1)),rewrite([102(2)])].
9.46/9.73	117 addition(one,coantidomain(A)) = one.  [para(36(a,1),55(a,1,2)),rewrite([34(3),36(7)])].
9.46/9.73	118 addition(one,antidomain(A)) = one.  [para(38(a,1),55(a,1,2)),rewrite([34(3),38(7)])].
9.46/9.73	122 coantidomain(multiplication(coantidomain(coantidomain(antidomain(A))),A)) = one.  [back_rewrite(99),rewrite([117(7)]),flip(a)].
9.46/9.73	124 antidomain(multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B))))) = one.  [back_rewrite(116),rewrite([118(8)]),flip(a)].
9.46/9.73	126 antidomain(multiplication(A,antidomain(antidomain(coantidomain(A))))) = one.  [back_rewrite(106),rewrite([118(7)]),flip(a)].
9.46/9.73	130 addition(A,multiplication(coantidomain(B),A)) = A.  [para(117(a,1),43(a,2,1)),rewrite([24(2),24(5)])].
9.46/9.73	131 addition(A,multiplication(A,antidomain(B))) = A.  [para(118(a,1),42(a,2,2)),rewrite([25(2),25(5)])].
9.46/9.73	132 addition(A,multiplication(antidomain(B),A)) = A.  [para(118(a,1),43(a,2,1)),rewrite([24(2),24(5)])].
9.46/9.73	175 multiplication(coantidomain(coantidomain(antidomain(A))),A) = zero.  [para(122(a,1),30(a,1,2)),rewrite([25(6)])].
9.46/9.73	179 multiplication(addition(A,coantidomain(coantidomain(antidomain(B)))),B) = multiplication(A,B).  [para(175(a,1),43(a,1,1)),rewrite([57(3),34(5)]),flip(a)].
9.46/9.73	181 multiplication(A,antidomain(antidomain(coantidomain(A)))) = zero.  [para(126(a,1),32(a,1,1)),rewrite([24(6)])].
9.46/9.73	184 multiplication(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = antidomain(coantidomain(A)).  [para(36(a,1),59(a,1,2)),rewrite([25(4)]),flip(a)].
9.46/9.73	189 multiplication(antidomain(multiplication(A,B)),multiplication(addition(A,C),B)) = multiplication(antidomain(multiplication(A,B)),multiplication(C,B)).  [para(43(a,1),59(a,1,2))].
9.46/9.73	193 multiplication(antidomain(A),multiplication(antidomain(B),A)) = zero.  [para(132(a,1),59(a,1,2)),rewrite([32(2)]),flip(a)].
9.46/9.73	196 multiplication(A,addition(B,antidomain(antidomain(coantidomain(A))))) = multiplication(A,B).  [para(181(a,1),42(a,1,1)),rewrite([57(3),34(5)]),flip(a)].
9.46/9.73	235 multiplication(addition(A,antidomain(B)),multiplication(antidomain(C),B)) = multiplication(A,multiplication(antidomain(C),B)).  [para(193(a,1),43(a,1,1)),rewrite([57(5),34(5)]),flip(a)].
9.46/9.73	258 multiplication(addition(A,B),coantidomain(A)) = multiplication(B,coantidomain(A)).  [para(34(a,1),61(a,1,1))].
9.46/9.73	259 multiplication(coantidomain(A),coantidomain(coantidomain(coantidomain(A)))) = coantidomain(coantidomain(coantidomain(A))).  [para(36(a,1),61(a,1,1)),rewrite([24(5)]),flip(a)].
9.46/9.73	260 multiplication(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))).  [para(38(a,1),61(a,1,1)),rewrite([24(5)]),flip(a)].
9.46/9.73	515 multiplication(antidomain(A),antidomain(antidomain(multiplication(A,B)))) = zero.  [para(124(a,1),32(a,1,1)),rewrite([24(7)])].
9.46/9.73	523 multiplication(antidomain(A),addition(B,antidomain(antidomain(multiplication(A,C))))) = multiplication(antidomain(A),B).  [para(515(a,1),42(a,1,1)),rewrite([57(4),34(7)]),flip(a)].
9.46/9.73	680 addition(antidomain(coantidomain(A)),coantidomain(coantidomain(A))) = coantidomain(coantidomain(A)).  [para(184(a,1),132(a,1,2)),rewrite([34(5)])].
9.46/9.73	876 multiplication(antidomain(antidomain(A)),coantidomain(antidomain(A))) = coantidomain(antidomain(A)).  [para(38(a,1),258(a,1,1)),rewrite([24(4)]),flip(a)].
9.46/9.73	2901 multiplication(coantidomain(antidomain(A)),A) = A.  [para(36(a,1),179(a,1,1)),rewrite([24(2)]),flip(a)].
9.46/9.73	2941 addition(antidomain(A),coantidomain(antidomain(antidomain(A)))) = coantidomain(antidomain(antidomain(A))).  [para(2901(a,1),131(a,1,2)),rewrite([34(5)])].
9.46/9.73	2952 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(coantidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [para(2901(a,1),78(a,1,2,1)),rewrite([34(13),2901(22)])].
9.46/9.73	2955 multiplication(antidomain(multiplication(A,coantidomain(antidomain(B)))),multiplication(A,B)) = zero.  [para(2901(a,1),112(a,1,2,2))].
9.46/9.73	3750 multiplication(A,antidomain(coantidomain(A))) = A.  [para(38(a,1),196(a,1,2)),rewrite([25(2)]),flip(a)].
9.46/9.73	3780 multiplication(A,multiplication(antidomain(coantidomain(A)),B)) = multiplication(A,B).  [para(3750(a,1),39(a,1,1)),flip(a)].
9.46/9.73	3781 multiplication(A,multiplication(B,antidomain(coantidomain(multiplication(A,B))))) = multiplication(A,B).  [para(3750(a,1),39(a,1)),flip(a)].
9.46/9.73	3787 addition(coantidomain(A),antidomain(coantidomain(coantidomain(A)))) = antidomain(coantidomain(coantidomain(A))).  [para(3750(a,1),130(a,1,2)),rewrite([34(5)])].
9.46/9.73	3981 multiplication(A,coantidomain(coantidomain(A))) = A.  [para(184(a,1),3780(a,1,2)),rewrite([3750(3)]),flip(a)].
9.46/9.73	4027 coantidomain(coantidomain(coantidomain(A))) = coantidomain(A).  [back_rewrite(259),rewrite([3981(5)]),flip(a)].
9.46/9.73	4082 antidomain(coantidomain(coantidomain(A))) = coantidomain(A).  [para(4027(a,1),680(a,1,2)),rewrite([34(5),3787(5),4027(6)])].
9.46/9.73	4104 coantidomain(coantidomain(A)) = antidomain(coantidomain(A)).  [para(4082(a,1),876(a,1,1,1)),rewrite([4082(5),184(5),4082(5)]),flip(a)].
9.46/9.73	4106 coantidomain(antidomain(antidomain(coantidomain(A)))) = antidomain(coantidomain(A)).  [para(4082(a,1),876(a,2,1)),rewrite([4104(2),4104(6),876(9),4104(6)])].
9.46/9.73	4115 coantidomain(antidomain(coantidomain(A))) = antidomain(antidomain(coantidomain(A))).  [para(4027(a,1),4082(a,1,1,1)),rewrite([4104(2),4104(5)]),flip(a)].
9.46/9.73	4116 antidomain(antidomain(coantidomain(A))) = coantidomain(A).  [para(4027(a,1),4082(a,2)),rewrite([4104(2),4115(3),4106(4)])].
9.46/9.73	5039 multiplication(antidomain(multiplication(antidomain(A),B)),multiplication(antidomain(antidomain(A)),B)) = multiplication(antidomain(multiplication(antidomain(A),B)),B).  [para(38(a,1),189(a,1,2,1)),rewrite([24(5)]),flip(a)].
9.46/9.73	5510 coantidomain(antidomain(antidomain(A))) = antidomain(A).  [para(260(a,1),56(a,1,2)),rewrite([2941(5),34(9),117(9),25(6)])].
9.46/9.73	5522 coantidomain(antidomain(A)) = antidomain(antidomain(A)).  [para(5510(a,1),4104(a,1,1)),rewrite([5510(5)])].
9.46/9.73	5523 antidomain(antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(A)).  [para(5510(a,1),4104(a,2,1)),rewrite([5522(3),5522(4)])].
9.46/9.73	5524 antidomain(antidomain(antidomain(A))) = antidomain(A).  [para(5510(a,1),4116(a,2)),rewrite([5522(3),5523(4)])].
9.46/9.73	5692 multiplication(antidomain(multiplication(A,antidomain(antidomain(B)))),multiplication(A,B)) = zero.  [back_rewrite(2955),rewrite([5522(2)])].
9.46/9.73	5693 addition(antidomain(multiplication(A,antidomain(antidomain(B)))),antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [back_rewrite(2952),rewrite([5522(9)])].
9.46/9.73	8573 multiplication(antidomain(A),multiplication(antidomain(B),antidomain(A))) = multiplication(antidomain(B),antidomain(A)).  [para(38(a,1),235(a,1,1)),rewrite([24(5)]),flip(a)].
9.46/9.73	17182 multiplication(antidomain(A),antidomain(multiplication(A,B))) = antidomain(A).  [para(38(a,1),523(a,1,2)),rewrite([25(3)]),flip(a)].
9.46/9.73	17330 multiplication(A,antidomain(multiplication(coantidomain(A),B))) = A.  [para(17182(a,1),3780(a,1,2)),rewrite([3750(3)]),flip(a)].
9.46/9.73	17352 multiplication(antidomain(multiplication(A,B)),antidomain(A)) = antidomain(A).  [para(17182(a,1),3781(a,1,2,2,1,1)),rewrite([5522(5),5524(6),8573(6),17182(8)])].
9.46/9.73	17409 addition(antidomain(A),antidomain(multiplication(antidomain(antidomain(A)),B))) = antidomain(multiplication(antidomain(antidomain(A)),B)).  [para(17330(a,1),132(a,1,2)),rewrite([5522(2),34(6),5522(8)])].
9.46/9.73	17444 antidomain(multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B))) = antidomain(multiplication(A,antidomain(antidomain(B)))).  [back_rewrite(5693),rewrite([17409(13)])].
9.46/9.73	17554 multiplication(antidomain(multiplication(A,B)),multiplication(antidomain(A),C)) = multiplication(antidomain(A),C).  [para(17352(a,1),39(a,1,1)),flip(a)].
9.46/9.73	17584 multiplication(antidomain(multiplication(antidomain(A),B)),B) = multiplication(antidomain(antidomain(A)),B).  [back_rewrite(5039),rewrite([17554(7)]),flip(a)].
9.46/9.73	18897 multiplication(antidomain(antidomain(multiplication(A,antidomain(antidomain(B))))),multiplication(A,B)) = multiplication(A,B).  [para(5692(a,1),17584(a,1,1,1)),rewrite([102(2),24(3)]),flip(a)].
9.46/9.73	18952 antidomain(multiplication(A,antidomain(antidomain(B)))) = antidomain(multiplication(A,B)).  [back_rewrite(17444),rewrite([18897(7)]),flip(a)].
9.46/9.73	18986 $F # answer(goals).  [back_rewrite(49),rewrite([18952(6)]),xx(a)].
9.46/9.73	
9.46/9.73	% SZS output end Refutation
9.46/9.73	============================== end of proof ==========================
9.46/9.73	
9.46/9.73	============================== STATISTICS ============================
9.46/9.73	
9.46/9.73	Given=928. Generated=452426. Kept=18956. proofs=1.
9.46/9.73	Usable=684. Sos=8820. Demods=9073. Limbo=34, Disabled=9440. Hints=0.
9.46/9.73	Megabytes=18.48.
9.46/9.73	User_CPU=9.08, System_CPU=0.22, Wall_clock=9.
9.46/9.73	
9.46/9.73	============================== end of statistics =====================
9.46/9.73	
9.46/9.73	============================== end of search =========================
9.46/9.73	
9.46/9.73	THEOREM PROVED
9.46/9.73	% SZS status Theorem
9.46/9.73	
9.46/9.73	Exiting with 1 proof.
9.46/9.73	
9.46/9.73	Process 57734 exit (max_proofs) Sat Jul 14 05:49:34 2018
9.46/9.73	Prover9 interrupted
9.46/9.74	EOF