0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.34	% Computer   : n005.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 960
0.12/0.34	% DateTime   : Thu Jul  2 08:30:53 EDT 2020
0.12/0.34	% CPUTime    : 
0.43/0.98	============================== Prover9 ===============================
0.43/0.98	Prover9 (32) version 2009-11A, November 2009.
0.43/0.98	Process 18566 was started by sandbox2 on n005.cluster.edu,
0.43/0.98	Thu Jul  2 08:30:53 2020
0.43/0.98	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_18412_n005.cluster.edu".
0.43/0.98	============================== end of head ===========================
0.43/0.98	
0.43/0.98	============================== INPUT =================================
0.43/0.98	
0.43/0.98	% Reading from file /tmp/Prover9_18412_n005.cluster.edu
0.43/0.98	
0.43/0.98	set(prolog_style_variables).
0.43/0.98	set(auto2).
0.43/0.98	    % set(auto2) -> set(auto).
0.43/0.98	    % set(auto) -> set(auto_inference).
0.43/0.98	    % set(auto) -> set(auto_setup).
0.43/0.98	    % set(auto_setup) -> set(predicate_elim).
0.43/0.98	    % set(auto_setup) -> assign(eq_defs, unfold).
0.43/0.98	    % set(auto) -> set(auto_limits).
0.43/0.98	    % set(auto_limits) -> assign(max_weight, "100.000").
0.43/0.98	    % set(auto_limits) -> assign(sos_limit, 20000).
0.43/0.98	    % set(auto) -> set(auto_denials).
0.43/0.98	    % set(auto) -> set(auto_process).
0.43/0.98	    % set(auto2) -> assign(new_constants, 1).
0.43/0.98	    % set(auto2) -> assign(fold_denial_max, 3).
0.43/0.98	    % set(auto2) -> assign(max_weight, "200.000").
0.43/0.98	    % set(auto2) -> assign(max_hours, 1).
0.43/0.98	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.43/0.98	    % set(auto2) -> assign(max_seconds, 0).
0.43/0.98	    % set(auto2) -> assign(max_minutes, 5).
0.43/0.98	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.43/0.98	    % set(auto2) -> set(sort_initial_sos).
0.43/0.98	    % set(auto2) -> assign(sos_limit, -1).
0.43/0.98	    % set(auto2) -> assign(lrs_ticks, 3000).
0.43/0.98	    % set(auto2) -> assign(max_megs, 400).
0.43/0.98	    % set(auto2) -> assign(stats, some).
0.43/0.98	    % set(auto2) -> clear(echo_input).
0.43/0.98	    % set(auto2) -> set(quiet).
0.43/0.98	    % set(auto2) -> clear(print_initial_clauses).
0.43/0.98	    % set(auto2) -> clear(print_given).
0.43/0.98	assign(lrs_ticks,-1).
0.43/0.98	assign(sos_limit,10000).
0.43/0.98	assign(order,kbo).
0.43/0.98	set(lex_order_vars).
0.43/0.98	clear(print_given).
0.43/0.98	
0.43/0.98	% formulas(sos).  % not echoed (17 formulas)
0.43/0.98	
0.43/0.98	============================== end of input ==========================
0.43/0.98	
0.43/0.98	% From the command line: assign(max_seconds, 960).
0.43/0.98	
0.43/0.98	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.43/0.98	
0.43/0.98	% Formulas that are not ordinary clauses:
0.43/0.98	1 (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].
0.43/0.98	2 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	5 (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].
0.43/0.98	6 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	8 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	9 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	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].
0.43/0.98	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	12 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
0.43/0.98	14 (all X0 all X1 (complement(X1,X0) <-> zero = multiplication(X0,X1) & zero = multiplication(X1,X0) & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
3.21/3.49	15 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> X1 = c(X0)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
3.21/3.49	16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
3.21/3.49	17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(X0,X1) = multiplication(X1,X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
3.21/3.49	
3.21/3.49	============================== end of process non-clausal formulas ===
3.21/3.49	
3.21/3.49	============================== PROCESS INITIAL CLAUSES ===============
3.21/3.49	
3.21/3.49	============================== PREDICATE ELIMINATION =================
3.21/3.49	18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
3.21/3.49	19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
3.21/3.49	20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
3.21/3.49	21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
3.21/3.49	22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
3.21/3.49	Derived: complement(f1(c2),c2).  [resolve(18,a,19,a)].
3.21/3.49	Derived: complement(f1(c1),c1).  [resolve(18,a,20,a)].
3.21/3.49	Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,a,21,a)].
3.21/3.49	Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
3.21/3.49	23 -test(A) | -complement(A,B) | c(A) = B # label(test_3) # label(axiom).  [clausify(15)].
3.21/3.49	Derived: -complement(c2,A) | c(c2) = A.  [resolve(23,a,19,a)].
3.21/3.49	Derived: -complement(c1,A) | c(c1) = A.  [resolve(23,a,20,a)].
3.21/3.49	Derived: -complement(A,B) | c(A) = B | c(A) = zero.  [resolve(23,a,21,a)].
3.21/3.49	Derived: -complement(A,B) | c(A) = B | -complement(C,A).  [resolve(23,a,22,a)].
3.21/3.49	24 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom).  [clausify(15)].
3.21/3.49	Derived: complement(c2,A) | c(c2) != A.  [resolve(24,a,19,a)].
3.21/3.49	Derived: complement(c1,A) | c(c1) != A.  [resolve(24,a,20,a)].
3.21/3.49	Derived: complement(A,B) | c(A) != B | c(A) = zero.  [resolve(24,a,21,a)].
3.21/3.49	Derived: complement(A,B) | c(A) != B | -complement(C,A).  [resolve(24,a,22,a)].
3.21/3.49	25 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(8)].
3.21/3.49	26 -leq(A,B) | addition(A,B) = B # label(order) # label(axiom).  [clausify(8)].
3.21/3.49	
3.21/3.49	============================== end predicate elimination =============
3.21/3.49	
3.21/3.49	Auto_denials:  (non-Horn, no changes).
3.21/3.49	
3.21/3.49	Term ordering decisions:
3.21/3.49	Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
3.21/3.49	
3.21/3.49	============================== end of process initial clauses ========
3.21/3.49	
3.21/3.49	============================== CLAUSES FOR SEARCH ====================
3.21/3.49	
3.21/3.49	============================== end of clauses for search =============
3.21/3.49	
3.21/3.49	============================== SEARCH ================================
3.21/3.49	
3.21/3.49	% Starting search at 0.01 seconds.
3.21/3.49	
3.21/3.49	Low Water (keep): wt=74.000, iters=3467
3.21/3.49	
3.21/3.49	Low Water (keep): wt=68.000, iters=3437
3.21/3.49	
3.21/3.49	Low Water (keep): wt=64.000, iters=3368
3.21/3.49	
3.21/3.49	Low Water (keep): wt=58.000, iters=3363
3.21/3.49	
3.21/3.49	Low Water (keep): wt=54.000, iters=3419
3.21/3.49	
3.21/3.49	Low Water (keep): wt=53.000, iters=3352
3.21/3.49	
3.21/3.49	Low Water (keep): wt=52.000, iters=3348
3.21/3.49	
3.21/3.49	Low Water (keep): wt=51.000, iters=3347
3.21/3.49	
3.21/3.49	Low Water (keep): wt=50.000, iters=3417
3.21/3.49	
3.21/3.49	Low Water (keep): wt=48.000, iters=3380
3.21/3.49	
3.21/3.49	Low Water (keep): wt=46.000, iters=3333
3.21/3.49	
3.21/3.49	Low Water (keep): wt=45.000, iters=3358
3.21/3.49	
3.21/3.49	Low Water (keep): wt=42.000, iters=3403
3.21/3.49	
3.21/3.49	Low Water (keep): wt=40.000, iters=3354
3.21/3.49	
3.21/3.49	Low Water (keep): wt=38.000, iters=3351
3.21/3.49	
3.21/3.49	Low Water (keep): wt=37.000, iters=3352
3.21/3.49	
3.21/3.49	Low Water (keep): wt=36.000, iters=3364
3.21/3.49	
3.21/3.49	Low Water (keep): wt=35.000, iters=3347
3.21/3.49	
3.21/3.49	Low Water (keep): wt=34.000, iters=3335
3.21/3.49	
3.21/3.49	Low Water (keep): wt=33.000, iters=3350
3.21/3.49	
3.21/3.49	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 110 (0.00 of 1.88 sec).
3.21/3.49	
3.21/3.49	Low Water (keep): wt=32.000, iters=3406
3.21/3.49	
3.21/3.49	Low Water (keep): wt=31.000, iters=3403
3.21/3.49	
3.21/3.49	Low Water (keep): wt=30.000, iters=3348
3.21/3.49	
3.21/3.49	Low Water (keep): wt=29.000, iters=3361
3.21/3.49	
3.21/3.49	Low Water (keep): wt=28.000, iters=3481
3.21/3.49	
3.21/3.49	Low Water (keep): wt=27.000, iters=3396
3.21/3.49	
3.21/3.49	Low Water (keep): wt=26.000, iters=3352
3.21/3.49	
3.21/3.49	Low Water (keep): wt=25.000, iters=3356
3.21/3.49	
3.21/3.49	Low Water (keep): wt=24.000, iters=3341
3.21/3.49	
3.21/3.49	Low Water (displace): id=5970, wt=107.000
3.21/3.49	
3.21/3.49	Low Water (displace): id=11177, wt=23.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=11464, wt=21.000
8.77/9.11	
8.77/9.11	Low Water (keep): wt=23.000, iters=3338
8.77/9.11	
8.77/9.11	Low Water (displace): id=11630, wt=20.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=11683, wt=17.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=11700, wt=16.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=11711, wt=15.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=11819, wt=14.000
8.77/9.11	
8.77/9.11	Low Water (displace): id=12626, wt=13.000
8.77/9.11	
8.77/9.11	Low Water (keep): wt=22.000, iters=3334
8.77/9.11	
8.77/9.11	Low Water (keep): wt=21.000, iters=3341
8.77/9.11	
8.77/9.11	Low Water (keep): wt=20.000, iters=3339
8.77/9.11	
8.77/9.11	============================== PROOF =================================
8.77/9.11	% SZS status Theorem
8.77/9.11	% SZS output start Refutation
8.77/9.11	
8.77/9.11	% Proof 1 at 7.97 (+ 0.16) seconds.
8.77/9.11	% Length of proof is 67.
8.77/9.11	% Level of proof is 11.
8.77/9.11	% Maximum clause weight is 17.000.
8.77/9.11	% Given clauses 1139.
8.77/9.11	
8.77/9.11	1 (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].
8.77/9.11	2 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	5 (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].
8.77/9.11	6 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	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].
8.77/9.11	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	12 (all A all B all C multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C)) # label(multiplicative_associativity) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	14 (all X0 all X1 (complement(X1,X0) <-> zero = multiplication(X0,X1) & zero = multiplication(X1,X0) & addition(X0,X1) = one)) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	15 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> X1 = c(X0)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
8.77/9.11	17 -(all X0 all X1 (test(X1) & test(X0) -> multiplication(X0,X1) = multiplication(X1,X0))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
8.77/9.11	18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
8.77/9.11	19 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
8.77/9.11	20 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
8.77/9.11	24 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom).  [clausify(15)].
8.77/9.11	27 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(2)].
8.77/9.11	28 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(4)].
8.77/9.11	29 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(6)].
8.77/9.11	30 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(7)].
8.77/9.11	32 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(11)].
8.77/9.11	33 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(3)].
8.77/9.11	34 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(10)].
8.77/9.11	35 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(34),rewrite([33(2)]),flip(a)].
8.77/9.11	36 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(12)].
8.77/9.11	37 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(1)].
8.77/9.11	38 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(5)].
8.77/9.11	39 multiplication(c2,c1) != multiplication(c1,c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
8.77/9.11	41 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom).  [clausify(14)].
8.77/9.11	42 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
8.77/9.11	43 -complement(A,B) | addition(A,B) = one.  [copy(42),rewrite([33(2)])].
8.77/9.11	46 complement(f1(c2),c2).  [resolve(18,a,19,a)].
8.77/9.11	47 complement(f1(c1),c1).  [resolve(18,a,20,a)].
8.77/9.11	54 complement(c2,A) | c(c2) != A.  [resolve(24,a,19,a)].
8.77/9.11	55 complement(c1,A) | c(c1) != A.  [resolve(24,a,20,a)].
8.77/9.11	61 addition(A,addition(A,B)) = addition(A,B).  [para(35(a,1),29(a,1)),rewrite([33(1),33(2),35(2,R),29(1),33(3)])].
8.77/9.11	62 addition(A,multiplication(B,A)) = multiplication(addition(B,one),A).  [para(28(a,1),37(a,1,1)),rewrite([33(4)])].
8.77/9.11	63 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(30(a,1),37(a,2,1)),rewrite([32(3),33(3)])].
8.77/9.11	64 addition(multiplication(A,multiplication(B,C)),multiplication(D,C)) = multiplication(addition(D,multiplication(A,B)),C).  [para(36(a,1),37(a,1,1)),rewrite([33(6)])].
8.77/9.11	73 addition(c2,f1(c2)) = one.  [resolve(46,a,43,a),rewrite([33(4)])].
8.77/9.11	76 addition(c1,f1(c1)) = one.  [resolve(47,a,43,a),rewrite([33(4)])].
8.77/9.11	90 complement(c2,c(c2)).  [resolve(54,b,29,a(flip)),rewrite([29(6)])].
8.77/9.11	92 complement(c1,c(c1)).  [resolve(55,b,29,a(flip)),rewrite([29(6)])].
8.77/9.11	104 addition(c2,c(c2)) = one.  [resolve(90,a,43,a)].
8.77/9.11	105 multiplication(c2,c(c2)) = zero.  [resolve(90,a,41,a)].
8.77/9.11	110 addition(c1,c(c1)) = one.  [resolve(92,a,43,a)].
8.77/9.11	111 multiplication(c1,c(c1)) = zero.  [resolve(92,a,41,a)].
8.77/9.11	114 addition(A,addition(B,multiplication(C,A))) = addition(B,multiplication(addition(C,one),A)).  [para(62(a,1),35(a,2,2)),rewrite([33(2)])].
8.77/9.11	149 addition(one,c2) = one.  [para(73(a,1),61(a,1,2)),rewrite([33(3),73(7)])].
8.77/9.11	168 addition(one,c1) = one.  [para(76(a,1),61(a,1,2)),rewrite([33(3),76(7)])].
8.77/9.11	229 multiplication(c2,addition(A,c(c2))) = multiplication(c2,A).  [para(105(a,1),38(a,1,1)),rewrite([63(4),33(6)]),flip(a)].
8.77/9.11	257 multiplication(c1,addition(A,c(c1))) = multiplication(c1,A).  [para(111(a,1),38(a,1,1)),rewrite([63(4),33(6)]),flip(a)].
8.77/9.11	481 addition(multiplication(A,B),multiplication(addition(A,one),C)) = addition(C,multiplication(A,addition(C,B))).  [para(38(a,1),114(a,1,2)),rewrite([33(1)]),flip(a)].
8.77/9.11	667 multiplication(c2,addition(A,addition(B,c(c2)))) = multiplication(c2,addition(A,B)).  [para(229(a,1),38(a,1,1)),rewrite([38(5),33(8),35(8,R),33(7)]),flip(a)].
8.77/9.11	722 multiplication(c1,addition(A,addition(B,c(c1)))) = multiplication(c1,addition(A,B)).  [para(257(a,1),38(a,1,1)),rewrite([38(5),33(8),35(8,R),33(7)]),flip(a)].
8.77/9.11	728 multiplication(c1,c1) = c1.  [para(110(a,1),257(a,1,2)),rewrite([27(3)]),flip(a)].
8.77/9.11	733 multiplication(c1,multiplication(c1,A)) = multiplication(c1,A).  [para(728(a,1),36(a,1,1)),flip(a)].
8.77/9.11	781 multiplication(c1,addition(A,multiplication(c1,B))) = multiplication(c1,addition(B,A)).  [para(733(a,1),38(a,1,1)),rewrite([38(5),33(7)]),flip(a)].
8.77/9.11	15910 addition(A,multiplication(c2,addition(B,A))) = addition(A,multiplication(c2,B)).  [para(229(a,1),481(a,1,1)),rewrite([33(5),149(5),28(4),33(3),35(8,R),33(7),667(9)]),flip(a)].
8.77/9.11	15912 addition(A,multiplication(c1,addition(B,A))) = addition(A,multiplication(c1,B)).  [para(257(a,1),481(a,1,1)),rewrite([33(5),168(5),28(4),33(3),35(8,R),33(7),722(9)]),flip(a)].
8.77/9.11	18901 addition(c(c1),multiplication(c2,c1)) = addition(c2,c(c1)).  [para(110(a,1),15910(a,1,2,2)),rewrite([27(5),33(4)]),flip(a)].
8.77/9.11	18981 multiplication(c1,multiplication(c2,c1)) = multiplication(c1,c2).  [para(18901(a,1),781(a,2,2)),rewrite([111(8),33(6),63(6),257(11)])].
8.77/9.11	18998 addition(multiplication(c1,c2),multiplication(A,c1)) = multiplication(addition(A,multiplication(c1,c2)),c1).  [para(18981(a,1),64(a,1,1))].
8.77/9.11	19102 addition(c(c2),multiplication(c1,c2)) = addition(c1,c(c2)).  [para(104(a,1),15912(a,1,2,2)),rewrite([27(5),33(4)]),flip(a)].
8.77/9.11	19178 $F.  [para(19102(a,1),15910(a,1,2,2)),rewrite([229(9),18998(7),62(5),33(3),168(3),28(3),105(10),33(8),63(8)]),unit_del(a,39)].
8.77/9.11	
8.77/9.11	% SZS output end Refutation
8.77/9.11	============================== end of proof ==========================
8.77/9.11	
8.77/9.11	============================== STATISTICS ============================
8.77/9.11	
8.77/9.11	Given=1139. Generated=227679. Kept=19148. proofs=1.
8.77/9.11	Usable=950. Sos=9999. Demods=2319. Limbo=6, Disabled=8230. Hints=0.
8.77/9.11	Megabytes=17.63.
8.77/9.11	User_CPU=7.97, System_CPU=0.16, Wall_clock=8.
8.77/9.11	
8.77/9.11	============================== end of statistics =====================
8.77/9.11	
8.77/9.11	============================== end of search =========================
8.77/9.11	
8.77/9.11	THEOREM PROVED
8.77/9.11	% SZS status Theorem
8.77/9.11	
8.77/9.11	Exiting with 1 proof.
8.77/9.11	
8.77/9.11	Process 18566 exit (max_proofs) Thu Jul  2 08:31:01 2020
8.77/9.11	Prover9 interrupted
8.77/9.11	EOF