0.03/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.35	% Computer   : n024.cluster.edu
0.12/0.35	% Model      : x86_64 x86_64
0.12/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.35	% Memory     : 8042.1875MB
0.12/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.35	% CPULimit   : 960
0.12/0.35	% DateTime   : Thu Jul  2 08:29:05 EDT 2020
0.12/0.35	% CPUTime    : 
0.78/1.11	============================== Prover9 ===============================
0.78/1.11	Prover9 (32) version 2009-11A, November 2009.
0.78/1.11	Process 6169 was started by sandbox2 on n024.cluster.edu,
0.78/1.11	Thu Jul  2 08:29:06 2020
0.78/1.11	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_6015_n024.cluster.edu".
0.78/1.11	============================== end of head ===========================
0.78/1.11	
0.78/1.11	============================== INPUT =================================
0.78/1.11	
0.78/1.11	% Reading from file /tmp/Prover9_6015_n024.cluster.edu
0.78/1.11	
0.78/1.11	set(prolog_style_variables).
0.78/1.11	set(auto2).
0.78/1.11	    % set(auto2) -> set(auto).
0.78/1.11	    % set(auto) -> set(auto_inference).
0.78/1.11	    % set(auto) -> set(auto_setup).
0.78/1.11	    % set(auto_setup) -> set(predicate_elim).
0.78/1.11	    % set(auto_setup) -> assign(eq_defs, unfold).
0.78/1.11	    % set(auto) -> set(auto_limits).
0.78/1.11	    % set(auto_limits) -> assign(max_weight, "100.000").
0.78/1.11	    % set(auto_limits) -> assign(sos_limit, 20000).
0.78/1.11	    % set(auto) -> set(auto_denials).
0.78/1.11	    % set(auto) -> set(auto_process).
0.78/1.11	    % set(auto2) -> assign(new_constants, 1).
0.78/1.11	    % set(auto2) -> assign(fold_denial_max, 3).
0.78/1.11	    % set(auto2) -> assign(max_weight, "200.000").
0.78/1.11	    % set(auto2) -> assign(max_hours, 1).
0.78/1.11	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.78/1.11	    % set(auto2) -> assign(max_seconds, 0).
0.78/1.11	    % set(auto2) -> assign(max_minutes, 5).
0.78/1.11	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.78/1.11	    % set(auto2) -> set(sort_initial_sos).
0.78/1.11	    % set(auto2) -> assign(sos_limit, -1).
0.78/1.11	    % set(auto2) -> assign(lrs_ticks, 3000).
0.78/1.11	    % set(auto2) -> assign(max_megs, 400).
0.78/1.11	    % set(auto2) -> assign(stats, some).
0.78/1.11	    % set(auto2) -> clear(echo_input).
0.78/1.11	    % set(auto2) -> set(quiet).
0.78/1.11	    % set(auto2) -> clear(print_initial_clauses).
0.78/1.11	    % set(auto2) -> clear(print_given).
0.78/1.11	assign(lrs_ticks,-1).
0.78/1.11	assign(sos_limit,10000).
0.78/1.11	assign(order,kbo).
0.78/1.11	set(lex_order_vars).
0.78/1.11	clear(print_given).
0.78/1.11	
0.78/1.11	% formulas(sos).  % not echoed (17 formulas)
0.78/1.11	
0.78/1.11	============================== end of input ==========================
0.78/1.11	
0.78/1.11	% From the command line: assign(max_seconds, 960).
0.78/1.11	
0.78/1.11	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.78/1.11	
0.78/1.11	% Formulas that are not ordinary clauses:
0.78/1.11	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].
0.78/1.11	2 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	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].
0.78/1.11	6 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	8 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	9 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	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].
0.78/1.11	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	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].
0.78/1.11	13 (all X0 (test(X0) <-> (exists X1 complement(X1,X0)))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
0.78/1.11	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].
0.81/1.31	15 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> X1 = c(X0)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	16 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.81/1.31	
0.81/1.31	============================== end of process non-clausal formulas ===
0.81/1.31	
0.81/1.31	============================== PROCESS INITIAL CLAUSES ===============
0.81/1.31	
0.81/1.31	============================== PREDICATE ELIMINATION =================
0.81/1.31	18 -test(A) | complement(f1(A),A) # label(test_1) # label(axiom).  [clausify(13)].
0.81/1.31	19 test(c4) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.31	20 test(c5) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.31	21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(16)].
0.81/1.31	22 test(A) | -complement(B,A) # label(test_1) # label(axiom).  [clausify(13)].
0.81/1.31	Derived: complement(f1(c4),c4).  [resolve(18,a,19,a)].
0.81/1.31	Derived: complement(f1(c5),c5).  [resolve(18,a,20,a)].
0.81/1.31	Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,a,21,a)].
0.81/1.31	Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,a,22,a)].
0.81/1.31	23 -test(A) | -complement(A,B) | c(A) = B # label(test_3) # label(axiom).  [clausify(15)].
0.81/1.31	Derived: -complement(c4,A) | c(c4) = A.  [resolve(23,a,19,a)].
0.81/1.31	Derived: -complement(c5,A) | c(c5) = A.  [resolve(23,a,20,a)].
0.81/1.31	Derived: -complement(A,B) | c(A) = B | c(A) = zero.  [resolve(23,a,21,a)].
0.81/1.31	Derived: -complement(A,B) | c(A) = B | -complement(C,A).  [resolve(23,a,22,a)].
0.81/1.31	24 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom).  [clausify(15)].
0.81/1.31	Derived: complement(c4,A) | c(c4) != A.  [resolve(24,a,19,a)].
0.81/1.31	Derived: complement(c5,A) | c(c5) != A.  [resolve(24,a,20,a)].
0.81/1.31	Derived: complement(A,B) | c(A) != B | c(A) = zero.  [resolve(24,a,21,a)].
0.81/1.31	Derived: complement(A,B) | c(A) != B | -complement(C,A).  [resolve(24,a,22,a)].
0.81/1.31	
0.81/1.31	============================== end predicate elimination =============
0.81/1.31	
0.81/1.31	Auto_denials:  (non-Horn, no changes).
0.81/1.31	
0.81/1.31	Term ordering decisions:
0.81/1.31	Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. c3=1. c4=1. c5=1. multiplication=1. addition=1. c=1. f1=1.
0.81/1.31	
0.81/1.31	============================== end of process initial clauses ========
0.81/1.31	
0.81/1.31	============================== CLAUSES FOR SEARCH ====================
0.81/1.31	
0.81/1.31	============================== end of clauses for search =============
0.81/1.31	
0.81/1.31	============================== SEARCH ================================
0.81/1.31	
0.81/1.31	% Starting search at 0.01 seconds.
0.81/1.31	
0.81/1.31	============================== PROOF =================================
0.81/1.31	% SZS status Theorem
0.81/1.31	% SZS output start Refutation
0.81/1.31	
0.81/1.31	% Proof 1 at 0.21 (+ 0.01) seconds.
0.81/1.31	% Length of proof is 41.
0.81/1.31	% Level of proof is 8.
0.81/1.31	% Maximum clause weight is 48.000.
0.81/1.31	% Given clauses 234.
0.81/1.31	
0.81/1.31	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].
0.81/1.31	2 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	3 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	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].
0.81/1.31	6 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	7 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	8 (all A all B (leq(A,B) <-> B = addition(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	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].
0.81/1.31	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].
0.81/1.31	15 (all X0 all X1 (test(X0) -> (complement(X0,X1) <-> X1 = c(X0)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
0.81/1.31	17 -(all X0 all X1 all X2 all X3 all X4 (test(X3) & test(X4) -> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) & leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.81/1.31	19 test(c4) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.31	24 -test(A) | complement(A,B) | c(A) != B # label(test_3) # label(axiom).  [clausify(15)].
0.81/1.31	25 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(2)].
0.81/1.31	27 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(6)].
0.81/1.31	28 addition(A,zero) = A # label(additive_identity) # label(axiom).  [clausify(7)].
0.81/1.31	30 multiplication(zero,A) = zero # label(left_annihilation) # label(axiom).  [clausify(11)].
0.81/1.31	31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(3)].
0.81/1.31	34 multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) # label(multiplicative_associativity) # label(axiom).  [clausify(12)].
0.81/1.31	35 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(1)].
0.81/1.31	36 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(5)].
0.81/1.31	37 -leq(addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3)),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))),multiplication(c(c4),c3))) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.31	38 -leq(addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2)))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,addition(multiplication(c4,c1),multiplication(c(c4),c2))))).  [copy(37),rewrite([31(15),31(47)])].
0.81/1.31	40 leq(A,B) | addition(A,B) != B # label(order) # label(axiom).  [clausify(8)].
0.81/1.31	42 -complement(A,B) | multiplication(A,B) = zero # label(test_2) # label(axiom).  [clausify(14)].
0.81/1.31	43 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
0.81/1.31	44 -complement(A,B) | addition(A,B) = one.  [copy(43),rewrite([31(2)])].
0.81/1.31	55 complement(c4,A) | c(c4) != A.  [resolve(24,a,19,a)].
0.81/1.31	64 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(28(a,1),35(a,2,1)),rewrite([30(3),31(3)])].
0.81/1.31	69 leq(A,A).  [resolve(40,b,27,a)].
0.81/1.31	96 complement(c4,c(c4)).  [resolve(55,b,27,a(flip)),rewrite([27(6)])].
0.81/1.31	111 addition(c4,c(c4)) = one.  [resolve(96,a,44,a)].
0.81/1.31	112 multiplication(c4,c(c4)) = zero.  [resolve(96,a,42,a)].
0.81/1.31	277 multiplication(c4,multiplication(c(c4),A)) = zero.  [para(112(a,1),34(a,1,1)),rewrite([30(2)]),flip(a)].
0.81/1.31	279 multiplication(c4,addition(A,c(c4))) = multiplication(c4,A).  [para(112(a,1),36(a,1,1)),rewrite([64(4),31(6)]),flip(a)].
0.81/1.31	506 multiplication(c4,addition(A,multiplication(c(c4),B))) = multiplication(c4,A).  [para(277(a,1),36(a,1,1)),rewrite([64(4),31(7)]),flip(a)].
0.81/1.31	509 -leq(addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1))),addition(multiplication(c4,c1),multiplication(c(c4),c3))) | -leq(addition(multiplication(c4,c1),multiplication(c(c4),c3)),addition(multiplication(c(c4),c3),multiplication(c4,multiplication(c4,c1)))).  [back_rewrite(38),rewrite([506(14),506(41)])].
0.81/1.31	1365 multiplication(c4,c4) = c4.  [para(111(a,1),279(a,1,2)),rewrite([25(3)]),flip(a)].
0.81/1.31	1380 multiplication(c4,multiplication(c4,A)) = multiplication(c4,A).  [para(1365(a,1),34(a,1,1)),flip(a)].
0.81/1.31	1392 $F.  [back_rewrite(509),rewrite([1380(9),31(8),1380(34),31(33)]),merge(b),unit_del(a,69)].
0.81/1.31	
0.81/1.31	% SZS output end Refutation
0.81/1.31	============================== end of proof ==========================
0.81/1.31	
0.81/1.31	============================== STATISTICS ============================
0.81/1.31	
0.81/1.31	Given=234. Generated=5472. Kept=1363. proofs=1.
0.81/1.31	Usable=198. Sos=995. Demods=247. Limbo=12, Disabled=195. Hints=0.
0.81/1.31	Megabytes=1.58.
0.81/1.31	User_CPU=0.21, System_CPU=0.01, Wall_clock=0.
0.81/1.31	
0.81/1.31	============================== end of statistics =====================
0.81/1.31	
0.81/1.31	============================== end of search =========================
0.81/1.31	
0.81/1.31	THEOREM PROVED
0.81/1.31	% SZS status Theorem
0.81/1.31	
0.81/1.31	Exiting with 1 proof.
0.81/1.31	
0.81/1.31	Process 6169 exit (max_proofs) Thu Jul  2 08:29:06 2020
0.81/1.31	Prover9 interrupted
0.81/1.31	EOF