0.07/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n026.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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 16:11:59 EDT 2021
0.12/0.33	% CPUTime    : 
0.73/1.00	============================== Prover9 ===============================
0.73/1.00	Prover9 (32) version 2009-11A, November 2009.
0.73/1.00	Process 2794 was started by sandbox on n026.cluster.edu,
0.73/1.00	Tue Jul 13 16:11:59 2021
0.73/1.00	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_2641_n026.cluster.edu".
0.73/1.00	============================== end of head ===========================
0.73/1.00	
0.73/1.00	============================== INPUT =================================
0.73/1.00	
0.73/1.00	% Reading from file /tmp/Prover9_2641_n026.cluster.edu
0.73/1.00	
0.73/1.00	set(prolog_style_variables).
0.73/1.00	set(auto2).
0.73/1.00	    % set(auto2) -> set(auto).
0.73/1.00	    % set(auto) -> set(auto_inference).
0.73/1.00	    % set(auto) -> set(auto_setup).
0.73/1.00	    % set(auto_setup) -> set(predicate_elim).
0.73/1.00	    % set(auto_setup) -> assign(eq_defs, unfold).
0.73/1.00	    % set(auto) -> set(auto_limits).
0.73/1.00	    % set(auto_limits) -> assign(max_weight, "100.000").
0.73/1.00	    % set(auto_limits) -> assign(sos_limit, 20000).
0.73/1.00	    % set(auto) -> set(auto_denials).
0.73/1.00	    % set(auto) -> set(auto_process).
0.73/1.00	    % set(auto2) -> assign(new_constants, 1).
0.73/1.00	    % set(auto2) -> assign(fold_denial_max, 3).
0.73/1.00	    % set(auto2) -> assign(max_weight, "200.000").
0.73/1.00	    % set(auto2) -> assign(max_hours, 1).
0.73/1.00	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.73/1.00	    % set(auto2) -> assign(max_seconds, 0).
0.73/1.00	    % set(auto2) -> assign(max_minutes, 5).
0.73/1.00	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.73/1.00	    % set(auto2) -> set(sort_initial_sos).
0.73/1.00	    % set(auto2) -> assign(sos_limit, -1).
0.73/1.00	    % set(auto2) -> assign(lrs_ticks, 3000).
0.73/1.00	    % set(auto2) -> assign(max_megs, 400).
0.73/1.00	    % set(auto2) -> assign(stats, some).
0.73/1.00	    % set(auto2) -> clear(echo_input).
0.73/1.00	    % set(auto2) -> set(quiet).
0.73/1.00	    % set(auto2) -> clear(print_initial_clauses).
0.73/1.00	    % set(auto2) -> clear(print_given).
0.73/1.00	assign(lrs_ticks,-1).
0.73/1.00	assign(sos_limit,10000).
0.73/1.00	assign(order,kbo).
0.73/1.00	set(lex_order_vars).
0.73/1.00	clear(print_given).
0.73/1.00	
0.73/1.00	% formulas(sos).  % not echoed (17 formulas)
0.73/1.00	
0.73/1.00	============================== end of input ==========================
0.73/1.00	
0.73/1.00	% From the command line: assign(max_seconds, 1200).
0.73/1.00	
0.73/1.00	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.73/1.00	
0.73/1.00	% Formulas that are not ordinary clauses:
0.73/1.00	1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	2 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	3 (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].
0.73/1.00	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	5 (all A addition(A,zero) = A) # label(additive_identity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	6 (all A multiplication(A,zero) = zero) # label(right_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	7 (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].
0.73/1.00	8 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	10 (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].
0.73/1.00	11 (all A zero = multiplication(zero,A)) # label(left_annihilation) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	13 (all X0 (-test(X0) -> c(X0) = zero)) # label(test_4) # label(axiom) # label(non_clause).  [assumption].
0.73/1.00	14 (all X0 all X1 (complement(X1,X0) <-> zero = multiplication(X0,X1) & addition(X0,X1) = one & zero = multiplication(X1,X0))) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	15 (all X0 ((exists X1 complement(X1,X0)) <-> test(X0))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	16 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	17 -(all X0 all X1 (test(X0) & test(X1) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.81/1.09	
0.81/1.09	============================== end of process non-clausal formulas ===
0.81/1.09	
0.81/1.09	============================== PROCESS INITIAL CLAUSES ===============
0.81/1.09	
0.81/1.09	============================== PREDICATE ELIMINATION =================
0.81/1.09	18 complement(f1(A),A) | -test(A) # label(test_1) # label(axiom).  [clausify(15)].
0.81/1.09	19 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.09	20 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.09	21 test(A) | c(A) = zero # label(test_4) # label(axiom).  [clausify(13)].
0.81/1.09	22 -complement(A,B) | test(B) # label(test_1) # label(axiom).  [clausify(15)].
0.81/1.09	Derived: complement(f1(c1),c1).  [resolve(18,b,19,a)].
0.81/1.09	Derived: complement(f1(c2),c2).  [resolve(18,b,20,a)].
0.81/1.09	Derived: complement(f1(A),A) | c(A) = zero.  [resolve(18,b,21,a)].
0.81/1.09	Derived: complement(f1(A),A) | -complement(B,A).  [resolve(18,b,22,b)].
0.81/1.09	23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(16)].
0.81/1.09	Derived: c(c1) != A | complement(c1,A).  [resolve(23,a,19,a)].
0.81/1.09	Derived: c(c2) != A | complement(c2,A).  [resolve(23,a,20,a)].
0.81/1.09	Derived: c(A) != B | complement(A,B) | c(A) = zero.  [resolve(23,a,21,a)].
0.81/1.09	Derived: c(A) != B | complement(A,B) | -complement(C,A).  [resolve(23,a,22,b)].
0.81/1.09	24 -test(A) | c(A) = B | -complement(A,B) # label(test_3) # label(axiom).  [clausify(16)].
0.81/1.09	Derived: c(c1) = A | -complement(c1,A).  [resolve(24,a,19,a)].
0.81/1.09	Derived: c(c2) = A | -complement(c2,A).  [resolve(24,a,20,a)].
0.81/1.09	Derived: c(A) = B | -complement(A,B) | c(A) = zero.  [resolve(24,a,21,a)].
0.81/1.09	Derived: c(A) = B | -complement(A,B) | -complement(C,A).  [resolve(24,a,22,b)].
0.81/1.09	
0.81/1.09	============================== end predicate elimination =============
0.81/1.09	
0.81/1.09	Auto_denials:  (non-Horn, no changes).
0.81/1.09	
0.81/1.09	Term ordering decisions:
0.81/1.09	Function symbol KB weights:  zero=1. one=1. c1=1. c2=1. multiplication=1. addition=1. c=1. f1=1.
0.81/1.09	
0.81/1.09	============================== end of process initial clauses ========
0.81/1.09	
0.81/1.09	============================== CLAUSES FOR SEARCH ====================
0.81/1.09	
0.81/1.09	============================== end of clauses for search =============
0.81/1.09	
0.81/1.09	============================== SEARCH ================================
0.81/1.09	
0.81/1.09	% Starting search at 0.01 seconds.
0.81/1.09	
0.81/1.09	============================== PROOF =================================
0.81/1.09	% SZS status Theorem
0.81/1.09	% SZS output start Refutation
0.81/1.09	
0.81/1.09	% Proof 1 at 0.11 (+ 0.01) seconds.
0.81/1.09	% Length of proof is 53.
0.81/1.09	% Level of proof is 8.
0.81/1.09	% Maximum clause weight is 46.000.
0.81/1.09	% Given clauses 209.
0.81/1.09	
0.81/1.09	1 (all A multiplication(A,one) = A) # label(multiplicative_right_identity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	2 (all C all B all A addition(addition(A,B),C) = addition(A,addition(B,C))) # label(additive_associativity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	3 (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].
0.81/1.09	4 (all A multiplication(one,A) = A) # label(multiplicative_left_identity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	7 (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].
0.81/1.09	8 (all A all B (B = addition(A,B) <-> leq(A,B))) # label(order) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	9 (all A all B addition(B,A) = addition(A,B)) # label(additive_commutativity) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	12 (all A A = addition(A,A)) # label(additive_idempotence) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	14 (all X0 all X1 (complement(X1,X0) <-> zero = multiplication(X0,X1) & addition(X0,X1) = one & zero = multiplication(X1,X0))) # label(test_2) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	15 (all X0 ((exists X1 complement(X1,X0)) <-> test(X0))) # label(test_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	16 (all X0 all X1 (test(X0) -> (c(X0) = X1 <-> complement(X0,X1)))) # label(test_3) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	17 -(all X0 all X1 (test(X0) & test(X1) -> leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) & leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one))) # label(goals) # label(negated_conjecture) # label(non_clause).  [assumption].
0.81/1.09	18 complement(f1(A),A) | -test(A) # label(test_1) # label(axiom).  [clausify(15)].
0.81/1.09	19 test(c1) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.09	20 test(c2) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.09	23 -test(A) | c(A) != B | complement(A,B) # label(test_3) # label(axiom).  [clausify(16)].
0.81/1.09	25 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [clausify(1)].
0.81/1.09	26 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [clausify(4)].
0.81/1.09	30 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [clausify(12)].
0.81/1.09	31 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [clausify(9)].
0.81/1.09	32 addition(addition(A,B),C) = addition(A,addition(B,C)) # label(additive_associativity) # label(axiom).  [clausify(2)].
0.81/1.09	33 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(32),rewrite([31(2)]),flip(a)].
0.81/1.09	35 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) # label(right_distributivity) # label(axiom).  [clausify(3)].
0.81/1.09	36 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B) # label(left_distributivity) # label(axiom).  [clausify(7)].
0.81/1.09	37 -leq(one,addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2)))) | -leq(addition(addition(addition(addition(multiplication(c2,c1),multiplication(c(c2),c1)),multiplication(c1,c2)),multiplication(c(c1),c2)),multiplication(c(c1),c(c2))),one) # label(goals) # label(negated_conjecture).  [clausify(17)].
0.81/1.09	38 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1)))),one).  [copy(37),rewrite([36(9),31(11),31(16),33(16,R),31(15),31(22),33(22,R),31(21),33(21,R),31(20),36(31),31(33),31(38),33(38,R),31(37),31(44),33(44,R),31(43),33(43,R),31(42)])].
0.81/1.09	39 addition(A,B) != B | leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.81/1.09	40 addition(A,B) = B | -leq(A,B) # label(order) # label(axiom).  [clausify(8)].
0.81/1.09	42 -complement(A,B) | addition(B,A) = one # label(test_2) # label(axiom).  [clausify(14)].
0.81/1.09	43 -complement(A,B) | addition(A,B) = one.  [copy(42),rewrite([31(2)])].
0.81/1.09	47 complement(f1(c1),c1).  [resolve(18,b,19,a)].
0.81/1.09	48 complement(f1(c2),c2).  [resolve(18,b,20,a)].
0.81/1.09	51 c(c1) != A | complement(c1,A).  [resolve(23,a,19,a)].
0.81/1.09	52 c(c2) != A | complement(c2,A).  [resolve(23,a,20,a)].
0.81/1.09	62 addition(A,addition(A,B)) = addition(A,B).  [para(33(a,1),30(a,1)),rewrite([31(1),31(2),33(2,R),30(1),31(3)])].
0.81/1.09	68 -leq(one,addition(multiplication(c1,c2),addition(multiplication(c(c1),c2),addition(multiplication(c(c1),c(c2)),multiplication(addition(c2,c(c2)),c1))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one).  [para(33(a,1),38(b,1,2)),rewrite([35(42)])].
0.81/1.10	74 addition(A,addition(B,C)) != addition(A,B) | leq(C,addition(A,B)).  [para(33(a,2),39(a,1))].
0.81/1.10	84 addition(c1,f1(c1)) = one.  [resolve(47,a,43,a),rewrite([31(4)])].
0.81/1.10	87 addition(c2,f1(c2)) = one.  [resolve(48,a,43,a),rewrite([31(4)])].
0.81/1.10	92 complement(c1,c(c1)).  [resolve(51,a,30,a(flip)),rewrite([30(6)])].
0.81/1.10	94 complement(c2,c(c2)).  [resolve(52,a,30,a(flip)),rewrite([30(6)])].
0.81/1.10	105 leq(A,addition(A,B)).  [resolve(62,a,39,a)].
0.81/1.10	107 -leq(one,addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2)))))) | -leq(addition(multiplication(c1,c2),addition(multiplication(addition(c2,c(c2)),c1),multiplication(c(c1),addition(c2,c(c2))))),one).  [para(33(a,1),68(a,2,2)),rewrite([35(20)])].
0.81/1.10	120 addition(c1,c(c1)) = one.  [resolve(92,a,43,a)].
0.81/1.10	130 addition(c2,c(c2)) = one.  [resolve(94,a,43,a)].
0.81/1.10	134 -leq(addition(one,multiplication(c1,c2)),one).  [back_rewrite(107),rewrite([130(8),26(7),130(11),25(9),120(8),31(6),130(14),26(13),130(17),25(15),120(14),31(12)]),unit_del(a,105)].
0.81/1.10	150 addition(one,multiplication(c1,c2)) != one.  [ur(39,b,134,a),rewrite([31(7),62(7)])].
0.81/1.10	235 addition(one,c1) = one.  [para(84(a,1),62(a,1,2)),rewrite([31(3),84(7)])].
0.81/1.10	269 addition(A,multiplication(c1,A)) = A.  [para(235(a,1),36(a,2,1)),rewrite([26(2),26(5)])].
0.81/1.10	297 addition(one,c2) = one.  [para(87(a,1),62(a,1,2)),rewrite([31(3),87(7)])].
0.81/1.10	554 leq(multiplication(c1,A),addition(B,A)).  [para(269(a,1),74(a,1,2)),xx(a)].
0.81/1.10	628 leq(multiplication(c1,c2),one).  [para(297(a,1),554(a,2))].
0.81/1.10	671 $F.  [resolve(628,a,40,b),rewrite([31(5)]),unit_del(a,150)].
0.81/1.10	
0.81/1.10	% SZS output end Refutation
0.81/1.10	============================== end of proof ==========================
0.81/1.10	
0.81/1.10	============================== STATISTICS ============================
0.81/1.10	
0.81/1.10	Given=209. Generated=2425. Kept=642. proofs=1.
0.81/1.10	Usable=175. Sos=371. Demods=104. Limbo=0, Disabled=133. Hints=0.
0.81/1.10	Megabytes=0.66.
0.81/1.10	User_CPU=0.11, System_CPU=0.01, Wall_clock=1.
0.81/1.10	
0.81/1.10	============================== end of statistics =====================
0.81/1.10	
0.81/1.10	============================== end of search =========================
0.81/1.10	
0.81/1.10	THEOREM PROVED
0.81/1.10	% SZS status Theorem
0.81/1.10	
0.81/1.10	Exiting with 1 proof.
0.81/1.10	
0.81/1.10	Process 2794 exit (max_proofs) Tue Jul 13 16:12:00 2021
0.81/1.10	Prover9 interrupted
0.81/1.10	EOF