0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer   : n003.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% DateTime   : Tue Jul 13 17:15:24 EDT 2021
0.13/0.34	% CPUTime    : 
0.43/1.00	============================== Prover9 ===============================
0.43/1.00	Prover9 (32) version 2009-11A, November 2009.
0.43/1.00	Process 20946 was started by sandbox2 on n003.cluster.edu,
0.43/1.00	Tue Jul 13 17:15:25 2021
0.43/1.00	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_20604_n003.cluster.edu".
0.43/1.00	============================== end of head ===========================
0.43/1.00	
0.43/1.00	============================== INPUT =================================
0.43/1.00	
0.43/1.00	% Reading from file /tmp/Prover9_20604_n003.cluster.edu
0.43/1.00	
0.43/1.00	set(prolog_style_variables).
0.43/1.00	set(auto2).
0.43/1.00	    % set(auto2) -> set(auto).
0.43/1.00	    % set(auto) -> set(auto_inference).
0.43/1.00	    % set(auto) -> set(auto_setup).
0.43/1.00	    % set(auto_setup) -> set(predicate_elim).
0.43/1.00	    % set(auto_setup) -> assign(eq_defs, unfold).
0.43/1.00	    % set(auto) -> set(auto_limits).
0.43/1.00	    % set(auto_limits) -> assign(max_weight, "100.000").
0.43/1.00	    % set(auto_limits) -> assign(sos_limit, 20000).
0.43/1.00	    % set(auto) -> set(auto_denials).
0.43/1.00	    % set(auto) -> set(auto_process).
0.43/1.00	    % set(auto2) -> assign(new_constants, 1).
0.43/1.00	    % set(auto2) -> assign(fold_denial_max, 3).
0.43/1.00	    % set(auto2) -> assign(max_weight, "200.000").
0.43/1.00	    % set(auto2) -> assign(max_hours, 1).
0.43/1.00	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.43/1.00	    % set(auto2) -> assign(max_seconds, 0).
0.43/1.00	    % set(auto2) -> assign(max_minutes, 5).
0.43/1.00	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.43/1.00	    % set(auto2) -> set(sort_initial_sos).
0.43/1.00	    % set(auto2) -> assign(sos_limit, -1).
0.43/1.00	    % set(auto2) -> assign(lrs_ticks, 3000).
0.43/1.00	    % set(auto2) -> assign(max_megs, 400).
0.43/1.00	    % set(auto2) -> assign(stats, some).
0.43/1.00	    % set(auto2) -> clear(echo_input).
0.43/1.00	    % set(auto2) -> set(quiet).
0.43/1.00	    % set(auto2) -> clear(print_initial_clauses).
0.43/1.00	    % set(auto2) -> clear(print_given).
0.43/1.00	assign(lrs_ticks,-1).
0.43/1.00	assign(sos_limit,10000).
0.43/1.00	assign(order,kbo).
0.43/1.00	set(lex_order_vars).
0.43/1.00	clear(print_given).
0.43/1.00	
0.43/1.00	% formulas(sos).  % not echoed (11 formulas)
0.43/1.00	
0.43/1.00	============================== end of input ==========================
0.43/1.00	
0.43/1.00	% From the command line: assign(max_seconds, 1200).
0.43/1.00	
0.43/1.00	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.43/1.01	
0.43/1.01	% Formulas that are not ordinary clauses:
0.43/1.01	1 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	2 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	3 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) <-> in(A,C) & D = B)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	4 (all A all B all C all D (in(B,D) & A = C <-> in(ordered_pair(A,B),cartesian_product2(singleton(C),D)))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	5 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	6 (all A ((all B -in(B,A)) <-> A = empty_set)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	7 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	8 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	9 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.01	10 -(all A all B (A != empty_set -> cartesian_product2(singleton(B),A) != empty_set & empty_set != cartesian_product2(A,singleton(B)))) # label(t130_zfmisc_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.43/1.01	
0.43/1.01	============================== end of process non-clausal formulas ===
0.43/1.01	
0.43/1.01	============================== PROCESS INITIAL CLAUSES ===============
0.43/1.01	
0.43/1.01	============================== PREDICATE ELIMINATION =================
0.43/1.01	
0.43/1.01	============================== end predicate elimination =============
0.43/1.01	
0.43/1.01	Auto_denials:  (non-Horn, no changes).
0.43/1.01	
0.43/1.01	Term ordering decisions:
0.43/1.01	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. singleton=1. f1=1.
0.43/1.01	
0.43/1.01	============================== end of process initial clauses ========
0.43/1.02	
0.43/1.02	============================== CLAUSES FOR SEARCH ====================
0.43/1.02	
0.43/1.02	============================== end of clauses for search =============
0.43/1.02	
0.43/1.02	============================== SEARCH ================================
0.43/1.02	
0.43/1.02	% Starting search at 0.01 seconds.
0.43/1.02	
0.43/1.02	============================== PROOF =================================
0.43/1.02	% SZS status Theorem
0.43/1.02	% SZS output start Refutation
0.43/1.02	
0.43/1.02	% Proof 1 at 0.02 (+ 0.00) seconds.
0.43/1.02	% Length of proof is 25.
0.43/1.02	% Level of proof is 7.
0.43/1.02	% Maximum clause weight is 19.000.
0.43/1.02	% Given clauses 51.
0.43/1.02	
0.43/1.02	3 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) <-> in(A,C) & D = B)) # label(t129_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.02	4 (all A all B all C all D (in(B,D) & A = C <-> in(ordered_pair(A,B),cartesian_product2(singleton(C),D)))) # label(t128_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.02	5 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
0.43/1.02	6 (all A ((all B -in(B,A)) <-> A = empty_set)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.43/1.02	7 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.43/1.02	10 -(all A all B (A != empty_set -> cartesian_product2(singleton(B),A) != empty_set & empty_set != cartesian_product2(A,singleton(B)))) # label(t130_zfmisc_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.43/1.02	13 in(f1(A),A) | empty_set = A # label(d1_xboole_0) # label(axiom).  [clausify(6)].
0.43/1.02	14 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom).  [clausify(7)].
0.43/1.02	15 unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B) # label(d5_tarski) # label(axiom).  [clausify(5)].
0.43/1.02	16 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)).  [copy(15),rewrite([14(3)]),flip(a)].
0.43/1.02	17 cartesian_product2(singleton(c4),c3) = empty_set | cartesian_product2(c3,singleton(c4)) = empty_set # label(t130_zfmisc_1) # label(negated_conjecture).  [clausify(10)].
0.43/1.02	19 empty_set != c3 # label(t130_zfmisc_1) # label(negated_conjecture).  [clausify(10)].
0.43/1.02	20 c3 != empty_set.  [copy(19),flip(a)].
0.43/1.02	23 -in(A,B) | empty_set != B # label(d1_xboole_0) # label(axiom).  [clausify(6)].
0.43/1.02	33 in(ordered_pair(A,B),cartesian_product2(C,singleton(D))) | -in(A,C) | D != B # label(t129_zfmisc_1) # label(axiom).  [clausify(3)].
0.43/1.02	34 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,singleton(D))) | -in(A,C) | D != B.  [copy(33),rewrite([16(1)])].
0.43/1.02	35 -in(A,B) | C != D | in(ordered_pair(D,A),cartesian_product2(singleton(C),B)) # label(t128_zfmisc_1) # label(axiom).  [clausify(4)].
0.43/1.02	36 -in(A,B) | C != D | in(unordered_pair(singleton(D),unordered_pair(A,D)),cartesian_product2(singleton(C),B)).  [copy(35),rewrite([16(3),14(4)])].
0.43/1.02	38 -in(A,empty_set).  [ur(23,b,xx)].
0.43/1.02	44 in(unordered_pair(singleton(f1(A)),unordered_pair(B,f1(A))),cartesian_product2(A,singleton(C))) | C != B | empty_set = A.  [resolve(34,b,13,a),rewrite([14(4)])].
0.43/1.02	45 A != B | in(unordered_pair(singleton(B),unordered_pair(B,f1(C))),cartesian_product2(singleton(A),C)) | empty_set = C.  [resolve(36,a,13,a),rewrite([14(4)])].
0.43/1.02	61 in(unordered_pair(singleton(A),unordered_pair(A,f1(B))),cartesian_product2(singleton(A),B)) | empty_set = B.  [xx_res(45,a)].
0.43/1.02	68 cartesian_product2(c3,singleton(c4)) = empty_set.  [para(17(a,1),61(a,2)),flip(c),unit_del(b,38),unit_del(c,20)].
0.43/1.02	91 in(unordered_pair(singleton(f1(A)),unordered_pair(B,f1(A))),cartesian_product2(A,singleton(B))) | empty_set = A.  [xx_res(44,b)].
0.43/1.02	130 $F.  [para(68(a,1),91(a,2)),flip(b),unit_del(a,38),unit_del(b,20)].
0.43/1.02	
0.43/1.02	% SZS output end Refutation
0.43/1.02	============================== end of proof ==========================
0.43/1.02	
0.43/1.02	============================== STATISTICS ============================
0.43/1.02	
0.43/1.02	Given=51. Generated=241. Kept=110. proofs=1.
0.43/1.02	Usable=50. Sos=48. Demods=3. Limbo=4, Disabled=25. Hints=0.
0.43/1.02	Megabytes=0.17.
0.43/1.02	User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
0.43/1.02	
0.43/1.02	============================== end of statistics =====================
0.43/1.02	
0.43/1.02	============================== end of search =========================
0.43/1.02	
0.43/1.02	THEOREM PROVED
0.43/1.02	% SZS status Theorem
0.43/1.02	
0.43/1.02	Exiting with 1 proof.
0.43/1.02	
0.43/1.02	Process 20946 exit (max_proofs) Tue Jul 13 17:15:25 2021
0.43/1.02	Prover9 interrupted
0.43/1.02	EOF