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
0.02/0.24	% Computer   : n009.star.cs.uiowa.edu
0.02/0.24	% Model      : x86_64 x86_64
0.02/0.24	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.24	% Memory     : 32218.625MB
0.02/0.24	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.24	% CPULimit   : 300
0.02/0.24	% DateTime   : Sat Jul 14 04:22:55 CDT 2018
0.02/0.24	% CPUTime    : 
0.26/0.56	============================== Prover9 ===============================
0.26/0.56	Prover9 (32) version 2009-11A, November 2009.
0.26/0.56	Process 15355 was started by sandbox on n009.star.cs.uiowa.edu,
0.26/0.56	Sat Jul 14 04:22:55 2018
0.26/0.56	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15323_n009.star.cs.uiowa.edu".
0.26/0.56	============================== end of head ===========================
0.26/0.56	
0.26/0.56	============================== INPUT =================================
0.26/0.56	
0.26/0.56	% Reading from file /tmp/Prover9_15323_n009.star.cs.uiowa.edu
0.26/0.56	
0.26/0.56	set(prolog_style_variables).
0.26/0.56	set(auto2).
0.26/0.56	    % set(auto2) -> set(auto).
0.26/0.56	    % set(auto) -> set(auto_inference).
0.26/0.56	    % set(auto) -> set(auto_setup).
0.26/0.56	    % set(auto_setup) -> set(predicate_elim).
0.26/0.56	    % set(auto_setup) -> assign(eq_defs, unfold).
0.26/0.56	    % set(auto) -> set(auto_limits).
0.26/0.56	    % set(auto_limits) -> assign(max_weight, "100.000").
0.26/0.56	    % set(auto_limits) -> assign(sos_limit, 20000).
0.26/0.56	    % set(auto) -> set(auto_denials).
0.26/0.56	    % set(auto) -> set(auto_process).
0.26/0.56	    % set(auto2) -> assign(new_constants, 1).
0.26/0.56	    % set(auto2) -> assign(fold_denial_max, 3).
0.26/0.56	    % set(auto2) -> assign(max_weight, "200.000").
0.26/0.56	    % set(auto2) -> assign(max_hours, 1).
0.26/0.56	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.26/0.56	    % set(auto2) -> assign(max_seconds, 0).
0.26/0.56	    % set(auto2) -> assign(max_minutes, 5).
0.26/0.56	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.26/0.56	    % set(auto2) -> set(sort_initial_sos).
0.26/0.56	    % set(auto2) -> assign(sos_limit, -1).
0.26/0.56	    % set(auto2) -> assign(lrs_ticks, 3000).
0.26/0.56	    % set(auto2) -> assign(max_megs, 400).
0.26/0.56	    % set(auto2) -> assign(stats, some).
0.26/0.56	    % set(auto2) -> clear(echo_input).
0.26/0.56	    % set(auto2) -> set(quiet).
0.26/0.56	    % set(auto2) -> clear(print_initial_clauses).
0.26/0.56	    % set(auto2) -> clear(print_given).
0.26/0.56	assign(lrs_ticks,-1).
0.26/0.56	assign(sos_limit,10000).
0.26/0.56	assign(order,kbo).
0.26/0.56	set(lex_order_vars).
0.26/0.56	clear(print_given).
0.26/0.56	
0.26/0.56	% formulas(sos).  % not echoed (35 formulas)
0.26/0.56	
0.26/0.56	============================== end of input ==========================
0.26/0.56	
0.26/0.56	% From the command line: assign(max_seconds, 300).
0.26/0.56	
0.26/0.56	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.26/0.56	
0.26/0.56	% Formulas that are not ordinary clauses:
0.26/0.56	1 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	2 (exists A (-empty(A) & relation(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	3 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	4 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	5 (all A (-empty(A) -> (exists B (-empty(B) & element(B,powerset(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	6 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	7 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	8 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	9 (exists A (function(A) & relation(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	10 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	11 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	12 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	13 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	14 (all A (relation(A) & -empty(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	15 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	16 (all A all B (function(B) & relation(B) -> (A = relation_dom(B) & (all C (in(C,A) -> C = apply(B,C))) <-> B = identity_relation(A)))) # label(t34_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	17 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	18 (all A (empty(A) -> empty(relation_dom(A)) & relation(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	19 (all A all B -(A != B & empty(B) & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	20 (all A (relation(identity_relation(A)) & function(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	21 (all A (relation(A) & function(A) -> ((all B all C (in(C,relation_dom(A)) & apply(A,B) = apply(A,C) & in(B,relation_dom(A)) -> C = B)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	22 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	23 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	24 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	25 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	26 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	27 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	28 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.26/0.56	29 -(all A one_to_one(identity_relation(A))) # label(t52_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.26/0.56	
0.26/0.56	============================== end of process non-clausal formulas ===
0.26/0.56	
0.26/0.56	============================== PROCESS INITIAL CLAUSES ===============
0.26/0.56	
0.26/0.56	============================== PREDICATE ELIMINATION =================
0.26/0.56	30 -relation(A) | empty(A) | -empty(relation_dom(A)) # label(fc5_relat_1) # label(axiom).  [clausify(14)].
0.26/0.57	31 relation(c1) # label(rc2_relat_1) # label(axiom).  [clausify(2)].
0.26/0.57	32 relation(c2) # label(rc1_funct_1) # label(axiom).  [clausify(9)].
0.26/0.57	33 relation(empty_set) # label(fc4_relat_1_AndLHS) # label(axiom).  [assumption].
0.26/0.57	34 relation(c5) # label(rc3_relat_1) # label(axiom).  [clausify(17)].
0.26/0.57	35 relation(empty_set) # label(fc12_relat_1_AndRHS_AndRHS) # label(axiom).  [assumption].
0.26/0.57	36 relation(c6) # label(rc1_relat_1) # label(axiom).  [clausify(28)].
0.26/0.57	37 relation(identity_relation(A)) # label(dt_k6_relat_1) # label(axiom).  [clausify(3)].
0.26/0.57	38 relation(identity_relation(A)) # label(fc2_funct_1) # label(axiom).  [clausify(20)].
0.26/0.57	39 -empty(A) | relation(A) # label(cc1_relat_1) # label(axiom).  [clausify(25)].
0.26/0.57	40 -empty(A) | relation(relation_dom(A)) # label(fc7_relat_1) # label(axiom).  [clausify(18)].
0.26/0.57	Derived: empty(c1) | -empty(relation_dom(c1)).  [resolve(30,a,31,a)].
0.26/0.57	Derived: empty(c2) | -empty(relation_dom(c2)).  [resolve(30,a,32,a)].
0.26/0.57	Derived: empty(empty_set) | -empty(relation_dom(empty_set)).  [resolve(30,a,33,a)].
0.26/0.57	Derived: empty(c5) | -empty(relation_dom(c5)).  [resolve(30,a,34,a)].
0.26/0.57	Derived: empty(c6) | -empty(relation_dom(c6)).  [resolve(30,a,36,a)].
0.26/0.57	Derived: empty(identity_relation(A)) | -empty(relation_dom(identity_relation(A))).  [resolve(30,a,37,a)].
0.26/0.57	Derived: empty(relation_dom(A)) | -empty(relation_dom(relation_dom(A))) | -empty(A).  [resolve(30,a,40,b)].
0.26/0.57	41 -relation(A) | -function(A) | in(f6(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.26/0.57	Derived: -function(c1) | in(f6(c1),relation_dom(c1)) | one_to_one(c1).  [resolve(41,a,31,a)].
0.26/0.57	Derived: -function(c2) | in(f6(c2),relation_dom(c2)) | one_to_one(c2).  [resolve(41,a,32,a)].
0.26/0.57	Derived: -function(empty_set) | in(f6(empty_set),relation_dom(empty_set)) | one_to_one(empty_set).  [resolve(41,a,33,a)].
0.26/0.57	Derived: -function(c5) | in(f6(c5),relation_dom(c5)) | one_to_one(c5).  [resolve(41,a,34,a)].
0.26/0.57	Derived: -function(c6) | in(f6(c6),relation_dom(c6)) | one_to_one(c6).  [resolve(41,a,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | in(f6(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(41,a,37,a)].
0.26/0.57	Derived: -function(A) | in(f6(A),relation_dom(A)) | one_to_one(A) | -empty(A).  [resolve(41,a,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | in(f6(relation_dom(A)),relation_dom(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(41,a,40,b)].
0.26/0.57	42 -relation(A) | -function(A) | in(f5(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.26/0.57	Derived: -function(c1) | in(f5(c1),relation_dom(c1)) | one_to_one(c1).  [resolve(42,a,31,a)].
0.26/0.57	Derived: -function(c2) | in(f5(c2),relation_dom(c2)) | one_to_one(c2).  [resolve(42,a,32,a)].
0.26/0.57	Derived: -function(empty_set) | in(f5(empty_set),relation_dom(empty_set)) | one_to_one(empty_set).  [resolve(42,a,33,a)].
0.26/0.57	Derived: -function(c5) | in(f5(c5),relation_dom(c5)) | one_to_one(c5).  [resolve(42,a,34,a)].
0.26/0.57	Derived: -function(c6) | in(f5(c6),relation_dom(c6)) | one_to_one(c6).  [resolve(42,a,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | in(f5(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(42,a,37,a)].
0.26/0.57	Derived: -function(A) | in(f5(A),relation_dom(A)) | one_to_one(A) | -empty(A).  [resolve(42,a,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | in(f5(relation_dom(A)),relation_dom(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(42,a,40,b)].
0.26/0.57	43 -relation(A) | -function(A) | f6(A) != f5(A) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.26/0.57	Derived: -function(c1) | f6(c1) != f5(c1) | one_to_one(c1).  [resolve(43,a,31,a)].
0.26/0.57	Derived: -function(c2) | f6(c2) != f5(c2) | one_to_one(c2).  [resolve(43,a,32,a)].
0.26/0.57	Derived: -function(empty_set) | f6(empty_set) != f5(empty_set) | one_to_one(empty_set).  [resolve(43,a,33,a)].
0.26/0.57	Derived: -function(c5) | f6(c5) != f5(c5) | one_to_one(c5).  [resolve(43,a,34,a)].
0.26/0.57	Derived: -function(c6) | f6(c6) != f5(c6) | one_to_one(c6).  [resolve(43,a,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | f6(identity_relation(A)) != f5(identity_relation(A)) | one_to_one(identity_relation(A)).  [resolve(43,a,37,a)].
0.26/0.57	Derived: -function(A) | f6(A) != f5(A) | one_to_one(A) | -empty(A).  [resolve(43,a,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | f6(relation_dom(A)) != f5(relation_dom(A)) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(43,a,40,b)].
0.26/0.57	44 -function(A) | -relation(A) | relation_dom(A) = B | identity_relation(B) != A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.26/0.57	Derived: -function(c1) | relation_dom(c1) = A | identity_relation(A) != c1.  [resolve(44,b,31,a)].
0.26/0.57	Derived: -function(c2) | relation_dom(c2) = A | identity_relation(A) != c2.  [resolve(44,b,32,a)].
0.26/0.57	Derived: -function(empty_set) | relation_dom(empty_set) = A | identity_relation(A) != empty_set.  [resolve(44,b,33,a)].
0.26/0.57	Derived: -function(c5) | relation_dom(c5) = A | identity_relation(A) != c5.  [resolve(44,b,34,a)].
0.26/0.57	Derived: -function(c6) | relation_dom(c6) = A | identity_relation(A) != c6.  [resolve(44,b,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | relation_dom(identity_relation(A)) = B | identity_relation(B) != identity_relation(A).  [resolve(44,b,37,a)].
0.26/0.57	Derived: -function(A) | relation_dom(A) = B | identity_relation(B) != A | -empty(A).  [resolve(44,b,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | relation_dom(relation_dom(A)) = B | identity_relation(B) != relation_dom(A) | -empty(A).  [resolve(44,b,40,b)].
0.26/0.57	45 -relation(A) | -function(A) | apply(A,f6(A)) = apply(A,f5(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.26/0.57	Derived: -function(c1) | apply(c1,f6(c1)) = apply(c1,f5(c1)) | one_to_one(c1).  [resolve(45,a,31,a)].
0.26/0.57	Derived: -function(c2) | apply(c2,f6(c2)) = apply(c2,f5(c2)) | one_to_one(c2).  [resolve(45,a,32,a)].
0.26/0.57	Derived: -function(empty_set) | apply(empty_set,f6(empty_set)) = apply(empty_set,f5(empty_set)) | one_to_one(empty_set).  [resolve(45,a,33,a)].
0.26/0.57	Derived: -function(c5) | apply(c5,f6(c5)) = apply(c5,f5(c5)) | one_to_one(c5).  [resolve(45,a,34,a)].
0.26/0.57	Derived: -function(c6) | apply(c6,f6(c6)) = apply(c6,f5(c6)) | one_to_one(c6).  [resolve(45,a,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | apply(identity_relation(A),f6(identity_relation(A))) = apply(identity_relation(A),f5(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(45,a,37,a)].
0.26/0.57	Derived: -function(A) | apply(A,f6(A)) = apply(A,f5(A)) | one_to_one(A) | -empty(A).  [resolve(45,a,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | apply(relation_dom(A),f6(relation_dom(A))) = apply(relation_dom(A),f5(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(45,a,40,b)].
0.26/0.57	46 -function(A) | -relation(A) | -in(B,C) | apply(A,B) = B | identity_relation(C) != A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.26/0.57	Derived: -function(c1) | -in(A,B) | apply(c1,A) = A | identity_relation(B) != c1.  [resolve(46,b,31,a)].
0.26/0.57	Derived: -function(c2) | -in(A,B) | apply(c2,A) = A | identity_relation(B) != c2.  [resolve(46,b,32,a)].
0.26/0.57	Derived: -function(empty_set) | -in(A,B) | apply(empty_set,A) = A | identity_relation(B) != empty_set.  [resolve(46,b,33,a)].
0.26/0.57	Derived: -function(c5) | -in(A,B) | apply(c5,A) = A | identity_relation(B) != c5.  [resolve(46,b,34,a)].
0.26/0.57	Derived: -function(c6) | -in(A,B) | apply(c6,A) = A | identity_relation(B) != c6.  [resolve(46,b,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | -in(B,C) | apply(identity_relation(A),B) = B | identity_relation(C) != identity_relation(A).  [resolve(46,b,37,a)].
0.26/0.57	Derived: -function(A) | -in(B,C) | apply(A,B) = B | identity_relation(C) != A | -empty(A).  [resolve(46,b,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | -in(B,C) | apply(relation_dom(A),B) = B | identity_relation(C) != relation_dom(A) | -empty(A).  [resolve(46,b,40,b)].
0.26/0.57	47 -function(A) | -relation(A) | relation_dom(A) != B | in(f4(B,A),B) | identity_relation(B) = A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.26/0.57	Derived: -function(c1) | relation_dom(c1) != A | in(f4(A,c1),A) | identity_relation(A) = c1.  [resolve(47,b,31,a)].
0.26/0.57	Derived: -function(c2) | relation_dom(c2) != A | in(f4(A,c2),A) | identity_relation(A) = c2.  [resolve(47,b,32,a)].
0.26/0.57	Derived: -function(empty_set) | relation_dom(empty_set) != A | in(f4(A,empty_set),A) | identity_relation(A) = empty_set.  [resolve(47,b,33,a)].
0.26/0.57	Derived: -function(c5) | relation_dom(c5) != A | in(f4(A,c5),A) | identity_relation(A) = c5.  [resolve(47,b,34,a)].
0.26/0.57	Derived: -function(c6) | relation_dom(c6) != A | in(f4(A,c6),A) | identity_relation(A) = c6.  [resolve(47,b,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | relation_dom(identity_relation(A)) != B | in(f4(B,identity_relation(A)),B) | identity_relation(B) = identity_relation(A).  [resolve(47,b,37,a)].
0.26/0.57	Derived: -function(A) | relation_dom(A) != B | in(f4(B,A),B) | identity_relation(B) = A | -empty(A).  [resolve(47,b,39,b)].
0.26/0.57	Derived: -function(relation_dom(A)) | relation_dom(relation_dom(A)) != B | in(f4(B,relation_dom(A)),B) | identity_relation(B) = relation_dom(A) | -empty(A).  [resolve(47,b,40,b)].
0.26/0.57	48 -function(A) | -relation(A) | relation_dom(A) != B | apply(A,f4(B,A)) != f4(B,A) | identity_relation(B) = A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.26/0.57	Derived: -function(c1) | relation_dom(c1) != A | apply(c1,f4(A,c1)) != f4(A,c1) | identity_relation(A) = c1.  [resolve(48,b,31,a)].
0.26/0.57	Derived: -function(c2) | relation_dom(c2) != A | apply(c2,f4(A,c2)) != f4(A,c2) | identity_relation(A) = c2.  [resolve(48,b,32,a)].
0.26/0.57	Derived: -function(empty_set) | relation_dom(empty_set) != A | apply(empty_set,f4(A,empty_set)) != f4(A,empty_set) | identity_relation(A) = empty_set.  [resolve(48,b,33,a)].
0.26/0.57	Derived: -function(c5) | relation_dom(c5) != A | apply(c5,f4(A,c5)) != f4(A,c5) | identity_relation(A) = c5.  [resolve(48,b,34,a)].
0.26/0.57	Derived: -function(c6) | relation_dom(c6) != A | apply(c6,f4(A,c6)) != f4(A,c6) | identity_relation(A) = c6.  [resolve(48,b,36,a)].
0.26/0.57	Derived: -function(identity_relation(A)) | relation_dom(identity_relation(A)) != B | apply(identity_relation(A),f4(B,identity_relation(A))) != f4(B,identity_relation(A)) | identity_relation(B) = identity_relation(A).  [resolve(48,b,37,a)].
0.26/0.57	Derived: -function(A) | relation_dom(A) != B | apply(A,f4(B,A)) != f4(B,A) | identity_relation(B) = A | -empty(A).  [resolve(48,b,39,b)].
0.47/0.79	Derived: -function(relation_dom(A)) | relation_dom(relation_dom(A)) != B | apply(relation_dom(A),f4(B,relation_dom(A))) != f4(B,relation_dom(A)) | identity_relation(B) = relation_dom(A) | -empty(A).  [resolve(48,b,40,b)].
0.47/0.79	49 -relation(A) | -function(A) | -in(B,relation_dom(A)) | apply(A,B) != apply(A,C) | -in(C,relation_dom(A)) | B = C | -one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.47/0.79	Derived: -function(c1) | -in(A,relation_dom(c1)) | apply(c1,A) != apply(c1,B) | -in(B,relation_dom(c1)) | A = B | -one_to_one(c1).  [resolve(49,a,31,a)].
0.47/0.79	Derived: -function(c2) | -in(A,relation_dom(c2)) | apply(c2,A) != apply(c2,B) | -in(B,relation_dom(c2)) | A = B | -one_to_one(c2).  [resolve(49,a,32,a)].
0.47/0.79	Derived: -function(empty_set) | -in(A,relation_dom(empty_set)) | apply(empty_set,A) != apply(empty_set,B) | -in(B,relation_dom(empty_set)) | A = B | -one_to_one(empty_set).  [resolve(49,a,33,a)].
0.47/0.79	Derived: -function(c5) | -in(A,relation_dom(c5)) | apply(c5,A) != apply(c5,B) | -in(B,relation_dom(c5)) | A = B | -one_to_one(c5).  [resolve(49,a,34,a)].
0.47/0.79	Derived: -function(c6) | -in(A,relation_dom(c6)) | apply(c6,A) != apply(c6,B) | -in(B,relation_dom(c6)) | A = B | -one_to_one(c6).  [resolve(49,a,36,a)].
0.47/0.79	Derived: -function(identity_relation(A)) | -in(B,relation_dom(identity_relation(A))) | apply(identity_relation(A),B) != apply(identity_relation(A),C) | -in(C,relation_dom(identity_relation(A))) | B = C | -one_to_one(identity_relation(A)).  [resolve(49,a,37,a)].
0.47/0.79	Derived: -function(A) | -in(B,relation_dom(A)) | apply(A,B) != apply(A,C) | -in(C,relation_dom(A)) | B = C | -one_to_one(A) | -empty(A).  [resolve(49,a,39,b)].
0.47/0.79	Derived: -function(relation_dom(A)) | -in(B,relation_dom(relation_dom(A))) | apply(relation_dom(A),B) != apply(relation_dom(A),C) | -in(C,relation_dom(relation_dom(A))) | B = C | -one_to_one(relation_dom(A)) | -empty(A).  [resolve(49,a,40,b)].
0.47/0.79	50 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom).  [clausify(24)].
0.47/0.79	51 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom).  [clausify(26)].
0.47/0.79	52 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom).  [clausify(24)].
0.47/0.79	Derived: element(A,powerset(A)).  [resolve(50,b,51,a)].
0.47/0.79	
0.47/0.79	============================== end predicate elimination =============
0.47/0.79	
0.47/0.79	Auto_denials:  (non-Horn, no changes).
0.47/0.79	
0.47/0.79	Term ordering decisions:
0.47/0.79	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. apply=1. f4=1. relation_dom=1. identity_relation=1. powerset=1. f1=1. f2=1. f3=1. f5=1. f6=1.
0.47/0.79	
0.47/0.79	============================== end of process initial clauses ========
0.47/0.79	
0.47/0.79	============================== CLAUSES FOR SEARCH ====================
0.47/0.79	
0.47/0.79	============================== end of clauses for search =============
0.47/0.79	
0.47/0.79	============================== SEARCH ================================
0.47/0.79	
0.47/0.79	% Starting search at 0.02 seconds.
0.47/0.79	
0.47/0.79	============================== PROOF =================================
0.47/0.79	% SZS status Theorem
0.47/0.79	% SZS output start Refutation
0.47/0.79	
0.47/0.79	% Proof 1 at 0.23 (+ 0.01) seconds.
0.47/0.79	% Length of proof is 38.
0.47/0.79	% Level of proof is 11.
0.47/0.79	% Maximum clause weight is 18.000.
0.47/0.79	% Given clauses 404.
0.47/0.79	
0.47/0.79	3 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/0.79	16 (all A all B (function(B) & relation(B) -> (A = relation_dom(B) & (all C (in(C,A) -> C = apply(B,C))) <-> B = identity_relation(A)))) # label(t34_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/0.79	20 (all A (relation(identity_relation(A)) & function(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/0.79	21 (all A (relation(A) & function(A) -> ((all B all C (in(C,relation_dom(A)) & apply(A,B) = apply(A,C) & in(B,relation_dom(A)) -> C = B)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/0.79	29 -(all A one_to_one(identity_relation(A))) # label(t52_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.47/0.79	37 relation(identity_relation(A)) # label(dt_k6_relat_1) # label(axiom).  [clausify(3)].
0.47/0.79	41 -relation(A) | -function(A) | in(f6(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.47/0.79	42 -relation(A) | -function(A) | in(f5(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.47/0.79	43 -relation(A) | -function(A) | f6(A) != f5(A) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.47/0.79	44 -function(A) | -relation(A) | relation_dom(A) = B | identity_relation(B) != A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.47/0.79	45 -relation(A) | -function(A) | apply(A,f6(A)) = apply(A,f5(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(21)].
0.47/0.79	46 -function(A) | -relation(A) | -in(B,C) | apply(A,B) = B | identity_relation(C) != A # label(t34_funct_1) # label(axiom).  [clausify(16)].
0.47/0.79	58 function(identity_relation(A)) # label(fc2_funct_1) # label(axiom).  [clausify(20)].
0.47/0.79	65 -one_to_one(identity_relation(c7)) # label(t52_funct_1) # label(negated_conjecture).  [clausify(29)].
0.47/0.79	88 -function(identity_relation(A)) | in(f6(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(41,a,37,a)].
0.47/0.79	89 in(f6(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [copy(88),unit_del(a,58)].
0.47/0.79	98 -function(identity_relation(A)) | in(f5(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(42,a,37,a)].
0.47/0.79	99 in(f5(identity_relation(A)),relation_dom(identity_relation(A))) | one_to_one(identity_relation(A)).  [copy(98),unit_del(a,58)].
0.47/0.79	108 -function(identity_relation(A)) | f6(identity_relation(A)) != f5(identity_relation(A)) | one_to_one(identity_relation(A)).  [resolve(43,a,37,a)].
0.47/0.79	109 f6(identity_relation(A)) != f5(identity_relation(A)) | one_to_one(identity_relation(A)).  [copy(108),unit_del(a,58)].
0.47/0.79	118 -function(identity_relation(A)) | relation_dom(identity_relation(A)) = B | identity_relation(B) != identity_relation(A).  [resolve(44,b,37,a)].
0.47/0.79	119 relation_dom(identity_relation(A)) = B | identity_relation(B) != identity_relation(A).  [copy(118),unit_del(a,58)].
0.47/0.79	129 -function(identity_relation(A)) | apply(identity_relation(A),f6(identity_relation(A))) = apply(identity_relation(A),f5(identity_relation(A))) | one_to_one(identity_relation(A)).  [resolve(45,a,37,a)].
0.47/0.79	130 apply(identity_relation(A),f6(identity_relation(A))) = apply(identity_relation(A),f5(identity_relation(A))) | one_to_one(identity_relation(A)).  [copy(129),unit_del(a,58)].
0.47/0.79	139 -function(identity_relation(A)) | -in(B,C) | apply(identity_relation(A),B) = B | identity_relation(C) != identity_relation(A).  [resolve(46,b,37,a)].
0.47/0.79	140 -in(A,B) | apply(identity_relation(C),A) = A | identity_relation(B) != identity_relation(C).  [copy(139),unit_del(a,58)].
0.47/0.79	225 relation_dom(identity_relation(A)) = A.  [xx_res(119,b)].
0.47/0.79	235 in(f5(identity_relation(A)),A) | one_to_one(identity_relation(A)).  [back_rewrite(99),rewrite([225(4)])].
0.47/0.79	236 in(f6(identity_relation(A)),A) | one_to_one(identity_relation(A)).  [back_rewrite(89),rewrite([225(4)])].
0.47/0.79	239 apply(identity_relation(c7),f6(identity_relation(c7))) = apply(identity_relation(c7),f5(identity_relation(c7))).  [resolve(130,b,65,a)].
0.47/0.79	366 one_to_one(identity_relation(A)) | apply(identity_relation(B),f5(identity_relation(A))) = f5(identity_relation(A)) | identity_relation(A) != identity_relation(B).  [resolve(235,a,140,a)].
0.47/0.79	380 one_to_one(identity_relation(A)) | apply(identity_relation(B),f6(identity_relation(A))) = f6(identity_relation(A)) | identity_relation(A) != identity_relation(B).  [resolve(236,a,140,a)].
0.47/0.79	2073 one_to_one(identity_relation(A)) | apply(identity_relation(A),f5(identity_relation(A))) = f5(identity_relation(A)).  [xx_res(366,c)].
0.47/0.79	2503 apply(identity_relation(c7),f5(identity_relation(c7))) = f5(identity_relation(c7)).  [resolve(2073,a,65,a)].
0.47/0.79	2504 apply(identity_relation(c7),f6(identity_relation(c7))) = f5(identity_relation(c7)).  [back_rewrite(239),rewrite([2503(12)])].
0.47/0.79	2769 one_to_one(identity_relation(A)) | apply(identity_relation(A),f6(identity_relation(A))) = f6(identity_relation(A)).  [xx_res(380,c)].
0.47/0.79	2770 f6(identity_relation(c7)) = f5(identity_relation(c7)).  [resolve(2769,a,65,a),rewrite([2504(6)]),flip(a)].
0.47/0.79	2771 $F.  [resolve(2770,a,109,a),unit_del(a,65)].
0.47/0.79	
0.47/0.79	% SZS output end Refutation
0.47/0.79	============================== end of proof ==========================
0.47/0.79	
0.47/0.79	============================== STATISTICS ============================
0.47/0.79	
0.47/0.79	Given=404. Generated=4539. Kept=2695. proofs=1.
0.47/0.79	Usable=378. Sos=2075. Demods=30. Limbo=0, Disabled=373. Hints=0.
0.47/0.79	Megabytes=3.92.
0.47/0.79	User_CPU=0.23, System_CPU=0.01, Wall_clock=0.
0.47/0.79	
0.47/0.79	============================== end of statistics =====================
0.47/0.79	
0.47/0.79	============================== end of search =========================
0.47/0.79	
0.47/0.79	THEOREM PROVED
0.47/0.79	% SZS status Theorem
0.47/0.79	
0.47/0.79	Exiting with 1 proof.
0.47/0.79	
0.47/0.79	Process 15355 exit (max_proofs) Sat Jul 14 04:22:55 2018
0.47/0.79	Prover9 interrupted
0.47/0.80	EOF