0.11/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n019.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 11:49:07 EDT 2019
0.12/0.33	% CPUTime    : 
0.42/1.00	============================== Prover9 ===============================
0.42/1.00	Prover9 (32) version 2009-11A, November 2009.
0.42/1.00	Process 12312 was started by sandbox on n019.cluster.edu,
0.42/1.00	Thu Aug 29 11:49:08 2019
0.42/1.00	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_12142_n019.cluster.edu".
0.42/1.00	============================== end of head ===========================
0.42/1.00	
0.42/1.00	============================== INPUT =================================
0.42/1.00	
0.42/1.00	% Reading from file /tmp/Prover9_12142_n019.cluster.edu
0.42/1.00	
0.42/1.00	set(prolog_style_variables).
0.42/1.00	set(auto2).
0.42/1.00	    % set(auto2) -> set(auto).
0.42/1.00	    % set(auto) -> set(auto_inference).
0.42/1.00	    % set(auto) -> set(auto_setup).
0.42/1.00	    % set(auto_setup) -> set(predicate_elim).
0.42/1.00	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.00	    % set(auto) -> set(auto_limits).
0.42/1.00	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.00	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.00	    % set(auto) -> set(auto_denials).
0.42/1.00	    % set(auto) -> set(auto_process).
0.42/1.00	    % set(auto2) -> assign(new_constants, 1).
0.42/1.00	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.00	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.00	    % set(auto2) -> assign(max_hours, 1).
0.42/1.00	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.00	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.00	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.00	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.00	    % set(auto2) -> set(sort_initial_sos).
0.42/1.00	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.00	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.00	    % set(auto2) -> assign(max_megs, 400).
0.42/1.00	    % set(auto2) -> assign(stats, some).
0.42/1.00	    % set(auto2) -> clear(echo_input).
0.42/1.00	    % set(auto2) -> set(quiet).
0.42/1.00	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.00	    % set(auto2) -> clear(print_given).
0.42/1.00	assign(lrs_ticks,-1).
0.42/1.00	assign(sos_limit,10000).
0.42/1.00	assign(order,kbo).
0.42/1.00	set(lex_order_vars).
0.42/1.00	clear(print_given).
0.42/1.00	
0.42/1.00	% formulas(sos).  % not echoed (43 formulas)
0.42/1.00	
0.42/1.00	============================== end of input ==========================
0.42/1.00	
0.42/1.00	% From the command line: assign(max_seconds, 180).
0.42/1.00	
0.42/1.00	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.00	
0.42/1.00	% Formulas that are not ordinary clauses:
0.42/1.00	1 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	2 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	4 (all A (relation(A) & empty(A) & function(A) -> relation(A) & function(A) & one_to_one(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	5 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	6 (all A (relation(A) & function(A) -> ((all B all C (in(B,relation_dom(A)) & apply(A,C) = apply(A,B) & in(C,relation_dom(A)) -> B = C)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	7 (exists A (relation(A) & function(A) & one_to_one(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	9 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	10 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	11 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	12 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	13 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	14 (all A all B all C -(element(B,powerset(C)) & empty(C) & in(A,B))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	15 (all A all B -(empty(A) & empty(B) & A != B)) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.42/1.00	16 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	17 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	18 (all A all B (A = empty_set | A = singleton(B) <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	19 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	20 (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].
0.42/1.01	21 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	22 (all A (relation(A) & function(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D (in(D,relation_dom(A)) & apply(A,D) = C)))))))) # label(d5_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	23 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	24 (all A all B (function(B) & relation(B) -> (in(A,relation_dom(B)) -> relation_image(B,singleton(A)) = singleton(apply(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	25 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	26 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	27 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	28 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	29 (all A (empty(A) -> empty(relation_dom(A)) & relation(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	30 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	31 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	32 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	33 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	34 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	35 (all A all B (relation(B) -> (in(A,relation_rng(B)) <-> empty_set != relation_inverse_image(B,singleton(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	36 (exists A (relation(A) & function(A) & empty(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	37 -(all A (function(A) & relation(A) -> ((all B subset(relation_inverse_image(A,relation_image(A,B)),B)) -> one_to_one(A)))) # label(t153_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.42/1.01	
0.42/1.01	============================== end of process non-clausal formulas ===
0.42/1.01	
0.42/1.01	============================== PROCESS INITIAL CLAUSES ===============
0.42/1.01	
0.42/1.01	============================== PREDICATE ELIMINATION =================
0.42/1.01	38 -relation(A) | -in(B,relation_rng(A)) | relation_inverse_image(A,singleton(B)) != empty_set # label(t142_funct_1) # label(axiom).  [clausify(35)].
0.42/1.01	39 relation(empty_set) # label(fc12_relat_1_AndRHS_AndRHS) # label(axiom).  [assumption].
0.42/1.01	40 relation(c1) # label(rc3_funct_1) # label(axiom).  [clausify(7)].
0.42/1.01	41 relation(c3) # label(rc2_relat_1) # label(axiom).  [clausify(10)].
0.42/1.01	42 relation(c5) # label(rc3_relat_1) # label(axiom).  [clausify(21)].
0.42/1.01	43 relation(empty_set) # label(fc4_relat_1_AndRHS) # label(axiom).  [assumption].
0.42/1.01	44 relation(c6) # label(rc1_relat_1) # label(axiom).  [clausify(32)].
0.42/1.01	45 relation(c7) # label(rc1_funct_1) # label(axiom).  [clausify(33)].
0.42/1.01	46 relation(c8) # label(rc2_funct_1) # label(axiom).  [clausify(36)].
0.42/1.01	47 relation(c9) # label(t153_funct_1) # label(negated_conjecture).  [clausify(37)].
0.42/1.01	Derived: -in(A,relation_rng(empty_set)) | relation_inverse_image(empty_set,singleton(A)) != empty_set.  [resolve(38,a,39,a)].
0.42/1.01	Derived: -in(A,relation_rng(c1)) | relation_inverse_image(c1,singleton(A)) != empty_set.  [resolve(38,a,40,a)].
0.42/1.01	Derived: -in(A,relation_rng(c3)) | relation_inverse_image(c3,singleton(A)) != empty_set.  [resolve(38,a,41,a)].
0.42/1.01	Derived: -in(A,relation_rng(c5)) | relation_inverse_image(c5,singleton(A)) != empty_set.  [resolve(38,a,42,a)].
0.42/1.01	Derived: -in(A,relation_rng(c6)) | relation_inverse_image(c6,singleton(A)) != empty_set.  [resolve(38,a,44,a)].
0.42/1.01	Derived: -in(A,relation_rng(c7)) | relation_inverse_image(c7,singleton(A)) != empty_set.  [resolve(38,a,45,a)].
0.42/1.01	Derived: -in(A,relation_rng(c8)) | relation_inverse_image(c8,singleton(A)) != empty_set.  [resolve(38,a,46,a)].
0.42/1.01	Derived: -in(A,relation_rng(c9)) | relation_inverse_image(c9,singleton(A)) != empty_set.  [resolve(38,a,47,a)].
0.42/1.01	48 -empty(A) | relation(A) # label(cc1_relat_1) # label(axiom).  [clausify(19)].
0.42/1.01	Derived: -empty(A) | -in(B,relation_rng(A)) | relation_inverse_image(A,singleton(B)) != empty_set.  [resolve(48,b,38,a)].
0.42/1.01	49 -empty(A) | relation(relation_rng(A)) # label(fc8_relat_1) # label(axiom).  [clausify(2)].
0.42/1.01	Derived: -empty(A) | -in(B,relation_rng(relation_rng(A))) | relation_inverse_image(relation_rng(A),singleton(B)) != empty_set.  [resolve(49,b,38,a)].
0.42/1.01	50 -empty(A) | relation(relation_dom(A)) # label(fc7_relat_1) # label(axiom).  [clausify(29)].
0.42/1.01	Derived: -empty(A) | -in(B,relation_rng(relation_dom(A))) | relation_inverse_image(relation_dom(A),singleton(B)) != empty_set.  [resolve(50,b,38,a)].
0.42/1.01	51 empty(A) | -relation(A) | -empty(relation_dom(A)) # label(fc5_relat_1) # label(axiom).  [clausify(23)].
0.42/1.01	Derived: empty(empty_set) | -empty(relation_dom(empty_set)).  [resolve(51,b,39,a)].
0.42/1.01	Derived: empty(c1) | -empty(relation_dom(c1)).  [resolve(51,b,40,a)].
0.42/1.01	Derived: empty(c3) | -empty(relation_dom(c3)).  [resolve(51,b,41,a)].
0.42/1.01	Derived: empty(c5) | -empty(relation_dom(c5)).  [resolve(51,b,42,a)].
0.42/1.01	Derived: empty(c6) | -empty(relation_dom(c6)).  [resolve(51,b,44,a)].
0.42/1.01	Derived: empty(c7) | -empty(relation_dom(c7)).  [resolve(51,b,45,a)].
0.42/1.01	Derived: empty(c8) | -empty(relation_dom(c8)).  [resolve(51,b,46,a)].
0.42/1.01	Derived: empty(c9) | -empty(relation_dom(c9)).  [resolve(51,b,47,a)].
0.42/1.01	Derived: empty(relation_rng(A)) | -empty(relation_dom(relation_rng(A))) | -empty(A).  [resolve(51,b,49,b)].
0.42/1.01	Derived: empty(relation_dom(A)) | -empty(relation_dom(relation_dom(A))) | -empty(A).  [resolve(51,b,50,b)].
0.42/1.01	52 -relation(A) | empty(A) | -empty(relation_rng(A)) # label(fc6_relat_1) # label(axiom).  [clausify(26)].
0.42/1.01	Derived: empty(empty_set) | -empty(relation_rng(empty_set)).  [resolve(52,a,39,a)].
0.42/1.01	Derived: empty(c1) | -empty(relation_rng(c1)).  [resolve(52,a,40,a)].
0.42/1.01	Derived: empty(c3) | -empty(relation_rng(c3)).  [resolve(52,a,41,a)].
0.42/1.01	Derived: empty(c5) | -empty(relation_rng(c5)).  [resolve(52,a,42,a)].
0.42/1.01	Derived: empty(c6) | -empty(relation_rng(c6)).  [resolve(52,a,44,a)].
0.42/1.01	Derived: empty(c7) | -empty(relation_rng(c7)).  [resolve(52,a,45,a)].
0.42/1.01	Derived: empty(c8) | -empty(relation_rng(c8)).  [resolve(52,a,46,a)].
0.42/1.01	Derived: empty(c9) | -empty(relation_rng(c9)).  [resolve(52,a,47,a)].
0.42/1.01	Derived: empty(relation_rng(A)) | -empty(relation_rng(relation_rng(A))) | -empty(A).  [resolve(52,a,49,b)].
0.42/1.01	Derived: empty(relation_dom(A)) | -empty(relation_rng(relation_dom(A))) | -empty(A).  [resolve(52,a,50,b)].
0.42/1.01	53 -relation(A) | -empty(A) | -function(A) | one_to_one(A) # label(cc2_funct_1) # label(axiom).  [clausify(4)].
0.42/1.01	Derived: -empty(empty_set) | -function(empty_set) | one_to_one(empty_set).  [resolve(53,a,39,a)].
0.42/1.01	Derived: -empty(c1) | -function(c1) | one_to_one(c1).  [resolve(53,a,40,a)].
0.42/1.01	Derived: -empty(c3) | -function(c3) | one_to_one(c3).  [resolve(53,a,41,a)].
0.42/1.01	Derived: -empty(c5) | -function(c5) | one_to_one(c5).  [resolve(53,a,42,a)].
0.42/1.01	Derived: -empty(c6) | -function(c6) | one_to_one(c6).  [resolve(53,a,44,a)].
0.42/1.01	Derived: -empty(c7) | -function(c7) | one_to_one(c7).  [resolve(53,a,45,a)].
0.42/1.01	Derived: -empty(c8) | -function(c8) | one_to_one(c8).  [resolve(53,a,46,a)].
0.42/1.01	Derived: -empty(c9) | -function(c9) | one_to_one(c9).  [resolve(53,a,47,a)].
0.42/1.01	Derived: -empty(A) | -function(A) | one_to_one(A) | -empty(A).  [resolve(53,a,48,b)].
0.42/1.01	54 -relation(A) | -function(A) | in(f1(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.42/1.01	Derived: -function(empty_set) | in(f1(empty_set),relation_dom(empty_set)) | one_to_one(empty_set).  [resolve(54,a,39,a)].
0.42/1.01	Derived: -function(c1) | in(f1(c1),relation_dom(c1)) | one_to_one(c1).  [resolve(54,a,40,a)].
0.42/1.01	Derived: -function(c3) | in(f1(c3),relation_dom(c3)) | one_to_one(c3).  [resolve(54,a,41,a)].
0.42/1.01	Derived: -function(c5) | in(f1(c5),relation_dom(c5)) | one_to_one(c5).  [resolve(54,a,42,a)].
0.42/1.01	Derived: -function(c6) | in(f1(c6),relation_dom(c6)) | one_to_one(c6).  [resolve(54,a,44,a)].
0.42/1.01	Derived: -function(c7) | in(f1(c7),relation_dom(c7)) | one_to_one(c7).  [resolve(54,a,45,a)].
0.42/1.01	Derived: -function(c8) | in(f1(c8),relation_dom(c8)) | one_to_one(c8).  [resolve(54,a,46,a)].
0.42/1.01	Derived: -function(c9) | in(f1(c9),relation_dom(c9)) | one_to_one(c9).  [resolve(54,a,47,a)].
0.42/1.01	Derived: -function(relation_rng(A)) | in(f1(relation_rng(A)),relation_dom(relation_rng(A))) | one_to_one(relation_rng(A)) | -empty(A).  [resolve(54,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | in(f1(relation_dom(A)),relation_dom(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(54,a,50,b)].
0.42/1.01	55 -relation(A) | -function(A) | in(f2(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.42/1.01	Derived: -function(empty_set) | in(f2(empty_set),relation_dom(empty_set)) | one_to_one(empty_set).  [resolve(55,a,39,a)].
0.42/1.01	Derived: -function(c1) | in(f2(c1),relation_dom(c1)) | one_to_one(c1).  [resolve(55,a,40,a)].
0.42/1.01	Derived: -function(c3) | in(f2(c3),relation_dom(c3)) | one_to_one(c3).  [resolve(55,a,41,a)].
0.42/1.01	Derived: -function(c5) | in(f2(c5),relation_dom(c5)) | one_to_one(c5).  [resolve(55,a,42,a)].
0.42/1.01	Derived: -function(c6) | in(f2(c6),relation_dom(c6)) | one_to_one(c6).  [resolve(55,a,44,a)].
0.42/1.01	Derived: -function(c7) | in(f2(c7),relation_dom(c7)) | one_to_one(c7).  [resolve(55,a,45,a)].
0.42/1.01	Derived: -function(c8) | in(f2(c8),relation_dom(c8)) | one_to_one(c8).  [resolve(55,a,46,a)].
0.42/1.01	Derived: -function(c9) | in(f2(c9),relation_dom(c9)) | one_to_one(c9).  [resolve(55,a,47,a)].
0.42/1.01	Derived: -function(relation_rng(A)) | in(f2(relation_rng(A)),relation_dom(relation_rng(A))) | one_to_one(relation_rng(A)) | -empty(A).  [resolve(55,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | in(f2(relation_dom(A)),relation_dom(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(55,a,50,b)].
0.42/1.01	56 -relation(A) | -function(A) | f2(A) != f1(A) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.42/1.01	Derived: -function(empty_set) | f2(empty_set) != f1(empty_set) | one_to_one(empty_set).  [resolve(56,a,39,a)].
0.42/1.01	Derived: -function(c1) | f2(c1) != f1(c1) | one_to_one(c1).  [resolve(56,a,40,a)].
0.42/1.01	Derived: -function(c3) | f2(c3) != f1(c3) | one_to_one(c3).  [resolve(56,a,41,a)].
0.42/1.01	Derived: -function(c5) | f2(c5) != f1(c5) | one_to_one(c5).  [resolve(56,a,42,a)].
0.42/1.01	Derived: -function(c6) | f2(c6) != f1(c6) | one_to_one(c6).  [resolve(56,a,44,a)].
0.42/1.01	Derived: -function(c7) | f2(c7) != f1(c7) | one_to_one(c7).  [resolve(56,a,45,a)].
0.42/1.01	Derived: -function(c8) | f2(c8) != f1(c8) | one_to_one(c8).  [resolve(56,a,46,a)].
0.42/1.01	Derived: -function(c9) | f2(c9) != f1(c9) | one_to_one(c9).  [resolve(56,a,47,a)].
0.42/1.01	Derived: -function(relation_rng(A)) | f2(relation_rng(A)) != f1(relation_rng(A)) | one_to_one(relation_rng(A)) | -empty(A).  [resolve(56,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | f2(relation_dom(A)) != f1(relation_dom(A)) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(56,a,50,b)].
0.42/1.01	57 -relation(A) | in(B,relation_rng(A)) | relation_inverse_image(A,singleton(B)) = empty_set # label(t142_funct_1) # label(axiom).  [clausify(35)].
0.42/1.01	Derived: in(A,relation_rng(empty_set)) | relation_inverse_image(empty_set,singleton(A)) = empty_set.  [resolve(57,a,39,a)].
0.42/1.01	Derived: in(A,relation_rng(c1)) | relation_inverse_image(c1,singleton(A)) = empty_set.  [resolve(57,a,40,a)].
0.42/1.01	Derived: in(A,relation_rng(c3)) | relation_inverse_image(c3,singleton(A)) = empty_set.  [resolve(57,a,41,a)].
0.42/1.01	Derived: in(A,relation_rng(c5)) | relation_inverse_image(c5,singleton(A)) = empty_set.  [resolve(57,a,42,a)].
0.42/1.01	Derived: in(A,relation_rng(c6)) | relation_inverse_image(c6,singleton(A)) = empty_set.  [resolve(57,a,44,a)].
0.42/1.01	Derived: in(A,relation_rng(c7)) | relation_inverse_image(c7,singleton(A)) = empty_set.  [resolve(57,a,45,a)].
0.42/1.01	Derived: in(A,relation_rng(c8)) | relation_inverse_image(c8,singleton(A)) = empty_set.  [resolve(57,a,46,a)].
0.42/1.01	Derived: in(A,relation_rng(c9)) | relation_inverse_image(c9,singleton(A)) = empty_set.  [resolve(57,a,47,a)].
0.42/1.01	Derived: in(A,relation_rng(B)) | relation_inverse_image(B,singleton(A)) = empty_set | -empty(B).  [resolve(57,a,48,b)].
0.42/1.01	Derived: in(A,relation_rng(relation_rng(B))) | relation_inverse_image(relation_rng(B),singleton(A)) = empty_set | -empty(B).  [resolve(57,a,49,b)].
0.42/1.01	Derived: in(A,relation_rng(relation_dom(B))) | relation_inverse_image(relation_dom(B),singleton(A)) = empty_set | -empty(B).  [resolve(57,a,50,b)].
0.42/1.01	58 -relation(A) | -function(A) | apply(A,f2(A)) = apply(A,f1(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.42/1.01	Derived: -function(empty_set) | apply(empty_set,f2(empty_set)) = apply(empty_set,f1(empty_set)) | one_to_one(empty_set).  [resolve(58,a,39,a)].
0.42/1.01	Derived: -function(c1) | apply(c1,f2(c1)) = apply(c1,f1(c1)) | one_to_one(c1).  [resolve(58,a,40,a)].
0.42/1.01	Derived: -function(c3) | apply(c3,f2(c3)) = apply(c3,f1(c3)) | one_to_one(c3).  [resolve(58,a,41,a)].
0.42/1.01	Derived: -function(c5) | apply(c5,f2(c5)) = apply(c5,f1(c5)) | one_to_one(c5).  [resolve(58,a,42,a)].
0.42/1.01	Derived: -function(c6) | apply(c6,f2(c6)) = apply(c6,f1(c6)) | one_to_one(c6).  [resolve(58,a,44,a)].
0.42/1.01	Derived: -function(c7) | apply(c7,f2(c7)) = apply(c7,f1(c7)) | one_to_one(c7).  [resolve(58,a,45,a)].
0.42/1.01	Derived: -function(c8) | apply(c8,f2(c8)) = apply(c8,f1(c8)) | one_to_one(c8).  [resolve(58,a,46,a)].
0.42/1.01	Derived: -function(c9) | apply(c9,f2(c9)) = apply(c9,f1(c9)) | one_to_one(c9).  [resolve(58,a,47,a)].
0.42/1.01	Derived: -function(relation_rng(A)) | apply(relation_rng(A),f2(relation_rng(A))) = apply(relation_rng(A),f1(relation_rng(A))) | one_to_one(relation_rng(A)) | -empty(A).  [resolve(58,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | apply(relation_dom(A),f2(relation_dom(A))) = apply(relation_dom(A),f1(relation_dom(A))) | one_to_one(relation_dom(A)) | -empty(A).  [resolve(58,a,50,b)].
0.42/1.01	59 -function(A) | -relation(A) | -in(B,relation_dom(A)) | relation_image(A,singleton(B)) = singleton(apply(A,B)) # label(t117_funct_1) # label(axiom).  [clausify(24)].
0.42/1.01	Derived: -function(empty_set) | -in(A,relation_dom(empty_set)) | relation_image(empty_set,singleton(A)) = singleton(apply(empty_set,A)).  [resolve(59,b,39,a)].
0.42/1.01	Derived: -function(c1) | -in(A,relation_dom(c1)) | relation_image(c1,singleton(A)) = singleton(apply(c1,A)).  [resolve(59,b,40,a)].
0.42/1.01	Derived: -function(c3) | -in(A,relation_dom(c3)) | relation_image(c3,singleton(A)) = singleton(apply(c3,A)).  [resolve(59,b,41,a)].
0.42/1.01	Derived: -function(c5) | -in(A,relation_dom(c5)) | relation_image(c5,singleton(A)) = singleton(apply(c5,A)).  [resolve(59,b,42,a)].
0.42/1.01	Derived: -function(c6) | -in(A,relation_dom(c6)) | relation_image(c6,singleton(A)) = singleton(apply(c6,A)).  [resolve(59,b,44,a)].
0.42/1.01	Derived: -function(c7) | -in(A,relation_dom(c7)) | relation_image(c7,singleton(A)) = singleton(apply(c7,A)).  [resolve(59,b,45,a)].
0.42/1.01	Derived: -function(c8) | -in(A,relation_dom(c8)) | relation_image(c8,singleton(A)) = singleton(apply(c8,A)).  [resolve(59,b,46,a)].
0.42/1.01	Derived: -function(c9) | -in(A,relation_dom(c9)) | relation_image(c9,singleton(A)) = singleton(apply(c9,A)).  [resolve(59,b,47,a)].
0.42/1.01	Derived: -function(A) | -in(B,relation_dom(A)) | relation_image(A,singleton(B)) = singleton(apply(A,B)) | -empty(A).  [resolve(59,b,48,b)].
0.42/1.01	Derived: -function(relation_rng(A)) | -in(B,relation_dom(relation_rng(A))) | relation_image(relation_rng(A),singleton(B)) = singleton(apply(relation_rng(A),B)) | -empty(A).  [resolve(59,b,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | -in(B,relation_dom(relation_dom(A))) | relation_image(relation_dom(A),singleton(B)) = singleton(apply(relation_dom(A),B)) | -empty(A).  [resolve(59,b,50,b)].
0.42/1.01	60 -relation(A) | -function(A) | relation_rng(A) != B | -in(C,B) | in(f3(A,B,C),relation_dom(A)) # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.01	Derived: -function(empty_set) | relation_rng(empty_set) != A | -in(B,A) | in(f3(empty_set,A,B),relation_dom(empty_set)).  [resolve(60,a,39,a)].
0.42/1.01	Derived: -function(c1) | relation_rng(c1) != A | -in(B,A) | in(f3(c1,A,B),relation_dom(c1)).  [resolve(60,a,40,a)].
0.42/1.01	Derived: -function(c3) | relation_rng(c3) != A | -in(B,A) | in(f3(c3,A,B),relation_dom(c3)).  [resolve(60,a,41,a)].
0.42/1.01	Derived: -function(c5) | relation_rng(c5) != A | -in(B,A) | in(f3(c5,A,B),relation_dom(c5)).  [resolve(60,a,42,a)].
0.42/1.01	Derived: -function(c6) | relation_rng(c6) != A | -in(B,A) | in(f3(c6,A,B),relation_dom(c6)).  [resolve(60,a,44,a)].
0.42/1.01	Derived: -function(c7) | relation_rng(c7) != A | -in(B,A) | in(f3(c7,A,B),relation_dom(c7)).  [resolve(60,a,45,a)].
0.42/1.01	Derived: -function(c8) | relation_rng(c8) != A | -in(B,A) | in(f3(c8,A,B),relation_dom(c8)).  [resolve(60,a,46,a)].
0.42/1.01	Derived: -function(c9) | relation_rng(c9) != A | -in(B,A) | in(f3(c9,A,B),relation_dom(c9)).  [resolve(60,a,47,a)].
0.42/1.01	Derived: -function(A) | relation_rng(A) != B | -in(C,B) | in(f3(A,B,C),relation_dom(A)) | -empty(A).  [resolve(60,a,48,b)].
0.42/1.01	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) != B | -in(C,B) | in(f3(relation_rng(A),B,C),relation_dom(relation_rng(A))) | -empty(A).  [resolve(60,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) != B | -in(C,B) | in(f3(relation_dom(A),B,C),relation_dom(relation_dom(A))) | -empty(A).  [resolve(60,a,50,b)].
0.42/1.01	61 -relation(A) | -function(A) | relation_rng(A) != B | -in(C,B) | apply(A,f3(A,B,C)) = C # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.01	Derived: -function(empty_set) | relation_rng(empty_set) != A | -in(B,A) | apply(empty_set,f3(empty_set,A,B)) = B.  [resolve(61,a,39,a)].
0.42/1.01	Derived: -function(c1) | relation_rng(c1) != A | -in(B,A) | apply(c1,f3(c1,A,B)) = B.  [resolve(61,a,40,a)].
0.42/1.01	Derived: -function(c3) | relation_rng(c3) != A | -in(B,A) | apply(c3,f3(c3,A,B)) = B.  [resolve(61,a,41,a)].
0.42/1.01	Derived: -function(c5) | relation_rng(c5) != A | -in(B,A) | apply(c5,f3(c5,A,B)) = B.  [resolve(61,a,42,a)].
0.42/1.01	Derived: -function(c6) | relation_rng(c6) != A | -in(B,A) | apply(c6,f3(c6,A,B)) = B.  [resolve(61,a,44,a)].
0.42/1.01	Derived: -function(c7) | relation_rng(c7) != A | -in(B,A) | apply(c7,f3(c7,A,B)) = B.  [resolve(61,a,45,a)].
0.42/1.01	Derived: -function(c8) | relation_rng(c8) != A | -in(B,A) | apply(c8,f3(c8,A,B)) = B.  [resolve(61,a,46,a)].
0.42/1.01	Derived: -function(c9) | relation_rng(c9) != A | -in(B,A) | apply(c9,f3(c9,A,B)) = B.  [resolve(61,a,47,a)].
0.42/1.01	Derived: -function(A) | relation_rng(A) != B | -in(C,B) | apply(A,f3(A,B,C)) = C | -empty(A).  [resolve(61,a,48,b)].
0.42/1.01	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) != B | -in(C,B) | apply(relation_rng(A),f3(relation_rng(A),B,C)) = C | -empty(A).  [resolve(61,a,49,b)].
0.42/1.01	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) != B | -in(C,B) | apply(relation_dom(A),f3(relation_dom(A),B,C)) = C | -empty(A).  [resolve(61,a,50,b)].
0.42/1.01	62 -relation(A) | -function(A) | relation_rng(A) = B | in(f4(A,B),B) | in(f5(A,B),relation_dom(A)) # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.01	Derived: -function(empty_set) | relation_rng(empty_set) = A | in(f4(empty_set,A),A) | in(f5(empty_set,A),relation_dom(empty_set)).  [resolve(62,a,39,a)].
0.42/1.01	Derived: -function(c1) | relation_rng(c1) = A | in(f4(c1,A),A) | in(f5(c1,A),relation_dom(c1)).  [resolve(62,a,40,a)].
0.42/1.01	Derived: -function(c3) | relation_rng(c3) = A | in(f4(c3,A),A) | in(f5(c3,A),relation_dom(c3)).  [resolve(62,a,41,a)].
0.42/1.01	Derived: -function(c5) | relation_rng(c5) = A | in(f4(c5,A),A) | in(f5(c5,A),relation_dom(c5)).  [resolve(62,a,42,a)].
0.42/1.01	Derived: -function(c6) | relation_rng(c6) = A | in(f4(c6,A),A) | in(f5(c6,A),relation_dom(c6)).  [resolve(62,a,44,a)].
0.42/1.01	Derived: -function(c7) | relation_rng(c7) = A | in(f4(c7,A),A) | in(f5(c7,A),relation_dom(c7)).  [resolve(62,a,45,a)].
0.42/1.02	Derived: -function(c8) | relation_rng(c8) = A | in(f4(c8,A),A) | in(f5(c8,A),relation_dom(c8)).  [resolve(62,a,46,a)].
0.42/1.02	Derived: -function(c9) | relation_rng(c9) = A | in(f4(c9,A),A) | in(f5(c9,A),relation_dom(c9)).  [resolve(62,a,47,a)].
0.42/1.02	Derived: -function(A) | relation_rng(A) = B | in(f4(A,B),B) | in(f5(A,B),relation_dom(A)) | -empty(A).  [resolve(62,a,48,b)].
0.42/1.02	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) = B | in(f4(relation_rng(A),B),B) | in(f5(relation_rng(A),B),relation_dom(relation_rng(A))) | -empty(A).  [resolve(62,a,49,b)].
0.42/1.02	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) = B | in(f4(relation_dom(A),B),B) | in(f5(relation_dom(A),B),relation_dom(relation_dom(A))) | -empty(A).  [resolve(62,a,50,b)].
0.42/1.02	63 -relation(A) | -function(A) | relation_rng(A) != B | in(C,B) | -in(D,relation_dom(A)) | apply(A,D) != C # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.02	Derived: -function(empty_set) | relation_rng(empty_set) != A | in(B,A) | -in(C,relation_dom(empty_set)) | apply(empty_set,C) != B.  [resolve(63,a,39,a)].
0.42/1.02	Derived: -function(c1) | relation_rng(c1) != A | in(B,A) | -in(C,relation_dom(c1)) | apply(c1,C) != B.  [resolve(63,a,40,a)].
0.42/1.02	Derived: -function(c3) | relation_rng(c3) != A | in(B,A) | -in(C,relation_dom(c3)) | apply(c3,C) != B.  [resolve(63,a,41,a)].
0.42/1.02	Derived: -function(c5) | relation_rng(c5) != A | in(B,A) | -in(C,relation_dom(c5)) | apply(c5,C) != B.  [resolve(63,a,42,a)].
0.42/1.02	Derived: -function(c6) | relation_rng(c6) != A | in(B,A) | -in(C,relation_dom(c6)) | apply(c6,C) != B.  [resolve(63,a,44,a)].
0.42/1.02	Derived: -function(c7) | relation_rng(c7) != A | in(B,A) | -in(C,relation_dom(c7)) | apply(c7,C) != B.  [resolve(63,a,45,a)].
0.42/1.02	Derived: -function(c8) | relation_rng(c8) != A | in(B,A) | -in(C,relation_dom(c8)) | apply(c8,C) != B.  [resolve(63,a,46,a)].
0.42/1.02	Derived: -function(c9) | relation_rng(c9) != A | in(B,A) | -in(C,relation_dom(c9)) | apply(c9,C) != B.  [resolve(63,a,47,a)].
0.42/1.02	Derived: -function(A) | relation_rng(A) != B | in(C,B) | -in(D,relation_dom(A)) | apply(A,D) != C | -empty(A).  [resolve(63,a,48,b)].
0.42/1.02	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) != B | in(C,B) | -in(D,relation_dom(relation_rng(A))) | apply(relation_rng(A),D) != C | -empty(A).  [resolve(63,a,49,b)].
0.42/1.02	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) != B | in(C,B) | -in(D,relation_dom(relation_dom(A))) | apply(relation_dom(A),D) != C | -empty(A).  [resolve(63,a,50,b)].
0.42/1.02	64 -relation(A) | -function(A) | relation_rng(A) = B | in(f4(A,B),B) | apply(A,f5(A,B)) = f4(A,B) # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.02	Derived: -function(empty_set) | relation_rng(empty_set) = A | in(f4(empty_set,A),A) | apply(empty_set,f5(empty_set,A)) = f4(empty_set,A).  [resolve(64,a,39,a)].
0.42/1.02	Derived: -function(c1) | relation_rng(c1) = A | in(f4(c1,A),A) | apply(c1,f5(c1,A)) = f4(c1,A).  [resolve(64,a,40,a)].
0.42/1.02	Derived: -function(c3) | relation_rng(c3) = A | in(f4(c3,A),A) | apply(c3,f5(c3,A)) = f4(c3,A).  [resolve(64,a,41,a)].
0.42/1.02	Derived: -function(c5) | relation_rng(c5) = A | in(f4(c5,A),A) | apply(c5,f5(c5,A)) = f4(c5,A).  [resolve(64,a,42,a)].
0.42/1.02	Derived: -function(c6) | relation_rng(c6) = A | in(f4(c6,A),A) | apply(c6,f5(c6,A)) = f4(c6,A).  [resolve(64,a,44,a)].
0.42/1.02	Derived: -function(c7) | relation_rng(c7) = A | in(f4(c7,A),A) | apply(c7,f5(c7,A)) = f4(c7,A).  [resolve(64,a,45,a)].
0.42/1.02	Derived: -function(c8) | relation_rng(c8) = A | in(f4(c8,A),A) | apply(c8,f5(c8,A)) = f4(c8,A).  [resolve(64,a,46,a)].
0.42/1.02	Derived: -function(c9) | relation_rng(c9) = A | in(f4(c9,A),A) | apply(c9,f5(c9,A)) = f4(c9,A).  [resolve(64,a,47,a)].
0.42/1.02	Derived: -function(A) | relation_rng(A) = B | in(f4(A,B),B) | apply(A,f5(A,B)) = f4(A,B) | -empty(A).  [resolve(64,a,48,b)].
0.42/1.02	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) = B | in(f4(relation_rng(A),B),B) | apply(relation_rng(A),f5(relation_rng(A),B)) = f4(relation_rng(A),B) | -empty(A).  [resolve(64,a,49,b)].
0.42/1.02	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) = B | in(f4(relation_dom(A),B),B) | apply(relation_dom(A),f5(relation_dom(A),B)) = f4(relation_dom(A),B) | -empty(A).  [resolve(64,a,50,b)].
0.42/1.02	65 -relation(A) | -function(A) | -in(B,relation_dom(A)) | apply(A,C) != apply(A,B) | -in(C,relation_dom(A)) | C = B | -one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.42/1.02	Derived: -function(empty_set) | -in(A,relation_dom(empty_set)) | apply(empty_set,B) != apply(empty_set,A) | -in(B,relation_dom(empty_set)) | B = A | -one_to_one(empty_set).  [resolve(65,a,39,a)].
0.42/1.02	Derived: -function(c1) | -in(A,relation_dom(c1)) | apply(c1,B) != apply(c1,A) | -in(B,relation_dom(c1)) | B = A | -one_to_one(c1).  [resolve(65,a,40,a)].
0.42/1.02	Derived: -function(c3) | -in(A,relation_dom(c3)) | apply(c3,B) != apply(c3,A) | -in(B,relation_dom(c3)) | B = A | -one_to_one(c3).  [resolve(65,a,41,a)].
0.42/1.02	Derived: -function(c5) | -in(A,relation_dom(c5)) | apply(c5,B) != apply(c5,A) | -in(B,relation_dom(c5)) | B = A | -one_to_one(c5).  [resolve(65,a,42,a)].
0.42/1.02	Derived: -function(c6) | -in(A,relation_dom(c6)) | apply(c6,B) != apply(c6,A) | -in(B,relation_dom(c6)) | B = A | -one_to_one(c6).  [resolve(65,a,44,a)].
0.42/1.02	Derived: -function(c7) | -in(A,relation_dom(c7)) | apply(c7,B) != apply(c7,A) | -in(B,relation_dom(c7)) | B = A | -one_to_one(c7).  [resolve(65,a,45,a)].
0.42/1.02	Derived: -function(c8) | -in(A,relation_dom(c8)) | apply(c8,B) != apply(c8,A) | -in(B,relation_dom(c8)) | B = A | -one_to_one(c8).  [resolve(65,a,46,a)].
0.42/1.02	Derived: -function(c9) | -in(A,relation_dom(c9)) | apply(c9,B) != apply(c9,A) | -in(B,relation_dom(c9)) | B = A | -one_to_one(c9).  [resolve(65,a,47,a)].
0.42/1.02	Derived: -function(A) | -in(B,relation_dom(A)) | apply(A,C) != apply(A,B) | -in(C,relation_dom(A)) | C = B | -one_to_one(A) | -empty(A).  [resolve(65,a,48,b)].
0.42/1.02	Derived: -function(relation_rng(A)) | -in(B,relation_dom(relation_rng(A))) | apply(relation_rng(A),C) != apply(relation_rng(A),B) | -in(C,relation_dom(relation_rng(A))) | C = B | -one_to_one(relation_rng(A)) | -empty(A).  [resolve(65,a,49,b)].
0.42/1.02	Derived: -function(relation_dom(A)) | -in(B,relation_dom(relation_dom(A))) | apply(relation_dom(A),C) != apply(relation_dom(A),B) | -in(C,relation_dom(relation_dom(A))) | C = B | -one_to_one(relation_dom(A)) | -empty(A).  [resolve(65,a,50,b)].
0.42/1.02	66 -relation(A) | -function(A) | relation_rng(A) = B | -in(f4(A,B),B) | -in(C,relation_dom(A)) | apply(A,C) != f4(A,B) # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.42/1.02	Derived: -function(empty_set) | relation_rng(empty_set) = A | -in(f4(empty_set,A),A) | -in(B,relation_dom(empty_set)) | apply(empty_set,B) != f4(empty_set,A).  [resolve(66,a,39,a)].
0.42/1.02	Derived: -function(c1) | relation_rng(c1) = A | -in(f4(c1,A),A) | -in(B,relation_dom(c1)) | apply(c1,B) != f4(c1,A).  [resolve(66,a,40,a)].
0.42/1.02	Derived: -function(c3) | relation_rng(c3) = A | -in(f4(c3,A),A) | -in(B,relation_dom(c3)) | apply(c3,B) != f4(c3,A).  [resolve(66,a,41,a)].
0.42/1.02	Derived: -function(c5) | relation_rng(c5) = A | -in(f4(c5,A),A) | -in(B,relation_dom(c5)) | apply(c5,B) != f4(c5,A).  [resolve(66,a,42,a)].
0.42/1.02	Derived: -function(c6) | relation_rng(c6) = A | -in(f4(c6,A),A) | -in(B,relation_dom(c6)) | apply(c6,B) != f4(c6,A).  [resolve(66,a,44,a)].
0.42/1.02	Derived: -function(c7) | relation_rng(c7) = A | -in(f4(c7,A),A) | -in(B,relation_dom(c7)) | apply(c7,B) != f4(c7,A).  [resolve(66,a,45,a)].
0.42/1.02	Derived: -function(c8) | relation_rng(c8) = A | -in(f4(c8,A),A) | -in(B,relation_dom(c8)) | apply(c8,B) != f4(c8,A).  [resolve(66,a,46,a)].
0.42/1.02	Derived: -function(c9) | relation_rng(c9) = A | -in(f4(c9,A),A) | -in(B,relation_dom(c9)) | apply(c9,B) != f4(c9,A).  [resolve(66,a,47,a)].
0.42/1.02	Derived: -function(A) | relation_rng(A) = B | -in(f4(A,B),B) | -in(C,relation_dom(A)) | apply(A,C) != f4(A,B) | -empty(A).  [resolve(66,a,48,b)].
0.42/1.02	Derived: -function(relation_rng(A)) | relation_rng(relation_rng(A)) = B | -in(f4(relation_rng(A),B),B) | -in(C,relation_dom(relation_rng(A))) | apply(relation_rng(A),C) != f4(relation_rng(A),B) | -empty(A).  [resolve(66,a,49,b)].
0.42/1.02	Derived: -function(relation_dom(A)) | relation_rng(relation_dom(A)) = B | -in(f4(relation_dom(A),B),B) | -in(C,relation_dom(relation_dom(A))) | apply(relation_dom(A),C) != f4(relation_dom(A),B) | -empty(A).  [resolve(66,a,50,b)].
0.74/1.18	
0.74/1.18	============================== end predicate elimination =============
0.74/1.18	
0.74/1.18	Auto_denials:  (non-Horn, no changes).
0.74/1.18	
0.74/1.18	Term ordering decisions:
0.74/1.18	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. apply=1. relation_image=1. relation_inverse_image=1. f4=1. f5=1. relation_dom=1. relation_rng=1. singleton=1. powerset=1. f1=1. f2=1. f6=1. f7=1. f8=1. f3=1.
0.74/1.18	
0.74/1.18	============================== end of process initial clauses ========
0.74/1.18	
0.74/1.18	============================== CLAUSES FOR SEARCH ====================
0.74/1.18	
0.74/1.18	============================== end of clauses for search =============
0.74/1.18	
0.74/1.18	============================== SEARCH ================================
0.74/1.18	
0.74/1.18	% Starting search at 0.05 seconds.
0.74/1.18	
0.74/1.18	============================== PROOF =================================
0.74/1.18	% SZS status Theorem
0.74/1.18	% SZS output start Refutation
0.74/1.18	
0.74/1.18	% Proof 1 at 0.18 (+ 0.01) seconds.
0.74/1.18	% Length of proof is 49.
0.74/1.18	% Level of proof is 11.
0.74/1.18	% Maximum clause weight is 17.000.
0.74/1.18	% Given clauses 331.
0.74/1.18	
0.74/1.18	5 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	6 (all A (relation(A) & function(A) -> ((all B all C (in(B,relation_dom(A)) & apply(A,C) = apply(A,B) & in(C,relation_dom(A)) -> B = C)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	18 (all A all B (A = empty_set | A = singleton(B) <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	22 (all A (relation(A) & function(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D (in(D,relation_dom(A)) & apply(A,D) = C)))))))) # label(d5_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	24 (all A all B (function(B) & relation(B) -> (in(A,relation_dom(B)) -> relation_image(B,singleton(A)) = singleton(apply(B,A))))) # label(t117_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	35 (all A all B (relation(B) -> (in(A,relation_rng(B)) <-> empty_set != relation_inverse_image(B,singleton(A))))) # label(t142_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.74/1.18	37 -(all A (function(A) & relation(A) -> ((all B subset(relation_inverse_image(A,relation_image(A,B)),B)) -> one_to_one(A)))) # label(t153_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.74/1.18	38 -relation(A) | -in(B,relation_rng(A)) | relation_inverse_image(A,singleton(B)) != empty_set # label(t142_funct_1) # label(axiom).  [clausify(35)].
0.74/1.18	47 relation(c9) # label(t153_funct_1) # label(negated_conjecture).  [clausify(37)].
0.74/1.18	54 -relation(A) | -function(A) | in(f1(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.74/1.18	55 -relation(A) | -function(A) | in(f2(A),relation_dom(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.74/1.18	56 -relation(A) | -function(A) | f2(A) != f1(A) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.74/1.18	58 -relation(A) | -function(A) | apply(A,f2(A)) = apply(A,f1(A)) | one_to_one(A) # label(d8_funct_1) # label(axiom).  [clausify(6)].
0.74/1.18	59 -function(A) | -relation(A) | -in(B,relation_dom(A)) | relation_image(A,singleton(B)) = singleton(apply(A,B)) # label(t117_funct_1) # label(axiom).  [clausify(24)].
0.74/1.18	63 -relation(A) | -function(A) | relation_rng(A) != B | in(C,B) | -in(D,relation_dom(A)) | apply(A,D) != C # label(d5_funct_1) # label(axiom).  [clausify(22)].
0.74/1.18	75 function(c9) # label(t153_funct_1) # label(negated_conjecture).  [clausify(37)].
0.74/1.18	81 subset(relation_inverse_image(c9,relation_image(c9,A)),A) # label(t153_funct_1) # label(negated_conjecture).  [clausify(37)].
0.74/1.18	84 -one_to_one(c9) # label(t153_funct_1) # label(negated_conjecture).  [clausify(37)].
0.74/1.18	100 -subset(singleton(A),singleton(B)) | B = A # label(t6_zfmisc_1) # label(axiom).  [clausify(5)].
0.74/1.18	104 empty_set = A | singleton(B) = A | -subset(A,singleton(B)) # label(t39_zfmisc_1) # label(axiom).  [clausify(18)].
0.74/1.18	112 -in(A,relation_rng(c9)) | relation_inverse_image(c9,singleton(A)) != empty_set.  [resolve(38,a,47,a)].
0.74/1.18	148 -function(c9) | in(f1(c9),relation_dom(c9)) | one_to_one(c9).  [resolve(54,a,47,a)].
0.74/1.18	149 in(f1(c9),relation_dom(c9)).  [copy(148),unit_del(a,75),unit_del(c,84)].
0.74/1.18	158 -function(c9) | in(f2(c9),relation_dom(c9)) | one_to_one(c9).  [resolve(55,a,47,a)].
0.74/1.18	159 in(f2(c9),relation_dom(c9)).  [copy(158),unit_del(a,75),unit_del(c,84)].
0.74/1.18	168 -function(c9) | f2(c9) != f1(c9) | one_to_one(c9).  [resolve(56,a,47,a)].
0.74/1.18	169 f2(c9) != f1(c9).  [copy(168),unit_del(a,75),unit_del(c,84)].
0.74/1.18	189 -function(c9) | apply(c9,f2(c9)) = apply(c9,f1(c9)) | one_to_one(c9).  [resolve(58,a,47,a)].
0.74/1.18	190 apply(c9,f2(c9)) = apply(c9,f1(c9)).  [copy(189),unit_del(a,75),unit_del(c,84)].
0.74/1.18	207 -function(c9) | -in(A,relation_dom(c9)) | relation_image(c9,singleton(A)) = singleton(apply(c9,A)).  [resolve(59,b,47,a)].
0.74/1.18	208 -in(A,relation_dom(c9)) | singleton(apply(c9,A)) = relation_image(c9,singleton(A)).  [copy(207),flip(c),unit_del(a,75)].
0.74/1.18	270 -function(c9) | relation_rng(c9) != A | in(B,A) | -in(C,relation_dom(c9)) | apply(c9,C) != B.  [resolve(63,a,47,a)].
0.74/1.18	271 relation_rng(c9) != A | in(B,A) | -in(C,relation_dom(c9)) | apply(c9,C) != B.  [copy(270),unit_del(a,75)].
0.74/1.18	329 f2(c9) = c_0.  [new_symbol(169)].
0.74/1.18	341 apply(c9,f1(c9)) = apply(c9,c_0).  [back_rewrite(190),rewrite([329(3)]),flip(a)].
0.74/1.18	342 f1(c9) != c_0.  [back_rewrite(169),rewrite([329(2)]),flip(a)].
0.74/1.18	343 in(c_0,relation_dom(c9)).  [back_rewrite(159),rewrite([329(2)])].
0.74/1.18	393 relation_inverse_image(c9,relation_image(c9,singleton(A))) = empty_set | relation_inverse_image(c9,relation_image(c9,singleton(A))) = singleton(A).  [resolve(104,c,81,a),flip(a),flip(b)].
0.74/1.18	430 relation_image(c9,singleton(f1(c9))) = singleton(apply(c9,c_0)).  [resolve(208,a,149,a),rewrite([341(4)]),flip(a)].
0.74/1.18	748 relation_rng(c9) != A | in(B,A) | apply(c9,c_0) != B.  [resolve(271,c,149,a),rewrite([341(8)])].
0.74/1.18	1057 singleton(apply(c9,c_0)) = relation_image(c9,singleton(c_0)).  [resolve(343,a,208,a)].
0.74/1.18	1060 relation_image(c9,singleton(f1(c9))) = relation_image(c9,singleton(c_0)).  [back_rewrite(430),rewrite([1057(9)])].
0.74/1.18	1496 subset(relation_inverse_image(c9,relation_image(c9,singleton(c_0))),singleton(f1(c9))).  [para(1060(a,1),81(a,1,2))].
0.74/1.18	1596 relation_inverse_image(c9,relation_image(c9,singleton(c_0))) = empty_set | subset(singleton(c_0),singleton(f1(c9))).  [para(393(b,1),1496(a,1))].
0.74/1.18	1724 in(A,relation_rng(c9)) | apply(c9,c_0) != A.  [xx_res(748,a)].
0.74/1.18	1726 in(apply(c9,c_0),relation_rng(c9)).  [resolve(1724,b,341,a(flip)),rewrite([341(4)])].
0.74/1.18	1744 relation_inverse_image(c9,relation_image(c9,singleton(c_0))) != empty_set.  [resolve(1726,a,112,a),rewrite([1057(5)])].
0.74/1.18	1773 subset(singleton(c_0),singleton(f1(c9))).  [back_unit_del(1596),unit_del(a,1744)].
0.74/1.18	1791 $F.  [resolve(1773,a,100,a),unit_del(a,342)].
0.74/1.18	
0.74/1.18	% SZS output end Refutation
0.74/1.18	============================== end of proof ==========================
0.74/1.18	
0.74/1.18	============================== STATISTICS ============================
0.74/1.18	
0.74/1.18	Given=331. Generated=2425. Kept=1653. proofs=1.
0.74/1.18	Usable=307. Sos=1049. Demods=31. Limbo=1, Disabled=546. Hints=0.
0.74/1.18	Megabytes=2.76.
0.74/1.18	User_CPU=0.18, System_CPU=0.01, Wall_clock=0.
0.74/1.18	
0.74/1.18	============================== end of statistics =====================
0.74/1.18	
0.74/1.18	============================== end of search =========================
0.74/1.18	
0.74/1.18	THEOREM PROVED
0.74/1.18	% SZS status Theorem
0.74/1.18	
0.74/1.18	Exiting with 1 proof.
0.74/1.18	
0.74/1.18	Process 12312 exit (max_proofs) Thu Aug 29 11:49:08 2019
0.74/1.18	Prover9 interrupted
0.74/1.18	EOF