0.03/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.11	% Command    : tptp2X_and_run_prover9 %d %s
0.10/0.31	% Computer   : n009.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 1200
0.10/0.31	% DateTime   : Tue Jul 13 17:10:42 EDT 2021
0.10/0.31	% CPUTime    : 
1.01/1.31	============================== Prover9 ===============================
1.01/1.31	Prover9 (32) version 2009-11A, November 2009.
1.01/1.31	Process 27464 was started by sandbox on n009.cluster.edu,
1.01/1.31	Tue Jul 13 17:10:43 2021
1.01/1.31	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_27290_n009.cluster.edu".
1.01/1.31	============================== end of head ===========================
1.01/1.31	
1.01/1.31	============================== INPUT =================================
1.01/1.31	
1.01/1.31	% Reading from file /tmp/Prover9_27290_n009.cluster.edu
1.01/1.31	
1.01/1.31	set(prolog_style_variables).
1.01/1.31	set(auto2).
1.01/1.31	    % set(auto2) -> set(auto).
1.01/1.31	    % set(auto) -> set(auto_inference).
1.01/1.31	    % set(auto) -> set(auto_setup).
1.01/1.31	    % set(auto_setup) -> set(predicate_elim).
1.01/1.31	    % set(auto_setup) -> assign(eq_defs, unfold).
1.01/1.31	    % set(auto) -> set(auto_limits).
1.01/1.31	    % set(auto_limits) -> assign(max_weight, "100.000").
1.01/1.31	    % set(auto_limits) -> assign(sos_limit, 20000).
1.01/1.31	    % set(auto) -> set(auto_denials).
1.01/1.31	    % set(auto) -> set(auto_process).
1.01/1.31	    % set(auto2) -> assign(new_constants, 1).
1.01/1.31	    % set(auto2) -> assign(fold_denial_max, 3).
1.01/1.31	    % set(auto2) -> assign(max_weight, "200.000").
1.01/1.31	    % set(auto2) -> assign(max_hours, 1).
1.01/1.31	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
1.01/1.31	    % set(auto2) -> assign(max_seconds, 0).
1.01/1.31	    % set(auto2) -> assign(max_minutes, 5).
1.01/1.31	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
1.01/1.31	    % set(auto2) -> set(sort_initial_sos).
1.01/1.31	    % set(auto2) -> assign(sos_limit, -1).
1.01/1.31	    % set(auto2) -> assign(lrs_ticks, 3000).
1.01/1.31	    % set(auto2) -> assign(max_megs, 400).
1.01/1.31	    % set(auto2) -> assign(stats, some).
1.01/1.31	    % set(auto2) -> clear(echo_input).
1.01/1.31	    % set(auto2) -> set(quiet).
1.01/1.31	    % set(auto2) -> clear(print_initial_clauses).
1.01/1.31	    % set(auto2) -> clear(print_given).
1.01/1.31	assign(lrs_ticks,-1).
1.01/1.31	assign(sos_limit,10000).
1.01/1.31	assign(order,kbo).
1.01/1.31	set(lex_order_vars).
1.01/1.31	clear(print_given).
1.01/1.31	
1.01/1.31	% formulas(sos).  % not echoed (297 formulas)
1.01/1.31	
1.01/1.31	============================== end of input ==========================
1.01/1.31	
1.01/1.31	% From the command line: assign(max_seconds, 1200).
1.01/1.31	
1.01/1.31	============================== PROCESS NON-CLAUSAL FORMULAS ==========
1.01/1.31	
1.01/1.31	% Formulas that are not ordinary clauses:
1.01/1.31	1 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	2 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_difference(A,B,C) = set_difference(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	3 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),A) <-> in(ordered_pair(C,D),B))) <-> B = A))))) # label(d2_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	4 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	5 (all A (ordinal(A) <-> epsilon_connected(A) & epsilon_transitive(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	6 (all A all B -(empty(B) & A != B & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	7 (all A all B (element(B,powerset(powerset(A))) -> -(B != empty_set & empty_set = complements_of_subsets(A,B)))) # label(t46_setfam_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	8 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	9 (all A all B ((all C (in(C,A) -> in(C,B))) -> element(A,powerset(B)))) # label(l71_subset_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	10 (all A all B ((-empty(A) -> (element(B,A) <-> in(B,A))) & (empty(A) -> (element(B,A) <-> empty(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	11 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	12 (all A ((all B (in(B,A) -> subset(B,A) & ordinal(B))) -> ordinal(A))) # label(t31_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	13 (all A all B (subset(A,B) -> set_union2(A,set_difference(B,A)) = B)) # label(t45_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	14 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	15 (all A all B (element(B,powerset(powerset(A))) -> B = complements_of_subsets(A,complements_of_subsets(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	16 (all A all B all C (subset(B,C) & subset(A,B) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	17 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),A))) # label(t116_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	18 (all A all B (ordinal(B) -> -(subset(A,B) & empty_set != A & (all C (ordinal(C) -> -((all D (ordinal(D) -> (in(D,A) -> ordinal_subset(C,D)))) & in(C,A))))))) # label(t32_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	19 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	20 (all A ((all B (in(B,A) -> subset(B,A))) <-> epsilon_transitive(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	21 (all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	22 (all A all B (relation(B) -> relation(relation_rng_restriction(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	23 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_dom(A),relation_rng(B)) -> relation_rng(A) = relation_rng(relation_composition(B,A))))))) # label(t47_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	24 (all A all B all C all D (subset(C,D) & subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	25 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	26 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	27 (all A (empty(A) -> relation(relation_inverse(A)) & empty(relation_inverse(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	28 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	29 (all A (empty_set != A -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	30 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	31 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> ((all D all E ((exists F (in(ordered_pair(D,F),A) & in(ordered_pair(F,E),B))) <-> in(ordered_pair(D,E),C))) <-> C = relation_composition(A,B)))))))) # label(d8_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	32 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	33 (exists A (relation(A) & one_to_one(A) & function(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	34 (all A all B all C (function(C) & relation(C) -> (in(B,relation_dom(relation_dom_restriction(C,A))) <-> in(B,A) & in(B,relation_dom(C))))) # label(l82_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	35 (all A all B all C all D -(C != A & A != D & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.31	36 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	37 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.31	38 (all A all B (empty(A) & relation(B) -> empty(relation_composition(B,A)) & relation(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	39 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	40 (all A all B all C (C = set_difference(A,B) <-> (all D (-in(D,B) & in(D,A) <-> in(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	41 (all A all B (relation(B) -> relation_composition(identity_relation(A),B) = relation_dom_restriction(B,A))) # label(t94_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	42 (all A all B all C (relation(C) -> (subset(A,B) -> subset(relation_inverse_image(C,A),relation_inverse_image(C,B))))) # label(t178_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	43 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	44 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	45 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	46 (all A (relation(A) -> A = relation_inverse(relation_inverse(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	47 (all A (ordinal(A) -> epsilon_transitive(union(A)) & ordinal(union(A)) & epsilon_connected(union(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	48 (all A all B A = set_intersection2(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	49 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	50 (all A all B ((all C (in(C,B) <-> C = A)) <-> singleton(A) = B)) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	51 (all A (relation(A) -> relation_rng(A) = relation_image(A,relation_dom(A)))) # label(t146_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	52 (all A (function(A) & relation(A) -> (all B ((all C ((exists D (in(D,relation_dom(A)) & C = apply(A,D))) <-> in(C,B))) <-> B = relation_rng(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	53 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	54 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	55 (all A (relation(A) -> (all B (relation(B) -> subset(relation_dom(relation_composition(A,B)),relation_dom(A)))))) # label(t44_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	56 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(B,A) | ordinal_subset(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	57 (all A (relation(A) -> (all B all C (relation_image(A,B) = C <-> (all D (in(D,C) <-> (exists E (in(ordered_pair(E,D),A) & in(E,B))))))))) # label(d13_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	58 (exists A (relation(A) & one_to_one(A) & ordinal(A) & epsilon_connected(A) & epsilon_transitive(A) & empty(A) & function(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	59 (all A all B (function(B) & relation(B) -> subset(relation_image(B,relation_inverse_image(B,A)),A))) # label(t145_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	60 (all A (ordinal(A) -> -((all B (ordinal(B) -> A != succ(B))) & -being_limit_ordinal(A)) & -((exists B (ordinal(B) & A = succ(B))) & being_limit_ordinal(A)))) # label(t42_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	61 (all A all B (element(B,powerset(powerset(A))) -> element(meet_of_subsets(A,B),powerset(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	62 (all A (function(A) & relation(A) -> (one_to_one(A) -> relation_dom(A) = relation_rng(function_inverse(A)) & relation_rng(A) = relation_dom(function_inverse(A))))) # label(t55_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	63 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	64 (all A all B (relation(A) & relation(B) -> relation(set_difference(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	65 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(D,C),A))) <-> relation_inverse(A) = B))))) # label(d7_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	66 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	67 (all A all B (relation(B) -> ((all C all D (in(C,A) & D = C <-> in(ordered_pair(C,D),B))) <-> B = identity_relation(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	68 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(B,D) & in(A,C))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	69 (all A (function(A) & one_to_one(A) & relation(A) -> relation(relation_inverse(A)) & function(relation_inverse(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	70 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(A,relation_dom(relation_composition(C,B))) -> apply(relation_composition(C,B),A) = apply(B,apply(C,A))))))) # label(t22_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	71 (all A all B all C -(in(B,C) & in(C,A) & in(A,B))) # label(t3_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	72 (all A all B (relation(B) -> -(empty_set = relation_inverse_image(B,A) & subset(A,relation_rng(B)) & A != empty_set))) # label(t174_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	73 (all A all B (relation(B) & relation(A) -> relation(set_intersection2(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	74 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	75 (all A all B all C (relation(C) -> (in(A,B) & in(A,relation_rng(C)) <-> in(A,relation_rng(relation_rng_restriction(B,C)))))) # label(t115_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	76 (all A (relation(A) -> (is_transitive_in(A,relation_field(A)) <-> transitive(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	77 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	78 (all A (ordinal(A) -> (all B (ordinal(B) -> -(-in(A,B) & A != B & -in(B,A)))))) # label(t24_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	79 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	80 (all A all B (proper_subset(A,B) <-> A != B & subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	81 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	82 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	83 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) = union_of_subsets(A,complements_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	84 (all A (relation(A) -> (all B (is_transitive_in(A,B) <-> (all C all D all E (in(ordered_pair(C,D),A) & in(ordered_pair(D,E),A) & in(E,B) & in(D,B) & in(C,B) -> in(ordered_pair(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	85 (all A ((all B -(in(B,A) & (all C all D ordered_pair(C,D) != B))) <-> relation(A))) # label(d1_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	86 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	87 (all A all B all C (element(B,powerset(C)) & in(A,B) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	88 (exists A (relation(A) & empty(A) & function(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	89 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	90 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(A,C) & in(B,C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	91 (all A (relation(A) & function(A) -> (all B all C ((in(B,relation_dom(A)) -> (in(ordered_pair(B,C),A) <-> C = apply(A,B))) & (-in(B,relation_dom(A)) -> (C = apply(A,B) <-> C = empty_set)))))) # label(d4_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	92 (all A all B all C (relation(C) -> ((exists D (in(D,relation_rng(C)) & in(D,B) & in(ordered_pair(A,D),C))) <-> in(A,relation_inverse_image(C,B))))) # label(t166_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	93 (all A all B (relation(B) -> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A))) # label(t119_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	94 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	95 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	96 (all A (relation(A) -> (all B ((all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))) <-> B = relation_rng(A))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	97 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> ((all D (element(D,powerset(A)) -> (in(D,C) <-> in(subset_complement(A,D),B)))) <-> complements_of_subsets(A,B) = C))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	98 (all A (relation(A) -> ((all B (in(B,relation_field(A)) -> in(ordered_pair(B,B),A))) <-> reflexive(A)))) # label(l1_wellord1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	99 (all A (function(A) & relation(A) -> (one_to_one(A) -> (all B (relation(B) & function(B) -> (B = function_inverse(A) <-> (all C all D ((C = apply(A,D) & in(D,relation_dom(A)) -> apply(B,C) = D & in(C,relation_rng(A))) & (in(C,relation_rng(A)) & apply(B,C) = D -> apply(A,D) = C & in(D,relation_dom(A))))) & relation_rng(A) = relation_dom(B))))))) # label(t54_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	100 (all A (relation(A) & function(A) -> (one_to_one(A) -> one_to_one(function_inverse(A))))) # label(t62_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	101 (all A A = cast_to_subset(A)) # label(d4_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	102 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	103 (all A (relation(A) -> (empty_set = relation_dom(A) <-> relation_rng(A) = empty_set))) # label(t65_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	104 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	105 (all A all B all C (unordered_pair(B,C) = singleton(A) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	106 (all A all B (relation(B) -> subset(relation_rng_restriction(A,B),B))) # label(t117_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	107 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	108 (all A (relation(A) & function(A) -> (one_to_one(A) -> relation_inverse(A) = function_inverse(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	109 (all A all B set_union2(A,set_difference(B,A)) = set_union2(A,B)) # label(t39_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	110 (all A all B all C (subset(A,C) & subset(A,B) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	111 (all A all B (-((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)) & -(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	112 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	113 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	114 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	115 (all A (A = relation_dom(identity_relation(A)) & relation_rng(identity_relation(A)) = A)) # label(t71_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	116 (all A all B (element(B,powerset(A)) -> (all C (element(C,powerset(A)) -> (subset(B,subset_complement(A,C)) <-> disjoint(B,C)))))) # label(t43_subset_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	117 (all A all B (ordinal(B) & ordinal(A) -> (ordinal_subset(A,B) <-> subset(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	118 (all A all B (B = powerset(A) <-> (all C (in(C,B) <-> subset(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	119 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	120 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	121 (all A (relation(A) -> ((all B all C -in(ordered_pair(B,C),A)) -> A = empty_set))) # label(t56_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	122 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	123 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	124 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	125 (all A all B all C (element(C,powerset(A)) -> -(in(B,subset_complement(A,C)) & in(B,C)))) # label(t54_subset_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	126 (all A (relation(A) -> (all B (is_reflexive_in(A,B) <-> (all C (in(C,B) -> in(ordered_pair(C,C),A))))))) # label(d1_relat_2) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	127 (all A all B all C (relation(C) & function(C) -> (B = apply(C,A) & in(A,relation_dom(C)) <-> in(ordered_pair(A,B),C)))) # label(t8_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	128 (all A (relation(A) -> (all B (relation(B) -> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)))))) # label(t160_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	129 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	130 (all A (relation(A) -> (all B (relation(B) -> subset(relation_rng(relation_composition(A,B)),relation_rng(B)))))) # label(t45_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	131 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	132 (all A (function(A) & relation(A) -> function(function_inverse(A)) & relation(function_inverse(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	133 (all A (epsilon_transitive(A) -> (all B (ordinal(B) -> (proper_subset(A,B) -> in(A,B)))))) # label(t21_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	134 (all A (ordinal(A) -> (all B (ordinal(B) -> (ordinal_subset(succ(A),B) <-> in(A,B)))))) # label(t33_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	135 (all A (function(identity_relation(A)) & relation(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	136 (exists A (epsilon_connected(A) & ordinal(A) & epsilon_transitive(A) & -empty(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	137 (all A (relation(A) & function(A) -> (all B all C (relation_image(A,B) = C <-> (all D (in(D,C) <-> (exists E (in(E,relation_dom(A)) & in(E,B) & D = apply(A,E))))))))) # label(d12_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	138 (all A -empty(succ(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	139 (all A in(A,succ(A))) # label(t10_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	140 (all A (empty(A) -> epsilon_transitive(A) & ordinal(A) & epsilon_connected(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	141 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	142 (all A all B -(in(A,B) & disjoint(singleton(A),B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	143 (all A all B (A = B <-> subset(B,A) & subset(A,B))) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	144 (all A all B all C all D (in(A,C) & in(B,D) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	145 (all A exists B (in(A,B) & (all C -((all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))) & in(C,B))) & (all C -(subset(C,B) & -in(C,B) & -are_equipotent(C,B))) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	146 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	147 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	148 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	149 (all A all B (element(B,powerset(powerset(A))) -> union(B) = union_of_subsets(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	150 (all A (relation(A) -> relation_dom(relation_inverse(A)) = relation_rng(A) & relation_rng(relation_inverse(A)) = relation_dom(A))) # label(t37_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	151 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	152 (all A (relation(A) -> (all B all C (relation(C) -> ((all D all E (in(ordered_pair(D,E),A) & in(D,B) <-> in(ordered_pair(D,E),C))) <-> relation_dom_restriction(A,B) = C))))) # label(d11_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	153 (all A all B (relation(B) -> relation_image(B,set_intersection2(relation_dom(B),A)) = relation_image(B,A))) # label(t145_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	154 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	155 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_rng(A),relation_rng(B)) & subset(relation_dom(A),relation_dom(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	156 (all A all B (element(B,powerset(powerset(A))) -> meet_of_subsets(A,B) = set_meet(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	157 (all A all B all C ((all D (D = A | B = D <-> in(D,C))) <-> C = unordered_pair(A,B))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	158 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)))) # label(t118_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	159 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	160 (all A all B (element(B,powerset(powerset(A))) -> element(complements_of_subsets(A,B),powerset(powerset(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	161 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	162 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	163 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	164 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_rng(A),relation_dom(B)) -> relation_dom(relation_composition(A,B)) = relation_dom(A)))))) # label(t46_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	165 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	166 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	167 (all A all B set_intersection2(A,B) = set_difference(A,set_difference(A,B))) # label(t48_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	168 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	169 (all A all B all C -(in(A,B) & empty(C) & element(B,powerset(C)))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	170 (all A all B (relation(B) -> subset(relation_image(B,A),relation_rng(B)))) # label(t144_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	171 (all A (relation(A) & function(A) -> (all B all C (relation_inverse_image(A,B) = C <-> (all D (in(D,C) <-> in(D,relation_dom(A)) & in(apply(A,D),B))))))) # label(d13_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	172 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	173 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	174 (all A all B all C (function(C) & relation(C) -> (in(B,relation_dom(relation_dom_restriction(C,A))) -> apply(C,B) = apply(relation_dom_restriction(C,A),B)))) # label(t70_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	175 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(A,relation_dom(C)) & in(apply(C,A),relation_dom(B)) <-> in(A,relation_dom(relation_composition(C,B)))))))) # label(t21_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	176 (all A all B (relation(B) -> (subset(A,relation_dom(B)) -> subset(A,relation_inverse_image(B,relation_image(B,A)))))) # label(t146_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	177 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	178 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	179 (all A succ(A) = set_union2(A,singleton(A))) # label(d1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	180 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> B = D & A = C)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	181 (all A all B (function(A) & function(B) & relation(B) & relation(A) -> function(relation_composition(A,B)) & relation(relation_composition(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	182 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,B) & in(D,A))))) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	183 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	184 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	185 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.32	186 (all A all B (-((exists C (in(C,B) & in(C,A))) & disjoint(A,B)) & -((all C -(in(C,A) & in(C,B))) & -disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	187 (all A all B (function(B) & relation(B) -> (subset(A,relation_rng(B)) -> A = relation_image(B,relation_inverse_image(B,A))))) # label(t147_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	188 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.32	189 (all A (A = union(A) <-> being_limit_ordinal(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	190 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	191 (all A all B -((all C -((all D -(in(D,B) & in(D,C))) & in(C,B))) & in(A,B))) # label(t7_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	192 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	193 (all A all B (element(B,powerset(powerset(A))) -> element(union_of_subsets(A,B),powerset(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	194 (all A all B (function(B) & relation(B) -> (all C (relation(C) & function(C) -> ((all D (in(D,relation_dom(B)) -> apply(C,D) = apply(B,D))) & relation_dom(B) = set_intersection2(relation_dom(C),A) <-> B = relation_dom_restriction(C,A)))))) # label(t68_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	195 (all A all B all C (relation(C) -> relation_dom_restriction(relation_rng_restriction(A,C),B) = relation_rng_restriction(A,relation_dom_restriction(C,B)))) # label(t140_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	196 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	197 (all A (empty(A) -> relation(relation_dom(A)) & empty(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	198 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	199 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	200 (all A all B (relation(B) -> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A))) # label(t90_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	201 (all A all B ((A != empty_set -> (B = set_meet(A) <-> (all C ((all D (in(D,A) -> in(C,D))) <-> in(C,B))))) & (empty_set = A -> (set_meet(A) = B <-> empty_set = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	202 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	203 (all A all B (empty(A) & relation(B) -> relation(relation_composition(A,B)) & empty(relation_composition(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	204 (all A all B set_difference(A,B) = set_difference(set_union2(A,B),B)) # label(t40_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	205 (all A all B (relation(B) -> (all C (relation(C) -> ((all D all E (in(ordered_pair(D,E),C) <-> in(ordered_pair(D,E),B) & in(E,A))) <-> C = relation_rng_restriction(A,B)))))) # label(d12_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	206 (all A all B all C all D (relation(D) -> (in(A,C) & in(ordered_pair(A,B),D) <-> in(ordered_pair(A,B),relation_composition(identity_relation(C),D))))) # label(t74_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	207 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	208 (all A all B (relation(B) -> subset(relation_dom_restriction(B,A),B))) # label(t88_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	209 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	210 (all A all B all C ((all D (in(D,C) <-> in(D,A) | in(D,B))) <-> set_union2(A,B) = C)) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	211 (all A (relation(A) -> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	212 (all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	213 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),A) -> in(ordered_pair(C,D),B))) <-> subset(A,B)))))) # label(d3_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	214 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	215 (all A all B (relation(B) -> subset(relation_inverse_image(B,A),relation_dom(B)))) # label(t167_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	216 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	217 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	218 (all A (function(A) & empty(A) & relation(A) -> relation(A) & function(A) & one_to_one(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	219 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	220 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	221 (all A all B (relation(B) & function(B) -> (one_to_one(B) & in(A,relation_rng(B)) -> A = apply(relation_composition(function_inverse(B),B),A) & A = apply(B,apply(function_inverse(B),A))))) # label(t57_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	222 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	223 (all A (ordinal(A) -> epsilon_connected(A) & epsilon_transitive(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	224 (all A all B (A = set_difference(A,singleton(B)) <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	225 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	226 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	227 (all A all B ((all C (in(C,B) <-> (exists D (in(C,D) & in(D,A))))) <-> union(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	228 (all A (relation(A) & -empty(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	229 (all A all B all C (unordered_pair(B,C) = singleton(A) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	230 (all A (ordinal(A) -> ((all B (ordinal(B) -> (in(B,A) -> in(succ(B),A)))) <-> being_limit_ordinal(A)))) # label(t41_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	231 (all A ((all B all C -(in(B,A) & in(C,A) & C != B & -in(C,B) & -in(B,C))) <-> epsilon_connected(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	232 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	233 (all A (relation(A) -> (is_reflexive_in(A,relation_field(A)) <-> reflexive(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	234 (exists A (function(A) & relation(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	235 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	236 (all A all B (relation(B) -> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)))) # label(t99_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	237 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	238 (all A all B (relation(B) & function(B) -> (all C (function(C) & relation(C) -> (in(A,relation_dom(B)) -> apply(C,apply(B,A)) = apply(relation_composition(B,C),A)))))) # label(t23_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	239 (all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	240 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	241 (all A all B (relation(A) & function(A) -> function(relation_dom_restriction(A,B)) & relation(relation_dom_restriction(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	242 (all A (ordinal(A) -> -empty(succ(A)) & epsilon_transitive(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	243 (all A all B all C (relation(C) -> (in(A,relation_dom(relation_dom_restriction(C,B))) <-> in(A,B) & in(A,relation_dom(C))))) # label(t86_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	244 (all A all B all C ((all D ((exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))) <-> in(D,C))) <-> cartesian_product2(A,B) = C)) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	245 (all A exists B (in(A,B) & (all C (in(C,B) -> in(powerset(C),B))) & (all C -(-are_equipotent(C,B) & -in(C,B) & subset(C,B))) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	246 (all A all B (relation(B) & function(B) -> ((all C (in(C,A) -> apply(B,C) = C)) & A = relation_dom(B) <-> B = identity_relation(A)))) # label(t34_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	247 (all A all B (relation(A) & relation(B) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	248 (all A all B all C all D ((all E (in(E,D) <-> -(B != E & C != E & E != A))) <-> unordered_triple(A,B,C) = D)) # label(d1_enumset1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	249 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	250 (all A all B (element(B,powerset(A)) -> subset_complement(A,B) = set_difference(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	251 (all A all B (relation_empty_yielding(A) & relation(A) -> relation_empty_yielding(relation_dom_restriction(A,B)) & relation(relation_dom_restriction(A,B)))) # label(fc13_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	252 (all A all B all C (function(C) & relation(C) -> (in(B,A) -> apply(C,B) = apply(relation_dom_restriction(C,A),B)))) # label(t72_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	253 (all A (relation(A) -> (all B all C ((all D ((exists E (in(E,B) & in(ordered_pair(D,E),A))) <-> in(D,C))) <-> relation_inverse_image(A,B) = C)))) # label(d14_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	254 (all A all B (ordinal(B) -> (in(A,B) -> ordinal(A)))) # label(t23_ordinal1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	255 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	256 (exists A (function(A) & relation_empty_yielding(A) & relation(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	257 (all A all B all C (relation(C) -> (in(A,relation_image(C,B)) <-> (exists D (in(D,relation_dom(C)) & in(D,B) & in(ordered_pair(D,A),C)))))) # label(t143_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	258 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	259 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	260 (all A all B ((all C (in(C,B) <-> in(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	261 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	262 (all A (epsilon_connected(A) & epsilon_transitive(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	263 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	264 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.33	265 (all A (relation(A) -> (empty_set = relation_rng(A) | empty_set = relation_dom(A) -> A = empty_set))) # label(t64_relat_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.33	266 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	267 (all A all B all C (subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,C)) & subset(cartesian_product2(C,A),cartesian_product2(C,B)))) # label(t118_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	268 (exists A (epsilon_connected(A) & ordinal(A) & epsilon_transitive(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	269 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	270 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	271 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	272 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	273 (all A all B all C (subset(A,B) -> in(C,A) | subset(A,set_difference(B,singleton(C))))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	274 (all A (function(A) & relation(A) -> ((all B all C (in(C,relation_dom(A)) & apply(A,C) = apply(A,B) & in(B,relation_dom(A)) -> B = C)) <-> one_to_one(A)))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	275 (all A all B (A = empty_set | singleton(B) = A <-> subset(A,singleton(B)))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	276 (all A all B (in(B,A) -> apply(identity_relation(A),B) = B)) # label(t35_funct_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	277 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
1.01/1.34	278 (all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	279 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),union_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause).  [assumption].
1.01/1.34	280 -(all A (relation(A) -> ((all B all C all D (in(ordered_pair(B,C),A) & in(ordered_pair(C,D),A) -> in(ordered_pair(B,D),A))) <-> transitive(A)))) # label(l2_wellord1) # label(negated_conjecture) # label(non_clause).  [assumption].
1.01/1.34	
1.01/1.34	============================== end of process non-clausal formulas ===
1.01/1.34	
1.01/1.34	============================== PROCESS INITIAL CLAUSES ===============
1.01/1.34	
1.01/1.34	============================== PREDICATE ELIMINATION =================
1.01/1.34	281 ordinal(A) | -epsilon_connected(A) | -epsilon_transitive(A) # label(d4_ordinal1) # label(axiom).  [clausify(5)].
1.01/1.34	282 -ordinal(A) | epsilon_connected(A) # label(d4_ordinal1) # label(axiom).  [clausify(5)].
1.01/1.34	283 -ordinal(A) | epsilon_connected(union(A)) # label(fc4_ordinal1) # label(axiom).  [clausify(47)].
1.01/1.34	Derived: -ordinal(A) | ordinal(union(A)) | -epsilon_transitive(union(A)).  [resolve(283,b,281,b)].
1.01/1.34	284 epsilon_connected(c3) # label(rc2_ordinal1) # label(axiom).  [clausify(58)].
1.01/1.34	Derived: ordinal(c3) | -epsilon_transitive(c3).  [resolve(284,a,281,b)].
1.01/1.34	285 epsilon_connected(c5) # label(rc3_ordinal1) # label(axiom).  [clausify(136)].
1.01/1.34	286 -empty(A) | epsilon_connected(A) # label(cc3_ordinal1) # label(axiom).  [clausify(140)].
1.01/1.34	Derived: -empty(A) | ordinal(A) | -epsilon_transitive(A).  [resolve(286,b,281,b)].
1.01/1.34	287 epsilon_connected(empty_set) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom).  [assumption].
1.01/1.34	288 -ordinal(A) | epsilon_connected(A) # label(cc1_ordinal1) # label(axiom).  [clausify(223)].
1.01/1.34	289 in(f76(A),A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.34	Derived: in(f76(A),A) | ordinal(A) | -epsilon_transitive(A).  [resolve(289,b,281,b)].
1.01/1.34	290 in(f77(A),A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.34	Derived: in(f77(A),A) | ordinal(A) | -epsilon_transitive(A).  [resolve(290,b,281,b)].
1.01/1.34	291 f77(A) != f76(A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.34	Derived: f77(A) != f76(A) | ordinal(A) | -epsilon_transitive(A).  [resolve(291,b,281,b)].
1.01/1.34	292 -in(f77(A),f76(A)) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.37	Derived: -in(f77(A),f76(A)) | ordinal(A) | -epsilon_transitive(A).  [resolve(292,b,281,b)].
1.01/1.37	293 -in(f76(A),f77(A)) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.37	Derived: -in(f76(A),f77(A)) | ordinal(A) | -epsilon_transitive(A).  [resolve(293,b,281,b)].
1.01/1.37	294 -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | -epsilon_connected(B) # label(d3_ordinal1) # label(axiom).  [clausify(231)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | -ordinal(B).  [resolve(294,f,282,b)].
1.01/1.37	Derived: -in(A,union(B)) | -in(C,union(B)) | C = A | in(C,A) | in(A,C) | -ordinal(B).  [resolve(294,f,283,b)].
1.01/1.37	Derived: -in(A,c3) | -in(B,c3) | B = A | in(B,A) | in(A,B).  [resolve(294,f,284,a)].
1.01/1.37	Derived: -in(A,c5) | -in(B,c5) | B = A | in(B,A) | in(A,B).  [resolve(294,f,285,a)].
1.01/1.37	Derived: -in(A,empty_set) | -in(B,empty_set) | B = A | in(B,A) | in(A,B).  [resolve(294,f,287,a)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | in(f76(B),B).  [resolve(294,f,289,b)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | in(f77(B),B).  [resolve(294,f,290,b)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | f77(B) != f76(B).  [resolve(294,f,291,b)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | -in(f77(B),f76(B)).  [resolve(294,f,292,b)].
1.01/1.37	Derived: -in(A,B) | -in(C,B) | C = A | in(C,A) | in(A,C) | -in(f76(B),f77(B)).  [resolve(294,f,293,b)].
1.01/1.37	295 -ordinal(A) | epsilon_connected(succ(A)) # label(fc3_ordinal1) # label(axiom).  [clausify(242)].
1.01/1.37	Derived: -ordinal(A) | -in(B,succ(A)) | -in(C,succ(A)) | C = B | in(C,B) | in(B,C).  [resolve(295,b,294,f)].
1.01/1.37	296 -epsilon_connected(A) | -epsilon_transitive(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom).  [clausify(262)].
1.01/1.37	Derived: -epsilon_transitive(c5) | ordinal(c5).  [resolve(296,a,285,a)].
1.01/1.37	Derived: -epsilon_transitive(empty_set) | ordinal(empty_set).  [resolve(296,a,287,a)].
1.01/1.37	Derived: -epsilon_transitive(succ(A)) | ordinal(succ(A)) | -ordinal(A).  [resolve(296,a,295,b)].
1.01/1.37	297 epsilon_connected(c12) # label(rc1_ordinal1) # label(axiom).  [clausify(268)].
1.01/1.37	Derived: -in(A,c12) | -in(B,c12) | B = A | in(B,A) | in(A,B).  [resolve(297,a,294,f)].
1.01/1.37	298 -ordinal(A) | -ordinal(B) | succ(B) != A | -being_limit_ordinal(A) # label(t42_ordinal1) # label(lemma).  [clausify(60)].
1.01/1.37	299 -ordinal(A) | ordinal(f22(A)) | being_limit_ordinal(A) # label(t42_ordinal1) # label(lemma).  [clausify(60)].
1.01/1.37	300 -ordinal(A) | succ(f22(A)) = A | being_limit_ordinal(A) # label(t42_ordinal1) # label(lemma).  [clausify(60)].
1.01/1.37	Derived: -ordinal(A) | -ordinal(B) | succ(B) != A | -ordinal(A) | ordinal(f22(A)).  [resolve(298,d,299,c)].
1.01/1.37	Derived: -ordinal(A) | -ordinal(B) | succ(B) != A | -ordinal(A) | succ(f22(A)) = A.  [resolve(298,d,300,c)].
1.01/1.37	301 union(A) != A | being_limit_ordinal(A) # label(d6_ordinal1) # label(axiom).  [clausify(189)].
1.01/1.37	Derived: union(A) != A | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(301,b,298,d)].
1.01/1.37	302 union(A) = A | -being_limit_ordinal(A) # label(d6_ordinal1) # label(axiom).  [clausify(189)].
1.01/1.37	Derived: union(A) = A | -ordinal(A) | ordinal(f22(A)).  [resolve(302,b,299,c)].
1.01/1.37	Derived: union(A) = A | -ordinal(A) | succ(f22(A)) = A.  [resolve(302,b,300,c)].
1.01/1.37	303 -ordinal(A) | ordinal(f75(A)) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(230)].
1.01/1.37	Derived: -ordinal(A) | ordinal(f75(A)) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(303,c,298,d)].
1.01/1.37	Derived: -ordinal(A) | ordinal(f75(A)) | union(A) = A.  [resolve(303,c,302,b)].
1.01/1.37	304 -ordinal(A) | in(f75(A),A) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(230)].
1.01/1.37	Derived: -ordinal(A) | in(f75(A),A) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(304,c,298,d)].
1.01/1.37	Derived: -ordinal(A) | in(f75(A),A) | union(A) = A.  [resolve(304,c,302,b)].
1.01/1.37	305 -ordinal(A) | -in(succ(f75(A)),A) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(230)].
1.01/1.37	Derived: -ordinal(A) | -in(succ(f75(A)),A) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(305,c,298,d)].
2.27/2.61	Derived: -ordinal(A) | -in(succ(f75(A)),A) | union(A) = A.  [resolve(305,c,302,b)].
2.27/2.61	306 -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(230)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | ordinal(f22(A)).  [resolve(306,e,299,c)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | succ(f22(A)) = A.  [resolve(306,e,300,c)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | union(A) != A.  [resolve(306,e,301,b)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | ordinal(f75(A)).  [resolve(306,e,303,c)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | in(f75(A),A).  [resolve(306,e,304,c)].
2.27/2.61	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | -in(succ(f75(A)),A).  [resolve(306,e,305,c)].
2.27/2.61	307 -relation(A) | -in(B,relation_field(A)) | in(ordered_pair(B,B),A) | -reflexive(A) # label(l1_wellord1) # label(lemma).  [clausify(98)].
2.27/2.61	308 -relation(A) | in(f40(A),relation_field(A)) | reflexive(A) # label(l1_wellord1) # label(lemma).  [clausify(98)].
2.27/2.61	309 -relation(A) | -in(ordered_pair(f40(A),f40(A)),A) | reflexive(A) # label(l1_wellord1) # label(lemma).  [clausify(98)].
2.27/2.61	Derived: -relation(A) | -in(B,relation_field(A)) | in(ordered_pair(B,B),A) | -relation(A) | in(f40(A),relation_field(A)).  [resolve(307,d,308,c)].
2.27/2.61	Derived: -relation(A) | -in(B,relation_field(A)) | in(ordered_pair(B,B),A) | -relation(A) | -in(ordered_pair(f40(A),f40(A)),A).  [resolve(307,d,309,c)].
2.27/2.61	310 -relation(A) | -is_reflexive_in(A,relation_field(A)) | reflexive(A) # label(d9_relat_2) # label(axiom).  [clausify(233)].
2.27/2.61	Derived: -relation(A) | -is_reflexive_in(A,relation_field(A)) | -relation(A) | -in(B,relation_field(A)) | in(ordered_pair(B,B),A).  [resolve(310,c,307,d)].
2.27/2.61	311 -relation(A) | is_reflexive_in(A,relation_field(A)) | -reflexive(A) # label(d9_relat_2) # label(axiom).  [clausify(233)].
2.27/2.61	Derived: -relation(A) | is_reflexive_in(A,relation_field(A)) | -relation(A) | in(f40(A),relation_field(A)).  [resolve(311,c,308,c)].
2.27/2.61	Derived: -relation(A) | is_reflexive_in(A,relation_field(A)) | -relation(A) | -in(ordered_pair(f40(A),f40(A)),A).  [resolve(311,c,309,c)].
2.27/2.61	
2.27/2.61	============================== end predicate elimination =============
2.27/2.61	
2.27/2.61	Auto_denials:  (non-Horn, no changes).
2.27/2.61	
2.27/2.61	Term ordering decisions:
2.27/2.61	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. c10=1. c11=1. c12=1. c13=1. c14=1. c15=1. c16=1. ordered_pair=1. apply=1. relation_dom_restriction=1. relation_composition=1. set_difference=1. relation_image=1. set_intersection2=1. set_union2=1. relation_inverse_image=1. cartesian_product2=1. unordered_pair=1. relation_rng_restriction=1. complements_of_subsets=1. subset_complement=1. meet_of_subsets=1. union_of_subsets=1. f1=1. f2=1. f3=1. f5=1. f8=1. f9=1. f15=1. f16=1. f17=1. f23=1. f24=1. f25=1. f26=1. f27=1. f29=1. f30=1. f31=1. f33=1. f34=1. f36=1. f37=1. f41=1. f42=1. f43=1. f44=1. f47=1. f52=1. f60=1. f62=1. f65=1. f66=1. f70=1. f71=1. f72=1. f73=1. f84=1. f90=1. relation_dom=1. powerset=1. relation_rng=1. singleton=1. succ=1. union=1. identity_relation=1. function_inverse=1. relation_inverse=1. relation_field=1. set_meet=1. cast_to_subset=1. f4=1. f6=1. f22=1. f28=1. f32=1. f40=1. f45=1. f46=1. f51=1. f56=1. f57=1. f61=1. f75=1. f76=1. f77=1. f83=1. f91=1. f92=1. unordered_triple=1. subset_difference=1. f7=1. f10=1. f11=1. f12=1. f14=1. f18=1. f20=1. f21=1. f35=1. f38=1. f39=1. f49=1. f50=1. f53=1. f54=1. f55=1. f58=1. f59=1. f63=1. f64=1. f67=1. f68=1. f69=1. f74=1. f78=1. f79=1. f80=1. f86=1. f87=1. f89=1. f19=1. f48=1. f81=1. f82=1. f85=1. f88=1. f13=1.
2.27/2.61	
2.27/2.61	============================== end of process initial clauses ========
2.27/2.61	
2.27/2.61	============================== CLAUSES FOR SEARCH ====================
2.27/2.61	
2.27/2.61	============================== end of clauses for search =============
2.27/2.61	
2.27/2.61	============================== SEARCH ================================
2.27/2.61	
2.27/2.61	% Starting search at 0.30 seconds.
2.27/2.61	
2.27/2.61	Low Water (kAlarm clock 
119.60/120.11	Prover9 interrupted
119.60/120.12	EOF