0.04/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.34	% Computer   : n009.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 180
0.12/0.34	% DateTime   : Thu Aug 29 14:34:27 EDT 2019
0.12/0.34	% CPUTime    : 
0.98/1.25	============================== Prover9 ===============================
0.98/1.25	Prover9 (32) version 2009-11A, November 2009.
0.98/1.25	Process 5890 was started by sandbox on n009.cluster.edu,
0.98/1.25	Thu Aug 29 14:34:28 2019
0.98/1.25	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_5736_n009.cluster.edu".
0.98/1.25	============================== end of head ===========================
0.98/1.25	
0.98/1.25	============================== INPUT =================================
0.98/1.25	
0.98/1.25	% Reading from file /tmp/Prover9_5736_n009.cluster.edu
0.98/1.25	
0.98/1.25	set(prolog_style_variables).
0.98/1.25	set(auto2).
0.98/1.25	    % set(auto2) -> set(auto).
0.98/1.25	    % set(auto) -> set(auto_inference).
0.98/1.25	    % set(auto) -> set(auto_setup).
0.98/1.25	    % set(auto_setup) -> set(predicate_elim).
0.98/1.25	    % set(auto_setup) -> assign(eq_defs, unfold).
0.98/1.25	    % set(auto) -> set(auto_limits).
0.98/1.25	    % set(auto_limits) -> assign(max_weight, "100.000").
0.98/1.25	    % set(auto_limits) -> assign(sos_limit, 20000).
0.98/1.25	    % set(auto) -> set(auto_denials).
0.98/1.25	    % set(auto) -> set(auto_process).
0.98/1.25	    % set(auto2) -> assign(new_constants, 1).
0.98/1.25	    % set(auto2) -> assign(fold_denial_max, 3).
0.98/1.25	    % set(auto2) -> assign(max_weight, "200.000").
0.98/1.25	    % set(auto2) -> assign(max_hours, 1).
0.98/1.25	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.98/1.25	    % set(auto2) -> assign(max_seconds, 0).
0.98/1.25	    % set(auto2) -> assign(max_minutes, 5).
0.98/1.25	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.98/1.25	    % set(auto2) -> set(sort_initial_sos).
0.98/1.25	    % set(auto2) -> assign(sos_limit, -1).
0.98/1.25	    % set(auto2) -> assign(lrs_ticks, 3000).
0.98/1.25	    % set(auto2) -> assign(max_megs, 400).
0.98/1.25	    % set(auto2) -> assign(stats, some).
0.98/1.25	    % set(auto2) -> clear(echo_input).
0.98/1.25	    % set(auto2) -> set(quiet).
0.98/1.25	    % set(auto2) -> clear(print_initial_clauses).
0.98/1.25	    % set(auto2) -> clear(print_given).
0.98/1.25	assign(lrs_ticks,-1).
0.98/1.25	assign(sos_limit,10000).
0.98/1.25	assign(order,kbo).
0.98/1.25	set(lex_order_vars).
0.98/1.25	clear(print_given).
0.98/1.25	
0.98/1.25	% formulas(sos).  % not echoed (325 formulas)
0.98/1.25	
0.98/1.25	============================== end of input ==========================
0.98/1.25	
0.98/1.25	% From the command line: assign(max_seconds, 180).
0.98/1.25	
0.98/1.25	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.98/1.25	
0.98/1.25	% Formulas that are not ordinary clauses:
0.98/1.25	1 (all A (relation(A) -> (all B ((all C all D (in(C,B) & in(ordered_pair(C,D),A) & in(ordered_pair(D,C),A) & in(D,B) -> C = D)) <-> is_antisymmetric_in(A,B))))) # label(d4_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	2 (all A all B (relation(B) -> relation_rng_restriction(A,relation_dom_restriction(B,A)) = relation_restriction(B,A))) # label(t18_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.25	3 (all A all B ((all C (in(C,B) <-> (exists D (in(D,A) & in(C,D))))) <-> B = union(A))) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	4 (all A all B (relation(B) & empty(A) -> relation(relation_composition(B,A)) & empty(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	5 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	6 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	7 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	8 (all A all B all C (relation(C) -> (in(A,relation_rng(relation_rng_restriction(B,C))) <-> in(A,relation_rng(C)) & in(A,B)))) # label(t115_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.25	9 (all A (-empty(A) & relation(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.25	10 (all A exists B (in(A,B) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.25	11 (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].
0.98/1.25	12 (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].
0.98/1.26	13 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	14 (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].
0.98/1.26	15 (all A all B all C (relation(C) -> subset(fiber(relation_restriction(C,A),B),fiber(C,B)))) # label(t21_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	16 (all A all B all C all D ((all E (-(C != E & B != E & A != E) <-> in(E,D))) <-> D = unordered_triple(A,B,C))) # label(d1_enumset1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	17 (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].
0.98/1.26	18 (all A ((all B -((all C all D ordered_pair(C,D) != B) & in(B,A))) <-> relation(A))) # label(d1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	19 (all A (relation(A) -> set_union2(relation_dom(A),relation_rng(A)) = relation_field(A))) # label(d6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	20 (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].
0.98/1.26	21 (all A all B ((-empty(A) -> (in(B,A) <-> element(B,A))) & (empty(A) -> (element(B,A) <-> empty(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	22 (all A all B all C (relation(C) -> (in(A,relation_inverse_image(C,B)) <-> (exists D (in(D,B) & in(ordered_pair(A,D),C) & in(D,relation_rng(C))))))) # label(t166_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	23 (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].
0.98/1.26	24 (all A ((all B all C -(in(C,A) & -in(B,C) & C != B & -in(C,B) & in(B,A))) <-> epsilon_connected(A))) # label(d3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	25 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	26 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -(disjoint(A,B) & (exists C in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	27 (all A (relation(A) -> (transitive(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)))))) # label(l2_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	28 (all A (function(A) & relation(A) -> (all B all C ((all D (in(D,relation_dom(A)) & in(apply(A,D),B) <-> in(D,C))) <-> C = relation_inverse_image(A,B))))) # label(d13_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	29 (all A (empty(A) -> empty(relation_inverse(A)) & relation(relation_inverse(A)))) # label(fc11_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	30 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	31 (all A all B (subset(A,singleton(B)) <-> A = singleton(B) | empty_set = A)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	32 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C ((exists D in(ordered_pair(C,D),A)) <-> in(C,B))))))) # label(d4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	33 (all A all B (disjoint(A,B) <-> A = set_difference(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	34 (all A (relation(A) -> (empty_set = relation_dom(A) | relation_rng(A) = empty_set -> empty_set = A))) # label(t64_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	35 (all A all B (relation(B) & function(B) -> (one_to_one(B) & in(A,relation_rng(B)) -> A = apply(B,apply(function_inverse(B),A)) & A = apply(relation_composition(function_inverse(B),B),A)))) # label(t57_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	36 (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].
0.98/1.26	37 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	38 (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].
0.98/1.26	39 (all A all B (function(B) & relation(B) -> (all C (relation(C) & function(C) -> (set_intersection2(relation_dom(C),A) = relation_dom(B) & (all D (in(D,relation_dom(B)) -> apply(C,D) = apply(B,D))) <-> relation_dom_restriction(C,A) = B))))) # label(t68_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	40 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	41 (all A all B (ordinal(B) -> (in(A,B) -> ordinal(A)))) # label(t23_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	42 (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].
0.98/1.26	43 (all A all B (relation(B) -> subset(relation_dom(relation_rng_restriction(A,B)),relation_dom(B)))) # label(l29_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	44 (all A all B (in(B,A) -> apply(identity_relation(A),B) = B)) # label(t35_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	45 (all A -empty(succ(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	46 (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].
0.98/1.26	47 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(B,relation_field(C)) & in(A,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	48 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	49 (all A all B all C (unordered_pair(A,B) = C <-> (all D (D = A | D = B <-> in(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	50 (all A (relation(A) -> (antisymmetric(A) <-> is_antisymmetric_in(A,relation_field(A))))) # label(d12_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	51 (all A all B ((all C (in(C,B) <-> in(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	52 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	53 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	54 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	55 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	56 (exists A (function(A) & empty(A) & relation(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	57 (all A all B all C (relation(C) & function(C) -> (in(B,relation_dom(C)) & in(B,A) <-> in(B,relation_dom(relation_dom_restriction(C,A)))))) # label(l82_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	58 (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].
0.98/1.26	59 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	60 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> 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].
0.98/1.26	61 (all A all B (function(A) & relation(A) -> relation(relation_dom_restriction(A,B)) & function(relation_dom_restriction(A,B)))) # label(fc4_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	62 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	63 (all A all B (relation(A) & relation(B) -> relation(set_difference(A,B)))) # label(fc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	64 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	65 (all A all B (element(B,powerset(powerset(A))) -> set_meet(B) = meet_of_subsets(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	66 (all A (epsilon_transitive(A) & epsilon_connected(A) <-> ordinal(A))) # label(d4_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	67 (all A all B all C (in(B,C) & in(A,C) <-> subset(unordered_pair(A,B),C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	68 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	69 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	70 (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].
0.98/1.26	71 (all A (epsilon_transitive(A) <-> (all B (in(B,A) -> subset(B,A))))) # label(d2_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	72 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	73 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	74 (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].
0.98/1.26	75 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	76 (all A all B (relation(B) & function(B) -> (identity_relation(A) = B <-> A = relation_dom(B) & (all C (in(C,A) -> C = apply(B,C)))))) # label(t34_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	77 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	78 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	79 (all A (empty(A) -> relation(relation_dom(A)) & empty(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	80 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(relation_composition(C,B))) -> apply(B,apply(C,A)) = apply(relation_composition(C,B),A)))))) # label(t22_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	81 (all A (function(identity_relation(A)) & relation(identity_relation(A)))) # label(fc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	82 (all A all B (relation(B) -> relation(relation_rng_restriction(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	83 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	84 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	85 (all A all B all C ((all D (in(D,C) <-> (exists E exists F (D = ordered_pair(E,F) & in(F,B) & in(E,A))))) <-> C = cartesian_product2(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	86 (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].
0.98/1.26	87 (all A (ordinal(A) -> -(-being_limit_ordinal(A) & (all B (ordinal(B) -> A != succ(B)))) & -(being_limit_ordinal(A) & (exists B (ordinal(B) & A = succ(B)))))) # label(t42_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	88 (all A all B all C (relation(C) -> (in(A,relation_field(relation_restriction(C,B))) -> in(A,B) & in(A,relation_field(C))))) # label(t19_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	89 (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].
0.98/1.26	90 (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].
0.98/1.26	91 (all A all B (ordinal(B) -> -(A != empty_set & (all C (ordinal(C) -> -((all D (ordinal(D) -> (in(D,A) -> ordinal_subset(C,D)))) & in(C,A)))) & subset(A,B)))) # label(t32_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	92 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	93 (all A all B (function(A) & function(B) & relation(B) & relation(A) -> relation(relation_composition(A,B)) & function(relation_composition(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	94 (all A (relation(A) -> (well_ordering(A) <-> well_orders(A,relation_field(A))))) # label(t8_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	95 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	96 (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].
0.98/1.26	97 (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].
0.98/1.26	98 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	99 (all A all B (relation(B) -> -(relation_inverse_image(B,A) = empty_set & subset(A,relation_rng(B)) & A != empty_set))) # label(t174_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	100 (all A all B (subset(A,B) -> B = set_union2(A,B))) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	101 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	102 (all A all B all C (unordered_pair(B,C) = singleton(A) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	103 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	104 (all A (relation(A) -> (is_well_founded_in(A,relation_field(A)) <-> well_founded_relation(A)))) # label(t5_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	105 (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].
0.98/1.26	106 (all A all B all C (disjoint(B,C) & subset(A,B) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	107 (all A (relation(A) -> (all B all C (C = fiber(A,B) <-> (all D (in(ordered_pair(D,B),A) & B != D <-> in(D,C))))))) # label(d1_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	108 (all A all B (-in(B,A) <-> set_difference(A,singleton(B)) = A)) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	109 (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].
0.98/1.26	110 (all A all B (relation(B) -> subset(relation_dom_restriction(B,A),B))) # label(t88_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	111 (all A all B (element(B,powerset(powerset(A))) -> union_of_subsets(A,B) = union(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	112 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	113 (all A (relation(A) -> (all B (relation(B) -> relation_image(B,relation_rng(A)) = relation_rng(relation_composition(A,B)))))) # label(t160_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	114 (all A (epsilon_connected(A) & epsilon_transitive(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	115 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	116 (all A (A = union(A) <-> being_limit_ordinal(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	117 (all A (empty(A) -> empty(relation_rng(A)) & relation(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	118 (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].
0.98/1.26	119 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	120 (all A all B (function(B) & relation(B) -> (subset(A,relation_rng(B)) -> relation_image(B,relation_inverse_image(B,A)) = A))) # label(t147_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	121 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(B)) -> apply(relation_composition(B,C),A) = apply(C,apply(B,A))))))) # label(t23_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	122 (all A all B -(in(A,B) & (all C -((all D -(in(D,C) & in(D,B))) & in(C,B))))) # label(t7_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	123 (all A all B all C (subset(A,B) -> subset(cartesian_product2(C,A),cartesian_product2(C,B)) & subset(cartesian_product2(A,C),cartesian_product2(B,C)))) # label(t118_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	124 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	125 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	126 (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].
0.98/1.26	127 (all A all B all C (function(C) & relation(C) -> (in(ordered_pair(A,B),C) <-> in(A,relation_dom(C)) & B = apply(C,A)))) # label(t8_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	128 (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].
0.98/1.26	129 (all A all B all C (relation(C) -> (in(A,C) & in(A,cartesian_product2(B,B)) <-> in(A,relation_restriction(C,B))))) # label(t16_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	130 (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].
0.98/1.26	131 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	132 (all A all B all C (subset(A,B) & subset(B,C) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	133 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	134 (all A all B all C -(in(A,B) & in(B,C) & in(C,A))) # label(t3_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	135 (all A all B (relation(B) -> subset(relation_field(relation_restriction(B,A)),relation_field(B)) & subset(relation_field(relation_restriction(B,A)),A))) # label(t20_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.26	136 (all A (function(A) & relation(A) -> (one_to_one(A) <-> (all B all C (in(C,relation_dom(A)) & apply(A,B) = apply(A,C) & in(B,relation_dom(A)) -> C = B))))) # label(d8_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.26	137 (all A (relation(A) -> (antisymmetric(A) <-> (all B all C (in(ordered_pair(B,C),A) & in(ordered_pair(C,B),A) -> C = B))))) # label(l3_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	138 (exists A (relation(A) & function(A) & relation_empty_yielding(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	139 (exists A (-empty(A) & epsilon_transitive(A) & epsilon_connected(A) & ordinal(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	140 (all A all B all C (relation(C) -> relation_rng_restriction(A,relation_dom_restriction(C,B)) = relation_dom_restriction(relation_rng_restriction(A,C),B))) # label(t140_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	141 (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].
0.98/1.27	142 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	143 (all A (relation(A) -> (all B (relation_rng(A) = B <-> (all C ((exists D in(ordered_pair(D,C),A)) <-> in(C,B))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	144 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) <-> (all C all D (in(ordered_pair(C,D),A) -> in(ordered_pair(C,D),B)))))))) # label(d3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	145 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	146 (all A all B (singleton(A) = B <-> (all C (C = A <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	147 (all A A = cast_to_subset(A)) # label(d4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	148 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	149 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	150 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	151 (all A (function(A) & relation(A) -> (all B all C ((all D ((exists E (in(E,relation_dom(A)) & in(E,B) & apply(A,E) = D)) <-> in(D,C))) <-> C = relation_image(A,B))))) # label(d12_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	152 (all A all B ((empty_set != A -> (B = set_meet(A) <-> (all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))))) & (empty_set = A -> (B = set_meet(A) <-> B = empty_set)))) # label(d1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	153 (all A all B (element(B,powerset(A)) -> (all C (element(C,powerset(A)) -> (disjoint(B,C) <-> subset(B,subset_complement(A,C))))))) # label(t43_subset_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	154 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_rng(A),relation_dom(B)) -> relation_dom(A) = relation_dom(relation_composition(A,B))))))) # label(t46_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	155 (all A ((all B (in(B,A) -> ordinal(B) & subset(B,A))) -> ordinal(A))) # label(t31_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	156 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	157 (all A set_union2(A,singleton(A)) = succ(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	158 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	159 (all A all B (relation(A) & relation_empty_yielding(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].
0.98/1.27	160 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	161 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	162 (all A all B all C -(in(A,B) & empty(C) & element(B,powerset(C)))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	163 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	164 (all A all B (relation(A) -> relation(relation_restriction(A,B)))) # label(dt_k2_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	165 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	166 (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].
0.98/1.27	167 (all A (empty(A) -> ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	168 (all A all B ((all C (subset(C,A) <-> in(C,B))) <-> powerset(A) = B)) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	169 (all A (relation(A) -> (all B all C (C = relation_inverse_image(A,B) <-> (all D (in(D,C) <-> (exists E (in(E,B) & in(ordered_pair(D,E),A))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	170 (all A (relation(A) -> (is_transitive_in(A,relation_field(A)) <-> transitive(A)))) # label(d16_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	171 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> -in(D,B) & in(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	172 (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].
0.98/1.27	173 (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].
0.98/1.27	174 (all A (ordinal(A) -> -empty(succ(A)) & epsilon_connected(succ(A)) & ordinal(succ(A)) & epsilon_transitive(succ(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	175 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	176 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	177 (all A all B (empty_set = set_difference(A,B) <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	178 (all A all B (relation(B) -> (transitive(B) -> transitive(relation_restriction(B,A))))) # label(t24_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	179 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	180 (all A all B (-empty(B) & -empty(A) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	181 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	182 (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].
0.98/1.27	183 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	184 (all A (relation(A) -> (empty_set = relation_dom(A) <-> relation_rng(A) = empty_set))) # label(t65_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	185 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	186 (all A all B all C (relation(C) -> ((exists D (in(ordered_pair(D,A),C) & in(D,B) & in(D,relation_dom(C)))) <-> in(A,relation_image(C,B))))) # label(t143_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	187 (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].
0.98/1.27	188 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	189 (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].
0.98/1.27	190 (all A all B -(empty(B) & B != A & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	191 (all A (relation(A) -> (is_connected_in(A,relation_field(A)) <-> connected(A)))) # label(d14_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	192 (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].
0.98/1.27	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].
0.98/1.27	194 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	195 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	196 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(C,D),A))) <-> A = B))))) # label(d2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	197 (all A (relation(A) & function(A) -> (one_to_one(A) -> (all B (function(B) & relation(B) -> (relation_rng(A) = relation_dom(B) & (all C all D ((apply(B,C) = D & in(C,relation_rng(A)) -> in(D,relation_dom(A)) & C = apply(A,D)) & (C = apply(A,D) & in(D,relation_dom(A)) -> apply(B,C) = D & in(C,relation_rng(A))))) <-> function_inverse(A) = B)))))) # label(t54_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	198 (all A (relation(A) -> (all B ((all C all D -(C != D & -in(ordered_pair(C,D),A) & -in(ordered_pair(D,C),A) & in(D,B) & in(C,B))) <-> is_connected_in(A,B))))) # label(d6_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	199 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	200 (all A all B (B = A <-> subset(B,A) & subset(A,B))) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	201 (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].
0.98/1.27	202 (all A (relation(A) -> relation_dom(relation_inverse(A)) = relation_rng(A) & relation_dom(A) = relation_rng(relation_inverse(A)))) # label(t37_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	203 (all A (empty(A) & function(A) & relation(A) -> one_to_one(A) & function(A) & relation(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	204 (all A all B all C all D -(A != D & A != C & unordered_pair(C,D) = unordered_pair(A,B))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	205 (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].
0.98/1.27	206 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	207 (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].
0.98/1.27	208 (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].
0.98/1.27	209 (all A (relation(A) -> (all B relation_restriction(A,B) = set_intersection2(A,cartesian_product2(B,B))))) # label(d6_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	210 (all A (ordinal(A) -> ordinal(union(A)) & epsilon_connected(union(A)) & epsilon_transitive(union(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	211 (all A all B all C (relation(C) & function(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].
0.98/1.27	212 (all A (relation(A) -> (all B (is_transitive_in(A,B) <-> (all C all D all E (in(D,B) & in(ordered_pair(D,E),A) & in(ordered_pair(C,D),A) & in(E,B) & in(C,B) -> in(ordered_pair(C,E),A))))))) # label(d8_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	213 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	214 (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].
0.98/1.27	215 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	216 (all A all B (empty(A) & relation(B) -> empty(relation_composition(A,B)) & relation(relation_composition(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	217 (all A (relation(A) -> ((all B -(empty_set != B & (all C -(in(C,B) & disjoint(fiber(A,C),B))) & subset(B,relation_field(A)))) <-> well_founded_relation(A)))) # label(d2_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	218 (all A (relation(A) -> (all B (is_reflexive_in(A,B) & is_connected_in(A,B) & is_well_founded_in(A,B) & is_antisymmetric_in(A,B) & is_transitive_in(A,B) <-> well_orders(A,B))))) # label(d5_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	219 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	220 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	221 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	222 (all A empty_set = set_difference(empty_set,A)) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	223 (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].
0.98/1.27	224 (all A all B (relation(B) -> subset(relation_image(B,A),relation_rng(B)))) # label(t144_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	225 (exists A (relation(A) & one_to_one(A) & function(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	226 (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].
0.98/1.27	227 (all A (A != empty_set -> (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].
0.98/1.27	228 (all A all B (relation(B) -> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)))) # label(t145_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	229 (all A (relation(A) -> (is_reflexive_in(A,relation_field(A)) <-> reflexive(A)))) # label(d9_relat_2) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	230 (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].
0.98/1.27	231 (all A empty_set != singleton(A)) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	232 (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].
0.98/1.27	233 (all A exists B (in(A,B) & (all C -(in(C,B) & (all D -(in(D,B) & (all E (subset(E,C) -> in(E,D))))))) & (all C -(-in(C,B) & -are_equipotent(C,B) & subset(C,B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	234 (all A all B all C all D (in(B,D) & in(A,C) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	235 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	236 (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].
0.98/1.27	237 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	238 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	239 (all A all B (relation(B) & relation(A) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	240 (all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & empty_set != B))) # label(t46_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	241 (all A (ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	242 (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].
0.98/1.27	243 (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].
0.98/1.27	244 (all A all B (relation(B) -> (identity_relation(A) = B <-> (all C all D (C = D & in(C,A) <-> in(ordered_pair(C,D),B)))))) # label(d10_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	245 (all A (function(A) & relation(A) -> (one_to_one(A) -> relation_rng(function_inverse(A)) = relation_dom(A) & relation_dom(function_inverse(A)) = relation_rng(A)))) # label(t55_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	246 (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)))) <-> C = complements_of_subsets(A,B)))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	247 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	248 (all A all B (element(B,powerset(A)) -> B = subset_complement(A,subset_complement(A,B)))) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	249 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	250 (all A (relation(A) -> (well_ordering(A) <-> reflexive(A) & transitive(A) & connected(A) & well_founded_relation(A) & antisymmetric(A)))) # label(d4_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	251 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	252 (all A A = union(powerset(A))) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	253 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	254 (all A (relation(A) -> (all B all C ((all D (in(D,C) <-> (exists E (in(E,B) & in(ordered_pair(E,D),A))))) <-> C = relation_image(A,B))))) # label(d13_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	255 (all A all B (relation(B) -> subset(relation_rng_restriction(A,B),B))) # label(t117_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	256 $T # label(dt_k1_enumset1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	257 (all A all B all C all D (in(A,C) & in(B,D) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	258 (all A all B (relation(B) -> (reflexive(B) -> reflexive(relation_restriction(B,A))))) # label(t22_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	259 (all A (relation(A) -> (all B (is_well_founded_in(A,B) <-> (all C -(C != empty_set & (all D -(in(D,C) & disjoint(fiber(A,D),C))) & subset(C,B))))))) # label(d3_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	260 (all A all B all C (set_intersection2(A,B) = C <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	261 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	262 (exists A (ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	263 $T # label(dt_k1_wellord1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	264 (all A (relation(A) -> relation_rng(A) = relation_image(A,relation_dom(A)))) # label(t146_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	265 (all A all B (subset(A,B) & B != A <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	266 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	267 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	268 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	269 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	270 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	271 (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].
0.98/1.27	272 (all A (relation(A) -> ((all B all C -(in(C,relation_field(A)) & B != C & -in(ordered_pair(C,B),A) & -in(ordered_pair(B,C),A) & in(B,relation_field(A)))) <-> connected(A)))) # label(l4_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	273 (all A (function(A) & relation(A) -> (all B ((all C (in(C,B) <-> (exists D (in(D,relation_dom(A)) & C = apply(A,D))))) <-> B = relation_rng(A))))) # label(d5_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	274 (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)) -> (apply(A,B) = C <-> empty_set = C)))))) # label(d4_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	275 (all A all B (-((exists C (in(C,B) & in(C,A))) & disjoint(A,B)) & -(-disjoint(A,B) & (all C -(in(C,B) & in(C,A)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	276 (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].
0.98/1.27	277 (all A all B (empty_set = set_difference(A,B) <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	278 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	279 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	280 (all A all B (relation(B) & relation(A) -> relation(set_intersection2(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	281 (all A all B (function(B) & relation(B) -> (all C (relation(C) & function(C) -> (in(apply(C,A),relation_dom(B)) & in(A,relation_dom(C)) <-> in(A,relation_dom(relation_composition(C,B)))))))) # label(t21_funct_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	282 (all A all B (relation(B) -> (connected(B) -> connected(relation_restriction(B,A))))) # label(t23_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	283 (all A all B all C (relation(C) -> (in(A,relation_dom(relation_dom_restriction(C,B))) <-> in(A,relation_dom(C)) & in(A,B)))) # label(t86_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	284 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.27	285 (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].
0.98/1.27	286 (all A in(A,succ(A))) # label(t10_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	287 (all A all B (subset(A,singleton(B)) <-> empty_set = A | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.27	288 (all A (relation(A) & function(A) -> (one_to_one(A) -> function_inverse(A) = relation_inverse(A)))) # label(d9_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	289 (all A (one_to_one(A) & function(A) & relation(A) -> relation(relation_inverse(A)) & function(relation_inverse(A)))) # label(fc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	290 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	291 (all A all B (relation(B) & function(B) -> function(relation_rng_restriction(A,B)) & relation(relation_rng_restriction(A,B)))) # label(fc5_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	292 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(A,B) | ordinal_subset(B,A))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	293 (all A (ordinal(A) -> (all B (ordinal(B) -> -(B != A & -in(B,A) & -in(A,B)))))) # label(t24_ordinal1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	294 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	295 (all A all B all C all D (relation(D) -> (in(ordered_pair(A,B),D) & in(A,C) <-> in(ordered_pair(A,B),relation_composition(identity_relation(C),D))))) # label(t74_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	296 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (relation_composition(A,B) = C <-> (all D all E ((exists F (in(ordered_pair(F,E),B) & in(ordered_pair(D,F),A))) <-> in(ordered_pair(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	297 (all A (relation_rng(identity_relation(A)) = A & relation_dom(identity_relation(A)) = A)) # label(t71_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	298 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	299 (all A all B (relation(B) -> set_intersection2(relation_rng(B),A) = relation_rng(relation_rng_restriction(A,B)))) # label(t119_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	300 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> D = B & A = C)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	301 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	302 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	303 (all A all B (relation(B) -> relation_dom_restriction(relation_rng_restriction(A,B),A) = relation_restriction(B,A))) # label(t17_wellord1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	304 (all A (relation(A) & function(A) -> function(function_inverse(A)) & relation(function_inverse(A)))) # label(dt_k2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.98/1.32	305 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	306 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_dom(A),relation_rng(B)) -> relation_rng(relation_composition(B,A)) = relation_rng(A)))))) # label(t47_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	307 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.98/1.32	308 -(all A all B (relation(B) -> (antisymmetric(B) -> antisymmetric(relation_restriction(B,A))))) # label(t25_wellord1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.98/1.32	
0.98/1.32	============================== end of process non-clausal formulas ===
0.98/1.32	
0.98/1.32	============================== PROCESS INITIAL CLAUSES ===============
0.98/1.32	
0.98/1.32	============================== PREDICATE ELIMINATION =================
0.98/1.32	309 -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | -epsilon_connected(B) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.32	310 in(f15(A),A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.32	311 -in(f14(A),f15(A)) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.32	312 f15(A) != f14(A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.37	313 -in(f15(A),f14(A)) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.37	314 in(f14(A),A) | epsilon_connected(A) # label(d3_ordinal1) # label(axiom).  [clausify(24)].
0.98/1.37	Derived: -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | in(f15(B),B).  [resolve(309,f,310,b)].
0.98/1.37	Derived: -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | -in(f14(B),f15(B)).  [resolve(309,f,311,b)].
0.98/1.37	Derived: -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | f15(B) != f14(B).  [resolve(309,f,312,b)].
0.98/1.37	Derived: -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | -in(f15(B),f14(B)).  [resolve(309,f,313,b)].
0.98/1.37	Derived: -in(A,B) | in(C,A) | A = C | in(A,C) | -in(C,B) | in(f14(B),B).  [resolve(309,f,314,b)].
0.98/1.37	315 -epsilon_transitive(A) | -epsilon_connected(A) | ordinal(A) # label(d4_ordinal1) # label(axiom).  [clausify(66)].
0.98/1.37	Derived: -epsilon_transitive(A) | ordinal(A) | in(f15(A),A).  [resolve(315,b,310,b)].
0.98/1.37	Derived: -epsilon_transitive(A) | ordinal(A) | -in(f14(A),f15(A)).  [resolve(315,b,311,b)].
0.98/1.37	Derived: -epsilon_transitive(A) | ordinal(A) | f15(A) != f14(A).  [resolve(315,b,312,b)].
0.98/1.37	Derived: -epsilon_transitive(A) | ordinal(A) | -in(f15(A),f14(A)).  [resolve(315,b,313,b)].
0.98/1.37	Derived: -epsilon_transitive(A) | ordinal(A) | in(f14(A),A).  [resolve(315,b,314,b)].
0.98/1.37	316 epsilon_connected(A) | -ordinal(A) # label(d4_ordinal1) # label(axiom).  [clausify(66)].
0.98/1.37	Derived: -ordinal(A) | -in(B,A) | in(C,B) | B = C | in(B,C) | -in(C,A).  [resolve(316,a,309,f)].
0.98/1.37	317 -epsilon_connected(A) | -epsilon_transitive(A) | ordinal(A) # label(cc2_ordinal1) # label(axiom).  [clausify(114)].
0.98/1.37	318 epsilon_connected(c6) # label(rc3_ordinal1) # label(axiom).  [clausify(139)].
0.98/1.37	Derived: -in(A,c6) | in(B,A) | A = B | in(A,B) | -in(B,c6).  [resolve(318,a,309,f)].
0.98/1.37	319 -empty(A) | epsilon_connected(A) # label(cc3_ordinal1) # label(axiom).  [clausify(167)].
0.98/1.37	Derived: -empty(A) | -epsilon_transitive(A) | ordinal(A).  [resolve(319,b,315,b)].
0.98/1.37	320 epsilon_connected(c7) # label(rc2_ordinal1) # label(axiom).  [clausify(173)].
0.98/1.37	Derived: -in(A,c7) | in(B,A) | A = B | in(A,B) | -in(B,c7).  [resolve(320,a,309,f)].
0.98/1.37	Derived: -epsilon_transitive(c7) | ordinal(c7).  [resolve(320,a,315,b)].
0.98/1.37	321 -ordinal(A) | epsilon_connected(succ(A)) # label(fc3_ordinal1) # label(axiom).  [clausify(174)].
0.98/1.37	Derived: -ordinal(A) | -in(B,succ(A)) | in(C,B) | B = C | in(B,C) | -in(C,succ(A)).  [resolve(321,b,309,f)].
0.98/1.37	322 -ordinal(A) | epsilon_connected(union(A)) # label(fc4_ordinal1) # label(axiom).  [clausify(210)].
0.98/1.37	Derived: -ordinal(A) | -in(B,union(A)) | in(C,B) | B = C | in(B,C) | -in(C,union(A)).  [resolve(322,b,309,f)].
0.98/1.37	Derived: -ordinal(A) | -epsilon_transitive(union(A)) | ordinal(union(A)).  [resolve(322,b,315,b)].
0.98/1.37	323 epsilon_connected(empty_set) # label(fc2_ordinal1_AndRHS_AndRHS_AndLHS) # label(axiom).  [assumption].
0.98/1.37	Derived: -in(A,empty_set) | in(B,A) | A = B | in(A,B) | -in(B,empty_set).  [resolve(323,a,309,f)].
0.98/1.37	Derived: -epsilon_transitive(empty_set) | ordinal(empty_set).  [resolve(323,a,315,b)].
0.98/1.37	324 -ordinal(A) | epsilon_connected(A) # label(cc1_ordinal1) # label(axiom).  [clausify(241)].
0.98/1.37	325 epsilon_connected(c11) # label(rc1_ordinal1) # label(axiom).  [clausify(262)].
0.98/1.37	Derived: -in(A,c11) | in(B,A) | A = B | in(A,B) | -in(B,c11).  [resolve(325,a,309,f)].
0.98/1.37	Derived: -epsilon_transitive(c11) | ordinal(c11).  [resolve(325,a,315,b)].
0.98/1.37	326 -ordinal(A) | -being_limit_ordinal(A) | -ordinal(B) | succ(B) != A # label(t42_ordinal1) # label(lemma).  [clausify(87)].
0.98/1.37	327 -ordinal(A) | being_limit_ordinal(A) | ordinal(f38(A)) # label(t42_ordinal1) # label(lemma).  [clausify(87)].
0.98/1.37	328 -ordinal(A) | being_limit_ordinal(A) | succ(f38(A)) = A # label(t42_ordinal1) # label(lemma).  [clausify(87)].
0.98/1.37	Derived: -ordinal(A) | -ordinal(B) | succ(B) != A | -ordinal(A) | ordinal(f38(A)).  [resolve(326,b,327,b)].
0.98/1.37	Derived: -ordinal(A) | -ordinal(B) | succ(B) != A | -ordinal(A) | succ(f38(A)) = A.  [resolve(326,b,328,b)].
0.98/1.37	329 -ordinal(A) | ordinal(f41(A)) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(109)].
0.98/1.37	Derived: -ordinal(A) | ordinal(f41(A)) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(329,c,326,b)].
0.98/1.43	330 -ordinal(A) | in(f41(A),A) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(109)].
0.98/1.43	Derived: -ordinal(A) | in(f41(A),A) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(330,c,326,b)].
0.98/1.43	331 -ordinal(A) | -in(succ(f41(A)),A) | being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(109)].
0.98/1.43	Derived: -ordinal(A) | -in(succ(f41(A)),A) | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(331,c,326,b)].
0.98/1.43	332 -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -being_limit_ordinal(A) # label(t41_ordinal1) # label(lemma).  [clausify(109)].
0.98/1.43	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | ordinal(f38(A)).  [resolve(332,e,327,b)].
0.98/1.43	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | succ(f38(A)) = A.  [resolve(332,e,328,b)].
0.98/1.43	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | ordinal(f41(A)).  [resolve(332,e,329,c)].
0.98/1.43	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | in(f41(A),A).  [resolve(332,e,330,c)].
0.98/1.43	Derived: -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A) | -ordinal(A) | -in(succ(f41(A)),A).  [resolve(332,e,331,c)].
0.98/1.43	333 union(A) != A | being_limit_ordinal(A) # label(d6_ordinal1) # label(axiom).  [clausify(116)].
0.98/1.43	Derived: union(A) != A | -ordinal(A) | -ordinal(B) | succ(B) != A.  [resolve(333,b,326,b)].
0.98/1.43	Derived: union(A) != A | -ordinal(A) | -ordinal(B) | -in(B,A) | in(succ(B),A).  [resolve(333,b,332,e)].
0.98/1.43	334 union(A) = A | -being_limit_ordinal(A) # label(d6_ordinal1) # label(axiom).  [clausify(116)].
0.98/1.43	Derived: union(A) = A | -ordinal(A) | ordinal(f38(A)).  [resolve(334,b,327,b)].
0.98/1.43	Derived: union(A) = A | -ordinal(A) | succ(f38(A)) = A.  [resolve(334,b,328,b)].
0.98/1.43	Derived: union(A) = A | -ordinal(A) | ordinal(f41(A)).  [resolve(334,b,329,c)].
0.98/1.43	Derived: union(A) = A | -ordinal(A) | in(f41(A),A).  [resolve(334,b,330,c)].
0.98/1.43	Derived: union(A) = A | -ordinal(A) | -in(succ(f41(A)),A).  [resolve(334,b,331,c)].
0.98/1.43	335 -relation(A) | well_ordering(A) | -well_orders(A,relation_field(A)) # label(t8_wellord1) # label(lemma).  [clausify(94)].
0.98/1.43	336 -relation(A) | -well_ordering(A) | well_orders(A,relation_field(A)) # label(t8_wellord1) # label(lemma).  [clausify(94)].
0.98/1.43	337 -relation(A) | -well_ordering(A) | reflexive(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | reflexive(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(337,b,335,b)].
0.98/1.43	338 -relation(A) | -well_ordering(A) | transitive(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | transitive(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(338,b,335,b)].
0.98/1.43	339 -relation(A) | -well_ordering(A) | connected(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | connected(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(339,b,335,b)].
0.98/1.43	340 -relation(A) | -well_ordering(A) | well_founded_relation(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | well_founded_relation(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(340,b,335,b)].
0.98/1.43	341 -relation(A) | -well_ordering(A) | antisymmetric(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | antisymmetric(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(341,b,335,b)].
0.98/1.43	342 -relation(A) | well_ordering(A) | -reflexive(A) | -transitive(A) | -connected(A) | -well_founded_relation(A) | -antisymmetric(A) # label(d4_wellord1) # label(axiom).  [clausify(250)].
0.98/1.43	Derived: -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -well_founded_relation(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)).  [resolve(342,b,336,b)].
0.98/1.43	343 -relation(A) | is_well_founded_in(A,relation_field(A)) | -well_founded_relation(A) # label(t5_wellord1) # label(lemma).  [clausify(104)].
0.98/1.43	344 -relation(A) | -is_well_founded_in(A,relation_field(A)) | well_founded_relation(A) # label(t5_wellord1) # label(lemma).  [clausify(104)].
0.98/1.45	345 -relation(A) | empty_set != f82(A) | well_founded_relation(A) # label(d2_wellord1) # label(axiom).  [clausify(217)].
0.98/1.45	Derived: -relation(A) | empty_set != f82(A) | -relation(A) | is_well_founded_in(A,relation_field(A)).  [resolve(345,c,343,c)].
0.98/1.45	346 -relation(A) | -in(B,f82(A)) | -disjoint(fiber(A,B),f82(A)) | well_founded_relation(A) # label(d2_wellord1) # label(axiom).  [clausify(217)].
0.98/1.45	Derived: -relation(A) | -in(B,f82(A)) | -disjoint(fiber(A,B),f82(A)) | -relation(A) | is_well_founded_in(A,relation_field(A)).  [resolve(346,d,343,c)].
0.98/1.45	347 -relation(A) | subset(f82(A),relation_field(A)) | well_founded_relation(A) # label(d2_wellord1) # label(axiom).  [clausify(217)].
0.98/1.45	Derived: -relation(A) | subset(f82(A),relation_field(A)) | -relation(A) | is_well_founded_in(A,relation_field(A)).  [resolve(347,c,343,c)].
0.98/1.45	348 -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)) | -well_founded_relation(A) # label(d2_wellord1) # label(axiom).  [clausify(217)].
0.98/1.45	Derived: -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)) | -relation(A) | -is_well_founded_in(A,relation_field(A)).  [resolve(348,e,344,c)].
0.98/1.45	Derived: -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)) | -relation(A) | empty_set != f82(A).  [resolve(348,e,345,c)].
0.98/1.45	Derived: -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)) | -relation(A) | -in(C,f82(A)) | -disjoint(fiber(A,C),f82(A)).  [resolve(348,e,346,d)].
0.98/1.45	Derived: -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)) | -relation(A) | subset(f82(A),relation_field(A)).  [resolve(348,e,347,c)].
0.98/1.45	349 -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)) | -well_founded_relation(A) # label(d2_wellord1) # label(axiom).  [clausify(217)].
0.98/1.45	Derived: -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)) | -relation(A) | -is_well_founded_in(A,relation_field(A)).  [resolve(349,e,344,c)].
0.98/1.45	Derived: -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)) | -relation(A) | empty_set != f82(A).  [resolve(349,e,345,c)].
0.98/1.45	Derived: -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)) | -relation(A) | -in(C,f82(A)) | -disjoint(fiber(A,C),f82(A)).  [resolve(349,e,346,d)].
0.98/1.45	Derived: -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)) | -relation(A) | subset(f82(A),relation_field(A)).  [resolve(349,e,347,c)].
0.98/1.45	350 -relation(A) | well_founded_relation(A) | -relation(A) | -well_orders(A,relation_field(A)).  [resolve(340,b,335,b)].
0.98/1.45	Derived: -relation(A) | -relation(A) | -well_orders(A,relation_field(A)) | -relation(A) | is_well_founded_in(A,relation_field(A)).  [resolve(350,b,343,c)].
0.98/1.45	Derived: -relation(A) | -relation(A) | -well_orders(A,relation_field(A)) | -relation(A) | empty_set = B | in(f83(A,B),B) | -subset(B,relation_field(A)).  [resolve(350,b,348,e)].
0.98/1.45	Derived: -relation(A) | -relation(A) | -well_orders(A,relation_field(A)) | -relation(A) | empty_set = B | disjoint(fiber(A,f83(A,B)),B) | -subset(B,relation_field(A)).  [resolve(350,b,349,e)].
0.98/1.45	351 -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -well_founded_relation(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)).  [resolve(342,b,336,b)].
0.98/1.45	Derived: -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)) | -relation(A) | -is_well_founded_in(A,relation_field(A)).  [resolve(351,e,344,c)].
0.98/1.45	Derived: -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)) | -relation(A) | empty_set != f82(A).  [resolve(351,e,345,c)].
0.98/1.45	Derived: -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)) | -relation(A) | -in(B,f82(A)) | -disjoint(fiber(A,B),f82(A)).  [resolve(351,e,346,d)].
0.98/1.45	Derived: -relation(A) | -reflexive(A) | -transitive(A) | -connected(A) | -antisymmetric(A) | -relation(A) | well_orders(A,relation_field(A)) | -relation(A) | subset(f82(A),relation_field(A)).  [resolve(351,e,347,c)].
3.23/3.54	
3.23/3.54	============================== end predicate elimination =============
3.23/3.54	
3.23/3.54	Auto_denials:  (non-Horn, no changes).
3.23/3.54	
3.23/3.54	Term ordering decisions:
3.23/3.54	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. ordered_pair=1. apply=1. relation_dom_restriction=1. relation_composition=1. set_difference=1. set_intersection2=1. relation_image=1. cartesian_product2=1. set_union2=1. relation_inverse_image=1. relation_rng_restriction=1. fiber=1. unordered_pair=1. relation_restriction=1. complements_of_subsets=1. subset_complement=1. meet_of_subsets=1. union_of_subsets=1. f1=1. f2=1. f3=1. f4=1. f11=1. f12=1. f16=1. f22=1. f23=1. f27=1. f29=1. f32=1. f39=1. f42=1. f50=1. f51=1. f52=1. f53=1. f54=1. f55=1. f60=1. f61=1. f63=1. f68=1. f69=1. f73=1. f74=1. f75=1. f76=1. f77=1. f78=1. f79=1. f80=1. f81=1. f83=1. f85=1. f87=1. f88=1. f89=1. f95=1. f100=1. f101=1. f103=1. relation_dom=1. powerset=1. relation_rng=1. relation_field=1. singleton=1. succ=1. union=1. identity_relation=1. function_inverse=1. relation_inverse=1. set_meet=1. cast_to_subset=1. f6=1. f7=1. f8=1. f10=1. f14=1. f15=1. f17=1. f18=1. f19=1. f30=1. f31=1. f38=1. f41=1. f45=1. f46=1. f47=1. f48=1. f62=1. f71=1. f72=1. f82=1. f84=1. f86=1. f98=1. f99=1. f108=1. unordered_triple=1. subset_difference=1. f5=1. f13=1. f20=1. f21=1. f24=1. f25=1. f26=1. f28=1. f33=1. f34=1. f35=1. f40=1. f43=1. f44=1. f49=1. f56=1. f57=1. f59=1. f65=1. f66=1. f67=1. f70=1. f90=1. f91=1. f92=1. f94=1. f96=1. f97=1. f102=1. f105=1. f106=1. f107=1. f9=1. f36=1. f37=1. f58=1. f64=1. f93=1. f104=1.
3.23/3.54	
3.23/3.54	============================== end of process initial clauses ========
3.23/3.54	
3.23/3.54	============================== CLAUSES FOR SEARCH ====================
3.23/3.54	
3.23/3.54	============================== end of clauses for search =============
3.23/3.54	
3.23/3.54	============================== SEARCH ================================
3.23/3.54	
3.23/3.54	% Starting search at 0.37 seconds.
3.23/3.54	
3.23/3.54	Low Water (keep): wt=42.000, iters=3338
3.23/3.54	
3.23/3.54	Low Water (keep): wt=40.000, iters=3406
3.23/3.54	
3.23/3.54	Low Water (keep): wt=37.000, iters=3435
3.23/3.54	
3.23/3.54	Low Water (keep): wt=36.000, iters=3391
3.23/3.54	
3.23/3.54	Low Water (keep): wt=35.000, iters=3413
3.23/3.54	
3.23/3.54	Low Water (keep): wt=34.000, iters=3335
3.23/3.54	
3.23/3.54	Low Water (keep): wt=33.000, iters=3605
3.23/3.54	
3.23/3.54	Low Water (keep): wt=32.000, iters=3431
3.23/3.54	
3.23/3.54	Low Water (keep): wt=31.000, iters=3482
3.23/3.54	
3.23/3.54	Low Water (keep): wt=30.000, iters=3389
3.23/3.54	
3.23/3.54	Low Water (keep): wt=29.000, iters=3402
3.23/3.54	
3.23/3.54	Low Water (keep): wt=28.000, iters=3407
3.23/3.54	
3.23/3.54	Low Water (keep): wt=27.000, iters=3349
3.23/3.54	
3.23/3.54	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 76 (0.00 of 1.41 sec).
3.23/3.54	
3.23/3.54	Low Water (keep): wt=26.000, iters=3344
3.23/3.54	
3.23/3.54	Low Water (keep): wt=25.000, iters=3496
3.23/3.54	
3.23/3.54	Low Water (keep): wt=24.000, iters=3445
3.23/3.54	
3.23/3.54	Low Water (keep): wt=23.000, iters=3363
3.23/3.54	
3.23/3.54	Low Water (keep): wt=22.000, iters=3337
3.23/3.54	
3.23/3.54	Low Water (keep): wt=21.000, iters=3336
3.23/3.54	
3.23/3.54	Low Water (keep): wt=20.000, iters=3334
3.23/3.54	
3.23/3.54	Low Water (keep): wt=19.000, iters=3451
3.23/3.54	
3.23/3.54	Low Water (keep): wt=18.000, iters=3341
3.29/3.54	
3.29/3.54	Low Water (keep): wt=17.000, iters=3384
3.29/3.54	
3.29/3.54	Low Water (keep): wt=16.000, iters=3368
3.29/3.54	
3.29/3.54	Low Water (keep): wt=15.000, iters=3357
3.29/3.54	
3.29/3.54	Low Water (keep): wt=14.000, iters=3381
3.29/3.54	
3.29/3.54	Low Water (keep): wt=13.000, iters=3343
3.29/3.54	
3.29/3.54	Low Water (keep): wt=12.000, iters=3361
3.29/3.54	
3.29/3.54	Low Water (keep): wt=11.000, iters=3345
3.29/3.54	
3.29/3.54	Low Water (keep): wt=10.000, iters=3343
3.29/3.54	
3.29/3.54	Low Water (displace): id=3868, wt=79.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2194, wt=72.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=3874, wt=70.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2203, wt=68.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4158, wt=67.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4177, wt=65.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4170, wt=63.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2949, wt=62.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4185, wt=61.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2596, wt=60.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4203, wt=59.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2212, wt=58.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4179, wt=57.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=3851, wt=56.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=4227, wt=55.000
3.29/3.54	
3.29/3.54	Low Water (displace): id=2935, wt=54.000
3.29/3.54	
3.29/3.54	Low Water (displacCputime limit exceeded (core dumped)
180.05/180.34	EOF