0.07/0.13	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command  : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer : n014.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 960
0.13/0.34	% WCLimit  : 120
0.13/0.34	% DateTime : Tue Aug  9 07:31:31 EDT 2022
0.13/0.35	% CPUTime  : 
0.85/1.12	============================== Prover9 ===============================
0.85/1.12	Prover9 (32) version 2009-11A, November 2009.
0.85/1.12	Process 24211 was started by sandbox2 on n014.cluster.edu,
0.85/1.12	Tue Aug  9 07:31:31 2022
0.85/1.12	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_23996_n014.cluster.edu".
0.85/1.12	============================== end of head ===========================
0.85/1.12	
0.85/1.12	============================== INPUT =================================
0.85/1.12	
0.85/1.12	% Reading from file /tmp/Prover9_23996_n014.cluster.edu
0.85/1.12	
0.85/1.12	set(prolog_style_variables).
0.85/1.12	set(auto2).
0.85/1.12	    % set(auto2) -> set(auto).
0.85/1.12	    % set(auto) -> set(auto_inference).
0.85/1.12	    % set(auto) -> set(auto_setup).
0.85/1.12	    % set(auto_setup) -> set(predicate_elim).
0.85/1.12	    % set(auto_setup) -> assign(eq_defs, unfold).
0.85/1.12	    % set(auto) -> set(auto_limits).
0.85/1.12	    % set(auto_limits) -> assign(max_weight, "100.000").
0.85/1.12	    % set(auto_limits) -> assign(sos_limit, 20000).
0.85/1.12	    % set(auto) -> set(auto_denials).
0.85/1.12	    % set(auto) -> set(auto_process).
0.85/1.12	    % set(auto2) -> assign(new_constants, 1).
0.85/1.12	    % set(auto2) -> assign(fold_denial_max, 3).
0.85/1.12	    % set(auto2) -> assign(max_weight, "200.000").
0.85/1.12	    % set(auto2) -> assign(max_hours, 1).
0.85/1.12	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.85/1.12	    % set(auto2) -> assign(max_seconds, 0).
0.85/1.12	    % set(auto2) -> assign(max_minutes, 5).
0.85/1.12	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.85/1.12	    % set(auto2) -> set(sort_initial_sos).
0.85/1.12	    % set(auto2) -> assign(sos_limit, -1).
0.85/1.12	    % set(auto2) -> assign(lrs_ticks, 3000).
0.85/1.12	    % set(auto2) -> assign(max_megs, 400).
0.85/1.12	    % set(auto2) -> assign(stats, some).
0.85/1.12	    % set(auto2) -> clear(echo_input).
0.85/1.12	    % set(auto2) -> set(quiet).
0.85/1.12	    % set(auto2) -> clear(print_initial_clauses).
0.85/1.12	    % set(auto2) -> clear(print_given).
0.85/1.12	assign(lrs_ticks,-1).
0.85/1.12	assign(sos_limit,10000).
0.85/1.12	assign(order,kbo).
0.85/1.12	set(lex_order_vars).
0.85/1.12	clear(print_given).
0.85/1.12	
0.85/1.12	% formulas(sos).  % not echoed (182 formulas)
0.85/1.12	
0.85/1.12	============================== end of input ==========================
0.85/1.12	
0.85/1.12	% From the command line: assign(max_seconds, 960).
0.85/1.12	
0.85/1.12	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.85/1.12	
0.85/1.12	% Formulas that are not ordinary clauses:
0.85/1.12	1 (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].
0.85/1.12	2 (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].
0.85/1.12	3 (all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> A = C & D = B)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	4 (all A (relation(A) -> (all B all C (relation(C) -> (relation_dom_restriction(A,B) = C <-> (all D all E (in(ordered_pair(D,E),C) <-> in(ordered_pair(D,E),A) & in(D,B)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	5 (all A all B ((all C ((exists D (in(D,A) & in(C,D))) <-> in(C,B))) <-> B = union(A))) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	6 (all A all B (-in(B,A) <-> set_difference(A,singleton(B)) = A)) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	7 (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].
0.85/1.12	8 (all A all B -(A != B & empty(B) & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	9 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	10 (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].
0.85/1.12	11 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	12 (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].
0.85/1.12	13 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	14 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	15 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	16 (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].
0.85/1.12	17 (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].
0.85/1.12	18 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	19 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	20 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	21 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	22 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	23 (all A (relation(A) -> relation_rng(A) = relation_dom(relation_inverse(A)) & relation_rng(relation_inverse(A)) = relation_dom(A))) # label(t37_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	24 (all A all B ((all C (in(C,B) <-> subset(C,A))) <-> powerset(A) = B)) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	25 (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].
0.85/1.12	26 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	27 (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].
0.85/1.12	28 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	29 (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].
0.85/1.12	30 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	31 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	32 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	33 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	34 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	35 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	36 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> 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].
0.85/1.12	37 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	38 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	39 (all A all B (relation(B) & empty(A) -> empty(relation_composition(B,A)) & relation(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	40 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	41 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	42 (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].
0.85/1.12	43 (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].
0.85/1.12	44 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	45 (all A (relation(A) -> (all B ((all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))) <-> B = relation_dom(A))))) # label(d4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	46 (all A empty_set != singleton(A)) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	47 (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].
0.85/1.12	48 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	49 (all A (A = relation_rng(identity_relation(A)) & A = relation_dom(identity_relation(A)))) # label(t71_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	50 (all A all B (relation(B) -> (B = identity_relation(A) <-> (all C all D (D = C & in(C,A) <-> in(ordered_pair(C,D),B)))))) # label(d10_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	51 (all A all B all C (set_union2(A,B) = C <-> (all D (in(D,A) | in(D,B) <-> in(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	52 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	53 (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].
0.85/1.12	54 (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].
0.85/1.12	55 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	56 (all A all B (singleton(A) = B <-> (all C (C = A <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	57 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	58 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	59 (all A all B (empty_set = set_difference(A,B) <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	60 (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].
0.85/1.12	61 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	62 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	63 (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].
0.85/1.12	64 (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].
0.85/1.12	65 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	66 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	67 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	68 (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].
0.85/1.12	69 (all A all B (subset(A,B) & subset(B,A) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	70 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	71 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	72 (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].
0.85/1.12	73 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	74 (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].
0.85/1.12	75 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	76 (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].
0.85/1.12	77 (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].
0.85/1.12	78 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	79 (all A (relation(A) -> ((all B all C -in(ordered_pair(B,C),A)) -> empty_set = A))) # label(t56_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	80 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	81 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	82 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	83 (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].
0.85/1.12	84 (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].
0.85/1.12	85 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (C = relation_composition(A,B) <-> (all D all E (in(ordered_pair(D,E),C) <-> (exists F (in(ordered_pair(D,F),A) & in(ordered_pair(F,E),B)))))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	86 (all A (relation(A) -> (all B (relation(B) -> (relation_inverse(A) = B <-> (all C all D (in(ordered_pair(D,C),A) <-> in(ordered_pair(C,D),B)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	87 (all A all B all C (unordered_pair(B,C) = singleton(A) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	88 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	89 (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].
0.85/1.12	90 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	91 (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].
0.85/1.12	92 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	93 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	94 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	95 (all A all B (subset(A,singleton(B)) <-> A = singleton(B) | A = empty_set)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	96 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	97 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	98 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	99 (all A (relation(A) <-> (all B -(in(B,A) & (all C all D ordered_pair(C,D) != B))))) # label(d1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	100 (all A (relation(A) -> (relation_dom(A) = empty_set <-> empty_set = relation_rng(A)))) # label(t65_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	101 (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].
0.85/1.12	102 (all A all B all C ((all D (in(D,C) <-> (exists E exists F (in(E,A) & D = ordered_pair(E,F) & in(F,B))))) <-> cartesian_product2(A,B) = C)) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	103 (all A (empty(A) -> relation(relation_dom(A)) & empty(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	104 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	105 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	106 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	107 (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].
0.85/1.12	108 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	109 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	110 (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].
0.85/1.12	111 (all A (-empty(A) -> (exists B (-empty(B) & element(B,powerset(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	112 (all A all B ((empty_set = A -> (B = empty_set <-> set_meet(A) = B)) & (empty_set != A -> (set_meet(A) = B <-> (all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))))))) # label(d1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	113 (all A all B all C all D (subset(A,B) & subset(C,D) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	114 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	115 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	116 (all A all B (subset(A,B) & A != B <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	117 (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].
0.85/1.12	118 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	119 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	120 (all A exists B ((all C -((all D -(in(D,B) & (all E (subset(E,C) -> in(E,D))))) & in(C,B))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))) & in(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	121 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	122 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	123 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	124 (all A all B (-((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)) & -((all C -in(C,set_intersection2(A,B))) & -disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	125 (all A all B all C (C = unordered_pair(A,B) <-> (all D (A = D | B = D <-> in(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	126 (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].
0.85/1.12	127 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	128 (all A all B all C (subset(C,B) & subset(A,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	129 (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].
0.85/1.12	130 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	131 (all A all B (relation(B) & empty(A) -> empty(relation_composition(A,B)) & relation(relation_composition(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	132 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	133 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	134 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> ((all D (element(D,powerset(A)) -> (in(subset_complement(A,D),B) <-> in(D,C)))) <-> C = complements_of_subsets(A,B)))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	135 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	136 (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].
0.85/1.12	137 (all A all B ((empty(A) -> (empty(B) <-> element(B,A))) & (-empty(A) -> (element(B,A) <-> in(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	138 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	139 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	140 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	141 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,A) & -in(D,B) <-> in(D,C))))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	142 (all A all B (-empty(B) & -empty(A) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	143 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	144 (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].
0.85/1.12	145 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	146 (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].
0.85/1.12	147 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	148 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_dom(A),relation_dom(B)) & subset(relation_rng(A),relation_rng(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.12	149 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.12	150 (all A all B set_union2(A,B) = set_union2(A,set_difference(B,A))) # label(t39_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	151 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	152 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	153 (all A all B (subset(A,singleton(B)) <-> A = singleton(B) | A = empty_set)) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	154 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,B) & in(C,A))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	155 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	156 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C ((exists D in(ordered_pair(D,C),A)) <-> in(C,B))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	157 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	158 (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].
0.85/1.13	159 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	160 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	161 (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].
0.85/1.13	162 (all A A = cast_to_subset(A)) # label(d4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	163 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	164 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	165 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	166 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	167 (all A all B all C all D -(A != D & A != C & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	168 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	169 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	170 (all A all B all C -(empty(C) & element(B,powerset(C)) & in(A,B))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	171 (all A exists B (in(A,B) & (all C -(subset(C,B) & -in(C,B) & -are_equipotent(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].
0.85/1.13	172 (all A all B (relation(B) & relation(A) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	173 (all A all B (subset(A,B) -> B = set_union2(A,B))) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.85/1.13	174 (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].
0.85/1.13	175 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.85/1.13	176 -(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(negated_conjecture) # label(non_clause).  [assumption].
0.85/1.13	
0.85/1.13	============================== end of process non-clausal formulas ===
0.85/1.13	
0.85/1.13	============================== PROCESS INITIAL CLAUSES ===============
0.85/1.13	
0.85/1.13	============================== PREDICATE ELIMINATION =================
4.06/4.34	
4.06/4.34	============================== end predicate elimination =============
4.06/4.34	
4.06/4.34	Auto_denials:  (non-Horn, no changes).
4.06/4.34	
4.06/4.34	Term ordering decisions:
4.06/4.34	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. ordered_pair=1. set_difference=1. set_union2=1. cartesian_product2=1. set_intersection2=1. relation_composition=1. unordered_pair=1. complements_of_subsets=1. subset_complement=1. relation_dom_restriction=1. meet_of_subsets=1. union_of_subsets=1. f3=1. f4=1. f6=1. f7=1. f8=1. f9=1. f10=1. f12=1. f13=1. f15=1. f19=1. f24=1. f25=1. f28=1. f29=1. f38=1. f39=1. f41=1. f42=1. f47=1. f49=1. f50=1. powerset=1. singleton=1. relation_dom=1. relation_rng=1. identity_relation=1. union=1. relation_inverse=1. set_meet=1. cast_to_subset=1. relation_field=1. f17=1. f18=1. f26=1. f27=1. f30=1. f36=1. f40=1. f46=1. f51=1. subset_difference=1. f1=1. f2=1. f5=1. f11=1. f14=1. f16=1. f21=1. f22=1. f23=1. f31=1. f32=1. f33=1. f37=1. f43=1. f44=1. f45=1. f48=1. f34=1. f35=1. f20=1.
4.06/4.34	
4.06/4.34	============================== end of process initial clauses ========
4.06/4.34	
4.06/4.34	============================== CLAUSES FOR SEARCH ====================
4.06/4.34	
4.06/4.34	============================== end of clauses for search =============
4.06/4.34	
4.06/4.34	============================== SEARCH ================================
4.06/4.34	
4.06/4.34	% Starting search at 0.11 seconds.
4.06/4.34	
4.06/4.34	Low Water (keep): wt=50.000, iters=3500
4.06/4.34	
4.06/4.34	Low Water (keep): wt=46.000, iters=3367
4.06/4.34	
4.06/4.34	Low Water (keep): wt=44.000, iters=3369
4.06/4.34	
4.06/4.34	Low Water (keep): wt=42.000, iters=3342
4.06/4.34	
4.06/4.34	Low Water (keep): wt=40.000, iters=3357
4.06/4.34	
4.06/4.34	Low Water (keep): wt=38.000, iters=3399
4.06/4.34	
4.06/4.34	Low Water (keep): wt=36.000, iters=3395
4.06/4.34	
4.06/4.34	Low Water (keep): wt=35.000, iters=3342
4.06/4.34	
4.06/4.34	Low Water (keep): wt=34.000, iters=3333
4.06/4.34	
4.06/4.34	Low Water (keep): wt=32.000, iters=3351
4.06/4.34	
4.06/4.34	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 0.81 sec).
4.06/4.34	
4.06/4.34	Low Water (keep): wt=28.000, iters=3371
4.06/4.34	
4.06/4.34	Low Water (keep): wt=27.000, iters=3359
4.06/4.34	
4.06/4.34	Low Water (keep): wt=26.000, iters=3490
4.06/4.34	
4.06/4.34	Low Water (keep): wt=25.000, iters=3337
4.06/4.34	
4.06/4.34	Low Water (keep): wt=23.000, iters=3405
4.06/4.34	
4.06/4.34	Low Water (keep): wt=22.000, iters=3422
4.06/4.34	
4.06/4.34	Low Water (keep): wt=21.000, iters=3352
4.06/4.34	
4.06/4.34	Low Water (keep): wt=20.000, iters=3483
4.06/4.34	
4.06/4.34	Low Water (keep): wt=19.000, iters=3495
4.06/4.34	
4.06/4.34	Low Water (keep): wt=18.000, iters=3346
4.06/4.34	
4.06/4.34	Low Water (keep): wt=17.000, iters=3335
4.06/4.34	
4.06/4.34	Low Water (keep): wt=16.000, iters=3345
4.06/4.34	
4.06/4.34	Low Water (keep): wt=15.000, iters=3336
4.06/4.34	
4.06/4.34	Low Water (keep): wt=14.000, iters=3334
4.06/4.34	
4.06/4.34	Low Water (keep): wt=13.000, iters=3349
4.06/4.34	
4.06/4.34	Low Water (keep): wt=12.000, iters=3343
4.06/4.34	
4.06/4.34	Low Water (keep): wt=10.000, iters=3459
4.06/4.34	
4.06/4.34	Low Water (keep): wt=9.000, iters=3386
4.06/4.34	
4.06/4.34	Low Water (displace): id=3104, wt=129.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3112, wt=103.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3108, wt=96.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4065, wt=84.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4099, wt=82.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4064, wt=81.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4206, wt=80.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4126, wt=79.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4205, wt=77.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4063, wt=75.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3663, wt=74.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4097, wt=73.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4204, wt=71.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3791, wt=70.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3183, wt=69.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3173, wt=68.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3124, wt=67.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3668, wt=65.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3699, wt=64.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3705, wt=63.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3760, wt=62.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3876, wt=61.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4069, wt=60.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3969, wt=59.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4199, wt=58.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3891, wt=57.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4135, wt=56.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3237, wt=55.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4060, wt=54.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4053, wt=53.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4109, wt=52.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3782, wt=51.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4209, wt=50.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=3911, wt=49.000
4.06/4.34	
4.06/4.34	Low Water (displace): id=4062, wt=48.000
4.06/4.34	
4.06/4.34	Low WaAlarm clock 
119.84/120.09	Prover9 interrupted
119.84/120.09	EOF