0.11/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer : n015.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 960
0.12/0.33	% WCLimit  : 120
0.12/0.33	% DateTime : Tue Aug  9 03:41:11 EDT 2022
0.12/0.33	% CPUTime  : 
0.81/1.08	============================== Prover9 ===============================
0.81/1.08	Prover9 (32) version 2009-11A, November 2009.
0.81/1.08	Process 9762 was started by sandbox2 on n015.cluster.edu,
0.81/1.08	Tue Aug  9 03:41:11 2022
0.81/1.08	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_9609_n015.cluster.edu".
0.81/1.08	============================== end of head ===========================
0.81/1.08	
0.81/1.08	============================== INPUT =================================
0.81/1.08	
0.81/1.08	% Reading from file /tmp/Prover9_9609_n015.cluster.edu
0.81/1.08	
0.81/1.08	set(prolog_style_variables).
0.81/1.08	set(auto2).
0.81/1.08	    % set(auto2) -> set(auto).
0.81/1.08	    % set(auto) -> set(auto_inference).
0.81/1.08	    % set(auto) -> set(auto_setup).
0.81/1.08	    % set(auto_setup) -> set(predicate_elim).
0.81/1.08	    % set(auto_setup) -> assign(eq_defs, unfold).
0.81/1.08	    % set(auto) -> set(auto_limits).
0.81/1.08	    % set(auto_limits) -> assign(max_weight, "100.000").
0.81/1.08	    % set(auto_limits) -> assign(sos_limit, 20000).
0.81/1.08	    % set(auto) -> set(auto_denials).
0.81/1.08	    % set(auto) -> set(auto_process).
0.81/1.08	    % set(auto2) -> assign(new_constants, 1).
0.81/1.08	    % set(auto2) -> assign(fold_denial_max, 3).
0.81/1.08	    % set(auto2) -> assign(max_weight, "200.000").
0.81/1.08	    % set(auto2) -> assign(max_hours, 1).
0.81/1.08	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.81/1.08	    % set(auto2) -> assign(max_seconds, 0).
0.81/1.08	    % set(auto2) -> assign(max_minutes, 5).
0.81/1.08	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.81/1.08	    % set(auto2) -> set(sort_initial_sos).
0.81/1.08	    % set(auto2) -> assign(sos_limit, -1).
0.81/1.08	    % set(auto2) -> assign(lrs_ticks, 3000).
0.81/1.08	    % set(auto2) -> assign(max_megs, 400).
0.81/1.08	    % set(auto2) -> assign(stats, some).
0.81/1.08	    % set(auto2) -> clear(echo_input).
0.81/1.08	    % set(auto2) -> set(quiet).
0.81/1.08	    % set(auto2) -> clear(print_initial_clauses).
0.81/1.08	    % set(auto2) -> clear(print_given).
0.81/1.08	assign(lrs_ticks,-1).
0.81/1.08	assign(sos_limit,10000).
0.81/1.08	assign(order,kbo).
0.81/1.08	set(lex_order_vars).
0.81/1.08	clear(print_given).
0.81/1.08	
0.81/1.08	% formulas(sos).  % not echoed (150 formulas)
0.81/1.08	
0.81/1.08	============================== end of input ==========================
0.81/1.08	
0.81/1.08	% From the command line: assign(max_seconds, 960).
0.81/1.08	
0.81/1.08	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.81/1.08	
0.81/1.08	% Formulas that are not ordinary clauses:
0.81/1.08	1 (all A exists B ((all C all D (subset(D,C) & in(C,B) -> in(D,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C -(-are_equipotent(C,B) & -in(C,B) & subset(C,B))) & in(A,B))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	2 (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].
0.81/1.08	3 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,B) | in(D,A) <-> in(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	4 (all A all B (B = union(A) <-> (all C (in(C,B) <-> (exists D (in(D,A) & in(C,D))))))) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	5 (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].
0.81/1.08	6 (all A all B all C (subset(A,B) -> subset(A,set_difference(B,singleton(C))) | in(C,A))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	7 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	8 (all A all B ((A != empty_set -> (set_meet(A) = B <-> (all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))))) & (empty_set = A -> (B = set_meet(A) <-> empty_set = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	9 (all A A = union(powerset(A))) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	10 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	11 (all A all B A = set_intersection2(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	12 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	13 (all A all B (subset(A,singleton(B)) <-> singleton(B) = A | A = empty_set)) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	14 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	15 (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].
0.81/1.08	16 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	17 (all A all B ((empty(A) -> (element(B,A) <-> empty(B))) & (-empty(A) -> (in(B,A) <-> element(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	18 (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].
0.81/1.08	19 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	20 (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].
0.81/1.08	21 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	22 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	23 (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].
0.81/1.08	24 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	25 (all A all B all C (in(A,C) & in(B,C) <-> subset(unordered_pair(A,B),C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	26 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	27 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> (C = complements_of_subsets(A,B) <-> (all D (element(D,powerset(A)) -> (in(D,C) <-> in(subset_complement(A,D),B))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	28 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	29 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	30 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	31 (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].
0.81/1.08	32 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	33 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	34 (all A all B (subset(A,singleton(B)) <-> singleton(B) = A | A = empty_set)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	35 (all A all B (A = set_difference(A,B) <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	36 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	37 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	38 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	39 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	40 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	41 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	42 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	43 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	44 (all A all B all C (unordered_pair(A,B) = C <-> (all D (B = D | D = A <-> in(D,C))))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	45 (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].
0.81/1.08	46 (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].
0.81/1.08	47 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	48 (all A all B (-((all C -in(C,set_intersection2(A,B))) & -disjoint(A,B)) & -(disjoint(A,B) & (exists C in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	49 (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].
0.81/1.08	50 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	51 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	52 (all A all B all C (unordered_pair(B,C) = singleton(A) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	53 (all A all B ((all C (in(C,A) <-> in(C,B))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	54 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	55 (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].
0.81/1.08	56 (all A all B -(empty(A) & B != A & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	57 (all A all B set_intersection2(A,B) = set_difference(A,set_difference(A,B))) # label(t48_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	58 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	59 (all A all B all C (element(C,powerset(A)) -> -(in(B,C) & in(B,subset_complement(A,C))))) # label(t54_subset_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	60 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	61 (all A all B (subset(A,B) & A != B <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	62 (all A all B -(proper_subset(B,A) & subset(A,B))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	63 (all A exists B ((all C -(-in(C,B) & -are_equipotent(C,B) & subset(C,B))) & (all C -(in(C,B) & (all D -(in(D,B) & (all E (subset(E,C) -> in(E,D))))))) & (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].
0.81/1.08	64 (all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & B != empty_set))) # label(t46_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	65 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B)) = union_of_subsets(A,complements_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	66 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	67 (all A all B all C ((all D (in(D,B) & in(D,A) <-> in(D,C))) <-> set_intersection2(A,B) = C)) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	68 (all A all B all C -(in(A,B) & empty(C) & element(B,powerset(C)))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	69 (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].
0.81/1.08	70 (all A all B (subset(A,B) & subset(B,A) <-> A = B)) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	71 (all A empty_set != singleton(A)) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	72 (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].
0.81/1.08	73 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	74 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	75 (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].
0.81/1.08	76 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	77 (all A all B -(in(A,B) & disjoint(singleton(A),B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	78 (all A all B (relation(B) & relation(A) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	79 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	80 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	81 (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].
0.81/1.08	82 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	83 (all A empty_set = set_difference(empty_set,A)) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	84 (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].
0.81/1.08	85 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	86 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	87 (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].
0.81/1.08	88 (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].
0.81/1.08	89 (all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	90 (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].
0.81/1.08	91 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	92 (all A (-empty(A) -> (exists B (-empty(B) & element(B,powerset(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	93 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.08	94 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	95 (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].
0.81/1.08	96 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	97 (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].
0.81/1.08	98 (all A (relation(A) -> (all B ((all C ((exists D in(ordered_pair(D,C),A)) <-> in(C,B))) <-> relation_rng(A) = B)))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.08	99 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	100 (all A (relation(A) <-> (all B -((all C all D B != ordered_pair(C,D)) & in(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	101 (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].
0.81/1.09	102 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	103 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	104 (all A ((all B -in(B,A)) <-> empty_set = A)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	105 (all A all B (-in(B,A) <-> set_difference(A,singleton(B)) = A)) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	106 (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].
0.81/1.09	107 (all A all B all C ((all D ((exists E exists F (D = ordered_pair(E,F) & in(F,B) & in(E,A))) <-> in(D,C))) <-> C = cartesian_product2(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	108 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	109 (all A (subset(A,empty_set) -> empty_set = A)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	110 (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].
0.81/1.09	111 (all A all B (powerset(A) = B <-> (all C (subset(C,A) <-> in(C,B))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	112 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	113 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	114 (all A all B (singleton(A) = B <-> (all C (A = C <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	115 (all A (empty_set != A -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	116 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	117 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> set_difference(B,C) = subset_difference(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	118 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	119 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	120 (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].
0.81/1.09	121 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	122 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> C = A & D = B)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	123 (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].
0.81/1.09	124 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.09	125 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.09	126 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	127 (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].
0.81/1.13	128 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	129 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	130 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	131 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	132 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	133 (all A all B (-((exists C (in(C,B) & in(C,A))) & disjoint(A,B)) & -(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	134 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	135 (all A all B all C (set_difference(A,B) = C <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	136 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	137 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	138 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	139 (all A all B all C all D -(unordered_pair(C,D) = unordered_pair(A,B) & A != D & C != A)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	140 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	141 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	142 (all A all B (element(B,powerset(powerset(A))) -> complements_of_subsets(A,complements_of_subsets(A,B)) = B)) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	143 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	144 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	145 (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].
0.81/1.13	146 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	147 (all A all B all C (subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,C)) & subset(cartesian_product2(C,A),cartesian_product2(C,B)))) # label(t118_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	148 -(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(negated_conjecture) # label(non_clause).  [assumption].
0.81/1.13	
0.81/1.13	============================== end of process non-clausal formulas ===
0.81/1.13	
0.81/1.13	============================== PROCESS INITIAL CLAUSES ===============
0.81/1.13	
0.81/1.13	============================== PREDICATE ELIMINATION =================
0.81/1.13	
0.81/1.13	============================== end predicate elimination =============
0.81/1.13	
0.81/1.13	Auto_denials:  (non-Horn, no changes).
0.81/1.13	
0.81/1.13	Term ordering decisions:
0.81/1.13	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. set_difference=1. set_union2=1. cartesian_product2=1. set_intersection2=1. unordered_pair=1. complements_of_subsets=1. subset_complement=1. meet_of_subsets=1. union_of_subsets=1. f4=1. f5=1. f8=1. f9=1. f13=1. f14=1. f16=1. f18=1. f19=1. f21=1. f23=1. f24=1. f26=1. f27=1. f35=1. f36=1. f37=1. f39=1. powerset=1. singleton=1. union=1. relation_dom=1. relation_rng=1. set_meet=1. cast_to_subset=1. relation_field=1. f1=1. f6=1. f11=1. f15=1. f22=1. f28=1. f29=1. subset_difference=1. f2=1. f3=1. f7=1. f10=1. f12=1. f17=1. f20=1. f25=1. f30=1. f31=1. f32=1. f38=1. f33=1. f34=1.
0.81/1.13	
0.81/1.13	============================== end of process initial clauses ========
5.16/5.46	
5.16/5.46	============================== CLAUSES FOR SEARCH ====================
5.16/5.46	
5.16/5.46	============================== end of clauses for search =============
5.16/5.46	
5.16/5.46	============================== SEARCH ================================
5.16/5.46	
5.16/5.46	% Starting search at 0.07 seconds.
5.16/5.46	
5.16/5.46	Low Water (keep): wt=44.000, iters=3342
5.16/5.46	
5.16/5.46	Low Water (keep): wt=43.000, iters=3414
5.16/5.46	
5.16/5.46	Low Water (keep): wt=42.000, iters=3388
5.16/5.46	
5.16/5.46	Low Water (keep): wt=39.000, iters=3421
5.16/5.46	
5.16/5.46	Low Water (keep): wt=38.000, iters=3380
5.16/5.46	
5.16/5.46	Low Water (keep): wt=37.000, iters=3371
5.16/5.46	
5.16/5.46	Low Water (keep): wt=36.000, iters=3394
5.16/5.46	
5.16/5.46	Low Water (keep): wt=34.000, iters=3345
5.16/5.46	
5.16/5.46	Low Water (keep): wt=33.000, iters=3413
5.16/5.46	
5.16/5.46	Low Water (keep): wt=31.000, iters=3467
5.16/5.46	
5.16/5.46	Low Water (keep): wt=30.000, iters=3427
5.16/5.46	
5.16/5.46	Low Water (keep): wt=29.000, iters=3350
5.16/5.46	
5.16/5.46	Low Water (keep): wt=28.000, iters=3494
5.16/5.46	
5.16/5.46	Low Water (keep): wt=27.000, iters=3362
5.16/5.46	
5.16/5.46	Low Water (keep): wt=26.000, iters=3387
5.16/5.46	
5.16/5.46	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 0.77 sec).
5.16/5.46	
5.16/5.46	Low Water (keep): wt=25.000, iters=3358
5.16/5.46	
5.16/5.46	Low Water (keep): wt=24.000, iters=3441
5.16/5.46	
5.16/5.46	Low Water (keep): wt=23.000, iters=3381
5.16/5.46	
5.16/5.46	Low Water (keep): wt=22.000, iters=3351
5.16/5.46	
5.16/5.46	Low Water (keep): wt=21.000, iters=3342
5.16/5.46	
5.16/5.46	Low Water (keep): wt=20.000, iters=3422
5.16/5.46	
5.16/5.46	Low Water (keep): wt=19.000, iters=3342
5.16/5.46	
5.16/5.46	Low Water (keep): wt=18.000, iters=3350
5.16/5.46	
5.16/5.46	Low Water (keep): wt=17.000, iters=3336
5.16/5.46	
5.16/5.46	Low Water (keep): wt=16.000, iters=3339
5.16/5.46	
5.16/5.46	Low Water (keep): wt=15.000, iters=3335
5.16/5.46	
5.16/5.46	Low Water (keep): wt=14.000, iters=3345
5.16/5.46	
5.16/5.46	Low Water (keep): wt=13.000, iters=3340
5.16/5.46	
5.16/5.46	Low Water (keep): wt=12.000, iters=3339
5.16/5.46	
5.16/5.46	Low Water (keep): wt=11.000, iters=3400
5.16/5.46	
5.16/5.46	Low Water (displace): id=3942, wt=80.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3025, wt=74.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4034, wt=73.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3892, wt=72.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3951, wt=69.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3950, wt=68.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4025, wt=65.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3938, wt=64.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4027, wt=63.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4045, wt=62.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4044, wt=61.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4037, wt=60.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3943, wt=59.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4077, wt=58.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4030, wt=57.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4078, wt=56.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4004, wt=55.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3939, wt=54.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4081, wt=53.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4035, wt=52.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=2638, wt=51.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4079, wt=50.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4028, wt=49.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3897, wt=48.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4033, wt=47.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4050, wt=46.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3967, wt=45.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4127, wt=44.000
5.16/5.46	
5.16/5.46	Low Water (keep): wt=10.000, iters=3404
5.16/5.46	
5.16/5.46	Low Water (displace): id=4086, wt=43.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=3978, wt=42.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4374, wt=41.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4379, wt=40.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4394, wt=39.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=4460, wt=38.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=13914, wt=9.000
5.16/5.46	
5.16/5.46	Low Water (displace): id=14164, wt=8.000
5.16/5.46	
5.16/5.46	Low Water (keep): wt=9.000, iters=3352
5.16/5.46	
5.16/5.46	============================== PROOF =================================
5.16/5.46	% SZS status Theorem
5.16/5.46	% SZS output start Refutation
5.16/5.46	
5.16/5.46	% Proof 1 at 4.29 (+ 0.11) seconds.
5.16/5.46	% Length of proof is 37.
5.16/5.46	% Level of proof is 8.
5.16/5.46	% Maximum clause weight is 15.000.
5.16/5.46	% Given clauses 4243.
5.16/5.46	
5.16/5.46	18 (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].
5.16/5.46	47 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
5.16/5.46	88 (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].
5.16/5.46	99 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
5.16/5.46	101 (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].
5.16/5.46	119 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
5.16/5.46	124 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
5.16/5.46	146 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
5.16/5.46	148 -(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(negated_conjecture) # label(non_clause).  [assumption].
5.16/5.46	193 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom).  [clausify(18)].
5.16/5.46	194 -relation(A) | set_union2(relation_dom(A),relation_rng(A)) = relation_field(A).  [copy(193),flip(b)].
5.16/5.46	233 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom).  [clausify(47)].
5.16/5.46	292 -relation(A) | -in(ordered_pair(B,C),A) | in(B,relation_dom(A)) # label(t20_relat_1) # label(lemma).  [clausify(88)].
5.16/5.46	293 -relation(A) | -in(ordered_pair(B,C),A) | in(C,relation_rng(A)) # label(t20_relat_1) # label(lemma).  [clausify(88)].
5.16/5.46	309 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(lemma).  [clausify(99)].
5.16/5.46	314 unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B) # label(d5_tarski) # label(axiom).  [clausify(101)].
5.16/5.46	315 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)).  [copy(314),rewrite([233(3)]),flip(a)].
5.16/5.46	351 unordered_pair(A,A) = singleton(A) # label(t69_enumset1) # label(lemma).  [clausify(119)].
5.16/5.46	352 singleton(A) = unordered_pair(A,A).  [copy(351),flip(a)].
5.16/5.46	365 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom).  [clausify(124)].
5.16/5.46	396 -in(A,B) | in(A,C) | -subset(B,C) # label(d3_tarski) # label(axiom).  [clausify(146)].
5.16/5.46	399 relation(c6) # label(t30_relat_1) # label(negated_conjecture).  [clausify(148)].
5.16/5.46	400 in(ordered_pair(c4,c5),c6) # label(t30_relat_1) # label(negated_conjecture).  [clausify(148)].
5.16/5.46	401 in(unordered_pair(unordered_pair(c4,c4),unordered_pair(c4,c5)),c6).  [copy(400),rewrite([315(3),352(2)])].
5.16/5.46	402 -in(c5,relation_field(c6)) | -in(c4,relation_field(c6)) # label(t30_relat_1) # label(negated_conjecture).  [clausify(148)].
5.16/5.46	448 -relation(A) | -in(unordered_pair(unordered_pair(B,B),unordered_pair(B,C)),A) | in(C,relation_rng(A)).  [back_rewrite(293),rewrite([315(2),352(2)])].
5.16/5.46	449 -relation(A) | -in(unordered_pair(unordered_pair(B,B),unordered_pair(B,C)),A) | in(B,relation_dom(A)).  [back_rewrite(292),rewrite([315(2),352(2)])].
5.16/5.46	1988 -in(A,B) | in(A,set_union2(B,C)).  [resolve(396,c,309,a)].
5.16/5.46	2000 set_union2(relation_dom(c6),relation_rng(c6)) = relation_field(c6).  [resolve(399,a,194,a)].
5.16/5.46	2492 in(c5,relation_rng(c6)).  [resolve(448,b,401,a),unit_del(a,399)].
5.16/5.46	2496 in(c4,relation_dom(c6)).  [resolve(449,b,401,a),unit_del(a,399)].
5.16/5.46	10844 in(c5,set_union2(A,relation_rng(c6))).  [resolve(1988,a,2492,a),rewrite([365(4)])].
5.16/5.46	11107 subset(relation_dom(c6),relation_field(c6)).  [para(2000(a,1),309(a,2))].
5.16/5.46	11127 in(c5,relation_field(c6)).  [para(2000(a,1),10844(a,2))].
5.16/5.46	11135 -in(c4,relation_field(c6)).  [back_unit_del(402),unit_del(a,11127)].
5.16/5.46	11181 -in(A,relation_dom(c6)) | in(A,relation_field(c6)).  [resolve(11107,a,396,c)].
5.16/5.46	20299 $F.  [resolve(11181,a,2496,a),unit_del(a,11135)].
5.16/5.46	
5.16/5.46	% SZS output end Refutation
5.16/5.46	============================== end of proof ==========================
5.16/5.46	
5.16/5.46	============================== STATISTICS ============================
5.16/5.46	
5.16/5.46	Given=4243. Generated=204695. Kept=20125. proofs=1.
5.16/5.46	Usable=4137. Sos=9998. Demods=764. Limbo=9, Disabled=6223. Hints=0.
5.16/5.46	Megabytes=25.81.
5.16/5.46	User_CPU=4.29, System_CPU=0.11, Wall_clock=5.
5.16/5.46	
5.16/5.46	============================== end of statistics =====================
5.16/5.46	
5.16/5.46	============================== end of search =========================
5.16/5.46	
5.16/5.46	THEOREM PROVED
5.16/5.46	% SZS status Theorem
5.16/5.46	
5.16/5.46	Exiting with 1 proof.
5.16/5.46	
5.16/5.46	Process 9762 exit (max_proofs) Tue Aug  9 03:41:16 2022
5.16/5.46	Prover9 interrupted
5.16/5.47	EOF