0.03/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.14	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n002.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 1200
0.14/0.35	% DateTime   : Tue Jul 13 17:06:03 EDT 2021
0.14/0.35	% CPUTime    : 
0.77/1.06	============================== Prover9 ===============================
0.77/1.06	Prover9 (32) version 2009-11A, November 2009.
0.77/1.06	Process 11907 was started by sandbox2 on n002.cluster.edu,
0.77/1.06	Tue Jul 13 17:06:03 2021
0.77/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_11564_n002.cluster.edu".
0.77/1.06	============================== end of head ===========================
0.77/1.06	
0.77/1.06	============================== INPUT =================================
0.77/1.06	
0.77/1.06	% Reading from file /tmp/Prover9_11564_n002.cluster.edu
0.77/1.06	
0.77/1.06	set(prolog_style_variables).
0.77/1.06	set(auto2).
0.77/1.06	    % set(auto2) -> set(auto).
0.77/1.06	    % set(auto) -> set(auto_inference).
0.77/1.06	    % set(auto) -> set(auto_setup).
0.77/1.06	    % set(auto_setup) -> set(predicate_elim).
0.77/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.77/1.06	    % set(auto) -> set(auto_limits).
0.77/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.77/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.77/1.06	    % set(auto) -> set(auto_denials).
0.77/1.06	    % set(auto) -> set(auto_process).
0.77/1.06	    % set(auto2) -> assign(new_constants, 1).
0.77/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.77/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.77/1.06	    % set(auto2) -> assign(max_hours, 1).
0.77/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.77/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.77/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.77/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.77/1.06	    % set(auto2) -> set(sort_initial_sos).
0.77/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.77/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.77/1.06	    % set(auto2) -> assign(max_megs, 400).
0.77/1.06	    % set(auto2) -> assign(stats, some).
0.77/1.06	    % set(auto2) -> clear(echo_input).
0.77/1.06	    % set(auto2) -> set(quiet).
0.77/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.77/1.06	    % set(auto2) -> clear(print_given).
0.77/1.06	assign(lrs_ticks,-1).
0.77/1.06	assign(sos_limit,10000).
0.77/1.06	assign(order,kbo).
0.77/1.06	set(lex_order_vars).
0.77/1.06	clear(print_given).
0.77/1.06	
0.77/1.06	% formulas(sos).  % not echoed (122 formulas)
0.77/1.06	
0.77/1.06	============================== end of input ==========================
0.77/1.06	
0.77/1.06	% From the command line: assign(max_seconds, 1200).
0.77/1.06	
0.77/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.77/1.06	
0.77/1.06	% Formulas that are not ordinary clauses:
0.77/1.06	1 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	2 (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].
0.77/1.06	3 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> B = D & C = A)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	4 (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)))) <-> complements_of_subsets(A,B) = C))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	5 (all A all B all C all D -(A != C & D != A & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	6 (all A all B (B = singleton(A) <-> (all C (C = A <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	7 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	8 (all A all B (A = B <-> subset(B,A) & subset(A,B))) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	9 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	10 (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].
0.77/1.06	11 (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].
0.77/1.06	12 (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].
0.77/1.06	13 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	14 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	15 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	16 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	17 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	18 (all A ((all B -in(B,A)) <-> empty_set = A)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	19 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	20 (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].
0.77/1.06	21 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	22 (all A all B (singleton(B) = A | empty_set = A <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	23 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	24 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	25 (all A all B all C ((all D (in(D,A) | in(D,B) <-> in(D,C))) <-> C = set_union2(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	26 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	27 (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].
0.77/1.06	28 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	29 (all A all B (element(B,powerset(A)) -> set_difference(A,B) = subset_complement(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	30 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(A,C) & in(B,C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	31 (all A all B all C (C = cartesian_product2(A,B) <-> (all D ((exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))) <-> in(D,C))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	32 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	33 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	34 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	35 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	36 (all A all B (-((all C -(in(C,A) & in(C,B))) & -disjoint(A,B)) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	37 (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].
0.77/1.06	38 (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].
0.77/1.06	39 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	40 (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].
0.77/1.06	41 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.06	42 (all A all B ((all C ((exists D (in(C,D) & in(D,A))) <-> in(C,B))) <-> union(A) = B)) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.06	43 (all A (subset(A,empty_set) -> empty_set = A)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	44 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	45 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	46 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	47 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	48 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	49 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	50 (all A all B (subset(A,B) & A != B <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	51 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	52 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	53 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	54 (all A exists B ((all C all D (in(C,B) & subset(D,C) -> in(D,B))) & (all C -((all D -(in(D,B) & (all E (subset(E,C) -> in(E,D))))) & in(C,B))) & (all C -(-in(C,B) & -are_equipotent(C,B) & subset(C,B))) & in(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	55 (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].
0.77/1.07	56 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	57 (all A all B (-((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)) & -(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	58 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	59 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	60 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	61 (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].
0.77/1.07	62 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(B,D) & in(A,C))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	63 (all A all B (disjoint(A,B) <-> A = set_difference(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	64 (all A exists B (in(A,B) & (all C -(-are_equipotent(C,B) & -in(C,B) & subset(C,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	65 (all A all B all C -(empty(C) & element(B,powerset(C)) & in(A,B))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	66 (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].
0.77/1.07	67 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	68 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	69 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	70 (all A all B A = set_union2(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	71 (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].
0.77/1.07	72 (all A empty_set != singleton(A)) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	73 (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].
0.77/1.07	74 (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].
0.77/1.07	75 (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].
0.77/1.07	76 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	77 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	78 (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].
0.77/1.07	79 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	80 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	81 (all A all B -(empty(B) & B != A & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	82 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	83 (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].
0.77/1.07	84 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	85 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,A) & in(D,B) <-> in(D,C))))) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	86 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	87 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	88 (all A all B all C (singleton(A) = unordered_pair(B,C) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	89 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	90 (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].
0.77/1.07	91 (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].
0.77/1.07	92 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	93 (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].
0.77/1.07	94 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	95 (all A all B (-in(B,A) <-> A = set_difference(A,singleton(B)))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	96 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	97 (all A all B (subset(A,singleton(B)) <-> singleton(B) = A | empty_set = A)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.77/1.07	98 (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].
0.77/1.07	99 (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].
0.77/1.07	100 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.77/1.07	101 (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].
0.79/1.35	102 (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].
0.79/1.35	103 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	104 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	105 (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].
0.79/1.35	106 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.79/1.35	107 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	108 (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].
0.79/1.35	109 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	110 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	111 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	112 (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].
0.79/1.35	113 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	114 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.79/1.35	115 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	116 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	117 (all A all B all C ((all D (in(D,C) <-> B = D | A = D)) <-> C = unordered_pair(A,B))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	118 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	119 (all A all B ((all C (in(C,B) <-> in(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	120 -(all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & empty_set != B))) # label(t46_setfam_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.79/1.35	
0.79/1.35	============================== end of process non-clausal formulas ===
0.79/1.35	
0.79/1.35	============================== PROCESS INITIAL CLAUSES ===============
0.79/1.35	
0.79/1.35	============================== PREDICATE ELIMINATION =================
0.79/1.35	
0.79/1.35	============================== end predicate elimination =============
0.79/1.35	
0.79/1.35	Auto_denials:  (non-Horn, no changes).
0.79/1.35	
0.79/1.35	Term ordering decisions:
0.79/1.35	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. set_difference=1. set_union2=1. cartesian_product2=1. set_intersection2=1. unordered_pair=1. ordered_pair=1. subset_complement=1. complements_of_subsets=1. f2=1. f12=1. f13=1. f14=1. f15=1. f18=1. f19=1. f21=1. f23=1. f27=1. powerset=1. singleton=1. union=1. f3=1. f4=1. f17=1. f20=1. f24=1. f25=1. f1=1. f5=1. f6=1. f9=1. f10=1. f11=1. f16=1. f22=1. f26=1. f7=1. f8=1.
0.79/1.35	
0.79/1.35	============================== end of process initial clauses ========
0.79/1.35	
0.79/1.35	============================== CLAUSES FOR SEARCH ====================
0.79/1.35	
0.79/1.35	============================== end of clauses for search =============
0.79/1.35	
0.79/1.35	============================== SEARCH ================================
0.79/1.35	
0.79/1.35	% Starting search at 0.05 seconds.
0.79/1.35	
0.79/1.35	============================== PROOF =================================
0.79/1.35	% SZS status Theorem
0.79/1.35	% SZS output start Refutation
0.79/1.35	
0.79/1.35	% Proof 1 at 0.30 (+ 0.01) seconds.
0.79/1.35	% Length of proof is 51.
0.79/1.35	% Level of proof is 11.
0.79/1.35	% Maximum clause weight is 29.000.
0.79/1.35	% Given clauses 236.
0.79/1.35	
0.79/1.35	2 (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].
0.79/1.35	4 (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)))) <-> complements_of_subsets(A,B) = C))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	13 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.79/1.35	49 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	57 (all A all B (-((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)) & -(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.79/1.35	58 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	86 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	90 (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].
0.79/1.35	96 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	118 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.79/1.35	120 -(all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & empty_set != B))) # label(t46_setfam_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.79/1.35	122 -element(A,powerset(powerset(B))) | complements_of_subsets(B,complements_of_subsets(B,A)) = A # label(involutiveness_k7_setfam_1) # label(axiom).  [clausify(2)].
0.79/1.35	126 -element(A,powerset(powerset(B))) | -element(C,powerset(powerset(B))) | in(subset_complement(B,f1(B,A,C)),A) | in(f1(B,A,C),C) | complements_of_subsets(B,A) = C # label(d8_setfam_1) # label(axiom).  [clausify(4)].
0.79/1.35	142 subset(empty_set,A) # label(t2_xboole_1) # label(lemma).  [clausify(13)].
0.79/1.35	208 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom).  [clausify(49)].
0.79/1.35	219 -in(A,set_intersection2(B,C)) | -disjoint(B,C) # label(t4_xboole_0) # label(lemma).  [clausify(57)].
0.79/1.35	221 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom).  [clausify(58)].
0.79/1.35	266 set_intersection2(A,B) != empty_set | disjoint(A,B) # label(d7_xboole_0) # label(axiom).  [clausify(86)].
0.79/1.35	271 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma).  [clausify(90)].
0.79/1.35	272 set_intersection2(A,B) = set_difference(A,set_difference(A,B)).  [copy(271),flip(a)].
0.79/1.35	286 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom).  [clausify(96)].
0.79/1.35	287 set_difference(A,A) = empty_set.  [copy(286),rewrite([272(2),221(2)])].
0.79/1.35	326 set_difference(empty_set,A) = empty_set # label(t4_boole) # label(axiom).  [clausify(118)].
0.79/1.35	329 element(c4,powerset(powerset(c3))) # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.79/1.35	330 complements_of_subsets(c3,c4) = empty_set # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.79/1.35	331 empty_set = complements_of_subsets(c3,c4).  [copy(330),flip(a)].
0.79/1.35	332 empty_set != c4 # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.79/1.35	333 complements_of_subsets(c3,c4) != c4.  [copy(332),rewrite([331(1)])].
0.79/1.35	335 -element(A,powerset(powerset(B))) | in(subset_complement(B,f1(B,A,A)),A) | in(f1(B,A,A),A) | complements_of_subsets(B,A) = A.  [factor(126,a,b)].
0.79/1.35	391 set_difference(A,set_difference(A,B)) != complements_of_subsets(c3,c4) | disjoint(A,B).  [back_rewrite(266),rewrite([272(1),331(3)])].
0.79/1.35	401 -in(A,set_difference(B,set_difference(B,C))) | -disjoint(B,C).  [back_rewrite(219),rewrite([272(1)])].
0.79/1.35	407 set_difference(complements_of_subsets(c3,c4),A) = complements_of_subsets(c3,c4).  [back_rewrite(326),rewrite([331(1),331(5)])].
0.79/1.35	409 set_difference(A,A) = complements_of_subsets(c3,c4).  [back_rewrite(287),rewrite([331(2)])].
0.79/1.35	419 subset(complements_of_subsets(c3,c4),A).  [back_rewrite(142),rewrite([331(1)])].
0.79/1.35	1448 complements_of_subsets(c3,complements_of_subsets(c3,c4)) = c4.  [resolve(329,a,122,a)].
0.79/1.35	2734 disjoint(complements_of_subsets(c3,c4),A).  [resolve(407,a,391,a)].
0.79/1.35	2751 set_difference(A,A) != c4.  [para(409(a,2),333(a,1))].
0.79/1.35	2756 set_difference(set_difference(A,A),B) = complements_of_subsets(c3,c4).  [para(409(a,2),407(a,1,1))].
0.79/1.35	2757 set_difference(A,A) = set_difference(B,B).  [para(409(a,2),409(a,2))].
0.79/1.35	2758 set_difference(A,A) = c_0.  [new_symbol(2757)].
0.79/1.35	2759 set_difference(c_0,A) = complements_of_subsets(c3,c4).  [back_rewrite(2756),rewrite([2758(1)])].
0.79/1.35	2764 c_0 != c4.  [back_rewrite(2751),rewrite([2758(1)])].
0.79/1.35	2770 complements_of_subsets(c3,c4) = c_0.  [back_rewrite(409),rewrite([2758(1)]),flip(a)].
0.79/1.35	2772 set_difference(c_0,A) = c_0.  [back_rewrite(2759),rewrite([2770(5)])].
0.79/1.35	2785 disjoint(c_0,A).  [back_rewrite(2734),rewrite([2770(3)])].
0.79/1.35	2797 complements_of_subsets(c3,c_0) = c4.  [back_rewrite(1448),rewrite([2770(4)])].
0.79/1.35	2803 subset(c_0,A).  [back_rewrite(419),rewrite([2770(3)])].
0.79/1.35	2826 -in(A,c_0).  [resolve(2785,a,401,b),rewrite([2772(3),2758(3)])].
0.79/1.35	2899 element(c_0,powerset(A)).  [resolve(2803,a,208,b)].
0.79/1.35	3065 complements_of_subsets(A,c_0) = c_0.  [resolve(2899,a,335,a),unit_del(a,2826),unit_del(b,2826)].
0.79/1.35	3075 $F.  [back_rewrite(2797),rewrite([3065(3)]),unit_del(a,2764)].
0.79/1.35	
0.79/1.35	% SZS output end Refutation
0.79/1.35	============================== end of proof ==========================
0.79/1.35	
0.79/1.35	============================== STATISTICS ============================
0.79/1.35	
0.79/1.35	Given=236. Generated=4177. Kept=2928. proofs=1.
0.79/1.35	Usable=220. Sos=2447. Demods=50. Limbo=10, Disabled=451. Hints=0.
0.79/1.35	Megabytes=4.57.
0.79/1.35	User_CPU=0.30, System_CPU=0.01, Wall_clock=1.
0.79/1.35	
0.79/1.35	============================== end of statistics =====================
0.79/1.35	
0.79/1.35	============================== end of search =========================
0.79/1.35	
0.79/1.35	THEOREM PROVED
0.79/1.35	% SZS status Theorem
0.79/1.35	
0.79/1.35	Exiting with 1 proof.
0.79/1.35	
0.79/1.35	Process 11907 exit (max_proofs) Tue Jul 13 17:06:04 2021
0.79/1.35	Prover9 interrupted
0.79/1.35	EOF