0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : tptp2X_and_run_prover9 %d %s
0.02/0.23	% Computer   : n133.star.cs.uiowa.edu
0.02/0.23	% Model      : x86_64 x86_64
0.02/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.02/0.23	% Memory     : 32218.625MB
0.02/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.02/0.23	% CPULimit   : 300
0.02/0.23	% DateTime   : Sat Jul 14 04:53:54 CDT 2018
0.02/0.23	% CPUTime    : 
0.33/0.53	============================== Prover9 ===============================
0.33/0.53	Prover9 (32) version 2009-11A, November 2009.
0.33/0.53	Process 59153 was started by sandbox on n133.star.cs.uiowa.edu,
0.33/0.53	Sat Jul 14 04:53:55 2018
0.33/0.53	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_59121_n133.star.cs.uiowa.edu".
0.33/0.53	============================== end of head ===========================
0.33/0.53	
0.33/0.53	============================== INPUT =================================
0.33/0.53	
0.33/0.53	% Reading from file /tmp/Prover9_59121_n133.star.cs.uiowa.edu
0.33/0.53	
0.33/0.53	set(prolog_style_variables).
0.33/0.53	set(auto2).
0.33/0.53	    % set(auto2) -> set(auto).
0.33/0.53	    % set(auto) -> set(auto_inference).
0.33/0.53	    % set(auto) -> set(auto_setup).
0.33/0.53	    % set(auto_setup) -> set(predicate_elim).
0.33/0.53	    % set(auto_setup) -> assign(eq_defs, unfold).
0.33/0.53	    % set(auto) -> set(auto_limits).
0.33/0.53	    % set(auto_limits) -> assign(max_weight, "100.000").
0.33/0.53	    % set(auto_limits) -> assign(sos_limit, 20000).
0.33/0.53	    % set(auto) -> set(auto_denials).
0.33/0.53	    % set(auto) -> set(auto_process).
0.33/0.53	    % set(auto2) -> assign(new_constants, 1).
0.33/0.53	    % set(auto2) -> assign(fold_denial_max, 3).
0.33/0.53	    % set(auto2) -> assign(max_weight, "200.000").
0.33/0.53	    % set(auto2) -> assign(max_hours, 1).
0.33/0.53	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.33/0.53	    % set(auto2) -> assign(max_seconds, 0).
0.33/0.53	    % set(auto2) -> assign(max_minutes, 5).
0.33/0.53	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.33/0.53	    % set(auto2) -> set(sort_initial_sos).
0.33/0.53	    % set(auto2) -> assign(sos_limit, -1).
0.33/0.53	    % set(auto2) -> assign(lrs_ticks, 3000).
0.33/0.53	    % set(auto2) -> assign(max_megs, 400).
0.33/0.53	    % set(auto2) -> assign(stats, some).
0.33/0.53	    % set(auto2) -> clear(echo_input).
0.33/0.53	    % set(auto2) -> set(quiet).
0.33/0.53	    % set(auto2) -> clear(print_initial_clauses).
0.33/0.53	    % set(auto2) -> clear(print_given).
0.33/0.53	assign(lrs_ticks,-1).
0.33/0.53	assign(sos_limit,10000).
0.33/0.53	assign(order,kbo).
0.33/0.53	set(lex_order_vars).
0.33/0.53	clear(print_given).
0.33/0.53	
0.33/0.53	% formulas(sos).  % not echoed (122 formulas)
0.33/0.53	
0.33/0.53	============================== end of input ==========================
0.33/0.53	
0.33/0.53	% From the command line: assign(max_seconds, 300).
0.33/0.53	
0.33/0.53	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.33/0.53	
0.33/0.53	% Formulas that are not ordinary clauses:
0.33/0.53	1 (all A all B (A = singleton(B) | A = empty_set <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	2 (all A all B all C ((all D ((exists E exists F (in(E,A) & ordered_pair(E,F) = D & in(F,B))) <-> in(D,C))) <-> C = cartesian_product2(A,B))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	3 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	4 (all A all B ((all C (in(C,B) <-> in(C,A))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	5 (all A exists B ((all C all D (subset(D,C) & in(C,B) -> in(D,B))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & (all C -((all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))) & in(C,B))) & in(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	6 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	7 (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].
0.33/0.53	8 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	9 (all A (empty_set = A <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	10 (all A empty_set = set_difference(empty_set,A)) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	11 (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].
0.33/0.53	12 (all A all B A = set_union2(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	13 (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].
0.33/0.53	14 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	15 (all A all B ((all C (subset(C,A) <-> in(C,B))) <-> B = powerset(A))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	16 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	17 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	18 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	19 (all A all B -(in(A,B) & disjoint(singleton(A),B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	20 (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].
0.33/0.53	21 (all A all B all C all D (in(A,C) & in(B,D) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	22 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	23 (all A all B (empty_set = set_difference(A,B) <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	24 (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].
0.33/0.53	25 (all A all B (proper_subset(A,B) <-> subset(A,B) & B != A)) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	26 (all A all B ((-empty(A) -> (element(B,A) <-> in(B,A))) & (empty(A) -> (element(B,A) <-> empty(B))))) # label(d2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	27 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	28 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	29 (all A all B all C all D (subset(C,D) & subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	30 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	31 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	32 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	33 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	34 (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].
0.33/0.53	35 (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].
0.33/0.53	36 (all A all B all C ((all D (in(D,C) <-> in(D,A) & -in(D,B))) <-> C = set_difference(A,B))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	37 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	38 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	39 (all A all B (subset(A,B) <-> set_difference(A,B) = empty_set)) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	40 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.53	41 (all A all B all C ((all D (in(D,C) <-> in(D,B) & in(D,A))) <-> C = set_intersection2(A,B))) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	42 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	43 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.53	44 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	45 (all A all B all C (C = unordered_pair(A,B) <-> (all D (in(D,C) <-> D = A | D = B)))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	46 (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].
0.33/0.54	47 (all A all B (set_intersection2(A,B) = empty_set <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	48 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	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].
0.33/0.54	50 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	51 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	52 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	53 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	54 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	55 (all A all B (singleton(A) = B <-> (all C (C = A <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	56 (all A all B all C (unordered_pair(B,C) = singleton(A) -> C = B)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	57 (all A all B all C all D -(A != C & A != D & unordered_pair(A,B) = unordered_pair(C,D))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	58 (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].
0.33/0.54	59 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	60 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	61 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	62 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	63 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	64 (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].
0.33/0.54	65 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	66 (all A all B (set_difference(A,B) = A <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	67 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	68 (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(subset_complement(A,D),B) <-> in(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	69 (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].
0.33/0.54	70 (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].
0.33/0.54	71 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	72 (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].
0.33/0.54	73 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	74 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	75 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	76 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	77 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	78 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	79 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	80 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	81 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	82 (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].
0.33/0.54	83 (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].
0.33/0.54	84 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	85 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	86 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	87 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	88 (all A all B all C ((all D (in(D,C) <-> in(D,B) | in(D,A))) <-> C = set_union2(A,B))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	89 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	90 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	91 (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 -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))) & in(A,B))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	92 (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].
0.33/0.54	93 (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].
0.33/0.54	94 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	95 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	96 (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].
0.33/0.54	97 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	98 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	99 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	100 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.33/0.54	101 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	102 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.33/0.54	103 (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].
0.33/0.54	104 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	105 (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].
0.34/0.88	106 (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].
0.34/0.88	107 (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].
0.34/0.88	108 (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].
0.34/0.88	109 (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].
0.34/0.88	110 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -(disjoint(A,B) & (exists C (in(C,B) & in(C,A)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	111 (all A all B (-(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	112 (all A all B (A = empty_set | A = singleton(B) <-> subset(A,singleton(B)))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	113 (all A all B -(A != B & empty(B) & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	114 (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].
0.34/0.88	115 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	116 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(B,C) & in(A,C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	117 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	118 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	119 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	120 -(all A all B (element(B,powerset(powerset(A))) -> -(complements_of_subsets(A,B) = empty_set & empty_set != B))) # label(t46_setfam_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.34/0.88	
0.34/0.88	============================== end of process non-clausal formulas ===
0.34/0.88	
0.34/0.88	============================== PROCESS INITIAL CLAUSES ===============
0.34/0.88	
0.34/0.88	============================== PREDICATE ELIMINATION =================
0.34/0.88	
0.34/0.88	============================== end predicate elimination =============
0.34/0.88	
0.34/0.88	Auto_denials:  (non-Horn, no changes).
0.34/0.88	
0.34/0.88	Term ordering decisions:
0.34/0.88	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. f6=1. f8=1. f10=1. f11=1. f12=1. f18=1. f24=1. f25=1. f26=1. f27=1. powerset=1. singleton=1. union=1. f7=1. f9=1. f14=1. f20=1. f21=1. f23=1. f1=1. f2=1. f3=1. f13=1. f15=1. f16=1. f17=1. f19=1. f22=1. f4=1. f5=1.
0.34/0.88	
0.34/0.88	============================== end of process initial clauses ========
0.34/0.88	
0.34/0.88	============================== CLAUSES FOR SEARCH ====================
0.34/0.88	
0.34/0.88	============================== end of clauses for search =============
0.34/0.88	
0.34/0.88	============================== SEARCH ================================
0.34/0.88	
0.34/0.88	% Starting search at 0.03 seconds.
0.34/0.88	
0.34/0.88	============================== PROOF =================================
0.34/0.88	% SZS status Theorem
0.34/0.88	% SZS output start Refutation
0.34/0.88	
0.34/0.88	% Proof 1 at 0.35 (+ 0.01) seconds.
0.34/0.88	% Length of proof is 43.
0.34/0.88	% Level of proof is 10.
0.34/0.88	% Maximum clause weight is 29.000.
0.34/0.88	% Given clauses 226.
0.34/0.88	
0.34/0.88	18 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	34 (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].
0.34/0.88	52 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	66 (all A all B (set_difference(A,B) = A <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	68 (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(subset_complement(A,D),B) <-> in(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	84 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	95 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.34/0.88	108 (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].
0.34/0.88	110 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -(disjoint(A,B) & (exists C (in(C,B) & in(C,A)))))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.34/0.88	120 -(all A all B (element(B,powerset(powerset(A))) -> -(complements_of_subsets(A,B) = empty_set & empty_set != B))) # label(t46_setfam_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.34/0.88	157 subset(empty_set,A) # label(t2_xboole_1) # label(lemma).  [clausify(18)].
0.34/0.88	186 set_intersection2(A,B) = set_difference(A,set_difference(A,B)) # label(t48_xboole_1) # label(lemma).  [clausify(34)].
0.34/0.88	225 -subset(A,B) | element(A,powerset(B)) # label(t3_subset) # label(axiom).  [clausify(52)].
0.34/0.88	249 set_difference(A,B) != A | disjoint(A,B) # label(t83_xboole_1) # label(lemma).  [clausify(66)].
0.34/0.88	256 -element(A,powerset(powerset(B))) | -element(C,powerset(powerset(B))) | complements_of_subsets(B,A) = C | in(subset_complement(B,f19(B,A,C)),A) | in(f19(B,A,C),C) # label(d8_setfam_1) # label(axiom).  [clausify(68)].
0.34/0.88	281 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom).  [clausify(84)].
0.34/0.88	299 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom).  [clausify(95)].
0.34/0.88	300 set_difference(A,A) = empty_set.  [copy(299),rewrite([186(2),281(2)])].
0.34/0.88	318 -element(A,powerset(powerset(B))) | complements_of_subsets(B,complements_of_subsets(B,A)) = A # label(involutiveness_k7_setfam_1) # label(axiom).  [clausify(108)].
0.34/0.88	322 -disjoint(A,B) | -in(C,B) | -in(C,A) # label(t3_xboole_0) # label(lemma).  [clausify(110)].
0.34/0.88	344 element(c4,powerset(powerset(c3))) # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.34/0.88	345 complements_of_subsets(c3,c4) = empty_set # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.34/0.88	346 empty_set = complements_of_subsets(c3,c4).  [copy(345),flip(a)].
0.34/0.88	347 empty_set != c4 # label(t46_setfam_1) # label(negated_conjecture).  [clausify(120)].
0.34/0.88	348 complements_of_subsets(c3,c4) != c4.  [copy(347),rewrite([346(1)])].
0.34/0.88	395 -element(A,powerset(powerset(B))) | complements_of_subsets(B,A) = A | in(subset_complement(B,f19(B,A,A)),A) | in(f19(B,A,A),A).  [factor(256,a,b)].
0.34/0.88	405 -disjoint(A,A) | -in(B,A).  [factor(322,b,c)].
0.34/0.88	407 complements_of_subsets(c3,c4) = set_difference(A,A).  [back_rewrite(300),rewrite([346(2)]),flip(a)].
0.34/0.88	418 subset(complements_of_subsets(c3,c4),A).  [back_rewrite(157),rewrite([346(1)])].
0.34/0.88	1685 complements_of_subsets(c3,complements_of_subsets(c3,c4)) = c4.  [resolve(344,a,318,a)].
0.34/0.88	2731 disjoint(complements_of_subsets(c3,c4),complements_of_subsets(c3,c4)).  [resolve(407,a,249,a(flip))].
0.34/0.88	2734 set_difference(A,A) != c4.  [para(407(a,1),348(a,1))].
0.34/0.88	2740 set_difference(A,A) = set_difference(B,B).  [para(407(a,1),407(a,1))].
0.34/0.88	2741 set_difference(A,A) = c_0.  [new_symbol(2740)].
0.34/0.88	2746 c_0 != c4.  [back_rewrite(2734),rewrite([2741(1)])].
0.34/0.88	2752 complements_of_subsets(c3,c4) = c_0.  [back_rewrite(407),rewrite([2741(4)])].
0.34/0.88	2779 disjoint(c_0,c_0).  [back_rewrite(2731),rewrite([2752(3),2752(4)])].
0.34/0.88	2789 complements_of_subsets(c3,c_0) = c4.  [back_rewrite(1685),rewrite([2752(4)])].
0.34/0.88	2793 subset(c_0,A).  [back_rewrite(418),rewrite([2752(3)])].
0.34/0.88	2861 -in(A,c_0).  [resolve(2779,a,405,a)].
0.34/0.88	2869 element(c_0,powerset(A)).  [resolve(2793,a,225,a)].
0.34/0.88	3041 complements_of_subsets(A,c_0) = c_0.  [resolve(2869,a,395,a),unit_del(b,2861),unit_del(c,2861)].
0.34/0.88	3052 $F.  [back_rewrite(2789),rewrite([3041(3)]),unit_del(a,2746)].
0.34/0.88	
0.34/0.88	% SZS output end Refutation
0.34/0.88	============================== end of proof ==========================
0.34/0.88	
0.34/0.88	============================== STATISTICS ============================
0.34/0.88	
0.34/0.88	Given=226. Generated=4115. Kept=2890. proofs=1.
0.34/0.88	Usable=214. Sos=2386. Demods=50. Limbo=11, Disabled=479. Hints=0.
0.34/0.88	Megabytes=4.51.
0.34/0.88	User_CPU=0.35, System_CPU=0.01, Wall_clock=0.
0.34/0.88	
0.34/0.88	============================== end of statistics =====================
0.34/0.88	
0.34/0.88	============================== end of search =========================
0.34/0.88	
0.34/0.88	THEOREM PROVED
0.34/0.88	% SZS status Theorem
0.34/0.88	
0.34/0.88	Exiting with 1 proof.
0.34/0.88	
0.34/0.88	Process 59153 exit (max_proofs) Sat Jul 14 04:53:55 2018
0.34/0.88	Prover9 interrupted
0.34/0.89	EOF