0.04/0.14	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.14/0.15	% Command  : tptp2X_and_run_prover9 %d %s
0.14/0.36	% Computer : n004.cluster.edu
0.14/0.36	% Model    : x86_64 x86_64
0.14/0.36	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.36	% Memory   : 8042.1875MB
0.14/0.36	% OS       : Linux 3.10.0-693.el7.x86_64
0.14/0.36	% CPULimit : 1440
0.14/0.36	% WCLimit  : 180
0.14/0.36	% DateTime : Mon Jul  3 11:02:15 EDT 2023
0.14/0.36	% CPUTime  : 
0.81/1.13	============================== Prover9 ===============================
0.81/1.13	Prover9 (32) version 2009-11A, November 2009.
0.81/1.13	Process 28591 was started by sandbox on n004.cluster.edu,
0.81/1.13	Mon Jul  3 11:02:16 2023
0.81/1.13	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_28438_n004.cluster.edu".
0.81/1.13	============================== end of head ===========================
0.81/1.13	
0.81/1.13	============================== INPUT =================================
0.81/1.13	
0.81/1.13	% Reading from file /tmp/Prover9_28438_n004.cluster.edu
0.81/1.13	
0.81/1.13	set(prolog_style_variables).
0.81/1.13	set(auto2).
0.81/1.13	    % set(auto2) -> set(auto).
0.81/1.13	    % set(auto) -> set(auto_inference).
0.81/1.13	    % set(auto) -> set(auto_setup).
0.81/1.13	    % set(auto_setup) -> set(predicate_elim).
0.81/1.13	    % set(auto_setup) -> assign(eq_defs, unfold).
0.81/1.13	    % set(auto) -> set(auto_limits).
0.81/1.13	    % set(auto_limits) -> assign(max_weight, "100.000").
0.81/1.13	    % set(auto_limits) -> assign(sos_limit, 20000).
0.81/1.13	    % set(auto) -> set(auto_denials).
0.81/1.13	    % set(auto) -> set(auto_process).
0.81/1.13	    % set(auto2) -> assign(new_constants, 1).
0.81/1.13	    % set(auto2) -> assign(fold_denial_max, 3).
0.81/1.13	    % set(auto2) -> assign(max_weight, "200.000").
0.81/1.13	    % set(auto2) -> assign(max_hours, 1).
0.81/1.13	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.81/1.13	    % set(auto2) -> assign(max_seconds, 0).
0.81/1.13	    % set(auto2) -> assign(max_minutes, 5).
0.81/1.13	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.81/1.13	    % set(auto2) -> set(sort_initial_sos).
0.81/1.13	    % set(auto2) -> assign(sos_limit, -1).
0.81/1.13	    % set(auto2) -> assign(lrs_ticks, 3000).
0.81/1.13	    % set(auto2) -> assign(max_megs, 400).
0.81/1.13	    % set(auto2) -> assign(stats, some).
0.81/1.13	    % set(auto2) -> clear(echo_input).
0.81/1.13	    % set(auto2) -> set(quiet).
0.81/1.13	    % set(auto2) -> clear(print_initial_clauses).
0.81/1.13	    % set(auto2) -> clear(print_given).
0.81/1.13	assign(lrs_ticks,-1).
0.81/1.13	assign(sos_limit,10000).
0.81/1.13	assign(order,kbo).
0.81/1.13	set(lex_order_vars).
0.81/1.13	clear(print_given).
0.81/1.13	
0.81/1.13	% formulas(sos).  % not echoed (157 formulas)
0.81/1.13	
0.81/1.13	============================== end of input ==========================
0.81/1.13	
0.81/1.13	% From the command line: assign(max_seconds, 1440).
0.81/1.13	
0.81/1.13	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.81/1.13	
0.81/1.13	% Formulas that are not ordinary clauses:
0.81/1.13	1 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	2 (all A all B -(empty(B) & A != B & empty(A))) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	3 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	4 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	5 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	6 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	7 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	8 (all A all B all C (unordered_pair(B,C) = singleton(A) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	9 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	10 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	11 (all A all B all C (cartesian_product2(A,B) = C <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & ordered_pair(E,F) = D)))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	12 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	13 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	14 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	15 (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].
0.81/1.13	16 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	17 (all A exists B ((all C -(subset(C,B) & -in(C,B) & -are_equipotent(C,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))) & in(A,B))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	18 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	19 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	20 (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].
0.81/1.13	21 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> meet_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),union_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	22 (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].
0.81/1.13	23 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	24 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	25 (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].
0.81/1.13	26 (all A all B ((A != empty_set -> ((all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))) <-> set_meet(A) = B)) & (A = empty_set -> (empty_set = B <-> set_meet(A) = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	27 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	28 (all A all B (B = A <-> subset(B,A) & subset(A,B))) # label(d10_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	29 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	30 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	31 (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].
0.81/1.13	32 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	33 (all A all B (-(disjoint(A,B) & (exists C in(C,set_intersection2(A,B)))) & -(-disjoint(A,B) & (all C -in(C,set_intersection2(A,B)))))) # label(t4_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	34 (all A (A != empty_set -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	35 (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].
0.81/1.13	36 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	37 (all A A = set_union2(A,empty_set)) # label(t1_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	38 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	39 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	40 (all A all B (element(B,powerset(powerset(A))) -> set_meet(B) = meet_of_subsets(A,B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	41 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	42 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	43 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	44 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> -in(D,B) & in(D,A))))) # label(d4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	45 (all A all B all C (set_union2(A,B) = C <-> (all D (in(D,B) | in(D,A) <-> in(D,C))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	46 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_rng(A),relation_rng(B)) & subset(relation_dom(A),relation_dom(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	47 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	48 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	49 (all A all B (element(B,powerset(powerset(A))) -> union(B) = union_of_subsets(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	50 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	51 (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].
0.81/1.13	52 (all A all B (-empty(B) & -empty(A) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	53 (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].
0.81/1.13	54 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	55 (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].
0.81/1.13	56 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	57 (all A all B all C all D -(C != A & A != D & unordered_pair(C,D) = unordered_pair(A,B))) # label(t10_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	58 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	59 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	60 (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].
0.81/1.13	61 (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].
0.81/1.13	62 (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].
0.81/1.13	63 (all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & empty_set != B))) # label(t46_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	64 (all A all B all C all D (in(B,D) & in(A,C) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	65 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	66 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	67 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	68 (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].
0.81/1.13	69 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (relation_composition(A,B) = C <-> (all D all E (in(ordered_pair(D,E),C) <-> (exists F (in(ordered_pair(D,F),A) & in(ordered_pair(F,E),B)))))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	70 (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].
0.81/1.13	71 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	72 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	73 (all A (relation(A) -> relation_dom(A) = relation_rng(relation_inverse(A)) & relation_dom(relation_inverse(A)) = relation_rng(A))) # label(t37_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	74 (all A all B (singleton(A) = B <-> (all C (in(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	75 (all A empty_set != singleton(A)) # label(l1_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	76 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	77 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	78 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	79 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	80 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	81 (all A (relation(A) -> A = relation_inverse(relation_inverse(A)))) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	82 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	83 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> set_difference(B,C) = subset_difference(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	84 (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].
0.81/1.13	85 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	86 (all A ((all B -((all C all D B != ordered_pair(C,D)) & in(B,A))) <-> relation(A))) # label(d1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	87 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	88 (all A all B A = set_union2(A,A)) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	89 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(t46_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	90 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	91 (all A all B (subset(A,singleton(B)) <-> empty_set = A | singleton(B) = A)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	92 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	93 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	94 (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].
0.81/1.13	95 (all A all B all C (subset(A,C) & subset(A,B) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	96 (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].
0.81/1.13	97 (all A all B (A = set_difference(A,B) <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	98 (all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> D = B & C = A)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	99 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	100 (all A (empty_set = A <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	101 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	102 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	103 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	104 (all A all B all C (unordered_pair(A,B) = C <-> (all D (in(D,C) <-> A = D | B = D)))) # label(d2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	105 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	106 (all A all B (relation(B) & relation(A) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	107 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	108 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	109 (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].
0.81/1.13	110 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	111 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	112 (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].
0.81/1.13	113 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	114 (all A all B all C (set_intersection2(A,B) = C <-> (all D (in(D,A) & in(D,B) <-> in(D,C))))) # label(d3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	115 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	116 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.13	117 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	118 (all A all B (subset(A,B) & A != B <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	119 (all A all B A = set_intersection2(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	120 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	121 (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].
0.81/1.13	122 (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].
0.81/1.13	123 (all A all B (B = union(A) <-> (all C ((exists D (in(D,A) & in(C,D))) <-> in(C,B))))) # label(d4_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	124 (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].
0.81/1.13	125 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.13	126 (all A all B all C (subset(B,C) & subset(A,B) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	127 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	128 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	129 (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].
0.81/1.14	130 (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].
0.81/1.14	131 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(B,relation_rng(C)) & in(A,relation_dom(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	132 (all A all B (B = powerset(A) <-> (all C (in(C,B) <-> subset(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	133 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	134 (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].
0.81/1.14	135 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	136 (all A exists B (in(A,B) & (all C all D (subset(D,C) & in(C,B) -> in(D,B))) & (all C -(in(C,B) & (all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	137 (all A all B (-((exists C (in(C,A) & in(C,B))) & disjoint(A,B)) & -((all C -(in(C,B) & in(C,A))) & -disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	138 (all A all B all C (element(B,powerset(C)) & in(A,B) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	139 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	140 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	141 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	142 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	143 (all A all B set_union2(A,B) = set_union2(A,set_difference(B,A))) # label(t39_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	144 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	145 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(D,C),A) <-> in(ordered_pair(C,D),B))) <-> B = relation_inverse(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	146 (all A all B ((all C (in(C,B) <-> in(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	147 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	148 (all A all B all C (subset(A,B) -> in(C,A) | subset(A,set_difference(B,singleton(C))))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	149 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	150 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	151 (all A all B all C (unordered_pair(B,C) = singleton(A) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	152 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause).  [assumption].
0.81/1.14	153 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.81/1.14	154 (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].
3.63/3.91	155 -(all A (relation(A) -> (all B (relation(B) -> subset(relation_dom(relation_composition(A,B)),relation_dom(A)))))) # label(t44_relat_1) # label(negated_conjecture) # label(non_clause).  [assumption].
3.63/3.91	
3.63/3.91	============================== end of process non-clausal formulas ===
3.63/3.91	
3.63/3.91	============================== PROCESS INITIAL CLAUSES ===============
3.63/3.91	
3.63/3.91	============================== PREDICATE ELIMINATION =================
3.63/3.91	
3.63/3.91	============================== end predicate elimination =============
3.63/3.91	
3.63/3.91	Auto_denials:  (non-Horn, no changes).
3.63/3.91	
3.63/3.91	Term ordering decisions:
3.63/3.91	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=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. relation_composition=1. meet_of_subsets=1. union_of_subsets=1. f8=1. f9=1. f11=1. f12=1. f14=1. f18=1. f19=1. f24=1. f26=1. f27=1. f30=1. f31=1. f37=1. f38=1. f39=1. f41=1. f42=1. f43=1. f44=1. f45=1. powerset=1. singleton=1. relation_dom=1. relation_rng=1. union=1. relation_inverse=1. set_meet=1. cast_to_subset=1. relation_field=1. f6=1. f7=1. f25=1. f28=1. f33=1. f34=1. f40=1. subset_difference=1. f3=1. f4=1. f5=1. f10=1. f13=1. f15=1. f16=1. f17=1. f21=1. f22=1. f23=1. f29=1. f32=1. f35=1. f36=1. f1=1. f2=1. f20=1.
3.63/3.91	
3.63/3.91	============================== end of process initial clauses ========
3.63/3.91	
3.63/3.91	============================== CLAUSES FOR SEARCH ====================
3.63/3.91	
3.63/3.91	============================== end of clauses for search =============
3.63/3.91	
3.63/3.91	============================== SEARCH ================================
3.63/3.91	
3.63/3.91	% Starting search at 0.09 seconds.
3.63/3.91	
3.63/3.91	Low Water (keep): wt=67.000, iters=3638
3.63/3.91	
3.63/3.91	Low Water (keep): wt=47.000, iters=3489
3.63/3.91	
3.63/3.91	Low Water (keep): wt=45.000, iters=3354
3.63/3.91	
3.63/3.91	Low Water (keep): wt=44.000, iters=3335
3.63/3.91	
3.63/3.91	Low Water (keep): wt=43.000, iters=3493
3.63/3.91	
3.63/3.91	Low Water (keep): wt=41.000, iters=3395
3.63/3.91	
3.63/3.91	Low Water (keep): wt=40.000, iters=3368
3.63/3.91	
3.63/3.91	Low Water (keep): wt=39.000, iters=3336
3.63/3.91	
3.63/3.91	Low Water (keep): wt=38.000, iters=3348
3.63/3.91	
3.63/3.91	Low Water (keep): wt=36.000, iters=3424
3.63/3.91	
3.63/3.91	Low Water (keep): wt=35.000, iters=3397
3.63/3.91	
3.63/3.91	Low Water (keep): wt=34.000, iters=3360
3.63/3.91	
3.63/3.91	Low Water (keep): wt=33.000, iters=3501
3.63/3.91	
3.63/3.91	Low Water (keep): wt=32.000, iters=3453
3.63/3.91	
3.63/3.91	Low Water (keep): wt=31.000, iters=3353
3.63/3.91	
3.63/3.91	Low Water (keep): wt=30.000, iters=3648
3.63/3.91	
3.63/3.91	Low Water (keep): wt=28.000, iters=3398
3.63/3.91	
3.63/3.91	Low Water (keep): wt=27.000, iters=3353
3.63/3.91	
3.63/3.91	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 25 (0.00 of 0.82 sec).
3.63/3.91	
3.63/3.91	Low Water (keep): wt=26.000, iters=3353
3.63/3.91	
3.63/3.91	Low Water (keep): wt=25.000, iters=3480
3.63/3.91	
3.63/3.91	Low Water (keep): wt=24.000, iters=3346
3.63/3.91	
3.63/3.91	Low Water (keep): wt=23.000, iters=3402
3.63/3.91	
3.63/3.91	Low Water (keep): wt=22.000, iters=3552
3.63/3.91	
3.63/3.91	Low Water (keep): wt=21.000, iters=3403
3.63/3.91	
3.63/3.91	Low Water (keep): wt=20.000, iters=3345
3.63/3.91	
3.63/3.91	Low Water (keep): wt=19.000, iters=3339
3.63/3.91	
3.63/3.91	Low Water (keep): wt=18.000, iters=3336
3.63/3.91	
3.63/3.91	Low Water (keep): wt=17.000, iters=3601
3.63/3.91	
3.63/3.91	Low Water (keep): wt=16.000, iters=3566
3.63/3.91	
3.63/3.91	Low Water (keep): wt=14.000, iters=3342
3.63/3.91	
3.63/3.91	Low Water (keep): wt=13.000, iters=3333
3.63/3.91	
3.63/3.91	Low Water (keep): wt=12.000, iters=3341
3.63/3.91	
3.63/3.91	Low Water (keep): wt=11.000, iters=3335
3.63/3.91	
3.63/3.91	Low Water (keep): wt=10.000, iters=3335
3.63/3.91	
3.63/3.91	Low Water (keep): wt=9.000, iters=3334
3.63/3.91	
3.63/3.91	Low Water (displace): id=2527, wt=129.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4158, wt=105.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2541, wt=103.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2534, wt=96.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4178, wt=89.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4180, wt=87.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3270, wt=84.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2636, wt=82.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3271, wt=81.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2624, wt=80.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2637, wt=79.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4159, wt=78.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2625, wt=77.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3883, wt=76.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3272, wt=75.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3744, wt=74.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=2647, wt=73.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4165, wt=71.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=3302, wt=70.000
3.63/3.91	
3.63/3.91	Low Water (displace): id=4Alarm clock 
179.69/180.05	Prover9 interrupted
179.69/180.06	EOF