TSTP Solution File: SEU182+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU182+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 13:29:43 EDT 2022
% Result : Timeout 300.07s 300.77s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.30 % Computer : n012.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Sun Jun 19 12:55:22 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.85/1.15 ============================== Prover9 ===============================
% 0.85/1.15 Prover9 (32) version 2009-11A, November 2009.
% 0.85/1.15 Process 31849 was started by sandbox on n012.cluster.edu,
% 0.85/1.15 Sun Jun 19 12:55:23 2022
% 0.85/1.15 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31696_n012.cluster.edu".
% 0.85/1.15 ============================== end of head ===========================
% 0.85/1.15
% 0.85/1.15 ============================== INPUT =================================
% 0.85/1.15
% 0.85/1.15 % Reading from file /tmp/Prover9_31696_n012.cluster.edu
% 0.85/1.15
% 0.85/1.15 set(prolog_style_variables).
% 0.85/1.15 set(auto2).
% 0.85/1.15 % set(auto2) -> set(auto).
% 0.85/1.15 % set(auto) -> set(auto_inference).
% 0.85/1.15 % set(auto) -> set(auto_setup).
% 0.85/1.15 % set(auto_setup) -> set(predicate_elim).
% 0.85/1.15 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.85/1.15 % set(auto) -> set(auto_limits).
% 0.85/1.15 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.85/1.15 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.85/1.15 % set(auto) -> set(auto_denials).
% 0.85/1.15 % set(auto) -> set(auto_process).
% 0.85/1.15 % set(auto2) -> assign(new_constants, 1).
% 0.85/1.15 % set(auto2) -> assign(fold_denial_max, 3).
% 0.85/1.15 % set(auto2) -> assign(max_weight, "200.000").
% 0.85/1.15 % set(auto2) -> assign(max_hours, 1).
% 0.85/1.15 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.85/1.15 % set(auto2) -> assign(max_seconds, 0).
% 0.85/1.15 % set(auto2) -> assign(max_minutes, 5).
% 0.85/1.15 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.85/1.15 % set(auto2) -> set(sort_initial_sos).
% 0.85/1.15 % set(auto2) -> assign(sos_limit, -1).
% 0.85/1.15 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.85/1.15 % set(auto2) -> assign(max_megs, 400).
% 0.85/1.15 % set(auto2) -> assign(stats, some).
% 0.85/1.15 % set(auto2) -> clear(echo_input).
% 0.85/1.15 % set(auto2) -> set(quiet).
% 0.85/1.15 % set(auto2) -> clear(print_initial_clauses).
% 0.85/1.15 % set(auto2) -> clear(print_given).
% 0.85/1.15 assign(lrs_ticks,-1).
% 0.85/1.15 assign(sos_limit,10000).
% 0.85/1.15 assign(order,kbo).
% 0.85/1.15 set(lex_order_vars).
% 0.85/1.15 clear(print_given).
% 0.85/1.15
% 0.85/1.15 % formulas(sos). % not echoed (157 formulas)
% 0.85/1.15
% 0.85/1.15 ============================== end of input ==========================
% 0.85/1.15
% 0.85/1.15 % From the command line: assign(max_seconds, 300).
% 0.85/1.15
% 0.85/1.15 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.85/1.15
% 0.85/1.15 % Formulas that are not ordinary clauses:
% 0.85/1.15 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 7 (all A (relation(A) <-> (all B -(in(B,A) & (all C all D B != ordered_pair(C,D)))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 8 (all A all B ((A != empty_set -> (B = set_meet(A) <-> (all C (in(C,B) <-> (all D (in(D,A) -> in(C,D))))))) & (A = empty_set -> (B = set_meet(A) <-> B = empty_set)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 9 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 10 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 11 (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].
% 0.85/1.15 12 (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].
% 0.85/1.15 13 (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].
% 0.85/1.15 14 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 15 (all A all B all C (C = cartesian_product2(A,B) <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 16 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 17 (all A all B all C (C = set_intersection2(A,B) <-> (all D (in(D,C) <-> in(D,A) & in(D,B))))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 18 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 19 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 20 (all A all B (B = union(A) <-> (all C (in(C,B) <-> (exists D (in(C,D) & in(D,A))))))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 21 (all A all B all C (C = set_difference(A,B) <-> (all D (in(D,C) <-> in(D,A) & -in(D,B))))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 22 (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].
% 0.85/1.15 23 (all A all B (element(B,powerset(A)) -> subset_complement(A,B) = set_difference(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 24 (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].
% 0.85/1.15 25 (all A (relation(A) -> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 26 (all A (relation(A) -> (all B (relation(B) -> (B = relation_inverse(A) <-> (all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(D,C),A)))))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 27 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 28 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (C = relation_composition(A,B) <-> (all D all E (in(ordered_pair(D,E),C) <-> (exists F (in(ordered_pair(D,F),A) & in(ordered_pair(F,E),B)))))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 29 (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].
% 0.85/1.15 30 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 31 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 32 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 33 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 34 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 35 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 36 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 37 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 38 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 39 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 40 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 41 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 42 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 43 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 44 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 45 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 46 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 47 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 48 (all A all B (relation(A) & relation(B) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 49 (all A all B (element(B,powerset(powerset(A))) -> element(union_of_subsets(A,B),powerset(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 50 (all A all B (element(B,powerset(powerset(A))) -> element(meet_of_subsets(A,B),powerset(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 51 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 52 (all A all B (element(B,powerset(powerset(A))) -> element(complements_of_subsets(A,B),powerset(powerset(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 53 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 54 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 55 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 56 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 57 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 58 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 59 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 60 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 61 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 62 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 63 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 64 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 65 (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].
% 0.85/1.15 66 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 67 (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].
% 0.85/1.15 68 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 69 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 70 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 71 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 72 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 73 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 74 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 75 (all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 76 (all A all B all C (subset(A,B) -> in(C,A) | subset(A,set_difference(B,singleton(C))))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 77 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 78 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 79 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 80 (all A all B ((all C (in(C,A) -> in(C,B))) -> element(A,powerset(B)))) # label(l71_subset_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 81 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 82 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 83 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 84 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 85 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 86 (all A all B (element(B,powerset(powerset(A))) -> union_of_subsets(A,B) = union(B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 87 (all A all B (element(B,powerset(powerset(A))) -> meet_of_subsets(A,B) = set_meet(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 88 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> subset_difference(A,B,C) = set_difference(B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 89 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 90 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 91 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 92 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & A != C & A != D)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 93 (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].
% 0.85/1.15 94 (all A all B all C all D (subset(A,B) & subset(C,D) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 95 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 96 (all A exists B (in(A,B) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))) & (all C (in(C,B) -> in(powerset(C),B))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 97 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.15 98 (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].
% 0.85/1.15 99 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 100 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.15 101 (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].
% 0.85/1.16 102 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_dom(C)) & in(B,relation_rng(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 103 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 104 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_dom(A),relation_dom(B)) & subset(relation_rng(A),relation_rng(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 105 (all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 106 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 107 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 108 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 109 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 110 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 111 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 112 (all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 113 (all A all B all C all D (ordered_pair(A,B) = ordered_pair(C,D) -> A = C & B = D)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 114 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 115 (all A (relation(A) -> relation_rng(A) = relation_dom(relation_inverse(A)) & relation_dom(A) = relation_rng(relation_inverse(A)))) # label(t37_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 116 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 117 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 118 (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].
% 0.85/1.16 119 (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].
% 0.85/1.16 120 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 121 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 122 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 123 (all A all B (-(-disjoint(A,B) & (all C -(in(C,A) & in(C,B)))) & -((exists C (in(C,A) & in(C,B))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 124 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 125 (all A all B set_difference(set_union2(A,B),B) = set_difference(A,B)) # label(t40_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 126 (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].
% 0.85/1.16 127 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 128 (all A all B (element(B,powerset(powerset(A))) -> -(B != empty_set & complements_of_subsets(A,B) = empty_set))) # label(t46_setfam_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 129 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 130 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> 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].
% 0.85/1.16 131 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 132 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 133 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 134 (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].
% 0.85/1.16 135 (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].
% 0.85/1.16 136 (all A (A != empty_set -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 137 (all A all B all C (element(C,powerset(A)) -> -(in(B,subset_complement(A,C)) & in(B,C)))) # label(t54_subset_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 138 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 139 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 140 (all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 141 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 142 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 143 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 144 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 145 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 146 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 147 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 148 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 149 (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].
% 0.85/1.16 150 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 151 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 152 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.85/1.16 153 (all A exists B (in(A,B) & (all C all D (in(C,B) & subset(D,C) -> in(D,B))) & (all C -(in(C,B) & (all D -(in(D,B) & (all E (subset(E,C) -> in(E,D))))))) & (all C -(subset(C,B) & -are_equipotent(C,B) & -in(C,B))))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.85/1.16 154 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 5.75/6.12 155 -(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].
% 5.75/6.12
% 5.75/6.12 ============================== end of process non-clausal formulas ===
% 5.75/6.12
% 5.75/6.12 ============================== PROCESS INITIAL CLAUSES ===============
% 5.75/6.12
% 5.75/6.12 ============================== PREDICATE ELIMINATION =================
% 5.75/6.12
% 5.75/6.12 ============================== end predicate elimination =============
% 5.75/6.12
% 5.75/6.12 Auto_denials: (non-Horn, no changes).
% 5.75/6.12
% 5.75/6.12 Term ordering decisions:
% 5.75/6.12 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. f1=1. f2=1. f5=1. f6=1. f7=1. f9=1. f17=1. f20=1. f21=1. f23=1. f24=1. f27=1. f28=1. f29=1. f30=1. f37=1. f41=1. f42=1. f43=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. f3=1. f8=1. f36=1. f38=1. f39=1. f40=1. f44=1. subset_difference=1. f4=1. f10=1. f11=1. f14=1. f15=1. f16=1. f18=1. f19=1. f22=1. f25=1. f26=1. f32=1. f33=1. f34=1. f35=1. f12=1. f13=1. f31=1.
% 5.75/6.12
% 5.75/6.12 ============================== end of process initial clauses ========
% 5.75/6.12
% 5.75/6.12 ============================== CLAUSES FOR SEARCH ====================
% 5.75/6.12
% 5.75/6.12 ============================== end of clauses for search =============
% 5.75/6.12
% 5.75/6.12 ============================== SEARCH ================================
% 5.75/6.12
% 5.75/6.12 % Starting search at 0.07 seconds.
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=55.000, iters=3613
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=47.000, iters=3445
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=46.000, iters=3415
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=42.000, iters=3426
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=41.000, iters=3362
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=39.000, iters=3355
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=38.000, iters=3339
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=35.000, iters=3436
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=34.000, iters=3402
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=32.000, iters=3412
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=31.000, iters=3333
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=29.000, iters=3349
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=28.000, iters=3369
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=27.000, iters=3378
% 5.75/6.12
% 5.75/6.12 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 26 (0.00 of 1.50 sec).
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=24.000, iters=3388
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=22.000, iters=3560
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=21.000, iters=3360
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=20.000, iters=3335
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=19.000, iters=3348
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=18.000, iters=3440
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=17.000, iters=3351
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=16.000, iters=3426
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=14.000, iters=3345
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=13.000, iters=3339
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=12.000, iters=3431
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=11.000, iters=3348
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=10.000, iters=3348
% 5.75/6.12
% 5.75/6.12 Low Water (keep): wt=9.000, iters=3340
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2693, wt=129.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2699, wt=103.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2696, wt=96.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3640, wt=84.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3298, wt=82.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3641, wt=81.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3393, wt=80.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3297, wt=79.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3392, wt=77.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3906, wt=76.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3642, wt=75.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2615, wt=74.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3296, wt=73.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3391, wt=71.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3680, wt=70.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3925, wt=69.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3927, wt=68.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2710, wt=67.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2684, wt=65.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2516, wt=64.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=2644, wt=63.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3644, wt=62.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3913, wt=61.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3914, wt=60.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3926, wt=59.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): id=3924, wt=58.000
% 5.75/6.12
% 5.75/6.12 Low Water (displace): Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------