TSTP Solution File: SEU177+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:29:40 EDT 2022
% Result : Timeout 300.06s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jun 20 14:18:50 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.82/1.08 ============================== Prover9 ===============================
% 0.82/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.08 Process 24143 was started by sandbox on n018.cluster.edu,
% 0.82/1.08 Mon Jun 20 14:18:51 2022
% 0.82/1.08 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23885_n018.cluster.edu".
% 0.82/1.08 ============================== end of head ===========================
% 0.82/1.08
% 0.82/1.08 ============================== INPUT =================================
% 0.82/1.08
% 0.82/1.08 % Reading from file /tmp/Prover9_23885_n018.cluster.edu
% 0.82/1.08
% 0.82/1.08 set(prolog_style_variables).
% 0.82/1.08 set(auto2).
% 0.82/1.08 % set(auto2) -> set(auto).
% 0.82/1.08 % set(auto) -> set(auto_inference).
% 0.82/1.08 % set(auto) -> set(auto_setup).
% 0.82/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.08 % set(auto) -> set(auto_limits).
% 0.82/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.08 % set(auto) -> set(auto_denials).
% 0.82/1.08 % set(auto) -> set(auto_process).
% 0.82/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.08 % set(auto2) -> assign(stats, some).
% 0.82/1.08 % set(auto2) -> clear(echo_input).
% 0.82/1.08 % set(auto2) -> set(quiet).
% 0.82/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.08 % set(auto2) -> clear(print_given).
% 0.82/1.08 assign(lrs_ticks,-1).
% 0.82/1.08 assign(sos_limit,10000).
% 0.82/1.08 assign(order,kbo).
% 0.82/1.08 set(lex_order_vars).
% 0.82/1.08 clear(print_given).
% 0.82/1.08
% 0.82/1.08 % formulas(sos). % not echoed (142 formulas)
% 0.82/1.08
% 0.82/1.08 ============================== end of input ==========================
% 0.82/1.08
% 0.82/1.08 % From the command line: assign(max_seconds, 300).
% 0.82/1.08
% 0.82/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.08
% 0.82/1.08 % Formulas that are not ordinary clauses:
% 0.82/1.08 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 7 (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].
% 0.82/1.08 8 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 9 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 10 (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].
% 0.82/1.08 11 (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].
% 0.82/1.08 12 (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].
% 0.82/1.08 13 (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].
% 0.82/1.08 14 (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].
% 0.82/1.08 15 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 16 (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].
% 0.82/1.08 17 (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].
% 0.82/1.08 18 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 19 (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].
% 0.82/1.08 20 (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].
% 0.82/1.08 21 (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].
% 0.82/1.08 22 (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].
% 0.82/1.08 23 (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].
% 0.82/1.08 24 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 25 (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].
% 0.82/1.08 26 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 27 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 28 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 29 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 30 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 31 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 32 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 33 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 34 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 35 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 36 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 37 (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].
% 0.82/1.08 38 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 39 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 40 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 41 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 42 (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].
% 0.82/1.08 43 (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].
% 0.82/1.08 44 (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].
% 0.82/1.08 45 (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].
% 0.82/1.08 46 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 47 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 48 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 49 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 50 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 51 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 52 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 53 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 54 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 55 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 56 (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].
% 0.82/1.08 57 (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].
% 0.82/1.08 58 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 59 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 60 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 61 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 62 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 63 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 64 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 65 (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].
% 0.82/1.08 66 (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].
% 0.82/1.08 67 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 68 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 69 (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].
% 0.82/1.08 70 (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].
% 0.82/1.08 71 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 72 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 73 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 74 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 75 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 76 (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].
% 0.82/1.08 77 (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].
% 0.82/1.08 78 (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].
% 0.82/1.08 79 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 80 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 81 (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].
% 0.82/1.08 82 (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].
% 0.82/1.08 83 (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].
% 0.82/1.08 84 (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].
% 0.82/1.08 85 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 86 (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].
% 0.82/1.08 87 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 88 (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].
% 0.82/1.08 89 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 90 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 91 (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].
% 0.82/1.08 92 (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].
% 0.82/1.08 93 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 94 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 95 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 96 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 97 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 98 (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].
% 0.82/1.08 99 (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].
% 0.82/1.08 100 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 101 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 102 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 103 (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].
% 0.82/1.08 104 (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].
% 0.82/1.08 105 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 106 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 107 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 108 (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].
% 0.82/1.08 109 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 110 (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].
% 0.82/1.08 111 (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].
% 0.82/1.08 112 (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].
% 0.82/1.08 113 (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].
% 0.82/1.08 114 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 115 (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].
% 0.82/1.08 116 (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].
% 0.82/1.08 117 (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].
% 0.82/1.08 118 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 119 (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].
% 0.82/1.08 120 (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].
% 0.82/1.08 121 (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].
% 0.82/1.08 122 (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].
% 0.82/1.08 123 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 124 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 125 (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].
% 0.82/1.08 126 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 127 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.08 128 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 129 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 130 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 131 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 132 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 133 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.09 134 (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].
% 0.82/1.09 135 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 136 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 137 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 138 (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].
% 0.82/1.09 139 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.09 140 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.09
% 0.82/1.09 ============================== end of process non-clausal formulas ===
% 0.82/1.09
% 0.82/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.09
% 0.82/1.09 ============================== PREDICATE ELIMINATION =================
% 0.82/1.09 141 relation(c1) # label(rc1_relat_1) # label(axiom). [clausify(71)].
% 0.82/1.09 142 -relation(A) | relation_dom(A) != B | -in(C,B) | in(ordered_pair(C,f16(A,B,C)),A) # label(d4_relat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 143 -relation(A) | relation_dom(A) != B | in(C,B) | -in(ordered_pair(C,D),A) # label(d4_relat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 144 -relation(A) | relation_dom(A) = B | in(f17(A,B),B) | in(ordered_pair(f17(A,B),f18(A,B)),A) # label(d4_relat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 145 -relation(A) | relation_dom(A) = B | -in(f17(A,B),B) | -in(ordered_pair(f17(A,B),C),A) # label(d4_relat_1) # label(axiom). [clausify(17)].
% 0.82/1.09 146 -relation(A) | relation_rng(A) != B | -in(C,B) | in(ordered_pair(f23(A,B,C),C),A) # label(d5_relat_1) # label(axiom). [clausify(21)].
% 0.82/1.09 147 -relation(A) | relation_rng(A) != B | in(C,B) | -in(ordered_pair(D,C),A) # label(d5_relat_1) # label(axiom). [clausify(21)].
% 0.82/1.09 148 -relation(A) | relation_rng(A) = B | in(f24(A,B),B) | in(ordered_pair(f25(A,B),f24(A,B)),A) # label(d5_relat_1) # label(axiom). [clausify(21)].
% 0.82/1.09 149 -relation(A) | relation_rng(A) = B | -in(f24(A,B),B) | -in(ordered_pair(C,f24(A,B)),A) # label(d5_relat_1) # label(axiom). [clausify(21)].
% 0.82/1.09 Derived: relation_dom(c1) != A | -in(B,A) | in(ordered_pair(B,f16(c1,A,B)),c1). [resolve(141,a,142,a)].
% 0.82/1.09 Derived: relation_dom(c1) != A | in(B,A) | -in(ordered_pair(B,C),c1). [resolve(141,a,143,a)].
% 0.82/1.09 Derived: relation_dom(c1) = A | in(f17(c1,A),A) | in(ordered_pair(f17(c1,A),f18(c1,A)),c1). [resolve(141,a,144,a)].
% 0.82/1.09 Derived: relation_dom(c1) = A | -in(f17(c1,A),A) | -in(ordered_pair(f17(c1,A),B),c1). [resolve(141,a,145,a)].
% 0.82/1.09 Derived: relation_rng(c1) != A | -in(B,A) | in(ordered_pair(f23(c1,A,B),B),c1). [resolve(141,a,146,a)].
% 0.82/1.09 Derived: relation_rng(c1) != A | in(B,A) | -in(ordered_pair(C,B),c1). [resolve(141,a,147,a)].
% 0.82/1.09 Derived: relation_rng(c1) = A | in(f24(c1,A),A) | in(ordered_pair(f25(c1,A),f24(c1,A)),c1). [resolve(141,a,148,a)].
% 0.82/1.09 Derived: relation_rng(c1) = A | -in(f24(c1,A),A) | -in(ordered_pair(B,f24(c1,A)),c1). [resolve(141,a,149,a)].
% 0.82/1.09 150 relation(c6) # label(t20_relat_1) # label(negated_conjecture). [clausify(140)].
% 2.45/2.72 Derived: relation_dom(c6) != A | -in(B,A) | in(ordered_pair(B,f16(c6,A,B)),c6). [resolve(150,a,142,a)].
% 2.45/2.72 Derived: relation_dom(c6) != A | in(B,A) | -in(ordered_pair(B,C),c6). [resolve(150,a,143,a)].
% 2.45/2.72 Derived: relation_dom(c6) = A | in(f17(c6,A),A) | in(ordered_pair(f17(c6,A),f18(c6,A)),c6). [resolve(150,a,144,a)].
% 2.45/2.72 Derived: relation_dom(c6) = A | -in(f17(c6,A),A) | -in(ordered_pair(f17(c6,A),B),c6). [resolve(150,a,145,a)].
% 2.45/2.72 Derived: relation_rng(c6) != A | -in(B,A) | in(ordered_pair(f23(c6,A,B),B),c6). [resolve(150,a,146,a)].
% 2.45/2.72 Derived: relation_rng(c6) != A | in(B,A) | -in(ordered_pair(C,B),c6). [resolve(150,a,147,a)].
% 2.45/2.72 Derived: relation_rng(c6) = A | in(f24(c6,A),A) | in(ordered_pair(f25(c6,A),f24(c6,A)),c6). [resolve(150,a,148,a)].
% 2.45/2.72 Derived: relation_rng(c6) = A | -in(f24(c6,A),A) | -in(ordered_pair(B,f24(c6,A)),c6). [resolve(150,a,149,a)].
% 2.45/2.72
% 2.45/2.72 ============================== end predicate elimination =============
% 2.45/2.72
% 2.45/2.72 Auto_denials: (non-Horn, no changes).
% 2.45/2.72
% 2.45/2.72 Term ordering decisions:
% 2.45/2.72 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. set_difference=1. set_union2=1. cartesian_product2=1. set_intersection2=1. unordered_pair=1. complements_of_subsets=1. subset_complement=1. meet_of_subsets=1. union_of_subsets=1. f2=1. f3=1. f4=1. f6=1. f14=1. f17=1. f18=1. f20=1. f21=1. f24=1. f25=1. f28=1. f32=1. f33=1. f34=1. f36=1. powerset=1. singleton=1. union=1. set_meet=1. relation_dom=1. relation_rng=1. cast_to_subset=1. f5=1. f27=1. f29=1. f30=1. f31=1. f35=1. subset_difference=1. f1=1. f7=1. f8=1. f11=1. f12=1. f13=1. f15=1. f16=1. f19=1. f22=1. f23=1. f26=1. f9=1. f10=1.
% 2.45/2.72
% 2.45/2.72 ============================== end of process initial clauses ========
% 2.45/2.72
% 2.45/2.72 ============================== CLAUSES FOR SEARCH ====================
% 2.45/2.72
% 2.45/2.72 ============================== end of clauses for search =============
% 2.45/2.72
% 2.45/2.72 ============================== SEARCH ================================
% 2.45/2.72
% 2.45/2.72 % Starting search at 0.07 seconds.
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=58.000, iters=3756
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=40.000, iters=3355
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=38.000, iters=3371
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=36.000, iters=3411
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=35.000, iters=3417
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=34.000, iters=3388
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=32.000, iters=3342
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=31.000, iters=3436
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=28.000, iters=3385
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=26.000, iters=3343
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=25.000, iters=3362
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=24.000, iters=3358
% 2.45/2.72
% 2.45/2.72 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 33 (0.00 of 0.81 sec).
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=23.000, iters=3380
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=22.000, iters=3357
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=21.000, iters=3341
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=20.000, iters=3375
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=19.000, iters=3372
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=18.000, iters=3341
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=17.000, iters=3384
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=16.000, iters=3368
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=15.000, iters=3346
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=14.000, iters=3340
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=13.000, iters=3335
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=12.000, iters=3334
% 2.45/2.72
% 2.45/2.72 Low Water (keep): wt=11.000, iters=3352
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2580, wt=109.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2110, wt=88.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=1796, wt=87.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=1999, wt=82.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2022, wt=81.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2371, wt=77.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2635, wt=76.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2572, wt=74.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2474, wt=71.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2525, wt=70.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=3279, wt=65.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2465, wt=64.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2437, wt=63.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2598, wt=62.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2581, wt=60.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2590, wt=59.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2881, wt=58.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=3667, wt=57.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2601, wt=56.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2398, wt=55.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2577, wt=54.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=3615, wt=53.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=3731, wt=52.000
% 2.45/2.72
% 2.45/2.72 Low Water (displace): id=2070, wt=51.000
% 300.06/300.32 Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------