TSTP Solution File: SEU180+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 13:29:42 EDT 2022
% Result : Theorem 4.66s 4.94s
% Output : Refutation 4.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU180+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 13:28:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.06 ============================== Prover9 ===============================
% 0.42/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.06 Process 3819 was started by sandbox2 on n017.cluster.edu,
% 0.42/1.06 Sun Jun 19 13:28:14 2022
% 0.42/1.06 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3665_n017.cluster.edu".
% 0.42/1.06 ============================== end of head ===========================
% 0.42/1.06
% 0.42/1.06 ============================== INPUT =================================
% 0.42/1.06
% 0.42/1.06 % Reading from file /tmp/Prover9_3665_n017.cluster.edu
% 0.42/1.06
% 0.42/1.06 set(prolog_style_variables).
% 0.42/1.06 set(auto2).
% 0.42/1.06 % set(auto2) -> set(auto).
% 0.42/1.06 % set(auto) -> set(auto_inference).
% 0.42/1.06 % set(auto) -> set(auto_setup).
% 0.42/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.06 % set(auto) -> set(auto_limits).
% 0.42/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.06 % set(auto) -> set(auto_denials).
% 0.42/1.06 % set(auto) -> set(auto_process).
% 0.42/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.06 % set(auto2) -> assign(stats, some).
% 0.42/1.06 % set(auto2) -> clear(echo_input).
% 0.42/1.06 % set(auto2) -> set(quiet).
% 0.42/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.06 % set(auto2) -> clear(print_given).
% 0.42/1.06 assign(lrs_ticks,-1).
% 0.42/1.06 assign(sos_limit,10000).
% 0.42/1.06 assign(order,kbo).
% 0.42/1.06 set(lex_order_vars).
% 0.42/1.06 clear(print_given).
% 0.42/1.06
% 0.42/1.06 % formulas(sos). % not echoed (150 formulas)
% 0.42/1.06
% 0.42/1.06 ============================== end of input ==========================
% 0.42/1.06
% 0.42/1.06 % From the command line: assign(max_seconds, 300).
% 0.42/1.06
% 0.42/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.06
% 0.42/1.06 % Formulas that are not ordinary clauses:
% 0.42/1.06 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 9 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 10 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 19 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 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].
% 0.42/1.06 26 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 27 (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].
% 0.42/1.06 28 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 29 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 30 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 31 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 32 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 33 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 34 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 35 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 36 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 37 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 38 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 39 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 40 (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].
% 0.42/1.06 41 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 42 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 43 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 44 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 45 (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].
% 0.42/1.06 46 (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].
% 0.42/1.06 47 (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].
% 0.42/1.06 48 (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].
% 0.42/1.06 49 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 50 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 51 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 52 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 53 (all A all B (relation(A) & relation(B) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 54 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 55 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 56 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 57 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 58 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 59 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 60 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 61 (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].
% 0.42/1.06 62 (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].
% 0.42/1.06 63 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 64 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 65 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 66 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 67 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 68 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 69 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 70 (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].
% 0.42/1.06 71 (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].
% 0.42/1.06 72 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 73 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 74 (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].
% 0.42/1.06 75 (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].
% 0.42/1.06 76 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 77 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 78 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 79 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 80 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 81 (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].
% 0.42/1.06 82 (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].
% 0.42/1.06 83 (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].
% 0.42/1.06 84 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 85 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 86 (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].
% 0.42/1.06 87 (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].
% 0.42/1.06 88 (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].
% 0.42/1.06 89 (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].
% 0.42/1.06 90 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 91 (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].
% 0.42/1.06 92 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 93 (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].
% 0.42/1.06 94 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 95 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 96 (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].
% 0.42/1.06 97 (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].
% 0.42/1.06 98 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 99 (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].
% 0.42/1.06 100 (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].
% 0.42/1.06 101 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 102 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 103 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 104 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 105 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 106 (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].
% 0.42/1.06 107 (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].
% 0.42/1.06 108 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 109 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 110 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 111 (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].
% 0.42/1.06 112 (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].
% 0.42/1.06 113 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 114 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 115 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 116 (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].
% 0.42/1.06 117 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 118 (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].
% 0.42/1.06 119 (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].
% 0.42/1.06 120 (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].
% 0.42/1.06 121 (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].
% 0.42/1.06 122 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.42/1.06 123 (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].
% 0.42/1.06 124 (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].
% 0.42/1.06 125 (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].
% 0.42/1.06 126 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.06 127 (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].
% 0.42/1.06 128 (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].
% 0.82/1.11 129 (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].
% 0.82/1.11 130 (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].
% 0.82/1.11 131 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.11 132 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 133 (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].
% 0.82/1.11 134 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 135 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 136 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.11 137 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 138 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.11 139 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 140 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 141 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.11 142 (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].
% 0.82/1.11 143 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 144 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 145 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 146 (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].
% 0.82/1.11 147 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.82/1.11 148 -(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(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.11
% 0.82/1.11 ============================== end of process non-clausal formulas ===
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.11
% 0.82/1.11 ============================== PREDICATE ELIMINATION =================
% 0.82/1.11
% 0.82/1.11 ============================== end predicate elimination =============
% 0.82/1.11
% 0.82/1.11 Auto_denials: (non-Horn, no changes).
% 0.82/1.11
% 0.82/1.11 Term ordering decisions:
% 0.82/1.11 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. 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. f31=1. f35=1. f36=1. f37=1. f39=1. powerset=1. singleton=1. union=1. relation_dom=1. relation_rng=1. set_meet=1. cast_to_subset=1. relation_field=1. f3=1. f8=1. f30=1. f32=1. f33=1. f34=1. f38=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. f29=1. f12=1. f13=1.
% 0.82/1.11
% 0.82/1.11 ============================== end of process initial clauses ========
% 4.66/4.94
% 4.66/4.94 ============================== CLAUSES FOR SEARCH ====================
% 4.66/4.94
% 4.66/4.94 ============================== end of clauses for search =============
% 4.66/4.94
% 4.66/4.94 ============================== SEARCH ================================
% 4.66/4.94
% 4.66/4.94 % Starting search at 0.07 seconds.
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=42.000, iters=3452
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=41.000, iters=3393
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=40.000, iters=3360
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=38.000, iters=3380
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=34.000, iters=3435
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=32.000, iters=3423
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=31.000, iters=3438
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=30.000, iters=3400
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=29.000, iters=3333
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=28.000, iters=3421
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=26.000, iters=3372
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=24.000, iters=3333
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=23.000, iters=3391
% 4.66/4.94
% 4.66/4.94 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 37 (0.00 of 0.88 sec).
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=22.000, iters=3488
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=21.000, iters=3412
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=20.000, iters=3334
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=19.000, iters=3388
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=18.000, iters=3339
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=17.000, iters=3359
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=16.000, iters=3344
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=15.000, iters=3337
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=14.000, iters=3339
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=13.000, iters=3341
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=12.000, iters=3342
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=11.000, iters=3342
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2547, wt=74.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2406, wt=65.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2446, wt=64.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2577, wt=63.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2571, wt=62.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4039, wt=60.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3944, wt=59.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2886, wt=58.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3725, wt=57.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=2575, wt=56.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3889, wt=55.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4012, wt=54.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3476, wt=53.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3289, wt=52.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4080, wt=51.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4045, wt=50.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4081, wt=49.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4043, wt=48.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3991, wt=47.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3899, wt=46.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3947, wt=45.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3888, wt=44.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4091, wt=43.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4044, wt=42.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4052, wt=41.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4163, wt=40.000
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=10.000, iters=3457
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4296, wt=39.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4318, wt=38.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3988, wt=37.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=4010, wt=36.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=3224, wt=19.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=10558, wt=16.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=13846, wt=9.000
% 4.66/4.94
% 4.66/4.94 Low Water (displace): id=14350, wt=8.000
% 4.66/4.94
% 4.66/4.94 Low Water (keep): wt=9.000, iters=3333
% 4.66/4.94
% 4.66/4.94 ============================== PROOF =================================
% 4.66/4.94 % SZS status Theorem
% 4.66/4.94 % SZS output start Refutation
% 4.66/4.94
% 4.66/4.94 % Proof 1 at 3.81 (+ 0.09) seconds.
% 4.66/4.94 % Length of proof is 70.
% 4.66/4.94 % Level of proof is 10.
% 4.66/4.94 % Maximum clause weight is 15.000.
% 4.66/4.94 % Given clauses 4065.
% 4.66/4.94
% 4.66/4.94 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 10 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 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].
% 4.66/4.94 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].
% 4.66/4.94 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].
% 4.66/4.94 84 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 96 (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].
% 4.66/4.94 97 (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].
% 4.66/4.94 101 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 4.66/4.94 102 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 111 (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].
% 4.66/4.94 114 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 4.66/4.94 125 (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].
% 4.66/4.94 134 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 4.66/4.94 135 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 4.66/4.94 139 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 4.66/4.94 148 -(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(negated_conjecture) # label(non_clause). [assumption].
% 4.66/4.94 151 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(3)].
% 4.66/4.94 152 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(4)].
% 4.66/4.94 153 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(5)].
% 4.66/4.94 173 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(10)].
% 4.66/4.94 204 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(16)].
% 4.66/4.94 235 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(24)].
% 4.66/4.94 236 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(235),rewrite([151(4)])].
% 4.66/4.94 237 -relation(A) | relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) # label(d6_relat_1) # label(axiom). [clausify(25)].
% 4.66/4.94 238 -relation(A) | set_union2(relation_dom(A),relation_rng(A)) = relation_field(A). [copy(237),flip(b)].
% 4.66/4.94 305 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(84)].
% 4.66/4.94 322 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(96)].
% 4.66/4.94 325 -relation(A) | -in(ordered_pair(B,C),A) | in(B,relation_dom(A)) # label(t20_relat_1) # label(lemma). [clausify(97)].
% 4.66/4.94 326 -relation(A) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),A) | in(B,relation_dom(A)). [copy(325),rewrite([236(2)])].
% 4.66/4.94 327 -relation(A) | -in(ordered_pair(B,C),A) | in(C,relation_rng(A)) # label(t20_relat_1) # label(lemma). [clausify(97)].
% 4.66/4.94 328 -relation(A) | -in(unordered_pair(singleton(B),unordered_pair(B,C)),A) | in(C,relation_rng(A)). [copy(327),rewrite([236(2)])].
% 4.66/4.94 333 -subset(A,B) | set_intersection2(A,B) = A # label(t28_xboole_1) # label(lemma). [clausify(101)].
% 4.66/4.94 334 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom). [clausify(102)].
% 4.66/4.94 344 -subset(unordered_pair(A,B),C) | in(A,C) # label(t38_zfmisc_1) # label(lemma). [clausify(111)].
% 4.66/4.94 346 subset(unordered_pair(A,B),C) | -in(A,C) | -in(B,C) # label(t38_zfmisc_1) # label(lemma). [clausify(111)].
% 4.66/4.94 348 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(114)].
% 4.66/4.94 365 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma). [clausify(125)].
% 4.66/4.94 366 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(365),flip(a)].
% 4.66/4.94 379 set_difference(A,singleton(B)) = A | in(B,A) # label(t65_zfmisc_1) # label(lemma). [clausify(134)].
% 4.66/4.94 380 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(135)].
% 4.66/4.94 385 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(lemma). [clausify(139)].
% 4.66/4.94 399 relation(c6) # label(t30_relat_1) # label(negated_conjecture). [clausify(148)].
% 4.66/4.94 400 in(ordered_pair(c4,c5),c6) # label(t30_relat_1) # label(negated_conjecture). [clausify(148)].
% 4.66/4.94 401 in(unordered_pair(unordered_pair(c4,c4),unordered_pair(c4,c5)),c6). [copy(400),rewrite([236(3),380(2)])].
% 4.66/4.94 402 -in(c4,relation_field(c6)) | -in(c5,relation_field(c6)) # label(t30_relat_1) # label(negated_conjecture). [clausify(148)].
% 4.66/4.94 459 subset(unordered_pair(A,A),B) | -in(A,B). [factor(346,b,c)].
% 4.66/4.94 463 set_difference(A,A) = empty_set. [back_rewrite(334),rewrite([366(2),348(2)])].
% 4.66/4.94 464 -subset(A,B) | set_difference(A,set_difference(A,B)) = A. [back_rewrite(333),rewrite([366(2)])].
% 4.66/4.94 474 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(153),rewrite([366(1),366(3)])].
% 4.66/4.94 475 set_difference(A,unordered_pair(B,B)) = A | in(B,A). [back_rewrite(379),rewrite([380(1)])].
% 4.66/4.94 479 -relation(A) | -in(unordered_pair(unordered_pair(B,B),unordered_pair(B,C)),A) | in(C,relation_rng(A)). [back_rewrite(328),rewrite([380(2)])].
% 4.66/4.94 480 -relation(A) | -in(unordered_pair(unordered_pair(B,B),unordered_pair(B,C)),A) | in(B,relation_dom(A)). [back_rewrite(326),rewrite([380(2)])].
% 4.66/4.94 1479 in(A,unordered_pair(A,B)). [resolve(344,a,305,a)].
% 4.66/4.94 1658 -in(A,B) | in(A,set_union2(B,C)). [resolve(385,a,204,a)].
% 4.66/4.94 1739 set_union2(relation_dom(c6),relation_rng(c6)) = relation_field(c6). [resolve(399,a,238,a)].
% 4.66/4.94 3251 in(c5,relation_rng(c6)). [resolve(479,b,401,a),unit_del(a,399)].
% 4.66/4.94 3256 in(c4,relation_dom(c6)). [resolve(480,b,401,a),unit_del(a,399)].
% 4.66/4.94 3833 subset(unordered_pair(c4,c4),relation_dom(c6)). [resolve(3256,a,459,b)].
% 4.66/4.94 4419 unordered_pair(A,B) != empty_set. [resolve(1479,a,173,b),flip(a)].
% 4.66/4.94 11191 in(c5,set_union2(A,relation_rng(c6))). [resolve(1658,a,3251,a),rewrite([152(4)])].
% 4.66/4.94 11749 subset(relation_dom(c6),relation_field(c6)). [para(1739(a,1),385(a,2))].
% 4.66/4.94 11771 in(c5,relation_field(c6)). [para(1739(a,1),11191(a,2))].
% 4.66/4.94 11779 -in(c4,relation_field(c6)). [back_unit_del(402),unit_del(b,11771)].
% 4.66/4.94 11811 set_difference(relation_field(c6),unordered_pair(c4,c4)) = relation_field(c6). [resolve(11779,a,475,b)].
% 4.66/4.94 11817 -subset(A,relation_dom(c6)) | subset(A,relation_field(c6)). [resolve(11749,a,322,b)].
% 4.66/4.94 21276 subset(unordered_pair(c4,c4),relation_field(c6)). [resolve(11817,a,3833,a)].
% 4.66/4.94 21284 $F. [resolve(21276,a,464,a),rewrite([474(10),11811(8),463(5)]),flip(a),unit_del(a,4419)].
% 4.66/4.94
% 4.66/4.94 % SZS output end Refutation
% 4.66/4.94 ============================== end of proof ==========================
% 4.66/4.94
% 4.66/4.94 ============================== STATISTICS ============================
% 4.66/4.94
% 4.66/4.94 Given=4065. Generated=164709. Kept=21105. proofs=1.
% 4.66/4.94 Usable=3956. Sos=9998. Demods=792. Limbo=7, Disabled=7386. Hints=0.
% 4.66/4.94 Megabytes=24.36.
% 4.66/4.94 User_CPU=3.81, System_CPU=0.09, Wall_clock=4.
% 4.66/4.94
% 4.66/4.94 ============================== end of statistics =====================
% 4.66/4.94
% 4.66/4.94 ============================== end of search =========================
% 4.66/4.94
% 4.66/4.94 THEOREM PROVED
% 4.66/4.94 % SZS status Theorem
% 4.66/4.94
% 4.66/4.94 Exiting with 1 proof.
% 4.66/4.94
% 4.66/4.94 Process 3819 exit (max_proofs) Sun Jun 19 13:28:18 2022
% 4.66/4.94 Prover9 interrupted
%------------------------------------------------------------------------------