TSTP Solution File: SEU172+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU172+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 13:29:38 EDT 2022
% Result : Theorem 0.52s 1.05s
% Output : Refutation 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU172+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.08 % Command : tptp2X_and_run_prover9 %d %s
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 600
% 0.07/0.26 % DateTime : Sun Jun 19 06:07:47 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.50/0.79 ============================== Prover9 ===============================
% 0.50/0.79 Prover9 (32) version 2009-11A, November 2009.
% 0.50/0.79 Process 24007 was started by sandbox2 on n032.cluster.edu,
% 0.50/0.79 Sun Jun 19 06:07:48 2022
% 0.50/0.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23771_n032.cluster.edu".
% 0.50/0.79 ============================== end of head ===========================
% 0.50/0.79
% 0.50/0.79 ============================== INPUT =================================
% 0.50/0.79
% 0.50/0.79 % Reading from file /tmp/Prover9_23771_n032.cluster.edu
% 0.50/0.79
% 0.50/0.79 set(prolog_style_variables).
% 0.50/0.79 set(auto2).
% 0.50/0.79 % set(auto2) -> set(auto).
% 0.50/0.79 % set(auto) -> set(auto_inference).
% 0.50/0.79 % set(auto) -> set(auto_setup).
% 0.50/0.79 % set(auto_setup) -> set(predicate_elim).
% 0.50/0.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.50/0.79 % set(auto) -> set(auto_limits).
% 0.50/0.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.50/0.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.50/0.79 % set(auto) -> set(auto_denials).
% 0.50/0.79 % set(auto) -> set(auto_process).
% 0.50/0.79 % set(auto2) -> assign(new_constants, 1).
% 0.50/0.79 % set(auto2) -> assign(fold_denial_max, 3).
% 0.50/0.79 % set(auto2) -> assign(max_weight, "200.000").
% 0.50/0.79 % set(auto2) -> assign(max_hours, 1).
% 0.50/0.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.50/0.79 % set(auto2) -> assign(max_seconds, 0).
% 0.50/0.79 % set(auto2) -> assign(max_minutes, 5).
% 0.50/0.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.50/0.79 % set(auto2) -> set(sort_initial_sos).
% 0.50/0.79 % set(auto2) -> assign(sos_limit, -1).
% 0.50/0.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.50/0.79 % set(auto2) -> assign(max_megs, 400).
% 0.50/0.79 % set(auto2) -> assign(stats, some).
% 0.50/0.79 % set(auto2) -> clear(echo_input).
% 0.50/0.79 % set(auto2) -> set(quiet).
% 0.50/0.79 % set(auto2) -> clear(print_initial_clauses).
% 0.50/0.79 % set(auto2) -> clear(print_given).
% 0.50/0.79 assign(lrs_ticks,-1).
% 0.50/0.79 assign(sos_limit,10000).
% 0.50/0.79 assign(order,kbo).
% 0.50/0.79 set(lex_order_vars).
% 0.50/0.79 clear(print_given).
% 0.50/0.79
% 0.50/0.79 % formulas(sos). % not echoed (112 formulas)
% 0.50/0.79
% 0.50/0.79 ============================== end of input ==========================
% 0.50/0.79
% 0.50/0.79 % From the command line: assign(max_seconds, 300).
% 0.50/0.79
% 0.50/0.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.50/0.79
% 0.50/0.79 % Formulas that are not ordinary clauses:
% 0.50/0.79 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 9 (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].
% 0.50/0.79 10 (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].
% 0.50/0.79 11 (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].
% 0.50/0.79 12 (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].
% 0.50/0.79 13 (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].
% 0.50/0.79 14 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 15 (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].
% 0.50/0.79 16 (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].
% 0.50/0.79 17 (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].
% 0.50/0.79 18 (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].
% 0.50/0.79 19 (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].
% 0.50/0.79 20 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 21 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 22 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 23 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 24 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 25 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 26 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 27 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 28 (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].
% 0.50/0.79 29 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 30 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 31 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 32 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 33 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 34 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 35 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 36 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 37 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 38 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 39 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 40 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 41 (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].
% 0.50/0.79 42 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 43 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 44 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 45 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 46 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 47 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 48 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 49 (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].
% 0.50/0.79 50 (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].
% 0.50/0.79 51 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 52 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 53 (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].
% 0.50/0.79 54 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 55 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 56 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 57 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 58 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 59 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 60 (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].
% 0.50/0.79 61 (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].
% 0.50/0.79 62 (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].
% 0.50/0.79 63 (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].
% 0.50/0.79 64 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 65 (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].
% 0.50/0.79 66 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 67 (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].
% 0.50/0.79 68 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 69 (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].
% 0.50/0.79 70 (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].
% 0.50/0.79 71 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 72 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 73 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 74 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 75 (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].
% 0.50/0.79 76 (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].
% 0.50/0.79 77 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 78 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 79 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 80 (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].
% 0.50/0.79 81 (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].
% 0.50/0.79 82 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 83 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 84 (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].
% 0.50/0.79 85 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 86 (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].
% 0.50/0.79 87 (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].
% 0.50/0.79 88 (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].
% 0.50/0.79 89 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 90 (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].
% 0.50/0.79 91 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 92 (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].
% 0.50/0.79 93 (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].
% 0.50/0.79 94 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 95 (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].
% 0.50/0.79 96 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 97 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 98 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 99 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 100 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 101 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 102 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.50/0.79 103 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.50/0.79 104 (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].
% 0.50/0.79 105 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.52/1.05 106 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.52/1.05 107 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.52/1.05 108 (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].
% 0.52/1.05 109 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.52/1.05 110 -(all A all B all C (element(C,powerset(A)) -> -(in(B,subset_complement(A,C)) & in(B,C)))) # label(t54_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.52/1.05
% 0.52/1.05 ============================== end of process non-clausal formulas ===
% 0.52/1.05
% 0.52/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.52/1.05
% 0.52/1.05 ============================== PREDICATE ELIMINATION =================
% 0.52/1.05
% 0.52/1.05 ============================== end predicate elimination =============
% 0.52/1.05
% 0.52/1.05 Auto_denials: (non-Horn, no changes).
% 0.52/1.05
% 0.52/1.05 Term ordering decisions:
% 0.52/1.05 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. set_union2=1. cartesian_product2=1. set_intersection2=1. unordered_pair=1. ordered_pair=1. subset_complement=1. f1=1. f3=1. f11=1. f14=1. f15=1. f21=1. f22=1. f23=1. f25=1. singleton=1. powerset=1. union=1. f2=1. f17=1. f18=1. f19=1. f20=1. f24=1. f4=1. f5=1. f8=1. f9=1. f10=1. f12=1. f13=1. f16=1. f6=1. f7=1.
% 0.52/1.05
% 0.52/1.05 ============================== end of process initial clauses ========
% 0.52/1.05
% 0.52/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.52/1.05
% 0.52/1.05 ============================== end of clauses for search =============
% 0.52/1.05
% 0.52/1.05 ============================== SEARCH ================================
% 0.52/1.05
% 0.52/1.05 % Starting search at 0.03 seconds.
% 0.52/1.05
% 0.52/1.05 ============================== PROOF =================================
% 0.52/1.05 % SZS status Theorem
% 0.52/1.05 % SZS output start Refutation
% 0.52/1.05
% 0.52/1.05 % Proof 1 at 0.27 (+ 0.01) seconds.
% 0.52/1.05 % Length of proof is 12.
% 0.52/1.05 % Level of proof is 4.
% 0.52/1.05 % Maximum clause weight is 11.000.
% 0.52/1.05 % Given clauses 256.
% 0.52/1.05
% 0.52/1.05 17 (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].
% 0.52/1.05 18 (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].
% 0.52/1.05 110 -(all A all B all C (element(C,powerset(A)) -> -(in(B,subset_complement(A,C)) & in(B,C)))) # label(t54_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.52/1.05 170 set_difference(A,B) != C | -in(D,C) | -in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(17)].
% 0.52/1.05 175 -element(A,powerset(B)) | subset_complement(B,A) = set_difference(B,A) # label(d5_subset_1) # label(axiom). [clausify(18)].
% 0.52/1.05 296 element(c5,powerset(c3)) # label(t54_subset_1) # label(negated_conjecture). [clausify(110)].
% 0.52/1.05 297 in(c4,subset_complement(c3,c5)) # label(t54_subset_1) # label(negated_conjecture). [clausify(110)].
% 0.52/1.05 298 in(c4,c5) # label(t54_subset_1) # label(negated_conjecture). [clausify(110)].
% 0.52/1.05 1241 subset_complement(c3,c5) = set_difference(c3,c5). [resolve(296,a,175,a)].
% 0.52/1.05 1247 in(c4,set_difference(c3,c5)). [back_rewrite(297),rewrite([1241(4)])].
% 0.52/1.05 1252 set_difference(A,c5) != B | -in(c4,B). [resolve(298,a,170,c)].
% 0.52/1.05 3085 $F. [resolve(1247,a,1252,b),flip(a),xx(a)].
% 0.52/1.05
% 0.52/1.05 % SZS output end Refutation
% 0.52/1.05 ============================== end of proof ==========================
% 0.52/1.05
% 0.52/1.05 ============================== STATISTICS ============================
% 0.52/1.05
% 0.52/1.05 Given=256. Generated=4415. Kept=2953. proofs=1.
% 0.52/1.05 Usable=240. Sos=2524. Demods=65. Limbo=0, Disabled=373. Hints=0.
% 0.52/1.05 Megabytes=4.48.
% 0.52/1.05 User_CPU=0.27, System_CPU=0.01, Wall_clock=0.
% 0.52/1.05
% 0.52/1.05 ============================== end of statistics =====================
% 0.52/1.05
% 0.52/1.05 ============================== end of search =========================
% 0.52/1.05
% 0.52/1.05 THEOREM PROVED
% 0.52/1.05 % SZS status Theorem
% 0.52/1.05
% 0.52/1.05 Exiting with 1 proof.
% 0.52/1.05
% 0.52/1.05 Process 24007 exit (max_proofs) Sun Jun 19 06:07:48 2022
% 0.52/1.05 Prover9 interrupted
%------------------------------------------------------------------------------