TSTP Solution File: SEU171+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 13:29:37 EDT 2022
% Result : Theorem 41.74s 42.03s
% Output : Refutation 41.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 01:59:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.07 ============================== Prover9 ===============================
% 0.80/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.07 Process 32080 was started by sandbox2 on n012.cluster.edu,
% 0.80/1.07 Sun Jun 19 01:59:54 2022
% 0.80/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31926_n012.cluster.edu".
% 0.80/1.07 ============================== end of head ===========================
% 0.80/1.07
% 0.80/1.07 ============================== INPUT =================================
% 0.80/1.07
% 0.80/1.07 % Reading from file /tmp/Prover9_31926_n012.cluster.edu
% 0.80/1.07
% 0.80/1.07 set(prolog_style_variables).
% 0.80/1.07 set(auto2).
% 0.80/1.07 % set(auto2) -> set(auto).
% 0.80/1.07 % set(auto) -> set(auto_inference).
% 0.80/1.07 % set(auto) -> set(auto_setup).
% 0.80/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.07 % set(auto) -> set(auto_limits).
% 0.80/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.07 % set(auto) -> set(auto_denials).
% 0.80/1.07 % set(auto) -> set(auto_process).
% 0.80/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.07 % set(auto2) -> assign(stats, some).
% 0.80/1.07 % set(auto2) -> clear(echo_input).
% 0.80/1.07 % set(auto2) -> set(quiet).
% 0.80/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.07 % set(auto2) -> clear(print_given).
% 0.80/1.07 assign(lrs_ticks,-1).
% 0.80/1.07 assign(sos_limit,10000).
% 0.80/1.07 assign(order,kbo).
% 0.80/1.07 set(lex_order_vars).
% 0.80/1.07 clear(print_given).
% 0.80/1.07
% 0.80/1.07 % formulas(sos). % not echoed (111 formulas)
% 0.80/1.07
% 0.80/1.07 ============================== end of input ==========================
% 0.80/1.07
% 0.80/1.07 % From the command line: assign(max_seconds, 300).
% 0.80/1.07
% 0.80/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.07
% 0.80/1.07 % Formulas that are not ordinary clauses:
% 0.80/1.07 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 20 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 21 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 22 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 23 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 24 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 25 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 26 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 27 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 29 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 30 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 31 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 32 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 33 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 34 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 35 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 36 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 37 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 38 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 39 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 40 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 42 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 43 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 44 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 45 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 46 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 47 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 48 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 52 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 54 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 55 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 56 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 57 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 58 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 59 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 64 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 66 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 68 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 71 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 72 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 73 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 74 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 77 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 78 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 79 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 83 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 85 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 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].
% 0.80/1.07 89 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 91 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 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].
% 0.80/1.07 93 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 94 (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].
% 0.80/1.07 95 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 96 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 97 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 98 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 99 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 100 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 101 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 102 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.80/1.07 103 (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].
% 0.80/1.07 104 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.80/1.07 105 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 106 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 107 (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].
% 41.74/42.03 108 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 109 -(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(negated_conjecture) # label(non_clause). [assumption].
% 41.74/42.03
% 41.74/42.03 ============================== end of process non-clausal formulas ===
% 41.74/42.03
% 41.74/42.03 ============================== PROCESS INITIAL CLAUSES ===============
% 41.74/42.03
% 41.74/42.03 ============================== PREDICATE ELIMINATION =================
% 41.74/42.03
% 41.74/42.03 ============================== end predicate elimination =============
% 41.74/42.03
% 41.74/42.03 Auto_denials: (non-Horn, no changes).
% 41.74/42.03
% 41.74/42.03 Term ordering decisions:
% 41.74/42.03 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.
% 41.74/42.03
% 41.74/42.03 ============================== end of process initial clauses ========
% 41.74/42.03
% 41.74/42.03 ============================== CLAUSES FOR SEARCH ====================
% 41.74/42.03
% 41.74/42.03 ============================== end of clauses for search =============
% 41.74/42.03
% 41.74/42.03 ============================== SEARCH ================================
% 41.74/42.03
% 41.74/42.03 % Starting search at 0.04 seconds.
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=45.000, iters=3533
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=40.000, iters=3433
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=38.000, iters=3345
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=35.000, iters=3404
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=32.000, iters=3345
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=31.000, iters=3398
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=29.000, iters=3402
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=28.000, iters=3432
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=27.000, iters=3436
% 41.74/42.03
% 41.74/42.03 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 0.56 sec).
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=26.000, iters=3404
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=25.000, iters=3355
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=23.000, iters=3405
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=21.000, iters=3354
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=20.000, iters=3345
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=19.000, iters=3541
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=18.000, iters=3399
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=17.000, iters=3349
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=16.000, iters=3342
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=15.000, iters=3337
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=14.000, iters=3333
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=13.000, iters=3382
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=12.000, iters=3337
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=11.000, iters=3440
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=10.000, iters=3340
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1875, wt=74.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1778, wt=64.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=3287, wt=63.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1898, wt=62.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=3299, wt=59.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=2129, wt=58.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1901, wt=56.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1418, wt=55.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=1880, wt=54.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=2656, wt=53.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=2479, wt=52.000
% 41.74/42.03
% 41.74/42.03 Low Water (displace): id=13339, wt=9.000
% 41.74/42.03
% 41.74/42.03 Low Water (keep): wt=9.000, iters=3334
% 41.74/42.03
% 41.74/42.03 ============================== PROOF =================================
% 41.74/42.03 % SZS status Theorem
% 41.74/42.03 % SZS output start Refutation
% 41.74/42.03
% 41.74/42.03 % Proof 1 at 40.03 (+ 0.95) seconds.
% 41.74/42.03 % Length of proof is 110.
% 41.74/42.03 % Level of proof is 11.
% 41.74/42.03 % Maximum clause weight is 16.000.
% 41.74/42.03 % Given clauses 20616.
% 41.74/42.03
% 41.74/42.03 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 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].
% 41.74/42.03 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].
% 41.74/42.03 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].
% 41.74/42.03 21 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 35 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 48 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 52 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 58 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 64 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 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].
% 41.74/42.03 72 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 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].
% 41.74/42.03 77 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 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].
% 41.74/42.03 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].
% 41.74/42.03 83 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 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].
% 41.74/42.03 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].
% 41.74/42.03 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].
% 41.74/42.03 91 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 93 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 95 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 96 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 99 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 41.74/42.03 100 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 101 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 106 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 41.74/42.03 107 (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].
% 41.74/42.03 109 -(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(negated_conjecture) # label(non_clause). [assumption].
% 41.74/42.03 113 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(4)].
% 41.74/42.03 114 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(5)].
% 41.74/42.03 122 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(8)].
% 41.74/42.03 123 empty_set = A | in(f2(A),A) # label(d1_xboole_0) # label(axiom). [clausify(8)].
% 41.74/42.03 128 empty(A) | -element(B,A) | in(B,A) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 41.74/42.03 138 set_union2(A,B) != C | -in(D,C) | in(D,A) | in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(12)].
% 41.74/42.03 174 -element(A,powerset(B)) | subset_complement(B,A) = set_difference(B,A) # label(d5_subset_1) # label(axiom). [clausify(18)].
% 41.74/42.03 181 proper_subset(A,B) | -subset(A,B) | B = A # label(d8_xboole_0) # label(axiom). [clausify(21)].
% 41.74/42.03 184 -empty(powerset(A)) # label(fc1_subset_1) # label(axiom). [clausify(35)].
% 41.74/42.03 202 set_difference(A,B) = empty_set | -subset(A,B) # label(l32_xboole_1) # label(lemma). [clausify(48)].
% 41.74/42.03 207 -in(A,B) | subset(A,union(B)) # label(l50_zfmisc_1) # label(lemma). [clausify(52)].
% 41.74/42.03 220 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(58)].
% 41.74/42.03 229 -subset(A,B) | set_union2(A,B) = B # label(t12_xboole_1) # label(lemma). [clausify(64)].
% 41.74/42.03 234 -subset(A,B) | -subset(A,C) | subset(A,set_intersection2(B,C)) # label(t19_xboole_1) # label(lemma). [clausify(67)].
% 41.74/42.03 240 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom). [clausify(72)].
% 41.74/42.03 244 -subset(A,B) | subset(set_difference(A,C),set_difference(B,C)) # label(t33_xboole_1) # label(lemma). [clausify(75)].
% 41.74/42.03 249 subset(set_difference(A,B),A) # label(t36_xboole_1) # label(lemma). [clausify(77)].
% 41.74/42.03 250 -subset(unordered_pair(A,B),C) | in(A,C) # label(t38_zfmisc_1) # label(lemma). [clausify(80)].
% 41.74/42.03 252 subset(unordered_pair(A,B),C) | -in(A,C) | -in(B,C) # label(t38_zfmisc_1) # label(lemma). [clausify(80)].
% 41.74/42.03 253 set_union2(A,set_difference(B,A)) = set_union2(A,B) # label(t39_xboole_1) # label(lemma). [clausify(81)].
% 41.74/42.03 254 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(83)].
% 41.74/42.03 257 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma). [clausify(84)].
% 41.74/42.03 259 set_difference(set_union2(A,B),B) = set_difference(A,B) # label(t40_xboole_1) # label(lemma). [clausify(86)].
% 41.74/42.03 264 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma). [clausify(90)].
% 41.74/42.03 265 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(264),flip(a)].
% 41.74/42.03 266 set_difference(empty_set,A) = empty_set # label(t4_boole) # label(axiom). [clausify(91)].
% 41.74/42.03 271 -subset(A,B) | -proper_subset(B,A) # label(t60_xboole_1) # label(lemma). [clausify(93)].
% 41.74/42.03 274 set_difference(A,singleton(B)) = A | in(B,A) # label(t65_zfmisc_1) # label(lemma). [clausify(95)].
% 41.74/42.03 275 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(96)].
% 41.74/42.03 279 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(99)].
% 41.74/42.03 280 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(lemma). [clausify(100)].
% 41.74/42.03 282 disjoint(A,B) | set_difference(A,B) != A # label(t83_xboole_1) # label(lemma). [clausify(101)].
% 41.74/42.03 287 union(powerset(A)) = A # label(t99_zfmisc_1) # label(lemma). [clausify(106)].
% 41.74/42.03 288 in(A,f24(A)) # label(t9_tarski) # label(axiom). [clausify(107)].
% 41.74/42.03 294 empty_set != c3 # label(t50_subset_1) # label(negated_conjecture). [clausify(109)].
% 41.74/42.03 295 c3 != empty_set. [copy(294),flip(a)].
% 41.74/42.03 296 element(c4,powerset(c3)) # label(t50_subset_1) # label(negated_conjecture). [clausify(109)].
% 41.74/42.03 297 element(c5,c3) # label(t50_subset_1) # label(negated_conjecture). [clausify(109)].
% 41.74/42.03 298 -in(c5,c4) # label(t50_subset_1) # label(negated_conjecture). [clausify(109)].
% 41.74/42.03 299 -in(c5,subset_complement(c3,c4)) # label(t50_subset_1) # label(negated_conjecture). [clausify(109)].
% 41.74/42.03 335 subset(unordered_pair(A,A),B) | -in(A,B). [factor(252,b,c)].
% 41.74/42.03 336 -in(A,B) | -disjoint(B,B). [factor(257,a,b)].
% 41.74/42.03 339 set_difference(A,A) = empty_set. [back_rewrite(240),rewrite([265(2),254(2)])].
% 41.74/42.03 342 -subset(A,B) | -subset(A,C) | subset(A,set_difference(B,set_difference(B,C))). [back_rewrite(234),rewrite([265(3)])].
% 41.74/42.03 350 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(114),rewrite([265(1),265(3)])].
% 41.74/42.03 351 set_difference(A,unordered_pair(B,B)) = A | in(B,A). [back_rewrite(274),rewrite([275(1)])].
% 41.74/42.03 402 set_union2(A,B) != C | in(f2(C),A) | in(f2(C),B) | empty_set = C. [resolve(138,b,123,b)].
% 41.74/42.03 1051 proper_subset(set_difference(A,B),A) | set_difference(A,B) = A. [resolve(249,a,181,b),flip(b)].
% 41.74/42.03 1055 in(A,unordered_pair(A,B)). [resolve(250,a,220,a)].
% 41.74/42.03 1090 set_difference(set_union2(A,B),set_difference(B,A)) = set_difference(A,set_difference(B,A)). [para(253(a,1),259(a,1,1))].
% 41.74/42.03 1151 set_difference(A,set_union2(A,B)) = empty_set. [resolve(280,a,202,b)].
% 41.74/42.03 1159 disjoint(empty_set,A). [resolve(282,b,266,a)].
% 41.74/42.03 1232 subset_complement(c3,c4) = set_difference(c3,c4). [resolve(296,a,174,a)].
% 41.74/42.03 1233 in(c4,powerset(c3)). [resolve(296,a,128,b),unit_del(a,184)].
% 41.74/42.03 1237 -in(c5,set_difference(c3,c4)). [back_rewrite(299),rewrite([1232(4)])].
% 41.74/42.03 1239 empty(c3) | in(c5,c3). [resolve(297,a,128,b)].
% 41.74/42.03 1941 subset(unordered_pair(A,A),f24(A)). [resolve(335,b,288,a)].
% 41.74/42.03 1978 -subset(A,B) | subset(A,set_difference(B,set_difference(B,A))). [resolve(342,b,220,a)].
% 41.74/42.03 2349 set_difference(A,set_difference(B,A)) = A. [para(259(a,1),350(a,2,2)),rewrite([113(1),1151(2),254(2),113(1),1090(3)]),flip(a)].
% 41.74/42.03 2389 set_difference(c4,unordered_pair(c5,c5)) = c4. [resolve(351,b,298,a)].
% 41.74/42.03 2661 -in(A,empty_set). [resolve(1159,a,336,b)].
% 41.74/42.03 2733 set_difference(set_difference(c3,c4),unordered_pair(c5,c5)) = set_difference(c3,c4). [resolve(1237,a,351,b)].
% 41.74/42.03 2756 subset(c4,c3). [resolve(1233,a,207,a),rewrite([287(4)])].
% 41.74/42.03 2785 set_union2(c3,c4) = c3. [resolve(2756,a,229,a),rewrite([113(3)])].
% 41.74/42.03 2790 set_difference(c4,c3) = empty_set. [resolve(2756,a,202,b)].
% 41.74/42.03 3000 unordered_pair(A,B) != empty_set. [resolve(1055,a,122,b),flip(a)].
% 41.74/42.03 3041 empty(c3) | subset(unordered_pair(c5,c5),c3). [resolve(1239,b,335,b)].
% 41.74/42.03 3128 set_union2(empty_set,c3) = c3. [para(2785(a,1),253(a,2)),rewrite([2790(4),113(3)])].
% 41.74/42.03 3440 set_difference(unordered_pair(A,A),f24(A)) = empty_set. [resolve(1941,a,202,b)].
% 41.74/42.03 4694 in(f2(c3),c3). [resolve(402,a,3128,a),flip(c),unit_del(a,2661),unit_del(c,295)].
% 41.74/42.03 4721 -empty(c3). [resolve(4694,a,279,a)].
% 41.74/42.03 4797 subset(unordered_pair(c5,c5),c3). [back_unit_del(3041),unit_del(a,4721)].
% 41.74/42.03 4839 subset(set_difference(unordered_pair(c5,c5),A),set_difference(c3,A)). [resolve(4797,a,244,a)].
% 41.74/42.03 4981 set_difference(unordered_pair(c5,c5),c4) = unordered_pair(c5,c5). [para(2389(a,1),2349(a,1,2))].
% 41.74/42.03 21660 proper_subset(empty_set,unordered_pair(A,A)). [para(3440(a,1),1051(a,1)),rewrite([3440(6)]),flip(b),unit_del(b,3000)].
% 41.74/42.03 21681 -subset(unordered_pair(A,A),empty_set). [resolve(21660,a,271,b)].
% 41.74/42.03 53203 subset(unordered_pair(c5,c5),set_difference(c3,c4)). [para(4981(a,1),4839(a,1))].
% 41.74/42.03 53205 $F. [resolve(53203,a,1978,a),rewrite([2733(13),339(10)]),unit_del(a,21681)].
% 41.74/42.03
% 41.74/42.03 % SZS output end Refutation
% 41.74/42.03 ============================== end of proof ==========================
% 41.74/42.03
% 41.74/42.03 ============================== STATISTICS ============================
% 41.74/42.03
% 41.74/42.03 Given=20616. Generated=1726851. Kept=53073. proofs=1.
% 41.74/42.03 Usable=20395. Sos=9864. Demods=781. Limbo=1, Disabled=22998. Hints=0.
% 41.74/42.03 Megabytes=32.79.
% 41.74/42.03 User_CPU=40.03, System_CPU=0.95, Wall_clock=41.
% 41.74/42.03
% 41.74/42.03 ============================== end of statistics =====================
% 41.74/42.03
% 41.74/42.03 ============================== end of search =========================
% 41.74/42.03
% 41.74/42.03 THEOREM PROVED
% 41.74/42.03 % SZS status Theorem
% 41.74/42.03
% 41.74/42.03 Exiting with 1 proof.
% 41.74/42.03
% 41.74/42.03 Process 32080 exit (max_proofs) Sun Jun 19 02:00:35 2022
% 41.74/42.03 Prover9 interrupted
%------------------------------------------------------------------------------