TSTP Solution File: SEU169+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 13:29:36 EDT 2022
% Result : Theorem 1.23s 1.50s
% Output : Refutation 1.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU169+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n014.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
% 0.13/0.35 % DateTime : Sun Jun 19 04:23:48 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.84/1.10 ============================== Prover9 ===============================
% 0.84/1.10 Prover9 (32) version 2009-11A, November 2009.
% 0.84/1.10 Process 23415 was started by sandbox on n014.cluster.edu,
% 0.84/1.10 Sun Jun 19 04:23:49 2022
% 0.84/1.10 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23262_n014.cluster.edu".
% 0.84/1.10 ============================== end of head ===========================
% 0.84/1.10
% 0.84/1.10 ============================== INPUT =================================
% 0.84/1.10
% 0.84/1.10 % Reading from file /tmp/Prover9_23262_n014.cluster.edu
% 0.84/1.10
% 0.84/1.10 set(prolog_style_variables).
% 0.84/1.10 set(auto2).
% 0.84/1.10 % set(auto2) -> set(auto).
% 0.84/1.10 % set(auto) -> set(auto_inference).
% 0.84/1.10 % set(auto) -> set(auto_setup).
% 0.84/1.10 % set(auto_setup) -> set(predicate_elim).
% 0.84/1.10 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.84/1.10 % set(auto) -> set(auto_limits).
% 0.84/1.10 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.84/1.10 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.84/1.10 % set(auto) -> set(auto_denials).
% 0.84/1.10 % set(auto) -> set(auto_process).
% 0.84/1.10 % set(auto2) -> assign(new_constants, 1).
% 0.84/1.10 % set(auto2) -> assign(fold_denial_max, 3).
% 0.84/1.10 % set(auto2) -> assign(max_weight, "200.000").
% 0.84/1.10 % set(auto2) -> assign(max_hours, 1).
% 0.84/1.10 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.84/1.10 % set(auto2) -> assign(max_seconds, 0).
% 0.84/1.10 % set(auto2) -> assign(max_minutes, 5).
% 0.84/1.10 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.84/1.10 % set(auto2) -> set(sort_initial_sos).
% 0.84/1.10 % set(auto2) -> assign(sos_limit, -1).
% 0.84/1.10 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.84/1.10 % set(auto2) -> assign(max_megs, 400).
% 0.84/1.10 % set(auto2) -> assign(stats, some).
% 0.84/1.10 % set(auto2) -> clear(echo_input).
% 0.84/1.10 % set(auto2) -> set(quiet).
% 0.84/1.10 % set(auto2) -> clear(print_initial_clauses).
% 0.84/1.10 % set(auto2) -> clear(print_given).
% 0.84/1.10 assign(lrs_ticks,-1).
% 0.84/1.10 assign(sos_limit,10000).
% 0.84/1.10 assign(order,kbo).
% 0.84/1.10 set(lex_order_vars).
% 0.84/1.10 clear(print_given).
% 0.84/1.10
% 0.84/1.10 % formulas(sos). % not echoed (105 formulas)
% 0.84/1.10
% 0.84/1.10 ============================== end of input ==========================
% 0.84/1.10
% 0.84/1.10 % From the command line: assign(max_seconds, 300).
% 0.84/1.10
% 0.84/1.10 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.84/1.10
% 0.84/1.10 % Formulas that are not ordinary clauses:
% 0.84/1.10 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 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].
% 0.84/1.10 18 (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].
% 0.84/1.10 19 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 20 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 21 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 22 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 23 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 24 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 25 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 26 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 27 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 28 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 29 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 30 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 31 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 32 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 33 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 34 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 35 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 36 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 37 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 38 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 39 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 40 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 41 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 42 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 43 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 44 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 45 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 46 (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].
% 0.84/1.10 47 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 48 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 49 (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].
% 0.84/1.10 50 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 51 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 52 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 53 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 54 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 55 (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].
% 0.84/1.10 56 (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].
% 0.84/1.10 57 (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].
% 0.84/1.10 58 (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].
% 0.84/1.10 59 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 60 (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].
% 0.84/1.10 61 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 62 (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].
% 0.84/1.10 63 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 64 (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].
% 0.84/1.10 65 (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].
% 0.84/1.10 66 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 67 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 68 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 69 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 70 (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].
% 0.84/1.10 71 (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].
% 0.84/1.10 72 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 73 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 74 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 75 (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].
% 0.84/1.10 76 (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].
% 0.84/1.10 77 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 78 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 79 (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].
% 0.84/1.10 80 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 81 (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].
% 0.84/1.10 82 (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].
% 0.84/1.10 83 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 84 (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].
% 0.84/1.10 85 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 86 (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].
% 0.84/1.10 87 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 88 (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].
% 0.84/1.10 89 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 90 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 91 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 92 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 93 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 94 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 95 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 96 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.84/1.10 97 (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].
% 0.84/1.10 98 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 99 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 100 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 101 (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].
% 0.84/1.10 102 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.84/1.10 103 -(all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.84/1.10
% 0.84/1.10 ============================== end of process non-clausal formulas ===
% 0.84/1.10
% 0.84/1.10 ============================== PROCESS INITIAL CLAUSES ===============
% 0.84/1.10
% 0.84/1.10 ============================== PREDICATE ELIMINATION =================
% 0.84/1.10 104 empty(A) | element(B,A) | -in(B,A) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 1.23/1.50 105 empty(A) | -element(B,A) | in(B,A) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 1.23/1.50 106 -empty(A) | -element(B,A) | empty(B) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 1.23/1.50 107 -empty(A) | element(B,A) | -empty(B) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 1.23/1.50 108 element(f17(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(32)].
% 1.23/1.50 Derived: empty(A) | in(f17(A),A). [resolve(108,a,105,b)].
% 1.23/1.50 Derived: -empty(A) | empty(f17(A)). [resolve(108,a,106,b)].
% 1.23/1.50 109 empty(A) | element(f18(A),powerset(A)) # label(rc1_subset_1) # label(axiom). [clausify(50)].
% 1.23/1.50 Derived: empty(A) | empty(powerset(A)) | in(f18(A),powerset(A)). [resolve(109,b,105,b)].
% 1.23/1.50 Derived: empty(A) | -empty(powerset(A)) | empty(f18(A)). [resolve(109,b,106,b)].
% 1.23/1.50 110 element(c4,powerset(c3)) # label(l3_subset_1) # label(negated_conjecture). [clausify(103)].
% 1.23/1.50 Derived: empty(powerset(c3)) | in(c4,powerset(c3)). [resolve(110,a,105,b)].
% 1.23/1.50 Derived: -empty(powerset(c3)) | empty(c4). [resolve(110,a,106,b)].
% 1.23/1.50
% 1.23/1.50 ============================== end predicate elimination =============
% 1.23/1.50
% 1.23/1.50 Auto_denials: (non-Horn, no changes).
% 1.23/1.50
% 1.23/1.50 Term ordering decisions:
% 1.23/1.50 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. f1=1. f3=1. f11=1. f14=1. f15=1. f20=1. f21=1. f22=1. f24=1. singleton=1. powerset=1. union=1. f2=1. f17=1. f18=1. f19=1. f23=1. f4=1. f5=1. f8=1. f9=1. f10=1. f12=1. f13=1. f16=1. f6=1. f7=1.
% 1.23/1.50
% 1.23/1.50 ============================== end of process initial clauses ========
% 1.23/1.50
% 1.23/1.50 ============================== CLAUSES FOR SEARCH ====================
% 1.23/1.50
% 1.23/1.50 ============================== end of clauses for search =============
% 1.23/1.50
% 1.23/1.50 ============================== SEARCH ================================
% 1.23/1.50
% 1.23/1.50 % Starting search at 0.05 seconds.
% 1.23/1.50
% 1.23/1.50 ============================== PROOF =================================
% 1.23/1.50 % SZS status Theorem
% 1.23/1.50 % SZS output start Refutation
% 1.23/1.50
% 1.23/1.50 % Proof 1 at 0.41 (+ 0.01) seconds.
% 1.23/1.50 % Length of proof is 51.
% 1.23/1.50 % Level of proof is 7.
% 1.23/1.50 % Maximum clause weight is 11.000.
% 1.23/1.50 % Given clauses 276.
% 1.23/1.50
% 1.23/1.50 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 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].
% 1.23/1.50 33 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 48 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.23/1.50 53 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 64 (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].
% 1.23/1.50 66 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.23/1.50 67 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 75 (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].
% 1.23/1.50 78 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 1.23/1.50 84 (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].
% 1.23/1.50 89 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.23/1.50 90 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 1.23/1.50 100 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.23/1.50 103 -(all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.23/1.50 105 empty(A) | -element(B,A) | in(B,A) # label(d2_subset_1) # label(axiom). [clausify(10)].
% 1.23/1.50 110 element(c4,powerset(c3)) # label(l3_subset_1) # label(negated_conjecture). [clausify(103)].
% 1.23/1.50 115 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(5)].
% 1.23/1.50 123 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(8)].
% 1.23/1.50 178 -empty(powerset(A)) # label(fc1_subset_1) # label(axiom). [clausify(33)].
% 1.23/1.50 199 -in(A,B) | subset(A,union(B)) # label(l50_zfmisc_1) # label(lemma). [clausify(48)].
% 1.23/1.50 209 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(53)].
% 1.23/1.50 225 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(64)].
% 1.23/1.50 228 -subset(A,B) | set_intersection2(A,B) = A # label(t28_xboole_1) # label(lemma). [clausify(66)].
% 1.23/1.50 229 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom). [clausify(67)].
% 1.23/1.50 239 -subset(unordered_pair(A,B),C) | in(A,C) # label(t38_zfmisc_1) # label(lemma). [clausify(75)].
% 1.23/1.50 241 subset(unordered_pair(A,B),C) | -in(A,C) | -in(B,C) # label(t38_zfmisc_1) # label(lemma). [clausify(75)].
% 1.23/1.50 243 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(78)].
% 1.23/1.50 251 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma). [clausify(84)].
% 1.23/1.50 252 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(251),flip(a)].
% 1.23/1.50 261 set_difference(A,singleton(B)) = A | in(B,A) # label(t65_zfmisc_1) # label(lemma). [clausify(89)].
% 1.23/1.50 262 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(90)].
% 1.23/1.50 274 union(powerset(A)) = A # label(t99_zfmisc_1) # label(lemma). [clausify(100)].
% 1.23/1.50 281 in(c5,c4) # label(l3_subset_1) # label(negated_conjecture). [clausify(103)].
% 1.23/1.50 282 -in(c5,c3) # label(l3_subset_1) # label(negated_conjecture). [clausify(103)].
% 1.23/1.50 287 empty(powerset(c3)) | in(c4,powerset(c3)). [resolve(110,a,105,b)].
% 1.23/1.50 288 in(c4,powerset(c3)). [copy(287),unit_del(a,178)].
% 1.23/1.50 323 subset(unordered_pair(A,A),B) | -in(A,B). [factor(241,b,c)].
% 1.23/1.50 325 set_difference(A,A) = empty_set. [back_rewrite(229),rewrite([252(2),243(2)])].
% 1.23/1.50 326 -subset(A,B) | set_difference(A,set_difference(A,B)) = A. [back_rewrite(228),rewrite([252(2)])].
% 1.23/1.50 336 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(115),rewrite([252(1),252(3)])].
% 1.23/1.50 337 set_difference(A,unordered_pair(B,B)) = A | in(B,A). [back_rewrite(261),rewrite([262(1)])].
% 1.23/1.50 995 in(A,unordered_pair(A,B)). [resolve(239,a,209,a)].
% 1.23/1.50 1214 subset(c4,c3). [resolve(288,a,199,a),rewrite([274(4)])].
% 1.23/1.50 1975 subset(unordered_pair(c5,c5),c4). [resolve(323,b,281,a)].
% 1.23/1.50 2429 set_difference(c3,unordered_pair(c5,c5)) = c3. [resolve(337,b,282,a)].
% 1.23/1.50 2756 -subset(A,c4) | subset(A,c3). [resolve(1214,a,225,b)].
% 1.23/1.50 2899 unordered_pair(A,B) != empty_set. [resolve(995,a,123,b),flip(a)].
% 1.23/1.50 3301 subset(unordered_pair(c5,c5),c3). [resolve(2756,a,1975,a)].
% 1.23/1.50 3418 $F. [resolve(3301,a,326,a),rewrite([336(9),2429(6),325(3)]),flip(a),unit_del(a,2899)].
% 1.23/1.50
% 1.23/1.50 % SZS output end Refutation
% 1.23/1.50 ============================== end of proof ==========================
% 1.23/1.50
% 1.23/1.50 ============================== STATISTICS ============================
% 1.23/1.50
% 1.23/1.50 Given=276. Generated=5136. Kept=3284. proofs=1.
% 1.23/1.50 Usable=262. Sos=2873. Demods=76. Limbo=4, Disabled=326. Hints=0.
% 1.23/1.50 Megabytes=4.90.
% 1.23/1.50 User_CPU=0.41, System_CPU=0.01, Wall_clock=0.
% 1.23/1.50
% 1.23/1.50 ============================== end of statistics =====================
% 1.23/1.50
% 1.23/1.50 ============================== end of search =========================
% 1.23/1.50
% 1.23/1.50 THEOREM PROVED
% 1.23/1.50 % SZS status Theorem
% 1.23/1.50
% 1.23/1.50 Exiting with 1 proof.
% 1.23/1.50
% 1.23/1.50 Process 23415 exit (max_proofs) Sun Jun 19 04:23:49 2022
% 1.23/1.50 Prover9 interrupted
%------------------------------------------------------------------------------