TSTP Solution File: SEU167+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU167+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 13:29:35 EDT 2022
% Result : Theorem 33.49s 33.84s
% Output : Refutation 33.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU167+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 20 10:08:29 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.76/1.06 ============================== Prover9 ===============================
% 0.76/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.06 Process 5480 was started by sandbox on n025.cluster.edu,
% 0.76/1.06 Mon Jun 20 10:08:30 2022
% 0.76/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5327_n025.cluster.edu".
% 0.76/1.06 ============================== end of head ===========================
% 0.76/1.06
% 0.76/1.06 ============================== INPUT =================================
% 0.76/1.06
% 0.76/1.06 % Reading from file /tmp/Prover9_5327_n025.cluster.edu
% 0.76/1.06
% 0.76/1.06 set(prolog_style_variables).
% 0.76/1.06 set(auto2).
% 0.76/1.06 % set(auto2) -> set(auto).
% 0.76/1.06 % set(auto) -> set(auto_inference).
% 0.76/1.06 % set(auto) -> set(auto_setup).
% 0.76/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.06 % set(auto) -> set(auto_limits).
% 0.76/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.06 % set(auto) -> set(auto_denials).
% 0.76/1.06 % set(auto) -> set(auto_process).
% 0.76/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.06 % set(auto2) -> assign(stats, some).
% 0.76/1.06 % set(auto2) -> clear(echo_input).
% 0.76/1.06 % set(auto2) -> set(quiet).
% 0.76/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.06 % set(auto2) -> clear(print_given).
% 0.76/1.06 assign(lrs_ticks,-1).
% 0.76/1.06 assign(sos_limit,10000).
% 0.76/1.06 assign(order,kbo).
% 0.76/1.06 set(lex_order_vars).
% 0.76/1.06 clear(print_given).
% 0.76/1.06
% 0.76/1.06 % formulas(sos). % not echoed (97 formulas)
% 0.76/1.06
% 0.76/1.06 ============================== end of input ==========================
% 0.76/1.06
% 0.76/1.06 % From the command line: assign(max_seconds, 300).
% 0.76/1.06
% 0.76/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.06
% 0.76/1.06 % Formulas that are not ordinary clauses:
% 0.76/1.06 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 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].
% 0.76/1.06 10 (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].
% 0.76/1.06 11 (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].
% 0.76/1.06 12 (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].
% 0.76/1.06 13 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 14 (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].
% 0.76/1.06 15 (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].
% 0.76/1.06 16 (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].
% 0.76/1.06 17 (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].
% 0.76/1.06 18 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 19 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 20 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 21 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 22 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 23 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 24 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 25 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 26 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 27 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 28 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 29 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 30 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 31 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 32 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 33 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 34 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 35 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 36 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 37 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 38 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 39 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 40 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 41 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 42 (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].
% 0.76/1.06 43 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 44 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 45 (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].
% 0.76/1.06 46 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 47 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 48 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 49 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 50 (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].
% 0.76/1.06 51 (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].
% 0.76/1.06 52 (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].
% 0.76/1.06 53 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 54 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 55 (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].
% 0.76/1.06 56 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 57 (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].
% 0.76/1.06 58 (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].
% 0.76/1.06 59 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 60 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 61 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 62 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 63 (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].
% 0.76/1.06 64 (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].
% 0.76/1.06 65 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 66 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 67 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 68 (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].
% 0.76/1.06 69 (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].
% 0.76/1.06 70 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 71 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 72 (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].
% 0.76/1.06 73 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 74 (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].
% 0.76/1.06 75 (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].
% 0.76/1.06 76 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.76/1.06 77 (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].
% 1.29/1.62 78 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.62 79 (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].
% 1.29/1.62 80 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 81 (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].
% 1.29/1.62 82 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 83 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 84 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.62 85 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 86 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.62 87 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 88 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 89 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.62 90 (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].
% 1.29/1.62 91 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 92 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 93 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 94 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.62 95 -(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(negated_conjecture) # label(non_clause). [assumption].
% 1.29/1.62
% 1.29/1.62 ============================== end of process non-clausal formulas ===
% 1.29/1.62
% 1.29/1.62 ============================== PROCESS INITIAL CLAUSES ===============
% 1.29/1.62
% 1.29/1.62 ============================== PREDICATE ELIMINATION =================
% 1.29/1.62
% 1.29/1.62 ============================== end predicate elimination =============
% 1.29/1.62
% 1.29/1.62 Auto_denials: (non-Horn, no changes).
% 1.29/1.62
% 1.29/1.62 Term ordering decisions:
% 1.29/1.62 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. set_difference=1. set_union2=1. set_intersection2=1. cartesian_product2=1. unordered_pair=1. ordered_pair=1. f1=1. f3=1. f11=1. f14=1. f15=1. f17=1. f18=1. f19=1. singleton=1. union=1. powerset=1. f2=1. f4=1. f5=1. f8=1. f9=1. f10=1. f12=1. f13=1. f16=1. f6=1. f7=1.
% 1.29/1.62
% 1.29/1.62 ============================== end of process initial clauses ========
% 1.29/1.62
% 1.29/1.62 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.62
% 1.29/1.62 ============================== end of clauses for search =============
% 1.29/1.62
% 1.29/1.62 ============================== SEARCH ================================
% 1.29/1.62
% 1.29/1.62 % Starting search at 0.04 seconds.
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=53.000, iters=3690
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=43.000, iters=3474
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=41.000, iters=3421
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=38.000, iters=3369
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=36.000, iters=3345
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=34.000, iters=3340
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=32.000, iters=3359
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=31.000, iters=3386
% 1.29/1.62
% 1.29/1.62 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 0.54 sec).
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=30.000, iters=3733
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=27.000, iters=3479
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=25.000, iters=3352
% 1.29/1.62
% 1.29/1.62 Low Water (keep): wt=23.000, iters=3343
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=22.000, iters=3490
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=21.000, iters=3400
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=20.000, iters=3350
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=19.000, iters=3341
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=18.000, iters=3367
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=17.000, iters=3368
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=16.000, iters=3360
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=15.000, iters=3335
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=14.000, iters=3408
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=13.000, iters=3378
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=12.000, iters=3336
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=11.000, iters=3340
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=1618, wt=74.000
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=1525, wt=64.000
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=2874, wt=63.000
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=10624, wt=19.000
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=12403, wt=18.000
% 33.49/33.84
% 33.49/33.84 Low Water (displace): id=13857, wt=10.000
% 33.49/33.84
% 33.49/33.84 Low Water (keep): wt=10.000, iters=3348
% 33.49/33.84
% 33.49/33.84 ============================== PROOF =================================
% 33.49/33.84 % SZS status Theorem
% 33.49/33.84 % SZS output start Refutation
% 33.49/33.84
% 33.49/33.84 % Proof 1 at 31.94 (+ 0.85) seconds.
% 33.49/33.84 % Length of proof is 13.
% 33.49/33.84 % Level of proof is 4.
% 33.49/33.84 % Maximum clause weight is 10.000.
% 33.49/33.84 % Given clauses 15573.
% 33.49/33.84
% 33.49/33.84 52 (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].
% 33.49/33.84 57 (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].
% 33.49/33.84 95 -(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(negated_conjecture) # label(non_clause). [assumption].
% 33.49/33.84 198 -subset(A,B) | subset(cartesian_product2(A,C),cartesian_product2(B,C)) # label(t118_zfmisc_1) # label(lemma). [clausify(52)].
% 33.49/33.84 199 -subset(A,B) | subset(cartesian_product2(C,A),cartesian_product2(C,B)) # label(t118_zfmisc_1) # label(lemma). [clausify(52)].
% 33.49/33.84 204 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(57)].
% 33.49/33.84 256 subset(c3,c4) # label(t119_zfmisc_1) # label(negated_conjecture). [clausify(95)].
% 33.49/33.84 257 subset(c5,c6) # label(t119_zfmisc_1) # label(negated_conjecture). [clausify(95)].
% 33.49/33.84 258 -subset(cartesian_product2(c3,c5),cartesian_product2(c4,c6)) # label(t119_zfmisc_1) # label(negated_conjecture). [clausify(95)].
% 33.49/33.84 1004 subset(cartesian_product2(c3,A),cartesian_product2(c4,A)). [resolve(256,a,198,a)].
% 33.49/33.84 1015 subset(cartesian_product2(A,c5),cartesian_product2(A,c6)). [resolve(257,a,199,a)].
% 33.49/33.84 3630 -subset(A,cartesian_product2(c3,B)) | subset(A,cartesian_product2(c4,B)). [resolve(1004,a,204,b)].
% 33.49/33.84 54573 $F. [resolve(3630,a,1015,a),unit_del(a,258)].
% 33.49/33.84
% 33.49/33.84 % SZS output end Refutation
% 33.49/33.84 ============================== end of proof ==========================
% 33.49/33.84
% 33.49/33.84 ============================== STATISTICS ============================
% 33.49/33.84
% 33.49/33.84 Given=15573. Generated=1575918. Kept=54456. proofs=1.
% 33.49/33.84 Usable=15019. Sos=9869. Demods=911. Limbo=20, Disabled=29705. Hints=0.
% 33.49/33.84 Megabytes=33.84.
% 33.49/33.84 User_CPU=31.94, System_CPU=0.85, Wall_clock=33.
% 33.49/33.84
% 33.49/33.84 ============================== end of statistics =====================
% 33.49/33.84
% 33.49/33.84 ============================== end of search =========================
% 33.49/33.84
% 33.49/33.84 THEOREM PROVED
% 33.49/33.84 % SZS status Theorem
% 33.49/33.84
% 33.49/33.84 Exiting with 1 proof.
% 33.49/33.84
% 33.49/33.84 Process 5480 exit (max_proofs) Mon Jun 20 10:09:03 2022
% 33.49/33.84 Prover9 interrupted
%------------------------------------------------------------------------------