TSTP Solution File: SEU165+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 13:29:33 EDT 2022
% Result : Theorem 35.22s 35.51s
% Output : Refutation 35.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU165+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 21:30:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.45/1.03 ============================== Prover9 ===============================
% 0.45/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.03 Process 2105 was started by sandbox on n004.cluster.edu,
% 0.45/1.03 Sun Jun 19 21:30:54 2022
% 0.45/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1947_n004.cluster.edu".
% 0.45/1.03 ============================== end of head ===========================
% 0.45/1.03
% 0.45/1.03 ============================== INPUT =================================
% 0.45/1.03
% 0.45/1.03 % Reading from file /tmp/Prover9_1947_n004.cluster.edu
% 0.45/1.03
% 0.45/1.03 set(prolog_style_variables).
% 0.45/1.03 set(auto2).
% 0.45/1.03 % set(auto2) -> set(auto).
% 0.45/1.03 % set(auto) -> set(auto_inference).
% 0.45/1.03 % set(auto) -> set(auto_setup).
% 0.45/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.03 % set(auto) -> set(auto_limits).
% 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.03 % set(auto) -> set(auto_denials).
% 0.45/1.03 % set(auto) -> set(auto_process).
% 0.45/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.03 % set(auto2) -> assign(stats, some).
% 0.45/1.03 % set(auto2) -> clear(echo_input).
% 0.45/1.03 % set(auto2) -> set(quiet).
% 0.45/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.03 % set(auto2) -> clear(print_given).
% 0.45/1.03 assign(lrs_ticks,-1).
% 0.45/1.03 assign(sos_limit,10000).
% 0.45/1.03 assign(order,kbo).
% 0.45/1.03 set(lex_order_vars).
% 0.45/1.03 clear(print_given).
% 0.45/1.03
% 0.45/1.03 % formulas(sos). % not echoed (95 formulas)
% 0.45/1.03
% 0.45/1.03 ============================== end of input ==========================
% 0.45/1.03
% 0.45/1.03 % From the command line: assign(max_seconds, 300).
% 0.45/1.03
% 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.03
% 0.45/1.03 % Formulas that are not ordinary clauses:
% 0.45/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 18 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 19 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 20 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 21 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 22 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 23 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 24 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 25 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 26 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 27 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 28 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 29 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 30 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 31 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 32 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 33 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 34 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 35 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 36 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 37 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 38 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 39 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 40 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 41 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 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].
% 0.45/1.03 44 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 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].
% 0.45/1.03 46 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 47 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 48 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 49 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 50 (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].
% 0.45/1.03 51 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 52 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 53 (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].
% 0.45/1.03 54 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 55 (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].
% 0.45/1.03 56 (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].
% 0.45/1.03 57 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 58 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 59 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 60 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 61 (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].
% 0.45/1.03 62 (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].
% 0.45/1.03 63 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 64 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 65 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 66 (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].
% 0.45/1.03 67 (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].
% 0.45/1.03 68 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 69 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 70 (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].
% 0.45/1.03 71 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 72 (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].
% 0.45/1.03 73 (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].
% 0.45/1.03 74 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.45/1.03 75 (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].
% 0.45/1.03 76 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.03 77 (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].
% 0.45/1.03 78 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 79 (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].
% 2.82/3.07 80 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 81 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 82 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 2.82/3.07 83 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 84 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 2.82/3.07 85 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 86 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 87 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 2.82/3.07 88 (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].
% 2.82/3.07 89 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 90 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 91 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 92 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 2.82/3.07 93 -(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(negated_conjecture) # label(non_clause). [assumption].
% 2.82/3.07
% 2.82/3.07 ============================== end of process non-clausal formulas ===
% 2.82/3.07
% 2.82/3.07 ============================== PROCESS INITIAL CLAUSES ===============
% 2.82/3.07
% 2.82/3.07 ============================== PREDICATE ELIMINATION =================
% 2.82/3.07
% 2.82/3.07 ============================== end predicate elimination =============
% 2.82/3.07
% 2.82/3.07 Auto_denials: (non-Horn, no changes).
% 2.82/3.07
% 2.82/3.07 Term ordering decisions:
% 2.82/3.07 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. unordered_pair=1. ordered_pair=1. cartesian_product2=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.
% 2.82/3.07
% 2.82/3.07 ============================== end of process initial clauses ========
% 2.82/3.07
% 2.82/3.07 ============================== CLAUSES FOR SEARCH ====================
% 2.82/3.07
% 2.82/3.07 ============================== end of clauses for search =============
% 2.82/3.07
% 2.82/3.07 ============================== SEARCH ================================
% 2.82/3.07
% 2.82/3.07 % Starting search at 0.04 seconds.
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=39.000, iters=3370
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=37.000, iters=3333
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=36.000, iters=3337
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=31.000, iters=3441
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=28.000, iters=3470
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=26.000, iters=3461
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=25.000, iters=3337
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=22.000, iters=3430
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=21.000, iters=3358
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=20.000, iters=3379
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=19.000, iters=3350
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=18.000, iters=3333
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=17.000, iters=3346
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=16.000, iters=3337
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=15.000, iters=3350
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=14.000, iters=3333
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=13.000, iters=3336
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=12.000, iters=3341
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=11.000, iters=3333
% 2.82/3.07
% 2.82/3.07 Low Water (keep): wt=10.000, iters=3337
% 2.82/3.07
% 2.82/3.07 Low Water (displace): id=1653, wt=74.000
% 2.82/3.07
% 2.82/3.07 Low Water (displace): id=1552, wt=64.000
% 2.82/3.07
% 2.82/3.07 Low Water (displace): id=3037, wt=63.000
% 2.82/3.07
% 2.82/3.07 Low Water (displace): id=1676, wt=62.000
% 2.82/3.07
% 2.82/3.07 Low Water (displace): id=3049, wt=59.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=1890, wt=58.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=4220, wt=56.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=1200, wt=55.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=1658, wt=54.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=4095, wt=53.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=2234, wt=52.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=4357, wt=51.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=4349, wt=50.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=3909, wt=49.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=1984, wt=48.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=3265, wt=47.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=2264, wt=46.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=13954, wt=15.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=13939, wt=14.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=14067, wt=13.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=15842, wt=12.000
% 35.22/35.51
% 35.22/35.51 Low Water (displace): id=17606, wt=10.000
% 35.22/35.51
% 35.22/35.51 ============================== PROOF =================================
% 35.22/35.51 % SZS status Theorem
% 35.22/35.51 % SZS output start Refutation
% 35.22/35.51
% 35.22/35.51 % Proof 1 at 33.69 (+ 0.81) seconds.
% 35.22/35.51 % Length of proof is 30.
% 35.22/35.51 % Level of proof is 8.
% 35.22/35.51 % Maximum clause weight is 17.000.
% 35.22/35.51 % Given clauses 15060.
% 35.22/35.51
% 35.22/35.51 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 35.22/35.52 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].
% 35.22/35.52 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].
% 35.22/35.52 81 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 35.22/35.52 93 -(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(negated_conjecture) # label(non_clause). [assumption].
% 35.22/35.52 96 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(3)].
% 35.22/35.52 154 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(17)].
% 35.22/35.52 155 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(154),rewrite([96(4)])].
% 35.22/35.52 182 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(lemma). [clausify(45)].
% 35.22/35.52 183 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(182),rewrite([155(1)])].
% 35.22/35.52 184 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(lemma). [clausify(45)].
% 35.22/35.52 185 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(184),rewrite([155(1)])].
% 35.22/35.52 186 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(lemma). [clausify(45)].
% 35.22/35.52 187 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(186),rewrite([155(1)])].
% 35.22/35.52 234 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(81)].
% 35.22/35.52 249 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c3,c5) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(93)].
% 35.22/35.52 250 in(unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c3,c5). [copy(249),rewrite([155(3),234(2)])].
% 35.22/35.52 251 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(93)].
% 35.22/35.52 252 in(unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c4,c6). [copy(251),rewrite([155(3),234(2)])].
% 35.22/35.52 253 -in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(93)].
% 35.22/35.52 254 -in(unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6). [copy(253),rewrite([155(3),234(2)])].
% 35.22/35.52 307 in(unordered_pair(unordered_pair(A,A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [back_rewrite(187),rewrite([234(1)])].
% 35.22/35.52 308 -in(unordered_pair(unordered_pair(A,A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [back_rewrite(185),rewrite([234(1)])].
% 35.22/35.52 309 -in(unordered_pair(unordered_pair(A,A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [back_rewrite(183),rewrite([234(1)])].
% 35.22/35.52 2294 in(c4,c6). [resolve(308,a,252,a),merge(b)].
% 35.22/35.52 2299 -in(unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c3,c5). [back_unit_del(254),unit_del(c,2294)].
% 35.22/35.52 2301 in(c3,c5). [resolve(309,a,250,a),merge(b)].
% 35.22/35.52 2305 -in(unordered_pair(unordered_pair(c3,c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)). [back_unit_del(2299),unit_del(b,2301)].
% 35.22/35.52 2421 in(unordered_pair(unordered_pair(A,A),unordered_pair(A,c4)),cartesian_product2(B,c6)) | -in(A,B). [resolve(2294,a,307,c)].
% 35.22/35.52 43943 $F. [resolve(2421,b,2301,a),unit_del(a,2305)].
% 35.22/35.52
% 35.22/35.52 % SZS output end Refutation
% 35.22/35.52 ============================== end of proof ==========================
% 35.22/35.52
% 35.22/35.52 ============================== STATISTICS ============================
% 35.22/35.52
% 35.22/35.52 Given=15060. Generated=1450734. Kept=43828. proofs=1.
% 35.22/35.52 Usable=13762. Sos=9757. Demods=991. Limbo=0, Disabled=20461. Hints=0.
% 35.22/35.52 Megabytes=29.26.
% 35.22/35.52 User_CPU=33.69, System_CPU=0.81, Wall_clock=34.
% 35.22/35.52
% 35.22/35.52 ============================== end of statistics =====================
% 35.22/35.52
% 35.22/35.52 ============================== end of search =========================
% 35.22/35.52
% 35.22/35.52 THEOREM PROVED
% 35.22/35.52 % SZS status Theorem
% 35.22/35.52
% 35.22/35.52 Exiting with 1 proof.
% 35.22/35.52
% 35.22/35.52 Process 2105 exit (max_proofs) Sun Jun 19 21:31:28 2022
% 35.22/35.52 Prover9 interrupted
%------------------------------------------------------------------------------