TSTP Solution File: SEU160+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 13:29:29 EDT 2022
% Result : Theorem 1.29s 1.61s
% Output : Refutation 1.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU160+2 : TPTP v8.1.0. Released v3.3.0.
% 0.00/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.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 02:03:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.03 ============================== Prover9 ===============================
% 0.44/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.03 Process 28254 was started by sandbox on n007.cluster.edu,
% 0.44/1.03 Sun Jun 19 02:03:44 2022
% 0.44/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28101_n007.cluster.edu".
% 0.44/1.03 ============================== end of head ===========================
% 0.44/1.03
% 0.44/1.03 ============================== INPUT =================================
% 0.44/1.03
% 0.44/1.03 % Reading from file /tmp/Prover9_28101_n007.cluster.edu
% 0.44/1.03
% 0.44/1.03 set(prolog_style_variables).
% 0.44/1.03 set(auto2).
% 0.44/1.03 % set(auto2) -> set(auto).
% 0.44/1.03 % set(auto) -> set(auto_inference).
% 0.44/1.03 % set(auto) -> set(auto_setup).
% 0.44/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.03 % set(auto) -> set(auto_limits).
% 0.44/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.03 % set(auto) -> set(auto_denials).
% 0.44/1.03 % set(auto) -> set(auto_process).
% 0.44/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.03 % set(auto2) -> assign(stats, some).
% 0.44/1.03 % set(auto2) -> clear(echo_input).
% 0.44/1.03 % set(auto2) -> set(quiet).
% 0.44/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.03 % set(auto2) -> clear(print_given).
% 0.44/1.03 assign(lrs_ticks,-1).
% 0.44/1.03 assign(sos_limit,10000).
% 0.44/1.03 assign(order,kbo).
% 0.44/1.03 set(lex_order_vars).
% 0.44/1.03 clear(print_given).
% 0.44/1.03
% 0.44/1.03 % formulas(sos). % not echoed (90 formulas)
% 0.44/1.03
% 0.44/1.03 ============================== end of input ==========================
% 0.44/1.03
% 0.44/1.03 % From the command line: assign(max_seconds, 300).
% 0.44/1.03
% 0.44/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.03
% 0.44/1.03 % Formulas that are not ordinary clauses:
% 0.44/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 18 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 19 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 20 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 21 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 22 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 23 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 24 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 25 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 26 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 27 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 28 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 29 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 30 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 31 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 32 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 33 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 34 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 35 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 36 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 37 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 38 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 39 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 40 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 41 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 44 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 46 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 47 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 48 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 49 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 51 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 52 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 54 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 57 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 58 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 59 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 60 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 63 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 64 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 65 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 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].
% 0.44/1.03 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].
% 0.44/1.03 68 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 69 (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].
% 0.44/1.03 70 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 71 (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].
% 0.44/1.03 72 (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].
% 0.44/1.03 73 (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].
% 0.44/1.03 74 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.03 75 (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].
% 0.44/1.03 76 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.44/1.03 77 (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].
% 0.44/1.03 78 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 79 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.61 80 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 81 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.61 82 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 83 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 84 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.61 85 (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].
% 1.29/1.61 86 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 87 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 88 -(all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.29/1.61
% 1.29/1.61 ============================== end of process non-clausal formulas ===
% 1.29/1.61
% 1.29/1.61 ============================== PROCESS INITIAL CLAUSES ===============
% 1.29/1.61
% 1.29/1.61 ============================== PREDICATE ELIMINATION =================
% 1.29/1.61
% 1.29/1.61 ============================== end predicate elimination =============
% 1.29/1.61
% 1.29/1.61 Auto_denials: (non-Horn, no changes).
% 1.29/1.61
% 1.29/1.61 Term ordering decisions:
% 1.29/1.61 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=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.
% 1.29/1.61
% 1.29/1.61 ============================== end of process initial clauses ========
% 1.29/1.61
% 1.29/1.61 ============================== CLAUSES FOR SEARCH ====================
% 1.29/1.61
% 1.29/1.61 ============================== end of clauses for search =============
% 1.29/1.61
% 1.29/1.61 ============================== SEARCH ================================
% 1.29/1.61
% 1.29/1.61 % Starting search at 0.04 seconds.
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=55.000, iters=3664
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=41.000, iters=3380
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=39.000, iters=3364
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=37.000, iters=3335
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=35.000, iters=3339
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=33.000, iters=3350
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=31.000, iters=3373
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=30.000, iters=3420
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=28.000, iters=3399
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=27.000, iters=3353
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=26.000, iters=3379
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=25.000, iters=3342
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=23.000, iters=3451
% 1.29/1.61
% 1.29/1.61 Low Water (keep): wt=22.000, iters=3352
% 1.29/1.61
% 1.29/1.61 ============================== PROOF =================================
% 1.29/1.61 % SZS status Theorem
% 1.29/1.61 % SZS output start Refutation
% 1.29/1.61
% 1.29/1.61 % Proof 1 at 0.58 (+ 0.02) seconds.
% 1.29/1.61 % Length of proof is 36.
% 1.29/1.61 % Level of proof is 6.
% 1.29/1.61 % Maximum clause weight is 13.000.
% 1.29/1.61 % Given clauses 555.
% 1.29/1.61
% 1.29/1.61 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].
% 1.29/1.61 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].
% 1.29/1.61 48 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.61 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].
% 1.29/1.61 60 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 69 (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].
% 1.29/1.61 74 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 1.29/1.61 78 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 83 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.29/1.61 88 -(all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(t39_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.29/1.61 129 subset(A,B) | in(f11(A,B),A) # label(d3_tarski) # label(axiom). [clausify(13)].
% 1.29/1.61 174 -subset(A,singleton(B)) | empty_set = A | singleton(B) = A # label(l4_zfmisc_1) # label(lemma). [clausify(43)].
% 1.29/1.61 185 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(48)].
% 1.29/1.61 192 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(55)].
% 1.29/1.61 199 subset(empty_set,A) # label(t2_xboole_1) # label(lemma). [clausify(60)].
% 1.29/1.61 213 -in(A,B) | -in(A,C) | -disjoint(B,C) # label(t3_xboole_0) # label(lemma). [clausify(69)].
% 1.29/1.61 219 set_difference(empty_set,A) = empty_set # label(t4_boole) # label(axiom). [clausify(74)].
% 1.29/1.61 226 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(78)].
% 1.29/1.61 233 disjoint(A,B) | set_difference(A,B) != A # label(t83_xboole_1) # label(lemma). [clausify(83)].
% 1.29/1.61 240 subset(c3,singleton(c4)) | empty_set = c3 | singleton(c4) = c3 # label(t39_zfmisc_1) # label(negated_conjecture). [clausify(88)].
% 1.29/1.61 241 subset(c3,unordered_pair(c4,c4)) | c3 = empty_set | unordered_pair(c4,c4) = c3. [copy(240),rewrite([226(3),226(10)]),flip(b)].
% 1.29/1.61 242 -subset(c3,singleton(c4)) | empty_set != c3 # label(t39_zfmisc_1) # label(negated_conjecture). [clausify(88)].
% 1.29/1.61 243 -subset(c3,unordered_pair(c4,c4)) | c3 != empty_set. [copy(242),rewrite([226(3)]),flip(b)].
% 1.29/1.61 244 -subset(c3,singleton(c4)) | singleton(c4) != c3 # label(t39_zfmisc_1) # label(negated_conjecture). [clausify(88)].
% 1.29/1.61 245 -subset(c3,unordered_pair(c4,c4)) | unordered_pair(c4,c4) != c3. [copy(244),rewrite([226(3),226(7)])].
% 1.29/1.61 280 -in(A,B) | -disjoint(B,B). [factor(213,a,b)].
% 1.29/1.61 300 -subset(A,unordered_pair(B,B)) | empty_set = A | unordered_pair(B,B) = A. [back_rewrite(174),rewrite([226(1),226(5)])].
% 1.29/1.61 872 -subset(A,empty_set) | subset(A,B). [resolve(199,a,192,b)].
% 1.29/1.61 963 disjoint(empty_set,A). [resolve(233,b,219,a)].
% 1.29/1.61 2116 c3 = empty_set | unordered_pair(c4,c4) = c3. [resolve(300,a,241,a),flip(a),merge(c),merge(d)].
% 1.29/1.61 2223 -in(A,empty_set). [resolve(963,a,280,b)].
% 1.29/1.61 2328 subset(A,B) | in(f11(A,empty_set),A). [resolve(872,a,129,a)].
% 1.29/1.61 3885 c3 = empty_set | unordered_pair(c4,c4) != c3. [para(2116(b,1),245(a,2)),unit_del(b,185)].
% 1.29/1.61 4164 in(f11(c3,empty_set),c3) | c3 != empty_set. [resolve(2328,a,243,a)].
% 1.29/1.61 5699 c3 = empty_set. [resolve(3885,b,2116,b),merge(b)].
% 1.29/1.61 5700 $F. [back_rewrite(4164),rewrite([5699(1),5699(4),5699(6)]),xx(b),unit_del(a,2223)].
% 1.29/1.61
% 1.29/1.61 % SZS output end Refutation
% 1.29/1.61 ============================== end of proof ==========================
% 1.29/1.61
% 1.29/1.61 ============================== STATISTICS ============================
% 1.29/1.61
% 1.29/1.61 Given=555. Generated=11706. Kept=5591. proofs=1.
% 1.29/1.61 Usable=483. Sos=4324. Demods=154. Limbo=1, Disabled=927. Hints=0.
% 1.29/1.61 Megabytes=7.28.
% 1.29/1.61 User_CPU=0.58, System_CPU=0.02, Wall_clock=1.
% 1.29/1.61
% 1.29/1.61 ============================== end of statistics =====================
% 1.29/1.61
% 1.29/1.61 ============================== end of search =========================
% 1.29/1.61
% 1.29/1.61 THEOREM PROVED
% 1.29/1.61 % SZS status Theorem
% 1.29/1.61
% 1.29/1.61 Exiting with 1 proof.
% 1.29/1.61
% 1.29/1.61 Process 28254 exit (max_proofs) Sun Jun 19 02:03:45 2022
% 1.29/1.61 Prover9 interrupted
%------------------------------------------------------------------------------