TSTP Solution File: SEU154+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 13:29:25 EDT 2022
% Result : Theorem 1.59s 1.89s
% Output : Refutation 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU154+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 03:31:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/1.01 ============================== Prover9 ===============================
% 0.41/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.41/1.01 Process 4953 was started by sandbox on n020.cluster.edu,
% 0.41/1.01 Mon Jun 20 03:31:19 2022
% 0.41/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4800_n020.cluster.edu".
% 0.41/1.01 ============================== end of head ===========================
% 0.41/1.01
% 0.41/1.01 ============================== INPUT =================================
% 0.41/1.01
% 0.41/1.01 % Reading from file /tmp/Prover9_4800_n020.cluster.edu
% 0.41/1.01
% 0.41/1.01 set(prolog_style_variables).
% 0.41/1.01 set(auto2).
% 0.41/1.01 % set(auto2) -> set(auto).
% 0.41/1.01 % set(auto) -> set(auto_inference).
% 0.41/1.01 % set(auto) -> set(auto_setup).
% 0.41/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.41/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.41/1.01 % set(auto) -> set(auto_limits).
% 0.41/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.41/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.41/1.01 % set(auto) -> set(auto_denials).
% 0.41/1.01 % set(auto) -> set(auto_process).
% 0.41/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.41/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.41/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.41/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.41/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.41/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.41/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.41/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.41/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.41/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.41/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.41/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.41/1.01 % set(auto2) -> assign(stats, some).
% 0.41/1.01 % set(auto2) -> clear(echo_input).
% 0.41/1.01 % set(auto2) -> set(quiet).
% 0.41/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.41/1.01 % set(auto2) -> clear(print_given).
% 0.41/1.01 assign(lrs_ticks,-1).
% 0.41/1.01 assign(sos_limit,10000).
% 0.41/1.01 assign(order,kbo).
% 0.41/1.01 set(lex_order_vars).
% 0.41/1.01 clear(print_given).
% 0.41/1.01
% 0.41/1.01 % formulas(sos). % not echoed (77 formulas)
% 0.41/1.01
% 0.41/1.01 ============================== end of input ==========================
% 0.41/1.01
% 0.41/1.01 % From the command line: assign(max_seconds, 300).
% 0.41/1.01
% 0.41/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.41/1.01
% 0.41/1.01 % Formulas that are not ordinary clauses:
% 0.41/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 3 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 6 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 7 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 8 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 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].
% 0.41/1.01 12 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 13 (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].
% 0.41/1.01 14 (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].
% 0.41/1.01 15 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 16 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 17 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 18 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 19 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 20 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 21 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 22 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 23 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 24 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 25 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 26 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 27 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 28 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 29 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 30 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 31 (all A all B -(disjoint(singleton(A),B) & in(A,B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 32 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 33 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 34 (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].
% 0.41/1.01 35 (all A all B (subset(A,singleton(B)) <-> A = empty_set | A = singleton(B))) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 36 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 37 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 38 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 39 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 40 (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].
% 0.41/1.01 41 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 42 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 43 (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].
% 0.41/1.01 44 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.01 45 (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].
% 0.41/1.01 46 (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].
% 0.41/1.01 47 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.01 48 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 49 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 50 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 51 (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].
% 0.41/1.02 52 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 53 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 54 (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].
% 0.41/1.02 55 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 56 (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].
% 0.41/1.02 57 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 58 (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].
% 0.41/1.02 59 (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].
% 0.41/1.02 60 (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].
% 0.41/1.02 61 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 62 (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].
% 0.41/1.02 63 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 64 (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].
% 0.41/1.02 65 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 66 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 67 (all A all B (subset(singleton(A),singleton(B)) -> A = B)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 68 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 69 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 70 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 71 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.41/1.02 72 (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].
% 0.41/1.02 73 (all A all B all C (singleton(A) = unordered_pair(B,C) -> A = B)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 74 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption].
% 0.41/1.02 75 -(all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.41/1.02
% 0.41/1.02 ============================== end of process non-clausal formulas ===
% 0.41/1.02
% 0.41/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.41/1.02
% 0.41/1.02 ============================== PREDICATE ELIMINATION =================
% 0.41/1.02
% 0.41/1.02 ============================== end predicate elimination =============
% 0.41/1.02
% 0.41/1.02 Auto_denials: (non-Horn, no changes).
% 0.41/1.02
% 0.41/1.02 Term ordering decisions:
% 0.41/1.02 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. f1=1. f3=1. f6=1. f9=1. f10=1. f11=1. singleton=1. powerset=1. f2=1. f4=1. f5=1. f7=1. f8=1.
% 1.59/1.89
% 1.59/1.89 ============================== end of process initial clauses ========
% 1.59/1.89
% 1.59/1.89 ============================== CLAUSES FOR SEARCH ====================
% 1.59/1.89
% 1.59/1.89 ============================== end of clauses for search =============
% 1.59/1.89
% 1.59/1.89 ============================== SEARCH ================================
% 1.59/1.89
% 1.59/1.89 % Starting search at 0.03 seconds.
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=39.000, iters=3551
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=31.000, iters=3413
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=28.000, iters=3360
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=27.000, iters=3440
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=26.000, iters=3363
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=25.000, iters=3341
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=24.000, iters=3364
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=23.000, iters=3346
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=22.000, iters=3358
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=21.000, iters=3357
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=20.000, iters=3353
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=19.000, iters=3337
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=18.000, iters=3335
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=17.000, iters=3344
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=16.000, iters=3364
% 1.59/1.89
% 1.59/1.89 Low Water (keep): wt=15.000, iters=3368
% 1.59/1.89
% 1.59/1.89 ============================== PROOF =================================
% 1.59/1.89 % SZS status Theorem
% 1.59/1.89 % SZS output start Refutation
% 1.59/1.89
% 1.59/1.89 % Proof 1 at 0.87 (+ 0.03) seconds.
% 1.59/1.89 % Length of proof is 45.
% 1.59/1.89 % Level of proof is 10.
% 1.59/1.89 % Maximum clause weight is 13.000.
% 1.59/1.89 % Given clauses 1220.
% 1.59/1.89
% 1.59/1.89 4 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.89 5 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.89 33 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.59/1.89 34 (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].
% 1.59/1.89 38 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.89 39 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.89 54 (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].
% 1.59/1.89 55 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 1.59/1.89 58 (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].
% 1.59/1.89 60 (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].
% 1.59/1.89 64 (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].
% 1.59/1.89 65 (all A unordered_pair(A,A) = singleton(A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption].
% 1.59/1.89 69 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.59/1.89 70 (all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 1.59/1.89 75 -(all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.59/1.89 79 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(4)].
% 1.59/1.89 80 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(5)].
% 1.59/1.89 139 set_difference(A,B) = empty_set | -subset(A,B) # label(l32_xboole_1) # label(lemma). [clausify(33)].
% 1.59/1.89 140 -subset(A,B) | in(C,A) | subset(A,set_difference(B,singleton(C))) # label(l3_zfmisc_1) # label(lemma). [clausify(34)].
% 1.59/1.89 145 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(38)].
% 1.59/1.89 146 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom). [clausify(39)].
% 1.59/1.89 162 set_union2(A,set_difference(B,A)) = set_union2(A,B) # label(t39_xboole_1) # label(lemma). [clausify(54)].
% 1.59/1.89 163 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(55)].
% 1.59/1.89 168 set_difference(set_union2(A,B),B) = set_difference(A,B) # label(t40_xboole_1) # label(lemma). [clausify(58)].
% 1.59/1.89 170 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma). [clausify(60)].
% 1.59/1.89 171 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(170),flip(a)].
% 1.59/1.89 178 -subset(A,B) | -disjoint(B,C) | disjoint(A,C) # label(t63_xboole_1) # label(lemma). [clausify(64)].
% 1.59/1.89 179 singleton(A) = unordered_pair(A,A) # label(t69_enumset1) # label(lemma). [clausify(65)].
% 1.59/1.89 184 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(lemma). [clausify(69)].
% 1.59/1.89 186 disjoint(A,B) | set_difference(A,B) != A # label(t83_xboole_1) # label(lemma). [clausify(70)].
% 1.59/1.89 193 -in(c3,c4) # label(l28_zfmisc_1) # label(negated_conjecture). [clausify(75)].
% 1.59/1.89 194 -disjoint(singleton(c3),c4) # label(l28_zfmisc_1) # label(negated_conjecture). [clausify(75)].
% 1.59/1.89 195 -disjoint(unordered_pair(c3,c3),c4). [copy(194),rewrite([179(2)])].
% 1.59/1.89 231 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(80),rewrite([171(1),171(3)])].
% 1.59/1.89 235 -subset(A,B) | in(C,A) | subset(A,set_difference(B,unordered_pair(C,C))). [back_rewrite(140),rewrite([179(3)])].
% 1.59/1.89 572 set_difference(set_union2(A,B),set_difference(B,A)) = set_difference(A,set_difference(B,A)). [para(162(a,1),168(a,1,1))].
% 1.59/1.89 599 set_difference(A,set_union2(A,B)) = empty_set. [resolve(184,a,139,b)].
% 1.59/1.89 1030 set_difference(A,set_difference(B,A)) = A. [para(168(a,1),231(a,2,2)),rewrite([79(1),599(2),163(2),79(1),572(3)]),flip(a)].
% 1.59/1.89 1052 in(A,B) | subset(B,set_difference(B,unordered_pair(A,A))). [resolve(235,a,145,a)].
% 1.59/1.89 1507 disjoint(A,set_difference(B,A)). [resolve(1030,a,186,b)].
% 1.59/1.89 1515 disjoint(set_difference(A,B),B). [resolve(1507,a,146,a)].
% 1.59/1.89 1517 -subset(A,set_difference(B,C)) | disjoint(A,C). [resolve(1515,a,178,b)].
% 1.59/1.89 7944 in(A,B) | disjoint(B,unordered_pair(A,A)). [resolve(1052,b,1517,a)].
% 1.59/1.89 7970 in(A,B) | disjoint(unordered_pair(A,A),B). [resolve(7944,b,146,a)].
% 1.59/1.89 7991 $F. [resolve(7970,b,195,a),unit_del(a,193)].
% 1.59/1.89
% 1.59/1.89 % SZS output end Refutation
% 1.59/1.89 ============================== end of proof ==========================
% 1.59/1.89
% 1.59/1.89 ============================== STATISTICS ============================
% 1.59/1.89
% 1.59/1.89 Given=1220. Generated=37990. Kept=7905. proofs=1.
% 1.59/1.89 Usable=1133. Sos=6037. Demods=363. Limbo=1, Disabled=849. Hints=0.
% 1.59/1.89 Megabytes=7.34.
% 1.59/1.89 User_CPU=0.87, System_CPU=0.03, Wall_clock=0.
% 1.59/1.89
% 1.59/1.89 ============================== end of statistics =====================
% 1.59/1.89
% 1.59/1.89 ============================== end of search =========================
% 1.59/1.89
% 1.59/1.89 THEOREM PROVED
% 1.59/1.89 % SZS status Theorem
% 1.59/1.89
% 1.59/1.89 Exiting with 1 proof.
% 1.59/1.89
% 1.59/1.89 Process 4953 exit (max_proofs) Mon Jun 20 03:31:19 2022
% 1.59/1.89 Prover9 interrupted
%------------------------------------------------------------------------------