TSTP Solution File: SEU131+2 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU131+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 13:29:12 EDT 2022
% Result : Theorem 182.49s 182.83s
% Output : Refutation 182.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : SEU131+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 01:03:38 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.81/1.09 ============================== Prover9 ===============================
% 0.81/1.09 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.09 Process 23843 was started by sandbox2 on n011.cluster.edu,
% 0.81/1.09 Sun Jun 19 01:03:39 2022
% 0.81/1.09 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_23690_n011.cluster.edu".
% 0.81/1.09 ============================== end of head ===========================
% 0.81/1.09
% 0.81/1.09 ============================== INPUT =================================
% 0.81/1.09
% 0.81/1.09 % Reading from file /tmp/Prover9_23690_n011.cluster.edu
% 0.81/1.09
% 0.81/1.09 set(prolog_style_variables).
% 0.81/1.09 set(auto2).
% 0.81/1.09 % set(auto2) -> set(auto).
% 0.81/1.09 % set(auto) -> set(auto_inference).
% 0.81/1.09 % set(auto) -> set(auto_setup).
% 0.81/1.09 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.09 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.09 % set(auto) -> set(auto_limits).
% 0.81/1.09 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.09 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.09 % set(auto) -> set(auto_denials).
% 0.81/1.09 % set(auto) -> set(auto_process).
% 0.81/1.09 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.09 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.09 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.09 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.09 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.09 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.09 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.09 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.09 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.09 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.09 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.09 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.09 % set(auto2) -> assign(stats, some).
% 0.81/1.09 % set(auto2) -> clear(echo_input).
% 0.81/1.09 % set(auto2) -> set(quiet).
% 0.81/1.09 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.09 % set(auto2) -> clear(print_given).
% 0.81/1.09 assign(lrs_ticks,-1).
% 0.81/1.09 assign(sos_limit,10000).
% 0.81/1.09 assign(order,kbo).
% 0.81/1.09 set(lex_order_vars).
% 0.81/1.09 clear(print_given).
% 0.81/1.09
% 0.81/1.09 % formulas(sos). % not echoed (44 formulas)
% 0.81/1.09
% 0.81/1.09 ============================== end of input ==========================
% 0.81/1.09
% 0.81/1.09 % From the command line: assign(max_seconds, 300).
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.09
% 0.81/1.09 % Formulas that are not ordinary clauses:
% 0.81/1.09 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 4 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 5 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 6 (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].
% 0.81/1.09 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 8 (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].
% 0.81/1.09 9 (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].
% 0.81/1.09 10 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 11 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 12 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 13 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 14 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 15 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 16 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 17 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 18 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 19 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 20 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 21 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 22 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 23 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 24 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 25 (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].
% 0.81/1.09 26 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 27 (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].
% 0.81/1.09 28 (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].
% 0.81/1.09 29 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 30 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 31 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 32 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 33 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 34 (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].
% 0.81/1.09 35 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 36 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 37 (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].
% 0.81/1.09 38 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 39 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 40 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.81/1.09 41 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.81/1.09 42 (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].
% 0.81/1.09 43 -(all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.81/1.09
% 0.81/1.09 ============================== end of process non-clausal formulas ===
% 0.81/1.09
% 0.81/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.09
% 0.81/1.09 ============================== PREDICATE ELIMINATION =================
% 0.81/1.09
% 0.81/1.09 ============================== end predicate elimination =============
% 0.81/1.09
% 0.81/1.09 Auto_denials: (non-Horn, no changes).
% 0.81/1.09
% 0.81/1.09 Term ordering decisions:
% 0.81/1.09
% 0.81/1.09 % Assigning unary symbol f1 kb_weight 0 and highest precedence (21).
% 0.81/1.09 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_intersection2=1. set_union2=1. set_difference=1. f3=1. f6=1. f7=1. f8=1. f2=1. f4=1. f5=1. f1=0.
% 182.49/182.83
% 182.49/182.83 ============================== end of process initial clauses ========
% 182.49/182.83
% 182.49/182.83 ============================== CLAUSES FOR SEARCH ====================
% 182.49/182.83
% 182.49/182.83 ============================== end of clauses for search =============
% 182.49/182.83
% 182.49/182.83 ============================== SEARCH ================================
% 182.49/182.83
% 182.49/182.83 % Starting search at 0.02 seconds.
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=37.000, iters=3359
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=35.000, iters=3436
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=33.000, iters=3417
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=31.000, iters=3442
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=27.000, iters=3389
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=25.000, iters=3412
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=23.000, iters=3450
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=21.000, iters=3404
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=19.000, iters=3382
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=17.000, iters=3391
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=15.000, iters=3345
% 182.49/182.83
% 182.49/182.83 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 73 (0.00 of 11.46 sec).
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=2762, wt=43.000
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=10480, wt=39.000
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=10473, wt=35.000
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=3581, wt=33.000
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=16577, wt=15.000
% 182.49/182.83
% 182.49/182.83 Low Water (displace): id=16584, wt=13.000
% 182.49/182.83
% 182.49/182.83 Low Water (keep): wt=13.000, iters=3339
% 182.49/182.83
% 182.49/182.83 ============================== PROOF =================================
% 182.49/182.83 % SZS status Theorem
% 182.49/182.83 % SZS output start Refutation
% 182.49/182.83
% 182.49/182.83 % Proof 1 at 178.47 (+ 3.29) seconds.
% 182.49/182.83 % Length of proof is 63.
% 182.49/182.83 % Level of proof is 9.
% 182.49/182.83 % Maximum clause weight is 22.000.
% 182.49/182.83 % Given clauses 1401.
% 182.49/182.83
% 182.49/182.83 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 3 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 6 (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].
% 182.49/182.83 7 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 9 (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].
% 182.49/182.83 23 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 182.49/182.83 24 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 182.49/182.83 27 (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].
% 182.49/182.83 29 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 182.49/182.83 33 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 39 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 182.49/182.83 40 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 182.49/182.83 43 -(all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 182.49/182.83 44 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 182.49/182.83 50 subset(set_intersection2(A,B),A) # label(t17_xboole_1) # label(lemma). [clausify(24)].
% 182.49/182.83 53 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(33)].
% 182.49/182.83 55 subset(A,set_union2(A,B)) # label(t7_xboole_1) # label(lemma). [clausify(40)].
% 182.49/182.83 56 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(2)].
% 182.49/182.83 57 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(3)].
% 182.49/182.83 59 subset(A,B) | in(f3(A,B),A) # label(d3_tarski) # label(axiom). [clausify(7)].
% 182.49/182.83 62 set_difference(c3,c4) = empty_set | subset(c3,c4) # label(l32_xboole_1) # label(negated_conjecture). [clausify(43)].
% 182.49/182.83 67 set_difference(A,B) = C | in(f5(A,B,C),C) | in(f5(A,B,C),A) # label(d4_xboole_0) # label(axiom). [clausify(9)].
% 182.49/182.83 70 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(39)].
% 182.49/182.83 71 -in(A,B) | -in(B,A) # label(antisymmetry_r2_hidden) # label(axiom). [clausify(1)].
% 182.49/182.83 74 set_difference(c3,c4) != empty_set | -subset(c3,c4) # label(l32_xboole_1) # label(negated_conjecture). [clausify(43)].
% 182.49/182.83 85 subset(A,B) | -in(f3(A,B),B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 182.49/182.83 88 -subset(A,B) | set_union2(A,B) = B # label(t12_xboole_1) # label(lemma). [clausify(23)].
% 182.49/182.83 89 -subset(A,B) | set_intersection2(A,B) = A # label(t28_xboole_1) # label(lemma). [clausify(29)].
% 182.49/182.83 91 -subset(A,B) | -in(C,A) | in(C,B) # label(d3_tarski) # label(axiom). [clausify(7)].
% 182.49/182.83 92 -subset(A,B) | -subset(B,C) | subset(A,C) # label(t1_xboole_1) # label(lemma). [clausify(27)].
% 182.49/182.83 95 set_union2(A,B) != C | in(D,C) | -in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 182.49/182.83 98 set_difference(A,B) != C | -in(D,C) | in(D,A) # label(d4_xboole_0) # label(axiom). [clausify(9)].
% 182.49/182.83 102 set_union2(A,B) != C | -in(D,C) | in(D,A) | in(D,B) # label(d2_xboole_0) # label(axiom). [clausify(6)].
% 182.49/182.83 104 set_difference(A,B) != C | in(D,C) | -in(D,A) | in(D,B) # label(d4_xboole_0) # label(axiom). [clausify(9)].
% 182.49/182.83 107 set_difference(A,B) = C | in(f5(A,B,C),C) | -in(f5(A,B,C),B) # label(d4_xboole_0) # label(axiom). [clausify(9)].
% 182.49/182.83 116 -in(A,A). [factor(71,a,b)].
% 182.49/182.83 128 subset(set_intersection2(A,B),B). [para(57(a,1),50(a,1))].
% 182.49/182.83 141 -in(A,empty_set). [ur(70,b,44,a)].
% 182.49/182.83 177 set_difference(c3,c4) != empty_set | in(f3(c3,c4),c3). [resolve(74,b,59,a)].
% 182.49/182.83 230 set_intersection2(A,set_union2(A,B)) = A. [resolve(89,a,55,a)].
% 182.49/182.83 237 -in(A,c3) | in(A,c4) | set_difference(c3,c4) = empty_set. [resolve(91,a,62,b)].
% 182.49/182.83 244 -subset(A,B) | subset(set_intersection2(A,C),B). [resolve(92,a,50,a)].
% 182.49/182.83 658 set_difference(A,A) = B | in(f5(A,A,B),B). [resolve(107,c,67,c),merge(c),merge(d)].
% 182.49/182.83 793 -in(set_union2(A,B),A). [ur(95,a,56,a,b,116,a)].
% 182.49/182.83 794 -in(set_union2(A,B),B). [ur(95,a,53,a(flip),b,116,a),rewrite([53(3)])].
% 182.49/182.83 872 set_union2(A,set_intersection2(B,A)) = A. [resolve(128,a,88,a),rewrite([56(2)])].
% 182.49/182.83 911 -in(set_union2(A,B),set_difference(A,C)). [ur(98,a,53,a(flip),c,793,a),rewrite([53(4)])].
% 182.49/182.83 1309 -in(set_union2(A,B),set_union2(B,set_difference(A,C))). [ur(102,a,56,a,c,794,a,d,911,a),rewrite([56(3)])].
% 182.49/182.83 2197 subset(set_intersection2(A,set_intersection2(B,C)),C). [resolve(244,a,128,a),rewrite([57(2)])].
% 182.49/182.83 2229 subset(set_intersection2(A,B),set_union2(B,C)). [para(230(a,1),2197(a,1,2))].
% 182.49/182.83 2706 set_union2(set_intersection2(A,B),set_union2(B,C)) = set_union2(B,C). [resolve(2229,a,88,a)].
% 182.49/182.83 6754 -in(set_union2(A,B),set_union2(A,set_union2(B,set_difference(A,C)))). [ur(102,a,56,a,c,793,a,d,1309,a),rewrite([56(4)])].
% 182.49/182.83 12252 in(f5(c3,A,B),c4) | set_difference(c3,c4) = empty_set | set_difference(c3,A) = B | in(f5(c3,A,B),B). [resolve(237,a,67,c)].
% 182.49/182.83 12272 in(f5(c3,c4,empty_set),c4) | set_difference(c3,c4) = empty_set. [factor(12252,b,c),unit_del(c,141)].
% 182.49/182.83 12473 set_difference(A,A) = empty_set. [resolve(658,b,141,a)].
% 182.49/182.83 16462 -in(A,set_difference(set_intersection2(B,A),C)). [ur(95,a,2706,a(flip),b,6754,a),rewrite([56(2),872(2)])].
% 182.49/182.83 17782 set_difference(c3,c4) = empty_set. [resolve(12272,a,107,c),merge(b),unit_del(b,141)].
% 182.49/182.83 17786 in(f3(c3,c4),c3). [back_rewrite(177),rewrite([17782(3)]),xx(a)].
% 182.49/182.83 17787 -subset(c3,c4). [back_rewrite(74),rewrite([17782(3)]),xx(a)].
% 182.49/182.83 18110 -in(f3(c3,c4),c4). [ur(85,a,17787,a)].
% 182.49/182.83 19354 set_difference(set_intersection2(A,f3(c3,c4)),B) != empty_set. [ur(104,b,16462,a,c,17786,a,d,18110,a),rewrite([17782(3)]),flip(a)].
% 182.49/182.83 19355 $F. [resolve(19354,a,12473,a)].
% 182.49/182.83
% 182.49/182.83 % SZS output end Refutation
% 182.49/182.83 ============================== end of proof ==========================
% 182.49/182.83
% 182.49/182.83 ============================== STATISTICS ============================
% 182.49/182.83
% 182.49/182.83 Given=1401. Generated=6055732. Kept=19310. proofs=1.
% 182.49/182.83 Usable=1274. Sos=9951. Demods=173. Limbo=6, Disabled=8144. Hints=0.
% 182.49/182.83 Megabytes=12.66.
% 182.49/182.83 User_CPU=178.47, System_CPU=3.29, Wall_clock=181.
% 182.49/182.83
% 182.49/182.83 ============================== end of statistics =====================
% 182.49/182.83
% 182.49/182.83 ============================== end of search =========================
% 182.49/182.83
% 182.49/182.83 THEOREM PROVED
% 182.49/182.83 % SZS status Theorem
% 182.49/182.83
% 182.49/182.83 Exiting with 1 proof.
% 182.49/182.83
% 182.49/182.83 Process 23843 exit (max_proofs) Sun Jun 19 01:06:40 2022
% 182.49/182.83 Prover9 interrupted
%------------------------------------------------------------------------------