TSTP Solution File: SEU141+2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n003.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 13:29:17 EDT 2022
% Result : Theorem 23.33s 23.60s
% Output : Refutation 23.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU141+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n003.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 01:55:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.43/1.00 ============================== Prover9 ===============================
% 0.43/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.43/1.00 Process 1540 was started by sandbox on n003.cluster.edu,
% 0.43/1.00 Sun Jun 19 01:55:47 2022
% 0.43/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_1386_n003.cluster.edu".
% 0.43/1.00 ============================== end of head ===========================
% 0.43/1.00
% 0.43/1.00 ============================== INPUT =================================
% 0.43/1.00
% 0.43/1.00 % Reading from file /tmp/Prover9_1386_n003.cluster.edu
% 0.43/1.00
% 0.43/1.00 set(prolog_style_variables).
% 0.43/1.00 set(auto2).
% 0.43/1.00 % set(auto2) -> set(auto).
% 0.43/1.00 % set(auto) -> set(auto_inference).
% 0.43/1.00 % set(auto) -> set(auto_setup).
% 0.43/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.43/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/1.00 % set(auto) -> set(auto_limits).
% 0.43/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/1.00 % set(auto) -> set(auto_denials).
% 0.43/1.00 % set(auto) -> set(auto_process).
% 0.43/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.43/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.43/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.43/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.43/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.43/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.43/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.43/1.00 % set(auto2) -> assign(stats, some).
% 0.43/1.00 % set(auto2) -> clear(echo_input).
% 0.43/1.00 % set(auto2) -> set(quiet).
% 0.43/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.43/1.00 % set(auto2) -> clear(print_given).
% 0.43/1.00 assign(lrs_ticks,-1).
% 0.43/1.00 assign(sos_limit,10000).
% 0.43/1.00 assign(order,kbo).
% 0.43/1.00 set(lex_order_vars).
% 0.43/1.00 clear(print_given).
% 0.43/1.00
% 0.43/1.00 % formulas(sos). % not echoed (57 formulas)
% 0.43/1.00
% 0.43/1.00 ============================== end of input ==========================
% 0.43/1.00
% 0.43/1.00 % From the command line: assign(max_seconds, 300).
% 0.43/1.00
% 0.43/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/1.00
% 0.43/1.00 % Formulas that are not ordinary clauses:
% 0.43/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 2 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 4 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 5 (all A all B (A = B <-> subset(A,B) & subset(B,A))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 6 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 7 (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].
% 0.43/1.00 8 (all A all B (subset(A,B) <-> (all C (in(C,A) -> in(C,B))))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 9 (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].
% 0.43/1.00 10 (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].
% 0.43/1.00 11 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 12 (all A all B (proper_subset(A,B) <-> subset(A,B) & A != B)) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 13 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 14 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 15 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 16 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 17 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 18 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 19 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 20 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 21 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 22 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 23 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 24 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 25 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 27 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 28 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 29 (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].
% 0.43/1.00 30 (all A set_union2(A,empty_set) = A) # label(t1_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 31 (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].
% 0.43/1.00 32 (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].
% 0.43/1.00 33 (all A all B (subset(A,B) -> set_intersection2(A,B) = A)) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 34 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 35 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 36 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 37 (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].
% 0.43/1.00 38 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 39 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 40 (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].
% 0.43/1.00 41 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.43/1.00 42 (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].
% 0.43/1.00 43 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 0.43/1.00 44 (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].
% 0.43/1.00 45 (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].
% 0.43/1.00 46 (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].
% 0.43/1.00 47 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 48 (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].
% 23.33/23.60 49 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 23.33/23.60 50 (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].
% 23.33/23.60 51 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 52 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 53 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 23.33/23.60 54 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 55 (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].
% 23.33/23.60 56 -(all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 23.33/23.60
% 23.33/23.60 ============================== end of process non-clausal formulas ===
% 23.33/23.60
% 23.33/23.60 ============================== PROCESS INITIAL CLAUSES ===============
% 23.33/23.60
% 23.33/23.60 ============================== PREDICATE ELIMINATION =================
% 23.33/23.60
% 23.33/23.60 ============================== end predicate elimination =============
% 23.33/23.60
% 23.33/23.60 Auto_denials: (non-Horn, no changes).
% 23.33/23.60
% 23.33/23.60 Term ordering decisions:
% 23.33/23.60
% 23.33/23.60 % Assigning unary symbol f1 kb_weight 0 and highest precedence (22).
% 23.33/23.60 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. set_difference=1. set_intersection2=1. set_union2=1. f3=1. f6=1. f7=1. f8=1. f2=1. f4=1. f5=1. f1=0.
% 23.33/23.60
% 23.33/23.60 ============================== end of process initial clauses ========
% 23.33/23.60
% 23.33/23.60 ============================== CLAUSES FOR SEARCH ====================
% 23.33/23.60
% 23.33/23.60 ============================== end of clauses for search =============
% 23.33/23.60
% 23.33/23.60 ============================== SEARCH ================================
% 23.33/23.60
% 23.33/23.60 % Starting search at 0.02 seconds.
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=29.000, iters=3460
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=27.000, iters=3400
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=25.000, iters=3339
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=23.000, iters=3359
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=21.000, iters=3404
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=19.000, iters=3391
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=17.000, iters=3426
% 23.33/23.60
% 23.33/23.60 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 22 (0.00 of 7.95 sec).
% 23.33/23.60
% 23.33/23.60 Low Water (keep): wt=15.000, iters=3360
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5034, wt=37.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5040, wt=35.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=4932, wt=33.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5600, wt=31.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5452, wt=29.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5601, wt=27.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=5858, wt=25.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=6033, wt=23.000
% 23.33/23.60
% 23.33/23.60 Low Water (displace): id=12708, wt=18.000
% 23.33/23.60
% 23.33/23.60 ============================== PROOF =================================
% 23.33/23.60 % SZS status Theorem
% 23.33/23.60 % SZS output start Refutation
% 23.33/23.60
% 23.33/23.60 % Proof 1 at 22.00 (+ 0.61) seconds.
% 23.33/23.60 % Length of proof is 44.
% 23.33/23.60 % Level of proof is 6.
% 23.33/23.60 % Maximum clause weight is 14.000.
% 23.33/23.60 % Given clauses 851.
% 23.33/23.60
% 23.33/23.60 3 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 4 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 11 (all A all B (disjoint(A,B) <-> set_intersection2(A,B) = empty_set)) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 22 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 23.33/23.60 26 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 27 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 23.33/23.60 34 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 38 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption].
% 23.33/23.60 40 (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].
% 23.33/23.60 41 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 46 (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].
% 23.33/23.60 48 (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].
% 23.33/23.60 52 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 23.33/23.60 56 -(all A all B (disjoint(A,B) <-> set_difference(A,B) = A)) # label(t83_xboole_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 23.33/23.60 57 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 23.33/23.60 65 set_intersection2(A,empty_set) = empty_set # label(t2_boole) # label(axiom). [clausify(34)].
% 23.33/23.60 66 subset(set_difference(A,B),A) # label(t36_xboole_1) # label(lemma). [clausify(38)].
% 23.33/23.60 67 set_difference(A,empty_set) = A # label(t3_boole) # label(axiom). [clausify(41)].
% 23.33/23.60 70 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom). [clausify(3)].
% 23.33/23.60 71 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(4)].
% 23.33/23.60 76 disjoint(c3,c4) | set_difference(c3,c4) = c3 # label(t83_xboole_1) # label(negated_conjecture). [clausify(56)].
% 23.33/23.60 77 set_union2(A,set_difference(B,A)) = set_union2(A,B) # label(t39_xboole_1) # label(lemma). [clausify(40)].
% 23.33/23.60 79 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(lemma). [clausify(46)].
% 23.33/23.60 80 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(79),flip(a)].
% 23.33/23.60 81 disjoint(A,B) | in(f8(A,B),set_intersection2(A,B)) # label(t4_xboole_0) # label(lemma). [clausify(48)].
% 23.33/23.60 82 disjoint(A,B) | in(f8(A,B),set_difference(A,set_difference(A,B))). [copy(81),rewrite([80(3)])].
% 23.33/23.60 92 -in(A,B) | -empty(B) # label(t7_boole) # label(axiom). [clausify(52)].
% 23.33/23.60 100 -disjoint(c3,c4) | set_difference(c3,c4) != c3 # label(t83_xboole_1) # label(negated_conjecture). [clausify(56)].
% 23.33/23.60 109 -disjoint(A,B) | disjoint(B,A) # label(symmetry_r1_xboole_0) # label(axiom). [clausify(26)].
% 23.33/23.60 113 -disjoint(A,B) | set_intersection2(A,B) = empty_set # label(d7_xboole_0) # label(axiom). [clausify(11)].
% 23.33/23.60 114 -disjoint(A,B) | set_difference(A,set_difference(A,B)) = empty_set. [copy(113),rewrite([80(2)])].
% 23.33/23.60 118 set_difference(A,B) = empty_set | -subset(A,B) # label(l32_xboole_1) # label(lemma). [clausify(22)].
% 23.33/23.60 119 -subset(A,B) | set_union2(A,B) = B # label(t12_xboole_1) # label(lemma). [clausify(27)].
% 23.33/23.60 152 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(71),rewrite([80(1),80(3)])].
% 23.33/23.60 153 set_difference(A,A) = empty_set. [back_rewrite(65),rewrite([80(2),67(2)])].
% 23.33/23.60 188 -in(A,empty_set). [ur(92,b,57,a)].
% 23.33/23.60 269 disjoint(A,B) | in(f8(B,A),set_difference(B,set_difference(B,A))). [resolve(109,a,82,a)].
% 23.33/23.60 275 set_difference(c3,set_difference(c3,c4)) = empty_set | set_difference(c3,c4) = c3. [resolve(114,a,76,a)].
% 23.33/23.60 284 set_difference(set_difference(A,B),A) = empty_set. [resolve(118,b,66,a)].
% 23.33/23.60 286 set_union2(A,set_difference(A,B)) = A. [resolve(119,a,66,a),rewrite([70(2)])].
% 23.33/23.60 1039 set_union2(empty_set,set_difference(A,B)) = set_difference(A,B). [para(284(a,1),286(a,1,2)),rewrite([70(3)])].
% 23.33/23.60 12403 in(f8(c4,c3),set_difference(c3,set_difference(c3,c4))) | set_difference(c3,c4) != c3. [resolve(269,a,100,a),rewrite([152(8)])].
% 23.33/23.60 12710 set_difference(c3,c4) = c3. [para(275(a,1),77(a,1,2)),rewrite([70(10),1039(10),70(13),286(13)]),merge(b)].
% 23.33/23.60 12711 $F. [back_rewrite(12403),rewrite([12710(7),153(6),12710(8)]),xx(b),unit_del(a,188)].
% 23.33/23.60
% 23.33/23.60 % SZS output end Refutation
% 23.33/23.60 ============================== end of proof ==========================
% 23.33/23.60
% 23.33/23.60 ============================== STATISTICS ============================
% 23.33/23.60
% 23.33/23.60 Given=851. Generated=1134928. Kept=12638. proofs=1.
% 23.33/23.60 Usable=830. Sos=9992. Demods=107. Limbo=1, Disabled=1898. Hints=0.
% 23.33/23.60 Megabytes=9.17.
% 23.33/23.60 User_CPU=22.00, System_CPU=0.61, Wall_clock=23.
% 23.33/23.60
% 23.33/23.60 ============================== end of statistics =====================
% 23.33/23.60
% 23.33/23.60 ============================== end of search =========================
% 23.33/23.60
% 23.33/23.60 THEOREM PROVED
% 23.33/23.60 % SZS status Theorem
% 23.33/23.60
% 23.33/23.60 Exiting with 1 proof.
% 23.33/23.60
% 23.33/23.60 Process 1540 exit (max_proofs) Sun Jun 19 01:56:10 2022
% 23.33/23.60 Prover9 interrupted
%------------------------------------------------------------------------------