TSTP Solution File: SET945+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 04:33:36 EDT 2022
% Result : Theorem 198.67s 199.02s
% Output : Refutation 198.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET945+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 02:06:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.02 ============================== Prover9 ===============================
% 0.46/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.02 Process 2769 was started by sandbox on n023.cluster.edu,
% 0.46/1.02 Sun Jul 10 02:06:41 2022
% 0.46/1.02 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2615_n023.cluster.edu".
% 0.46/1.02 ============================== end of head ===========================
% 0.46/1.02
% 0.46/1.02 ============================== INPUT =================================
% 0.46/1.02
% 0.46/1.02 % Reading from file /tmp/Prover9_2615_n023.cluster.edu
% 0.46/1.02
% 0.46/1.02 set(prolog_style_variables).
% 0.46/1.02 set(auto2).
% 0.46/1.02 % set(auto2) -> set(auto).
% 0.46/1.02 % set(auto) -> set(auto_inference).
% 0.46/1.02 % set(auto) -> set(auto_setup).
% 0.46/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.02 % set(auto) -> set(auto_limits).
% 0.46/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.02 % set(auto) -> set(auto_denials).
% 0.46/1.02 % set(auto) -> set(auto_process).
% 0.46/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.02 % set(auto2) -> assign(stats, some).
% 0.46/1.02 % set(auto2) -> clear(echo_input).
% 0.46/1.02 % set(auto2) -> set(quiet).
% 0.46/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.02 % set(auto2) -> clear(print_given).
% 0.46/1.02 assign(lrs_ticks,-1).
% 0.46/1.02 assign(sos_limit,10000).
% 0.46/1.02 assign(order,kbo).
% 0.46/1.02 set(lex_order_vars).
% 0.46/1.02 clear(print_given).
% 0.46/1.02
% 0.46/1.02 % formulas(sos). % not echoed (10 formulas)
% 0.46/1.02
% 0.46/1.02 ============================== end of input ==========================
% 0.46/1.02
% 0.46/1.02 % From the command line: assign(max_seconds, 300).
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.02
% 0.46/1.02 % Formulas that are not ordinary clauses:
% 0.46/1.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 3 (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].
% 0.46/1.02 4 (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].
% 0.46/1.02 5 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 8 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 9 (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(axiom) # label(non_clause). [assumption].
% 0.46/1.02 10 -(all A all B ((all C (in(C,A) -> disjoint(C,B))) -> disjoint(union(A),B))) # label(t98_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.02
% 0.46/1.02 ============================== end of process non-clausal formulas ===
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.02
% 0.46/1.02 ============================== PREDICATE ELIMINATION =================
% 0.46/1.02
% 0.46/1.02 ============================== end predicate elimination =============
% 0.46/1.02
% 0.46/1.02 Auto_denials: (non-Horn, no changes).
% 0.46/1.02
% 0.46/1.02 Term ordering decisions:
% 0.46/1.02
% 0.46/1.02 % Assigning unary symbol union kb_weight 0 and highest precedence (15).
% 0.46/1.02 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. set_intersection2=1. f3=1. f4=1. f5=1. f1=1. f2=1. union=0.
% 0.46/1.02
% 0.46/1.02 ============================== end of process initial clauses ========
% 198.67/199.02
% 198.67/199.02 ============================== CLAUSES FOR SEARCH ====================
% 198.67/199.02
% 198.67/199.02 ============================== end of clauses for search =============
% 198.67/199.02
% 198.67/199.02 ============================== SEARCH ================================
% 198.67/199.02
% 198.67/199.02 % Starting search at 0.01 seconds.
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=43.000, iters=3393
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=29.000, iters=3359
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=27.000, iters=3337
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=26.000, iters=3348
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=25.000, iters=3341
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=23.000, iters=3335
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=22.000, iters=3390
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=21.000, iters=3337
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=20.000, iters=3367
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=19.000, iters=3335
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=18.000, iters=3352
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=7109, wt=50.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=2628, wt=48.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=6289, wt=44.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=6297, wt=40.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=7145, wt=39.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=5968, wt=38.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=6293, wt=37.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=6304, wt=35.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=6160, wt=34.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=7311, wt=33.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=8145, wt=32.000
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=17.000, iters=3341
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=7149, wt=31.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=7949, wt=30.000
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=16.000, iters=3335
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=8206, wt=29.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=8146, wt=28.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=8299, wt=27.000
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=15.000, iters=3429
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=15371, wt=22.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=15402, wt=14.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=15404, wt=13.000
% 198.67/199.02
% 198.67/199.02 Low Water (displace): id=16171, wt=12.000
% 198.67/199.02
% 198.67/199.02 Low Water (keep): wt=14.000, iters=3334
% 198.67/199.02
% 198.67/199.02 ============================== PROOF =================================
% 198.67/199.02 % SZS status Theorem
% 198.67/199.02 % SZS output start Refutation
% 198.67/199.02
% 198.67/199.02 % Proof 1 at 197.34 (+ 0.64) seconds.
% 198.67/199.02 % Length of proof is 81.
% 198.67/199.02 % Level of proof is 19.
% 198.67/199.02 % Maximum clause weight is 23.000.
% 198.67/199.02 % Given clauses 3986.
% 198.67/199.02
% 198.67/199.02 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 198.67/199.02 2 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 198.67/199.02 3 (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].
% 198.67/199.02 4 (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].
% 198.67/199.02 5 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 198.67/199.02 9 (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(axiom) # label(non_clause). [assumption].
% 198.67/199.02 10 -(all A all B ((all C (in(C,A) -> disjoint(C,B))) -> disjoint(union(A),B))) # label(t98_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 198.67/199.02 12 set_intersection2(A,A) = A # label(idempotence_k3_xboole_0) # label(axiom). [clausify(5)].
% 198.67/199.02 13 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(2)].
% 198.67/199.02 14 disjoint(A,B) | in(f5(A,B),set_intersection2(A,B)) # label(t4_xboole_0) # label(axiom). [clausify(9)].
% 198.67/199.02 15 union(A) = B | in(f3(A,B),B) | in(f4(A,B),A) # label(d4_tarski) # label(axiom). [clausify(4)].
% 198.67/199.02 17 set_intersection2(A,B) = C | in(f1(A,B,C),C) | in(f1(A,B,C),A) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 18 set_intersection2(A,B) = C | in(f1(A,B,C),C) | in(f1(A,B,C),B) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 20 -disjoint(union(c3),c4) # label(t98_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 198.67/199.02 21 -in(A,B) | -in(B,A) # label(antisymmetry_r2_hidden) # label(axiom). [clausify(1)].
% 198.67/199.02 22 -in(A,set_intersection2(B,C)) | -disjoint(B,C) # label(t4_xboole_0) # label(axiom). [clausify(9)].
% 198.67/199.02 24 -in(A,c3) | disjoint(A,c4) # label(t98_zfmisc_1) # label(negated_conjecture). [clausify(10)].
% 198.67/199.02 25 set_intersection2(A,B) != C | -in(D,C) | in(D,A) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 26 set_intersection2(A,B) != C | -in(D,C) | in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 27 union(A) != B | -in(C,B) | in(C,f2(A,B,C)) # label(d4_tarski) # label(axiom). [clausify(4)].
% 198.67/199.02 28 union(A) != B | -in(C,B) | in(f2(A,B,C),A) # label(d4_tarski) # label(axiom). [clausify(4)].
% 198.67/199.02 30 set_intersection2(A,B) != C | in(D,C) | -in(D,A) | -in(D,B) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 32 set_intersection2(A,B) = C | -in(f1(A,B,C),C) | -in(f1(A,B,C),A) | -in(f1(A,B,C),B) # label(d3_xboole_0) # label(axiom). [clausify(3)].
% 198.67/199.02 33 set_intersection2(A,B) = A | in(f1(A,B,A),A). [factor(17,b,c)].
% 198.67/199.02 34 set_intersection2(A,B) = B | in(f1(A,B,B),B). [factor(18,b,c)].
% 198.67/199.02 35 -in(A,A). [factor(21,a,b)].
% 198.67/199.02 36 A != B | in(C,B) | -in(C,A). [factor(30,c,d),rewrite([12(1)])].
% 198.67/199.02 38 set_intersection2(A,B) = A | -in(f1(A,B,A),A) | -in(f1(A,B,A),B). [factor(32,b,c)].
% 198.67/199.02 40 A = B | -in(f1(A,A,B),B) | -in(f1(A,A,B),A). [factor(32,c,d),rewrite([12(1)])].
% 198.67/199.02 41 in(f5(union(c3),c4),set_intersection2(c4,union(c3))). [resolve(20,a,14,a),rewrite([13(8)])].
% 198.67/199.02 49 -in(A,set_intersection2(B,C)) | in(f5(B,C),set_intersection2(B,C)). [resolve(22,b,14,a)].
% 198.67/199.02 59 set_intersection2(A,B) != C | in(f1(D,C,E),A) | set_intersection2(C,D) = E | in(f1(D,C,E),E). [resolve(25,b,18,c),rewrite([13(5)])].
% 198.67/199.02 60 set_intersection2(A,B) != C | in(f1(D,E,C),A) | set_intersection2(D,E) = C | in(f1(D,E,C),E). [resolve(25,b,18,b)].
% 198.67/199.02 157 -in(A,set_intersection2(A,B)). [ur(26,a,13,a,c,35,a)].
% 198.67/199.02 173 set_intersection2(A,B) = A | -in(f1(A,B,A),B). [resolve(38,b,33,b),merge(c)].
% 198.67/199.02 181 set_intersection2(c4,union(c3)) != set_intersection2(A,B) | in(f5(union(c3),c4),B). [resolve(41,a,26,b),flip(a)].
% 198.67/199.02 230 -in(A,B) | in(f5(B,B),B). [para(12(a,1),49(a,2)),rewrite([12(3)])].
% 198.67/199.02 231 -in(A,set_intersection2(B,C)) | in(f5(C,B),set_intersection2(B,C)). [para(13(a,1),49(a,2)),rewrite([13(4)])].
% 198.67/199.02 233 in(f5(A,A),A) | set_intersection2(A,B) = A. [resolve(230,a,34,b),rewrite([13(3)])].
% 198.67/199.02 239 in(f5(A,A),A) | union(A) = B | in(f3(A,B),B). [resolve(230,a,15,c)].
% 198.67/199.02 382 in(f5(union(c3),c4),c4). [resolve(181,a,13,a)].
% 198.67/199.02 383 in(f5(union(c3),c4),union(c3)). [xx_res(181,a)].
% 198.67/199.02 387 set_intersection2(A,c4) != B | in(f5(union(c3),c4),B) | -in(f5(union(c3),c4),A). [resolve(382,a,30,d)].
% 198.67/199.02 455 union(c3) != union(A) | in(f2(A,union(c3),f5(union(c3),c4)),A). [resolve(383,a,28,b),flip(a)].
% 198.67/199.02 456 union(c3) != union(A) | in(f5(union(c3),c4),f2(A,union(c3),f5(union(c3),c4))). [resolve(383,a,27,b),flip(a)].
% 198.67/199.02 515 in(f1(A,set_intersection2(B,C),D),B) | set_intersection2(A,set_intersection2(B,C)) = D | in(f1(A,set_intersection2(B,C),D),D). [resolve(59,a,12,a(flip)),rewrite([12(3),12(6),13(5),12(9)])].
% 198.67/199.02 518 in(f1(A,set_intersection2(B,C),B),B) | set_intersection2(A,set_intersection2(B,C)) = B. [factor(515,a,c)].
% 198.67/199.02 536 in(f1(A,B,set_intersection2(C,D)),D) | set_intersection2(A,B) = set_intersection2(C,D) | in(f1(A,B,set_intersection2(C,D)),B). [resolve(60,a,13,a)].
% 198.67/199.02 539 in(f1(A,B,set_intersection2(B,C)),B) | set_intersection2(B,C) = set_intersection2(A,B). [factor(536,a,c),rewrite([13(1),13(5)]),flip(b)].
% 198.67/199.02 751 in(f5(A,A),A) | union(A) = B | in(f5(B,B),B). [resolve(239,c,230,a)].
% 198.67/199.02 766 in(f5(A,A),A) | union(A) = A. [factor(751,a,c)].
% 198.67/199.02 1153 in(f2(c3,union(c3),f5(union(c3),c4)),c3). [xx_res(455,a)].
% 198.67/199.02 1154 in(f5(c3,c3),c3). [resolve(1153,a,230,a)].
% 198.67/199.02 1164 disjoint(f2(c3,union(c3),f5(union(c3),c4)),c4). [resolve(1153,a,24,a)].
% 198.67/199.02 1187 disjoint(f5(c3,c3),c4). [resolve(1154,a,24,a)].
% 198.67/199.02 1193 set_intersection2(A,f5(c3,c3)) != c3. [ur(36,b,157,a,c,1154,a),rewrite([13(5)]),flip(a)].
% 198.67/199.02 1202 -in(A,set_intersection2(c4,f5(c3,c3))). [resolve(1187,a,22,b),rewrite([13(5)])].
% 198.67/199.02 1205 -in(f1(c3,f5(c3,c3),c3),f5(c3,c3)). [ur(173,a,1193,a)].
% 198.67/199.02 1220 -in(A,set_intersection2(c4,f2(c3,union(c3),f5(union(c3),c4)))). [resolve(1164,a,22,b),rewrite([13(10)])].
% 198.67/199.02 1221 union(set_intersection2(c4,f5(c3,c3))) = set_intersection2(c4,f5(c3,c3)). [resolve(1202,a,766,a)].
% 198.67/199.02 1223 set_intersection2(c4,f5(c3,c3)) = A | in(f5(A,A),A). [resolve(1202,a,751,a),rewrite([1221(6)])].
% 198.67/199.02 1226 set_intersection2(A,set_intersection2(c4,f5(c3,c3))) = set_intersection2(c4,f5(c3,c3)). [resolve(1202,a,233,a),rewrite([13(6)])].
% 198.67/199.02 1567 set_intersection2(c4,f5(c3,c3)) = set_intersection2(A,B) | in(f5(B,A),set_intersection2(A,B)). [resolve(1223,b,231,a)].
% 198.67/199.02 1873 set_intersection2(A,B) = A | -in(f1(set_intersection2(A,B),set_intersection2(A,B),A),set_intersection2(A,B)). [resolve(518,a,40,b),rewrite([12(3)]),merge(b)].
% 198.67/199.02 1895 in(f1(c3,f5(c3,c3),c3),c3). [resolve(1205,a,18,c),unit_del(a,1193)].
% 198.67/199.02 1949 disjoint(f1(c3,f5(c3,c3),c3),c4). [resolve(1895,a,24,a)].
% 198.67/199.02 1956 -in(A,set_intersection2(c4,f1(c3,f5(c3,c3),c3))). [resolve(1949,a,22,b),rewrite([13(8)])].
% 198.67/199.02 2018 set_intersection2(A,B) = set_intersection2(A,C) | in(f5(A,A),A). [resolve(539,a,230,a),rewrite([13(2)])].
% 198.67/199.02 2021 set_intersection2(A,set_intersection2(A,B)) = set_intersection2(A,B). [resolve(539,a,173,b),rewrite([13(3),13(6)]),flip(a),merge(b)].
% 198.67/199.02 2810 set_intersection2(A,set_intersection2(c4,f1(c3,f5(c3,c3),c3))) = set_intersection2(B,set_intersection2(c4,f1(c3,f5(c3,c3),c3))). [resolve(1956,a,2018,b),rewrite([13(9),13(18)])].
% 198.67/199.02 2812 set_intersection2(c4,f1(c3,f5(c3,c3),c3)) = set_intersection2(c4,f5(c3,c3)). [resolve(1956,a,1223,b),flip(a)].
% 198.67/199.02 2820 set_intersection2(c4,f5(c3,c3)) = c_0. [new_symbol(2810),rewrite([2812(8),1226(6)])].
% 198.67/199.02 2823 -in(A,c_0). [back_rewrite(1956),rewrite([2812(8),2820(5)])].
% 198.67/199.02 3005 set_intersection2(A,B) = c_0 | in(f5(B,A),set_intersection2(A,B)). [back_rewrite(1567),rewrite([2820(5)]),flip(a)].
% 198.67/199.02 4210 set_intersection2(A,B) = c_0 | set_intersection2(C,D) != set_intersection2(A,B) | in(f5(B,A),C). [resolve(3005,b,25,b)].
% 198.67/199.02 16773 in(f5(union(c3),c4),f2(c3,union(c3),f5(union(c3),c4))). [xx_res(456,a)].
% 198.67/199.02 16788 set_intersection2(c4,f2(c3,union(c3),f5(union(c3),c4))) != c_0. [ur(387,b,2823,a,c,16773,a),rewrite([13(10)])].
% 198.67/199.02 17206 set_intersection2(A,B) = A | in(f1(set_intersection2(A,B),set_intersection2(A,B),A),A). [resolve(1873,b,18,c),rewrite([12(5)]),merge(b)].
% 198.67/199.02 18817 set_intersection2(A,B) = c_0 | in(f5(set_intersection2(A,B),A),A). [resolve(4210,b,2021,a(flip)),rewrite([2021(2)])].
% 198.67/199.02 20526 set_intersection2(A,set_intersection2(c4,f2(c3,union(c3),f5(union(c3),c4)))) = c_0. [resolve(1220,a,18817,b),rewrite([13(11)])].
% 198.67/199.02 20527 $F. [resolve(1220,a,17206,b),rewrite([13(11),20526(11)]),flip(a),unit_del(a,16788)].
% 198.67/199.02
% 198.67/199.02 % SZS output end Refutation
% 198.67/199.02 ============================== end of proof ==========================
% 198.67/199.02
% 198.67/199.02 ============================== STATISTICS ============================
% 198.67/199.02
% 198.67/199.02 Given=3986. Generated=1148313. Kept=20516. proofs=1.
% 198.67/199.02 Usable=3907. Sos=9996. Demods=164. Limbo=2, Disabled=6633. Hints=0.
% 198.67/199.02 Megabytes=16.86.
% 198.67/199.02 User_CPU=197.34, System_CPU=0.64, Wall_clock=198.
% 198.67/199.02
% 198.67/199.02 ============================== end of statistics =====================
% 198.67/199.02
% 198.67/199.02 ============================== end of search =========================
% 198.67/199.02
% 198.67/199.02 THEOREM PROVED
% 198.67/199.02 % SZS status Theorem
% 198.67/199.02
% 198.67/199.02 Exiting with 1 proof.
% 198.67/199.02
% 198.67/199.02 Process 2769 exit (max_proofs) Sun Jul 10 02:09:59 2022
% 198.67/199.03 Prover9 interrupted
%------------------------------------------------------------------------------