TSTP Solution File: SET619+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 04:30:50 EDT 2022
% Result : Theorem 58.10s 58.45s
% Output : Refutation 58.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n021.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 Jul 10 20:48:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.73/0.99 ============================== Prover9 ===============================
% 0.73/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.73/0.99 Process 12172 was started by sandbox on n021.cluster.edu,
% 0.73/0.99 Sun Jul 10 20:48:38 2022
% 0.73/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_11988_n021.cluster.edu".
% 0.73/0.99 ============================== end of head ===========================
% 0.73/0.99
% 0.73/0.99 ============================== INPUT =================================
% 0.73/0.99
% 0.73/0.99 % Reading from file /tmp/Prover9_11988_n021.cluster.edu
% 0.73/0.99
% 0.73/0.99 set(prolog_style_variables).
% 0.73/0.99 set(auto2).
% 0.73/0.99 % set(auto2) -> set(auto).
% 0.73/0.99 % set(auto) -> set(auto_inference).
% 0.73/0.99 % set(auto) -> set(auto_setup).
% 0.73/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.73/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/0.99 % set(auto) -> set(auto_limits).
% 0.73/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/0.99 % set(auto) -> set(auto_denials).
% 0.73/0.99 % set(auto) -> set(auto_process).
% 0.73/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.73/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.73/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.73/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.73/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.73/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.73/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.73/0.99 % set(auto2) -> assign(stats, some).
% 0.73/0.99 % set(auto2) -> clear(echo_input).
% 0.73/0.99 % set(auto2) -> set(quiet).
% 0.73/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.73/0.99 % set(auto2) -> clear(print_given).
% 0.73/0.99 assign(lrs_ticks,-1).
% 0.73/0.99 assign(sos_limit,10000).
% 0.73/0.99 assign(order,kbo).
% 0.73/0.99 set(lex_order_vars).
% 0.73/0.99 clear(print_given).
% 0.73/0.99
% 0.73/0.99 % formulas(sos). % not echoed (14 formulas)
% 0.73/0.99
% 0.73/0.99 ============================== end of input ==========================
% 0.73/0.99
% 0.73/0.99 % From the command line: assign(max_seconds, 300).
% 0.73/0.99
% 0.73/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/0.99
% 0.73/0.99 % Formulas that are not ordinary clauses:
% 0.73/0.99 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 2 (all B all C all D union(union(B,C),D) = union(B,union(C,D))) # label(associativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 3 (all B all C union(B,intersection(B,C)) = B) # label(union_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 4 (all B all C union(intersection(B,C),difference(B,C)) = B) # label(union_intersection_difference) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 5 (all B all C all D (member(D,union(B,C)) <-> member(D,B) | member(D,C))) # label(union_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 6 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 7 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 8 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 9 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 10 (all B all C symmetric_difference(B,C) = symmetric_difference(C,B)) # label(commutativity_of_symmetric_difference) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 11 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 12 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 13 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/0.99 14 -(all B all C union(B,C) = union(symmetric_difference(B,C),intersection(B,C))) # label(prove_th95) # label(negated_conjecture) # label(non_clause). [assumption].
% 58.10/58.45
% 58.10/58.45 ============================== end of process non-clausal formulas ===
% 58.10/58.45
% 58.10/58.45 ============================== PROCESS INITIAL CLAUSES ===============
% 58.10/58.45
% 58.10/58.45 ============================== PREDICATE ELIMINATION =================
% 58.10/58.45
% 58.10/58.45 ============================== end predicate elimination =============
% 58.10/58.45
% 58.10/58.45 Auto_denials: (non-Horn, no changes).
% 58.10/58.45
% 58.10/58.45 Term ordering decisions:
% 58.10/58.45 Function symbol KB weights: c1=1. c2=1. union=1. intersection=1. difference=1. symmetric_difference=1. f1=1. f2=1.
% 58.10/58.45
% 58.10/58.45 ============================== end of process initial clauses ========
% 58.10/58.45
% 58.10/58.45 ============================== CLAUSES FOR SEARCH ====================
% 58.10/58.45
% 58.10/58.45 ============================== end of clauses for search =============
% 58.10/58.45
% 58.10/58.45 ============================== SEARCH ================================
% 58.10/58.45
% 58.10/58.45 % Starting search at 0.01 seconds.
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=64.000, iters=3350
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=59.000, iters=3335
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=56.000, iters=3416
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=50.000, iters=3355
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=48.000, iters=3355
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=47.000, iters=3336
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=46.000, iters=3334
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=45.000, iters=3343
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=42.000, iters=3344
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=41.000, iters=3356
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=40.000, iters=3380
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=39.000, iters=3370
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=37.000, iters=3430
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=36.000, iters=3340
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=35.000, iters=3408
% 58.10/58.45
% 58.10/58.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 21 (0.00 of 1.83 sec).
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=34.000, iters=3336
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=33.000, iters=3340
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=32.000, iters=3360
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=31.000, iters=3333
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=30.000, iters=3337
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=29.000, iters=3375
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=28.000, iters=3345
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=5422, wt=88.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=5970, wt=78.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=2600, wt=76.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=4209, wt=71.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=4501, wt=70.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=4527, wt=67.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=4259, wt=65.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=6207, wt=64.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=5445, wt=62.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=4574, wt=61.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=6261, wt=60.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=11660, wt=26.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=11686, wt=21.000
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=27.000, iters=3357
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=12487, wt=19.000
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=26.000, iters=3335
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=25.000, iters=3341
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=24.000, iters=3346
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=16560, wt=18.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=19544, wt=17.000
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=23.000, iters=3334
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=22.000, iters=3337
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=21.000, iters=3340
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=26880, wt=15.000
% 58.10/58.45
% 58.10/58.45 Low Water (displace): id=27012, wt=13.000
% 58.10/58.45
% 58.10/58.45 Low Water (keep): wt=20.000, iters=3340
% 58.10/58.45
% 58.10/58.45 ============================== PROOF =================================
% 58.10/58.45 % SZS status Theorem
% 58.10/58.45 % SZS output start Refutation
% 58.10/58.45
% 58.10/58.45 % Proof 1 at 56.27 (+ 1.20) seconds.
% 58.18/58.45 % Length of proof is 74.
% 58.18/58.45 % Level of proof is 24.
% 58.18/58.45 % Maximum clause weight is 26.000.
% 58.18/58.45 % Given clauses 2428.
% 58.18/58.45
% 58.18/58.45 1 (all B all C symmetric_difference(B,C) = union(difference(B,C),difference(C,B))) # label(symmetric_difference_defn) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 2 (all B all C all D union(union(B,C),D) = union(B,union(C,D))) # label(associativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 3 (all B all C union(B,intersection(B,C)) = B) # label(union_intersection) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 4 (all B all C union(intersection(B,C),difference(B,C)) = B) # label(union_intersection_difference) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 5 (all B all C all D (member(D,union(B,C)) <-> member(D,B) | member(D,C))) # label(union_defn) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 6 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 8 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 9 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 11 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 58.18/58.45 14 -(all B all C union(B,C) = union(symmetric_difference(B,C),intersection(B,C))) # label(prove_th95) # label(negated_conjecture) # label(non_clause). [assumption].
% 58.18/58.45 16 union(A,intersection(A,B)) = A # label(union_intersection) # label(axiom). [clausify(3)].
% 58.18/58.45 17 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(8)].
% 58.18/58.45 18 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(9)].
% 58.18/58.45 21 union(intersection(A,B),difference(A,B)) = A # label(union_intersection_difference) # label(axiom). [clausify(4)].
% 58.18/58.45 22 union(difference(A,B),difference(B,A)) = symmetric_difference(A,B) # label(symmetric_difference_defn) # label(axiom). [clausify(1)].
% 58.18/58.45 23 symmetric_difference(A,B) = union(difference(A,B),difference(B,A)). [copy(22),flip(a)].
% 58.18/58.45 24 union(union(A,B),C) = union(A,union(B,C)) # label(associativity_of_union) # label(axiom). [clausify(2)].
% 58.18/58.45 25 union(A,union(B,C)) = union(C,union(A,B)). [copy(24),rewrite([17(2)]),flip(a)].
% 58.18/58.45 26 A = B | member(f1(B,A),B) | member(f1(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(11)].
% 58.18/58.45 27 union(symmetric_difference(c1,c2),intersection(c1,c2)) != union(c1,c2) # label(prove_th95) # label(negated_conjecture). [clausify(14)].
% 58.18/58.45 28 union(intersection(c1,c2),union(difference(c1,c2),difference(c2,c1))) != union(c1,c2). [copy(27),rewrite([23(3),17(11)])].
% 58.18/58.45 31 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(5)].
% 58.18/58.45 32 member(A,union(B,C)) | -member(A,C) # label(union_defn) # label(axiom). [clausify(5)].
% 58.18/58.45 33 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(6)].
% 58.18/58.45 40 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(5)].
% 58.18/58.45 41 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(6)].
% 58.18/58.45 42 A = B | -member(f1(B,A),B) | -member(f1(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(11)].
% 58.18/58.45 44 member(A,intersection(B,B)) | -member(A,B). [factor(41,b,c)].
% 58.18/58.45 45 union(intersection(A,B),difference(B,A)) = B. [para(18(a,1),21(a,1,1))].
% 58.18/58.45 46 union(A,union(B,intersection(A,C))) = union(A,B). [para(16(a,1),25(a,2,2)),rewrite([17(2),17(4)])].
% 58.18/58.45 47 union(c1,difference(c2,c1)) != union(c1,c2). [para(25(a,1),28(a,1)),rewrite([21(10),17(5)])].
% 58.18/58.45 49 member(f1(A,B),union(B,C)) | B = A | member(f1(A,B),A). [resolve(31,b,26,c)].
% 58.18/58.45 51 member(f1(union(A,B),A),union(A,B)) | union(A,B) = A. [factor(49,a,c),flip(b)].
% 58.18/58.45 53 member(f1(A,intersection(B,C)),B) | intersection(B,C) = A | member(f1(A,intersection(B,C)),A). [resolve(33,a,26,c)].
% 58.18/58.45 55 member(f1(A,intersection(A,B)),A) | intersection(A,B) = A. [factor(53,a,c)].
% 58.18/58.45 70 member(f1(union(A,B),C),A) | member(f1(union(A,B),C),B) | union(A,B) = C | member(f1(union(A,B),C),C). [resolve(40,a,26,b),flip(c)].
% 58.18/58.45 76 member(f1(union(A,A),B),A) | union(A,A) = B | member(f1(union(A,A),B),B). [factor(70,a,b)].
% 58.18/58.45 81 member(f1(union(A,A),A),A) | union(A,A) = A. [factor(76,a,c)].
% 58.18/58.45 93 union(intersection(A,B),union(difference(B,A),intersection(C,intersection(A,B)))) = B. [para(45(a,1),46(a,2)),rewrite([18(4)])].
% 58.18/58.45 124 intersection(A,B) = A | member(f1(A,intersection(A,B)),intersection(A,A)). [resolve(55,a,44,b)].
% 58.18/58.45 126 intersection(A,B) = A | -member(f1(A,intersection(A,B)),intersection(A,B)). [resolve(55,a,42,b),merge(b)].
% 58.18/58.45 127 intersection(A,B) = A | member(f1(A,intersection(A,B)),intersection(A,C)) | -member(f1(A,intersection(A,B)),C). [resolve(55,a,41,c),rewrite([18(5)])].
% 58.18/58.45 133 intersection(A,B) = A | member(f1(A,intersection(A,B)),union(A,C)). [resolve(55,a,32,b),rewrite([17(5)])].
% 58.18/58.45 219 union(A,B) = A | -member(f1(union(A,B),A),A). [resolve(51,a,42,b),flip(b),merge(b)].
% 58.18/58.46 226 member(f1(A,intersection(B,A)),A) | intersection(B,A) = A. [para(45(a,1),51(a,2)),rewrite([45(3),45(6)]),flip(b)].
% 58.18/58.46 227 union(A,A) = A. [resolve(219,b,81,a),merge(b)].
% 58.18/58.46 522 intersection(A,A) = A | -member(f1(A,intersection(A,A)),A). [resolve(124,b,42,c),merge(b)].
% 58.18/58.46 526 intersection(A,A) = A. [resolve(522,b,226,a),merge(b)].
% 58.18/58.46 2390 intersection(A,B) = A | member(f1(A,intersection(A,B)),intersection(A,union(A,C))). [resolve(127,c,133,b),merge(c)].
% 58.18/58.46 3406 intersection(A,union(A,B)) = A. [resolve(2390,b,126,b),merge(b)].
% 58.18/58.46 3431 union(A,difference(union(A,B),A)) = union(A,B). [para(3406(a,1),45(a,1,1))].
% 58.18/58.46 3432 intersection(A,intersection(B,A)) = intersection(B,A). [para(45(a,1),3406(a,1,2)),rewrite([18(2)])].
% 58.18/58.46 3461 union(intersection(A,B),difference(B,intersection(A,B))) = B. [para(3432(a,1),21(a,1,1))].
% 58.18/58.46 3487 union(A,union(B,difference(union(A,C),A))) = union(A,union(C,B)). [para(3431(a,1),25(a,2,2)),rewrite([17(3),25(6),17(5),25(6,R),17(5)])].
% 58.18/58.46 3592 union(intersection(A,B),union(intersection(C,intersection(A,B)),difference(B,intersection(A,B)))) = B. [para(93(a,1),3487(a,2)),rewrite([45(6)])].
% 58.18/58.46 9848 union(A,intersection(B,intersection(C,A))) = A. [para(3592(a,1),25(a,2)),rewrite([17(6),3461(6),17(3)])].
% 58.18/58.46 9892 union(union(A,B),intersection(A,C)) = union(A,B). [para(3406(a,1),9848(a,1,2,2)),rewrite([18(2)])].
% 58.18/58.46 9896 union(union(A,B),intersection(B,C)) = union(A,B). [para(17(a,1),9892(a,1,1)),rewrite([17(4)])].
% 58.18/58.46 9932 union(union(A,union(B,C)),intersection(D,union(A,C))) = union(A,union(B,C)). [para(25(a,1),9896(a,1,1)),rewrite([17(3),18(4),17(6),25(7,R),17(6)])].
% 58.18/58.46 9934 union(union(A,union(B,C)),intersection(D,union(A,B))) = union(A,union(B,C)). [para(25(a,2),9896(a,1,1)),rewrite([18(4),25(7),17(6),25(7,R),17(6)])].
% 58.18/58.46 16766 union(A,union(union(B,C),intersection(D,union(A,C)))) = union(A,union(B,C)). [para(9932(a,1),17(a,1)),rewrite([25(7,R)]),flip(a)].
% 58.18/58.46 16981 union(union(A,B),intersection(C,union(A,intersection(D,B)))) = union(A,B). [para(45(a,1),9934(a,2,2)),rewrite([45(3)])].
% 58.18/58.46 24262 union(intersection(A,B),union(union(C,difference(A,B)),intersection(A,D))) = union(A,C). [para(21(a,1),16766(a,1,2,2,2)),rewrite([18(4),25(10,R),17(9),21(9),17(7)])].
% 58.18/58.46 24269 union(A,union(B,intersection(C,union(A,B)))) = union(A,B). [para(227(a,1),16766(a,1,2,1)),rewrite([227(5)])].
% 58.18/58.46 24335 union(intersection(A,B),union(difference(A,B),intersection(A,C))) = A. [para(21(a,1),24269(a,1,2,2,2)),rewrite([18(3),21(8)])].
% 58.18/58.46 26333 intersection(intersection(A,B),union(A,C)) = intersection(A,B). [para(24262(a,1),3406(a,1,2))].
% 58.18/58.46 26376 intersection(union(A,B),intersection(A,C)) = intersection(A,C). [para(26333(a,1),18(a,1)),flip(a)].
% 58.18/58.46 26441 intersection(union(A,B),intersection(B,C)) = intersection(B,C). [para(17(a,1),26376(a,1,1))].
% 58.18/58.46 26552 intersection(A,union(B,A)) = A. [para(526(a,1),26441(a,1,2)),rewrite([18(2),526(3)])].
% 58.18/58.46 26793 intersection(A,union(difference(A,B),intersection(A,C))) = union(difference(A,B),intersection(A,C)). [para(24335(a,1),26552(a,1,2)),rewrite([18(4)])].
% 58.18/58.46 32195 union(A,union(difference(B,C),intersection(B,A))) = union(A,difference(B,C)). [para(26793(a,1),16981(a,1,2)),rewrite([17(2),25(6),17(5),25(5,R),227(4),25(4,R),17(6)])].
% 58.18/58.46 32664 union(A,union(intersection(A,B),difference(B,C))) = union(A,difference(B,C)). [para(17(a,1),32195(a,1,2)),rewrite([18(1)])].
% 58.18/58.46 32673 union(A,difference(B,A)) = union(A,B). [para(45(a,1),32664(a,1,2)),flip(a)].
% 58.18/58.46 32674 $F. [resolve(32673,a,47,a)].
% 58.18/58.46
% 58.18/58.46 % SZS output end Refutation
% 58.18/58.46 ============================== end of proof ==========================
% 58.18/58.46
% 58.18/58.46 ============================== STATISTICS ============================
% 58.18/58.46
% 58.18/58.46 Given=2428. Generated=2242683. Kept=32656. proofs=1.
% 58.18/58.46 Usable=2359. Sos=9999. Demods=5974. Limbo=2, Disabled=20320. Hints=0.
% 58.18/58.46 Megabytes=24.78.
% 58.18/58.46 User_CPU=56.27, System_CPU=1.20, Wall_clock=58.
% 58.18/58.46
% 58.18/58.46 ============================== end of statistics =====================
% 58.18/58.46
% 58.18/58.46 ============================== end of search =========================
% 58.18/58.46
% 58.18/58.46 THEOREM PROVED
% 58.18/58.46 % SZS status Theorem
% 58.18/58.46
% 58.18/58.46 Exiting with 1 proof.
% 58.18/58.46
% 58.18/58.46 Process 12172 exit (max_proofs) Sun Jul 10 20:49:36 2022
% 58.18/58.46 Prover9 interrupted
%------------------------------------------------------------------------------