TSTP Solution File: SET620+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 04:30:51 EDT 2022
% Result : Theorem 1.54s 1.81s
% Output : Refutation 1.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n013.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 Jul 11 05:47:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/1.00 ============================== Prover9 ===============================
% 0.42/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.00 Process 3471 was started by sandbox2 on n013.cluster.edu,
% 0.42/1.00 Mon Jul 11 05:48:00 2022
% 0.42/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3318_n013.cluster.edu".
% 0.42/1.00 ============================== end of head ===========================
% 0.42/1.00
% 0.42/1.00 ============================== INPUT =================================
% 0.42/1.00
% 0.42/1.00 % Reading from file /tmp/Prover9_3318_n013.cluster.edu
% 0.42/1.00
% 0.42/1.00 set(prolog_style_variables).
% 0.42/1.00 set(auto2).
% 0.42/1.00 % set(auto2) -> set(auto).
% 0.42/1.00 % set(auto) -> set(auto_inference).
% 0.42/1.00 % set(auto) -> set(auto_setup).
% 0.42/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.00 % set(auto) -> set(auto_limits).
% 0.42/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.00 % set(auto) -> set(auto_denials).
% 0.42/1.00 % set(auto) -> set(auto_process).
% 0.42/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.00 % set(auto2) -> assign(stats, some).
% 0.42/1.00 % set(auto2) -> clear(echo_input).
% 0.42/1.00 % set(auto2) -> set(quiet).
% 0.42/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.00 % set(auto2) -> clear(print_given).
% 0.42/1.00 assign(lrs_ticks,-1).
% 0.42/1.00 assign(sos_limit,10000).
% 0.42/1.00 assign(order,kbo).
% 0.42/1.00 set(lex_order_vars).
% 0.42/1.00 clear(print_given).
% 0.42/1.00
% 0.42/1.00 % formulas(sos). % not echoed (14 formulas)
% 0.42/1.00
% 0.42/1.00 ============================== end of input ==========================
% 0.42/1.00
% 0.42/1.00 % From the command line: assign(max_seconds, 300).
% 0.42/1.00
% 0.42/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.00
% 0.42/1.00 % Formulas that are not ordinary clauses:
% 0.42/1.00 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].
% 0.42/1.00 2 (all B all C difference(B,intersection(B,C)) = difference(B,C)) # label(difference_into_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 3 (all B all C all D difference(union(B,C),D) = union(difference(B,D),difference(C,D))) # label(difference_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 4 (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].
% 0.42/1.00 5 (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].
% 0.42/1.00 6 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 7 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 8 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 9 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 10 (all B all C symmetric_difference(B,C) = symmetric_difference(C,B)) # label(commutativity_of_symmetric_difference) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 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].
% 0.42/1.00 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].
% 0.42/1.00 13 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/1.00 14 -(all B all C symmetric_difference(B,C) = difference(union(B,C),intersection(B,C))) # label(prove_th96) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.54/1.81
% 1.54/1.81 ============================== end of process non-clausal formulas ===
% 1.54/1.81
% 1.54/1.81 ============================== PROCESS INITIAL CLAUSES ===============
% 1.54/1.81
% 1.54/1.81 ============================== PREDICATE ELIMINATION =================
% 1.54/1.81
% 1.54/1.81 ============================== end predicate elimination =============
% 1.54/1.81
% 1.54/1.81 Auto_denials: (non-Horn, no changes).
% 1.54/1.81
% 1.54/1.81 Term ordering decisions:
% 1.54/1.81 Function symbol KB weights: c1=1. c2=1. difference=1. union=1. intersection=1. symmetric_difference=1. f1=1. f2=1.
% 1.54/1.81
% 1.54/1.81 ============================== end of process initial clauses ========
% 1.54/1.81
% 1.54/1.81 ============================== CLAUSES FOR SEARCH ====================
% 1.54/1.81
% 1.54/1.81 ============================== end of clauses for search =============
% 1.54/1.81
% 1.54/1.81 ============================== SEARCH ================================
% 1.54/1.81
% 1.54/1.81 % Starting search at 0.01 seconds.
% 1.54/1.81
% 1.54/1.81 ============================== PROOF =================================
% 1.54/1.81 % SZS status Theorem
% 1.54/1.81 % SZS output start Refutation
% 1.54/1.81
% 1.54/1.81 % Proof 1 at 0.81 (+ 0.02) seconds.
% 1.54/1.81 % Length of proof is 100.
% 1.54/1.81 % Level of proof is 18.
% 1.54/1.81 % Maximum clause weight is 33.000.
% 1.54/1.81 % Given clauses 210.
% 1.54/1.81
% 1.54/1.81 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].
% 1.54/1.81 2 (all B all C difference(B,intersection(B,C)) = difference(B,C)) # label(difference_into_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 3 (all B all C all D difference(union(B,C),D) = union(difference(B,D),difference(C,D))) # label(difference_distributes_over_union) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 4 (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].
% 1.54/1.81 5 (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].
% 1.54/1.81 6 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 8 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 9 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.54/1.81 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].
% 1.54/1.81 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].
% 1.54/1.81 14 -(all B all C symmetric_difference(B,C) = difference(union(B,C),intersection(B,C))) # label(prove_th96) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.54/1.81 16 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(8)].
% 1.54/1.81 17 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(9)].
% 1.54/1.81 19 subset(A,B) | member(f2(A,B),A) # label(subset_defn) # label(axiom). [clausify(12)].
% 1.54/1.81 20 difference(A,intersection(A,B)) = difference(A,B) # label(difference_into_intersection) # label(axiom). [clausify(2)].
% 1.54/1.81 21 union(difference(A,B),difference(B,A)) = symmetric_difference(A,B) # label(symmetric_difference_defn) # label(axiom). [clausify(1)].
% 1.54/1.81 22 symmetric_difference(A,B) = union(difference(A,B),difference(B,A)). [copy(21),flip(a)].
% 1.54/1.81 23 union(difference(A,B),difference(C,B)) = difference(union(A,C),B) # label(difference_distributes_over_union) # label(axiom). [clausify(3)].
% 1.54/1.81 24 A = B | member(f1(B,A),B) | member(f1(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(11)].
% 1.54/1.81 25 -member(A,difference(B,C)) | -member(A,C) # label(difference_defn) # label(axiom). [clausify(6)].
% 1.54/1.81 26 symmetric_difference(c1,c2) != difference(union(c1,c2),intersection(c1,c2)) # label(prove_th96) # label(negated_conjecture). [clausify(14)].
% 1.54/1.81 27 union(difference(c1,c2),difference(c2,c1)) != difference(union(c1,c2),intersection(c1,c2)). [copy(26),rewrite([22(3)])].
% 1.54/1.81 30 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(4)].
% 1.54/1.81 32 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(5)].
% 1.54/1.81 33 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(5)].
% 1.54/1.81 34 -member(A,difference(B,C)) | member(A,B) # label(difference_defn) # label(axiom). [clausify(6)].
% 1.54/1.81 39 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(12)].
% 1.54/1.81 40 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(4)].
% 1.54/1.81 41 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(5)].
% 1.54/1.81 42 member(A,difference(B,C)) | -member(A,B) | member(A,C) # label(difference_defn) # label(axiom). [clausify(6)].
% 1.54/1.81 43 A = B | -member(f1(B,A),B) | -member(f1(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(11)].
% 1.54/1.81 44 -member(A,union(B,B)) | member(A,B). [factor(40,b,c)].
% 1.54/1.81 45 member(A,intersection(B,B)) | -member(A,B). [factor(41,b,c)].
% 1.54/1.81 46 union(difference(A,B),difference(C,intersection(A,B))) = difference(union(A,C),intersection(A,B)). [para(20(a,1),23(a,1,1))].
% 1.54/1.81 47 difference(union(A,B),intersection(C,union(A,B))) = difference(union(A,B),C). [para(20(a,1),23(a,2)),rewrite([17(2),17(5),23(7)])].
% 1.54/1.81 48 -member(f1(A,difference(B,C)),C) | difference(B,C) = A | member(f1(A,difference(B,C)),A). [resolve(25,a,24,c)].
% 1.54/1.81 51 member(f1(A,B),union(B,C)) | B = A | member(f1(A,B),A). [resolve(30,b,24,c)].
% 1.54/1.81 52 member(f1(A,B),union(A,C)) | B = A | member(f1(A,B),B). [resolve(30,b,24,b)].
% 1.54/1.81 53 member(f1(union(A,B),A),union(A,B)) | union(A,B) = A. [factor(51,a,c),flip(b)].
% 1.54/1.81 54 member(f1(A,union(A,B)),union(A,B)) | union(A,B) = A. [factor(52,a,c)].
% 1.54/1.81 55 member(f1(A,intersection(B,C)),B) | intersection(B,C) = A | member(f1(A,intersection(B,C)),A). [resolve(32,a,24,c)].
% 1.54/1.81 56 member(f1(intersection(A,B),C),A) | intersection(A,B) = C | member(f1(intersection(A,B),C),C). [resolve(32,a,24,b),flip(b)].
% 1.54/1.81 57 member(f1(A,intersection(A,B)),A) | intersection(A,B) = A. [factor(55,a,c)].
% 1.54/1.81 58 member(f1(intersection(A,B),A),A) | intersection(A,B) = A. [factor(56,a,c)].
% 1.54/1.81 60 member(f1(intersection(A,B),C),B) | intersection(A,B) = C | member(f1(intersection(A,B),C),C). [resolve(33,a,24,b),flip(b)].
% 1.54/1.81 61 member(f1(intersection(A,B),B),B) | intersection(A,B) = B. [factor(60,a,c)].
% 1.54/1.81 62 member(f1(A,difference(B,C)),B) | difference(B,C) = A | member(f1(A,difference(B,C)),A). [resolve(34,a,24,c)].
% 1.54/1.81 63 member(f1(difference(A,B),C),A) | difference(A,B) = C | member(f1(difference(A,B),C),C). [resolve(34,a,24,b),flip(b)].
% 1.54/1.81 65 member(f1(difference(A,B),A),A) | difference(A,B) = A. [factor(63,a,c)].
% 1.54/1.81 74 -member(A,B) | member(A,C) | member(f2(B,C),B). [resolve(39,a,19,a)].
% 1.54/1.81 75 member(f1(A,union(B,C)),B) | member(f1(A,union(B,C)),C) | union(B,C) = A | member(f1(A,union(B,C)),A). [resolve(40,a,24,c)].
% 1.54/1.81 76 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,24,b),flip(c)].
% 1.54/1.81 80 member(f1(union(A,A),B),A) | union(A,A) = B | member(f1(union(A,A),B),B). [factor(76,a,b)].
% 1.54/1.81 85 member(f1(union(A,A),A),A) | union(A,A) = A. [factor(80,a,c)].
% 1.54/1.81 101 difference(union(A,A),intersection(A,B)) = difference(union(A,A),B). [para(20(a,1),46(a,1,2)),rewrite([23(3)]),flip(a)].
% 1.54/1.81 112 union(difference(A,union(B,C)),difference(union(B,C),A)) = difference(union(A,union(B,C)),intersection(A,union(B,C))). [para(47(a,1),46(a,1,2))].
% 1.54/1.81 127 member(f1(A,B),C) | member(f2(A,C),A) | B = A | member(f1(A,B),B). [resolve(74,a,24,b)].
% 1.54/1.81 129 member(f1(A,B),B) | member(f2(A,B),A) | B = A. [factor(127,a,d)].
% 1.54/1.81 136 intersection(A,B) = A | member(f1(A,intersection(A,B)),intersection(A,A)). [resolve(57,a,45,b)].
% 1.54/1.81 137 intersection(A,union(B,B)) = union(B,B) | member(f1(union(B,B),intersection(A,union(B,B))),B). [resolve(57,a,44,a),rewrite([17(2),17(7)])].
% 1.54/1.81 170 intersection(A,B) = B | -member(f1(intersection(A,B),B),intersection(A,B)). [resolve(61,a,43,c),flip(b),merge(b)].
% 1.54/1.81 239 difference(A,B) = A | -member(f1(difference(A,B),A),difference(A,B)). [resolve(65,a,43,c),flip(b),merge(b)].
% 1.54/1.81 363 -member(A,difference(union(B,B),C)) | -member(A,intersection(B,C)). [para(101(a,1),25(a,2))].
% 1.54/1.81 522 -member(A,difference(difference(union(B,B),C),D)) | -member(A,intersection(D,difference(B,C))). [para(23(a,1),363(a,2,1)),rewrite([17(6)])].
% 1.54/1.81 561 -member(A,difference(difference(union(B,B),C),D)) | -member(A,intersection(D,difference(B,intersection(C,union(B,B))))). [para(20(a,1),522(a,2,1)),rewrite([17(6)])].
% 1.54/1.81 585 member(f2(A,B),A) | B = A | -member(f1(A,B),A). [resolve(129,a,43,c),merge(c)].
% 1.54/1.81 873 union(A,B) = A | -member(f1(union(A,B),A),A). [resolve(53,a,43,b),flip(b),merge(b)].
% 1.54/1.81 966 union(A,A) = A. [resolve(873,b,85,a),merge(b)].
% 1.54/1.81 1039 -member(A,difference(difference(B,C),D)) | -member(A,intersection(D,difference(B,C))). [back_rewrite(561),rewrite([966(1),966(4),17(4),20(5)])].
% 1.54/1.81 1074 intersection(A,B) = B | member(f1(B,intersection(A,B)),B). [back_rewrite(137),rewrite([966(1),966(2),966(3),966(3)])].
% 1.54/1.81 1093 union(A,B) = A | -member(f1(A,union(A,B)),A). [resolve(54,a,43,c),merge(b)].
% 1.54/1.81 1212 intersection(A,A) = A | -member(f1(A,intersection(A,A)),A). [resolve(136,b,43,c),merge(b)].
% 1.54/1.81 1273 intersection(A,A) = A. [resolve(1212,b,1074,b),merge(b)].
% 1.54/1.81 1381 difference(A,A) = B | member(f1(B,difference(A,A)),B). [resolve(62,a,48,a),merge(c),merge(d)].
% 1.54/1.81 1429 difference(A,A) = B | member(f2(B,difference(A,A)),B). [resolve(1381,b,585,c),merge(c)].
% 1.54/1.81 1430 difference(difference(A,A),B) = difference(A,A). [resolve(1381,b,239,b),flip(a),merge(b)].
% 1.54/1.81 1431 intersection(A,difference(B,B)) = difference(B,B). [resolve(1381,b,170,b),flip(a),merge(b)].
% 1.54/1.81 1446 union(difference(A,A),difference(B,C)) = difference(union(B,difference(A,A)),C). [para(1430(a,1),23(a,1,1)),rewrite([16(5)])].
% 1.54/1.81 1447 union(difference(A,B),difference(C,C)) = difference(union(A,difference(C,C)),B). [para(1430(a,1),23(a,1,2))].
% 1.54/1.81 1451 -member(A,difference(B,B)). [para(1430(a,1),1039(b,2,2)),rewrite([1430(2),1430(2),1431(4)]),merge(b)].
% 1.54/1.81 1452 member(f1(difference(A,A),B),B) | difference(A,A) = B. [para(1431(a,1),58(a,1,1)),rewrite([1431(5)])].
% 1.54/1.81 1519 difference(A,A) = difference(B,B). [resolve(1451,a,1429,b)].
% 1.54/1.81 1523 -member(A,difference(union(B,difference(C,C)),B)). [ur(40,b,1451,a,c,1451,a),rewrite([1446(3)])].
% 1.54/1.81 1524 difference(A,A) = c_0. [new_symbol(1519)].
% 1.54/1.81 1525 -member(A,difference(union(B,c_0),B)). [back_rewrite(1523),rewrite([1524(1)])].
% 1.54/1.81 1546 member(f1(c_0,A),A) | c_0 = A. [back_rewrite(1452),rewrite([1524(1),1524(4)])].
% 1.54/1.81 1547 -member(A,c_0). [back_rewrite(1451),rewrite([1524(1)])].
% 1.54/1.81 1549 union(c_0,difference(A,B)) = difference(union(A,c_0),B). [back_rewrite(1447),rewrite([1524(2),16(3),1524(4)])].
% 1.54/1.81 1583 -member(A,difference(union(c_0,union(B,c_0)),B)). [ur(42,a,1525,a,c,1525,a),rewrite([16(5),1549(5),16(4)])].
% 1.54/1.81 1599 -member(A,difference(union(c_0,union(c_0,union(B,c_0))),B)). [ur(42,a,1525,a,c,1583,a),rewrite([16(7),1549(7),16(6)])].
% 1.54/1.81 1603 difference(union(A,c_0),B) = difference(union(A,B),B). [para(1524(a,1),23(a,1,1)),rewrite([1549(3),16(4)])].
% 1.54/1.81 1618 difference(union(c_0,union(c_0,union(A,c_0))),A) = c_0. [resolve(1599,a,1546,a),flip(a)].
% 1.54/1.81 1671 union(difference(union(A,B),B),difference(B,union(A,c_0))) = difference(union(B,union(A,c_0)),intersection(B,union(A,c_0))). [para(1603(a,1),22(a,2,1)),rewrite([22(3),16(7),112(7)]),flip(a)].
% 1.54/1.81 1904 difference(union(A,union(c_0,union(c_0,union(B,c_0)))),intersection(B,union(c_0,union(c_0,union(B,c_0))))) = difference(union(A,c_0),intersection(B,union(c_0,union(c_0,union(B,c_0))))). [para(1618(a,1),46(a,1,1)),rewrite([17(8),1549(10),16(17),17(24)]),flip(a)].
% 1.54/1.81 1914 member(f1(A,union(B,c_0)),B) | union(B,c_0) = A | member(f1(A,union(B,c_0)),A). [resolve(75,a,1547,a),rewrite([16(2),16(6),16(9)])].
% 1.54/1.81 1964 member(f1(A,union(A,c_0)),A) | union(A,c_0) = A. [factor(1914,a,c)].
% 1.54/1.81 4204 union(A,c_0) = A. [resolve(1964,a,1093,b),merge(b)].
% 1.54/1.81 5475 difference(union(A,B),B) = difference(A,B). [back_rewrite(1904),rewrite([4204(4),16(3),4204(3),16(2),4204(2),4204(5),16(4),4204(4),16(3),4204(3),1273(2),4204(4),4204(6),16(5),4204(5),16(4),4204(4),1273(3)])].
% 1.54/1.81 5538 union(difference(A,B),difference(B,A)) = difference(union(A,B),intersection(A,B)). [back_rewrite(1671),rewrite([5475(2),4204(3),4204(5),16(4),4204(6),17(5)])].
% 1.54/1.81 5539 $F. [resolve(5538,a,27,a)].
% 1.54/1.81
% 1.54/1.81 % SZS output end Refutation
% 1.54/1.81 ============================== end of proof ==========================
% 1.54/1.81
% 1.54/1.81 ============================== STATISTICS ============================
% 1.54/1.81
% 1.54/1.81 Given=210. Generated=11807. Kept=5522. proofs=1.
% 1.54/1.81 Usable=139. Sos=1655. Demods=53. Limbo=1334, Disabled=2420. Hints=0.
% 1.54/1.81 Megabytes=6.38.
% 1.54/1.81 User_CPU=0.81, System_CPU=0.02, Wall_clock=1.
% 1.54/1.81
% 1.54/1.81 ============================== end of statistics =====================
% 1.54/1.81
% 1.54/1.81 ============================== end of search =========================
% 1.54/1.81
% 1.54/1.81 THEOREM PROVED
% 1.54/1.81 % SZS status Theorem
% 1.54/1.81
% 1.54/1.81 Exiting with 1 proof.
% 1.54/1.81
% 1.54/1.81 Process 3471 exit (max_proofs) Mon Jul 11 05:48:01 2022
% 1.54/1.81 Prover9 interrupted
%------------------------------------------------------------------------------