TSTP Solution File: SET635+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:31:02 EDT 2022
% Result : Theorem 1.08s 1.33s
% Output : Refutation 1.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n016.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 13:56:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/0.99 ============================== Prover9 ===============================
% 0.44/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.44/0.99 Process 28968 was started by sandbox on n016.cluster.edu,
% 0.44/0.99 Sun Jul 10 13:56:12 2022
% 0.44/0.99 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28815_n016.cluster.edu".
% 0.44/0.99 ============================== end of head ===========================
% 0.44/0.99
% 0.44/0.99 ============================== INPUT =================================
% 0.44/0.99
% 0.44/0.99 % Reading from file /tmp/Prover9_28815_n016.cluster.edu
% 0.44/0.99
% 0.44/0.99 set(prolog_style_variables).
% 0.44/0.99 set(auto2).
% 0.44/0.99 % set(auto2) -> set(auto).
% 0.44/0.99 % set(auto) -> set(auto_inference).
% 0.44/0.99 % set(auto) -> set(auto_setup).
% 0.44/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.44/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/0.99 % set(auto) -> set(auto_limits).
% 0.44/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/0.99 % set(auto) -> set(auto_denials).
% 0.44/0.99 % set(auto) -> set(auto_process).
% 0.44/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.44/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.44/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.44/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.44/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.44/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.44/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.44/0.99 % set(auto2) -> assign(stats, some).
% 0.44/0.99 % set(auto2) -> clear(echo_input).
% 0.44/0.99 % set(auto2) -> set(quiet).
% 0.44/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.44/0.99 % set(auto2) -> clear(print_given).
% 0.44/0.99 assign(lrs_ticks,-1).
% 0.44/0.99 assign(sos_limit,10000).
% 0.44/0.99 assign(order,kbo).
% 0.44/0.99 set(lex_order_vars).
% 0.44/0.99 clear(print_given).
% 0.44/0.99
% 0.44/0.99 % formulas(sos). % not echoed (16 formulas)
% 0.44/0.99
% 0.44/0.99 ============================== end of input ==========================
% 0.44/0.99
% 0.44/0.99 % From the command line: assign(max_seconds, 300).
% 0.44/0.99
% 0.44/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/0.99
% 0.44/0.99 % Formulas that are not ordinary clauses:
% 0.44/0.99 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 2 (all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(difference_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 3 (all B union(B,empty_set) = B) # label(union_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 4 (all B all C all D difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D))) # label(difference_and_intersection_and_union) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 5 (all B all C all D intersection(B,difference(C,D)) = difference(intersection(B,C),D)) # label(difference_and_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 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].
% 0.44/0.99 7 (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].
% 0.44/0.99 8 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 9 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 10 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 11 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 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].
% 0.44/0.99 13 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 14 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/0.99 15 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 16 -(all B all C all D intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D))) # label(prove_th117) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.08/1.33
% 1.08/1.33 ============================== end of process non-clausal formulas ===
% 1.08/1.33
% 1.08/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 1.08/1.33
% 1.08/1.33 ============================== PREDICATE ELIMINATION =================
% 1.08/1.33 17 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(15)].
% 1.08/1.33 18 empty(A) | member(f3(A),A) # label(empty_defn) # label(axiom). [clausify(15)].
% 1.08/1.33 Derived: -member(A,B) | member(f3(B),B). [resolve(17,a,18,a)].
% 1.08/1.33
% 1.08/1.33 ============================== end predicate elimination =============
% 1.08/1.33
% 1.08/1.33 Auto_denials: (non-Horn, no changes).
% 1.08/1.33
% 1.08/1.33 Term ordering decisions:
% 1.08/1.33
% 1.08/1.33 % Assigning unary symbol f3 kb_weight 0 and highest precedence (13).
% 1.08/1.33 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. difference=1. intersection=1. union=1. f1=1. f2=1. f3=0.
% 1.08/1.33
% 1.08/1.33 ============================== end of process initial clauses ========
% 1.08/1.33
% 1.08/1.33 ============================== CLAUSES FOR SEARCH ====================
% 1.08/1.33
% 1.08/1.33 ============================== end of clauses for search =============
% 1.08/1.33
% 1.08/1.33 ============================== SEARCH ================================
% 1.08/1.33
% 1.08/1.33 % Starting search at 0.01 seconds.
% 1.08/1.33
% 1.08/1.33 ============================== PROOF =================================
% 1.08/1.33 % SZS status Theorem
% 1.08/1.33 % SZS output start Refutation
% 1.08/1.33
% 1.08/1.33 % Proof 1 at 0.35 (+ 0.01) seconds.
% 1.08/1.33 % Length of proof is 70.
% 1.08/1.33 % Level of proof is 18.
% 1.08/1.33 % Maximum clause weight is 22.000.
% 1.08/1.33 % Given clauses 176.
% 1.08/1.33
% 1.08/1.33 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 2 (all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(difference_empty_set) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 3 (all B union(B,empty_set) = B) # label(union_empty_set) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 4 (all B all C all D difference(B,intersection(C,D)) = union(difference(B,C),difference(B,D))) # label(difference_and_intersection_and_union) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 5 (all B all C all D intersection(B,difference(C,D)) = difference(intersection(B,C),D)) # label(difference_and_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 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].
% 1.08/1.33 7 (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].
% 1.08/1.33 8 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 10 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 11 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 13 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 14 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 15 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 1.08/1.33 16 -(all B all C all D intersection(B,difference(C,D)) = difference(intersection(B,C),intersection(B,D))) # label(prove_th117) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.08/1.33 17 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(15)].
% 1.08/1.33 18 empty(A) | member(f3(A),A) # label(empty_defn) # label(axiom). [clausify(15)].
% 1.08/1.33 19 subset(A,A) # label(reflexivity_of_subset) # label(axiom). [clausify(13)].
% 1.08/1.33 20 subset(intersection(A,B),A) # label(intersection_is_subset) # label(axiom). [clausify(1)].
% 1.08/1.33 21 union(A,empty_set) = A # label(union_empty_set) # label(axiom). [clausify(3)].
% 1.08/1.33 23 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(11)].
% 1.08/1.33 25 difference(intersection(A,B),C) = intersection(A,difference(B,C)) # label(difference_and_intersection) # label(axiom). [clausify(5)].
% 1.08/1.33 26 intersection(A,difference(B,C)) = difference(intersection(A,B),C). [copy(25),flip(a)].
% 1.08/1.33 27 union(difference(A,B),difference(A,C)) = difference(A,intersection(B,C)) # label(difference_and_intersection_and_union) # label(axiom). [clausify(4)].
% 1.08/1.33 28 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(14)].
% 1.08/1.33 29 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(10)].
% 1.08/1.33 30 -member(A,difference(B,C)) | -member(A,C) # label(difference_defn) # label(axiom). [clausify(7)].
% 1.08/1.33 31 difference(intersection(c1,c2),intersection(c1,c3)) != intersection(c1,difference(c2,c3)) # label(prove_th117) # label(negated_conjecture). [clausify(16)].
% 1.08/1.33 32 difference(intersection(c1,c2),intersection(c1,c3)) != difference(intersection(c1,c2),c3). [copy(31),rewrite([26(12)])].
% 1.08/1.33 35 difference(A,B) != empty_set | subset(A,B) # label(difference_empty_set) # label(axiom). [clausify(2)].
% 1.08/1.33 36 difference(A,B) = empty_set | -subset(A,B) # label(difference_empty_set) # label(axiom). [clausify(2)].
% 1.08/1.33 38 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(6)].
% 1.08/1.33 41 A = B | -subset(B,A) | -subset(A,B) # label(equal_defn) # label(axiom). [clausify(8)].
% 1.08/1.33 46 member(A,difference(B,C)) | -member(A,B) | member(A,C) # label(difference_defn) # label(axiom). [clausify(7)].
% 1.08/1.33 48 -member(A,B) | member(f3(B),B). [resolve(17,a,18,a)].
% 1.08/1.33 50 subset(intersection(A,B),B). [para(23(a,1),20(a,1))].
% 1.08/1.33 51 subset(difference(intersection(A,B),C),A). [para(26(a,1),20(a,1))].
% 1.08/1.33 52 empty_set = A | member(f2(A,empty_set),A). [resolve(29,a,28,c)].
% 1.08/1.33 57 difference(intersection(A,B),A) = empty_set. [resolve(36,b,20,a)].
% 1.08/1.33 58 difference(A,A) = empty_set. [resolve(36,b,19,a)].
% 1.08/1.33 66 member(f2(intersection(A,B),C),B) | intersection(A,B) = C | member(f2(intersection(A,B),C),C). [resolve(38,a,28,b),flip(b)].
% 1.08/1.33 68 member(f2(intersection(A,B),B),B) | intersection(A,B) = B. [factor(66,a,c)].
% 1.08/1.33 100 intersection(A,B) = B | -subset(B,intersection(A,B)). [resolve(50,a,41,c)].
% 1.08/1.33 101 difference(intersection(A,B),B) = empty_set. [resolve(50,a,36,b)].
% 1.08/1.33 123 union(empty_set,difference(A,B)) = difference(A,intersection(A,B)). [para(58(a,1),27(a,1,1))].
% 1.08/1.33 133 union(empty_set,difference(intersection(A,B),C)) = difference(intersection(A,B),intersection(A,C)). [para(57(a,1),27(a,1,1))].
% 1.08/1.33 143 empty_set = A | member(f3(A),A). [resolve(52,b,48,a)].
% 1.08/1.33 158 intersection(A,B) = empty_set | member(f3(intersection(A,B)),B). [resolve(143,b,38,a),flip(a)].
% 1.08/1.33 522 -member(A,union(empty_set,difference(B,C))) | -member(A,intersection(B,C)). [para(123(a,2),30(a,2))].
% 1.08/1.33 525 difference(A,intersection(A,A)) = empty_set. [para(58(a,1),123(a,1,2)),rewrite([21(3)]),flip(a)].
% 1.08/1.33 548 subset(A,intersection(A,A)). [resolve(525,a,35,a)].
% 1.08/1.33 609 -member(A,union(empty_set,union(empty_set,difference(B,C)))) | -member(A,intersection(B,intersection(B,C))). [para(123(a,2),522(a,2,2))].
% 1.08/1.33 644 -member(A,union(empty_set,union(empty_set,difference(B,difference(C,D))))) | -member(A,difference(intersection(B,intersection(B,C)),D)). [para(26(a,1),609(b,2,2)),rewrite([26(10)])].
% 1.08/1.33 707 intersection(A,A) = A. [resolve(548,a,100,b)].
% 1.08/1.33 716 difference(difference(A,B),B) = difference(A,B). [para(707(a,1),26(a,1)),rewrite([23(3),26(3),707(2)]),flip(a)].
% 1.08/1.33 717 subset(difference(A,B),A). [para(707(a,1),51(a,1,1))].
% 1.08/1.33 727 difference(A,B) = A | -subset(A,difference(A,B)). [resolve(717,a,41,c)].
% 1.08/1.33 839 intersection(A,B) = B | member(f3(B),B). [resolve(68,a,48,a)].
% 1.08/1.33 930 union(empty_set,difference(A,B)) = difference(difference(A,B),empty_set). [para(716(a,1),123(a,1,2)),rewrite([23(6),26(6),23(5),101(6)])].
% 1.08/1.33 934 -member(A,difference(difference(B,difference(C,D)),empty_set)) | -member(A,difference(difference(intersection(B,intersection(B,C)),difference(C,D)),D)). [para(716(a,1),644(a,2,2,2)),rewrite([930(5),930(6),716(6),23(10),26(10),23(8),26(11),23(9),26(9),23(7),716(11)])].
% 1.08/1.34 1116 difference(difference(intersection(A,B),C),empty_set) = difference(intersection(A,B),intersection(A,C)). [back_rewrite(133),rewrite([930(4)])].
% 1.08/1.34 1724 intersection(A,B) = empty_set | member(f3(B),B). [resolve(158,b,48,a)].
% 1.08/1.34 2080 -member(A,difference(difference(B,difference(B,C)),empty_set)) | -member(A,difference(difference(B,difference(B,C)),C)). [para(707(a,1),934(b,2,1,1,2)),rewrite([707(6)])].
% 1.08/1.34 2082 -member(A,difference(difference(B,difference(B,empty_set)),empty_set)). [factor(2080,a,b)].
% 1.08/1.34 2087 -member(A,difference(B,difference(B,empty_set))). [ur(46,a,2082,a,c,29,a)].
% 1.08/1.34 2089 difference(intersection(A,B),difference(B,empty_set)) = empty_set. [resolve(2087,a,1724,b),rewrite([26(4)])].
% 1.08/1.34 2091 difference(A,difference(A,empty_set)) = empty_set. [resolve(2087,a,839,b),rewrite([26(4),2089(4)]),flip(a)].
% 1.08/1.34 2154 subset(A,difference(A,empty_set)). [resolve(2091,a,35,a)].
% 1.08/1.34 2162 difference(A,empty_set) = A. [resolve(2154,a,727,b)].
% 1.08/1.34 2769 difference(intersection(A,B),intersection(A,C)) = difference(intersection(A,B),C). [back_rewrite(1116),rewrite([2162(4)]),flip(a)].
% 1.08/1.34 2770 $F. [resolve(2769,a,32,a)].
% 1.08/1.34
% 1.08/1.34 % SZS output end Refutation
% 1.08/1.34 ============================== end of proof ==========================
% 1.08/1.34
% 1.08/1.34 ============================== STATISTICS ============================
% 1.08/1.34
% 1.08/1.34 Given=176. Generated=6639. Kept=2749. proofs=1.
% 1.08/1.34 Usable=134. Sos=817. Demods=49. Limbo=607, Disabled=1220. Hints=0.
% 1.08/1.34 Megabytes=2.83.
% 1.08/1.34 User_CPU=0.35, System_CPU=0.01, Wall_clock=0.
% 1.08/1.34
% 1.08/1.34 ============================== end of statistics =====================
% 1.08/1.34
% 1.08/1.34 ============================== end of search =========================
% 1.08/1.34
% 1.08/1.34 THEOREM PROVED
% 1.08/1.34 % SZS status Theorem
% 1.08/1.34
% 1.08/1.34 Exiting with 1 proof.
% 1.08/1.34
% 1.08/1.34 Process 28968 exit (max_proofs) Sun Jul 10 13:56:12 2022
% 1.08/1.34 Prover9 interrupted
%------------------------------------------------------------------------------