TSTP Solution File: SET601+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET601+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n014.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 04:30:37 EDT 2022
% Result : Theorem 0.70s 1.17s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET601+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 : n014.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 : Sun Jul 10 22:28:04 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.96 ============================== Prover9 ===============================
% 0.66/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.96 Process 28838 was started by sandbox on n014.cluster.edu,
% 0.66/0.96 Sun Jul 10 22:28:05 2022
% 0.66/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_28685_n014.cluster.edu".
% 0.66/0.96 ============================== end of head ===========================
% 0.66/0.96
% 0.66/0.96 ============================== INPUT =================================
% 0.66/0.96
% 0.66/0.96 % Reading from file /tmp/Prover9_28685_n014.cluster.edu
% 0.66/0.96
% 0.66/0.96 set(prolog_style_variables).
% 0.66/0.96 set(auto2).
% 0.66/0.96 % set(auto2) -> set(auto).
% 0.66/0.96 % set(auto) -> set(auto_inference).
% 0.66/0.96 % set(auto) -> set(auto_setup).
% 0.66/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.96 % set(auto) -> set(auto_limits).
% 0.66/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.96 % set(auto) -> set(auto_denials).
% 0.66/0.96 % set(auto) -> set(auto_process).
% 0.66/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.96 % set(auto2) -> assign(stats, some).
% 0.66/0.96 % set(auto2) -> clear(echo_input).
% 0.66/0.96 % set(auto2) -> set(quiet).
% 0.66/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.96 % set(auto2) -> clear(print_given).
% 0.66/0.96 assign(lrs_ticks,-1).
% 0.66/0.96 assign(sos_limit,10000).
% 0.66/0.96 assign(order,kbo).
% 0.66/0.96 set(lex_order_vars).
% 0.66/0.96 clear(print_given).
% 0.66/0.96
% 0.66/0.96 % formulas(sos). % not echoed (14 formulas)
% 0.66/0.96
% 0.66/0.96 ============================== end of input ==========================
% 0.66/0.96
% 0.66/0.96 % From the command line: assign(max_seconds, 300).
% 0.66/0.96
% 0.66/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.96
% 0.66/0.96 % Formulas that are not ordinary clauses:
% 0.66/0.96 1 (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].
% 0.66/0.96 2 (all B intersection(B,B) = B) # label(idempotency_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 3 (all B all C all D intersection(intersection(B,C),D) = intersection(B,intersection(C,D))) # label(associativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 4 (all B all C union(B,intersection(B,C)) = B) # label(union_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 5 (all B all C all D union(B,intersection(C,D)) = intersection(union(B,C),union(B,D))) # label(union_distributes_over_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 6 (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].
% 0.66/0.96 7 (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].
% 0.66/0.96 8 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 9 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 10 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 11 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 12 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 13 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 14 -(all B all C all D union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B))) # label(prove_th72) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.17
% 0.70/1.17 ============================== end of process non-clausal formulas ===
% 0.70/1.17
% 0.70/1.17 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.17
% 0.70/1.17 ============================== PREDICATE ELIMINATION =================
% 0.70/1.17
% 0.70/1.17 ============================== end predicate elimination =============
% 0.70/1.17
% 0.70/1.17 Auto_denials: (non-Horn, no changes).
% 0.70/1.17
% 0.70/1.17 Term ordering decisions:
% 0.70/1.17 Function symbol KB weights: c1=1. c2=1. c3=1. intersection=1. union=1. f1=1. f2=1.
% 0.70/1.17
% 0.70/1.17 ============================== end of process initial clauses ========
% 0.70/1.17
% 0.70/1.17 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.17
% 0.70/1.17 ============================== end of clauses for search =============
% 0.70/1.17
% 0.70/1.17 ============================== SEARCH ================================
% 0.70/1.17
% 0.70/1.17 % Starting search at 0.01 seconds.
% 0.70/1.17
% 0.70/1.17 ============================== PROOF =================================
% 0.70/1.17 % SZS status Theorem
% 0.70/1.17 % SZS output start Refutation
% 0.70/1.17
% 0.70/1.17 % Proof 1 at 0.21 (+ 0.01) seconds.
% 0.70/1.17 % Length of proof is 48.
% 0.70/1.17 % Level of proof is 13.
% 0.70/1.17 % Maximum clause weight is 23.000.
% 0.70/1.17 % Given clauses 117.
% 0.70/1.17
% 0.70/1.17 1 (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].
% 0.70/1.17 2 (all B intersection(B,B) = B) # label(idempotency_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 3 (all B all C all D intersection(intersection(B,C),D) = intersection(B,intersection(C,D))) # label(associativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 4 (all B all C union(B,intersection(B,C)) = B) # label(union_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 5 (all B all C all D union(B,intersection(C,D)) = intersection(union(B,C),union(B,D))) # label(union_distributes_over_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 9 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 10 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.70/1.17 14 -(all B all C all D union(union(intersection(B,C),intersection(C,D)),intersection(D,B)) = intersection(intersection(union(B,C),union(C,D)),union(D,B))) # label(prove_th72) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.70/1.17 16 intersection(A,A) = A # label(idempotency_of_intersection) # label(axiom). [clausify(2)].
% 0.70/1.17 17 union(A,intersection(A,B)) = A # label(union_intersection) # label(axiom). [clausify(4)].
% 0.70/1.17 18 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(9)].
% 0.70/1.17 19 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(10)].
% 0.70/1.17 21 union(union(A,B),C) = union(A,union(B,C)) # label(associativity_of_union) # label(axiom). [clausify(1)].
% 0.70/1.17 22 union(A,union(B,C)) = union(C,union(A,B)). [copy(21),rewrite([18(2)]),flip(a)].
% 0.70/1.17 23 intersection(intersection(A,B),C) = intersection(A,intersection(B,C)) # label(associativity_of_intersection) # label(axiom). [clausify(3)].
% 0.70/1.17 24 intersection(A,intersection(B,C)) = intersection(C,intersection(A,B)). [copy(23),rewrite([19(2)]),flip(a)].
% 0.70/1.17 25 intersection(union(A,B),union(A,C)) = union(A,intersection(B,C)) # label(union_distributes_over_intersection) # label(axiom). [clausify(5)].
% 0.70/1.17 27 intersection(intersection(union(c1,c2),union(c2,c3)),union(c3,c1)) != union(union(intersection(c1,c2),intersection(c2,c3)),intersection(c3,c1)) # label(prove_th72) # label(negated_conjecture). [clausify(14)].
% 0.70/1.17 28 union(intersection(c1,c2),union(intersection(c1,c3),intersection(c2,c3))) != intersection(union(c1,c2),intersection(union(c1,c3),union(c2,c3))). [copy(27),rewrite([18(10),19(11),24(11,R),19(10),19(21),18(22),22(22,R),18(21)]),flip(a)].
% 0.70/1.17 44 union(A,A) = A. [para(16(a,1),17(a,1,2))].
% 0.70/1.17 45 union(A,union(B,intersection(A,C))) = union(A,B). [para(17(a,1),22(a,2,2)),rewrite([18(2),18(4)])].
% 0.70/1.17 47 union(A,union(A,B)) = union(A,B). [para(25(a,1),17(a,1,2)),rewrite([22(4,R),22(3),18(2),45(3),18(1)])].
% 0.70/1.17 48 intersection(A,union(A,B)) = A. [para(17(a,1),25(a,1,1)),rewrite([19(4),24(4,R),19(3),17(5)])].
% 0.70/1.17 49 intersection(union(A,B),union(B,C)) = union(B,intersection(A,C)). [para(18(a,1),25(a,1,1))].
% 0.70/1.17 50 intersection(union(A,union(B,C)),union(B,D)) = union(B,intersection(D,union(A,C))). [para(22(a,1),25(a,1,1)),rewrite([18(5),19(6)])].
% 0.70/1.17 51 intersection(union(A,union(B,C)),union(C,D)) = union(C,intersection(D,union(A,B))). [para(22(a,2),25(a,1,1)),rewrite([19(6)])].
% 0.70/1.17 93 intersection(A,intersection(B,union(A,C))) = intersection(A,B). [para(48(a,1),24(a,2,2)),rewrite([19(2),19(4)])].
% 0.70/1.17 94 union(A,intersection(B,union(A,C))) = union(A,intersection(C,B)). [para(47(a,1),25(a,1,1)),rewrite([25(3),19(4)]),flip(a)].
% 0.70/1.17 126 union(intersection(A,B),intersection(A,C)) = intersection(A,union(C,intersection(A,B))). [para(17(a,1),49(a,1,1)),rewrite([18(2)]),flip(a)].
% 0.70/1.17 130 union(A,intersection(B,A)) = intersection(A,union(B,A)). [para(44(a,1),49(a,1,2)),rewrite([19(2)]),flip(a)].
% 0.70/1.17 137 union(A,intersection(intersection(A,B),union(C,D))) = intersection(A,union(C,union(A,D))). [para(17(a,1),50(a,1,2)),rewrite([19(3)]),flip(a)].
% 0.70/1.17 150 union(A,intersection(intersection(A,B),union(C,D))) = A. [back_rewrite(137),rewrite([22(6,R),18(5),48(7)])].
% 0.70/1.17 156 intersection(intersection(A,B),union(C,intersection(A,B))) = intersection(A,union(intersection(B,C),intersection(A,B))). [para(24(a,1),130(a,1,2)),rewrite([19(2),24(3,R),19(2),126(4)]),flip(a)].
% 0.70/1.17 160 union(A,intersection(B,intersection(intersection(A,C),union(D,E)))) = A. [para(150(a,1),25(a,1,1)),rewrite([48(2),19(4)]),flip(a)].
% 0.70/1.17 162 intersection(A,union(B,A)) = A. [para(150(a,1),49(a,1,2)),rewrite([19(2),160(7)])].
% 0.70/1.17 166 intersection(A,union(intersection(B,C),intersection(A,B))) = intersection(A,B). [back_rewrite(156),rewrite([162(4)]),flip(a)].
% 0.70/1.17 173 union(intersection(A,B),intersection(C,union(A,D))) = intersection(union(A,D),union(C,intersection(A,B))). [para(45(a,1),51(a,1,1)),rewrite([18(3)]),flip(a)].
% 0.70/1.17 863 intersection(A,union(B,intersection(A,B))) = intersection(A,B). [para(16(a,1),166(a,1,2,1))].
% 0.70/1.17 865 intersection(A,union(intersection(B,C),intersection(A,C))) = intersection(A,C). [para(19(a,1),166(a,1,2,1))].
% 0.70/1.17 877 intersection(union(A,B),union(C,B)) = union(B,intersection(A,C)). [para(863(a,1),51(a,2,2)),rewrite([19(1),18(2),45(3),18(2),19(4)])].
% 0.70/1.17 878 union(intersection(c1,c2),union(intersection(c1,c3),intersection(c2,c3))) != intersection(union(c1,c2),union(c3,intersection(c1,c2))). [back_rewrite(28),rewrite([877(21)])].
% 0.70/1.17 970 union(intersection(A,B),intersection(B,C)) = intersection(B,union(C,intersection(A,B))). [para(865(a,1),25(a,1)),rewrite([18(2),19(3),18(6),19(7),93(8),19(5)]),flip(a)].
% 0.70/1.17 973 intersection(A,union(B,intersection(A,C))) = intersection(A,union(B,C)). [para(48(a,1),865(a,1,2,1)),rewrite([94(3),19(1)])].
% 0.70/1.17 974 union(intersection(A,B),intersection(C,B)) = intersection(B,union(C,intersection(A,B))). [para(865(a,1),49(a,1)),rewrite([19(3),19(7),93(8)]),flip(a)].
% 0.70/1.17 990 union(intersection(A,B),intersection(A,C)) = intersection(A,union(B,C)). [back_rewrite(126),rewrite([973(6),18(4)])].
% 0.70/1.17 991 union(intersection(c1,c2),intersection(c3,union(c2,intersection(c1,c3)))) != intersection(union(c1,c2),union(c3,intersection(c1,c2))). [back_rewrite(878),rewrite([974(10)])].
% 0.70/1.17 1027 intersection(A,union(B,intersection(C,A))) = intersection(A,union(C,B)). [para(19(a,1),990(a,1,1)),rewrite([970(3)])].
% 0.70/1.17 1049 $F. [back_rewrite(991),rewrite([1027(10),173(9)]),xx(a)].
% 0.70/1.17
% 0.70/1.17 % SZS output end Refutation
% 0.70/1.17 ============================== end of proof ==========================
% 0.70/1.17
% 0.70/1.17 ============================== STATISTICS ============================
% 0.70/1.17
% 0.70/1.17 Given=117. Generated=5117. Kept=1031. proofs=1.
% 0.70/1.17 Usable=104. Sos=837. Demods=140. Limbo=22, Disabled=93. Hints=0.
% 0.70/1.17 Megabytes=0.94.
% 0.70/1.17 User_CPU=0.21, System_CPU=0.01, Wall_clock=0.
% 0.70/1.17
% 0.70/1.17 ============================== end of statistics =====================
% 0.70/1.17
% 0.70/1.17 ============================== end of search =========================
% 0.70/1.17
% 0.70/1.17 THEOREM PROVED
% 0.70/1.17 % SZS status Theorem
% 0.70/1.17
% 0.70/1.17 Exiting with 1 proof.
% 0.70/1.17
% 0.70/1.17 Process 28838 exit (max_proofs) Sun Jul 10 22:28:05 2022
% 0.92/1.17 Prover9 interrupted
%------------------------------------------------------------------------------