TSTP Solution File: SET598+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:30:35 EDT 2022
% Result : Theorem 0.78s 1.10s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n010.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 : Mon Jul 11 08:36:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.47/1.04 ============================== Prover9 ===============================
% 0.47/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.04 Process 31699 was started by sandbox2 on n010.cluster.edu,
% 0.47/1.04 Mon Jul 11 08:36:46 2022
% 0.47/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31546_n010.cluster.edu".
% 0.47/1.04 ============================== end of head ===========================
% 0.47/1.04
% 0.47/1.04 ============================== INPUT =================================
% 0.47/1.04
% 0.47/1.04 % Reading from file /tmp/Prover9_31546_n010.cluster.edu
% 0.47/1.04
% 0.47/1.04 set(prolog_style_variables).
% 0.47/1.04 set(auto2).
% 0.47/1.04 % set(auto2) -> set(auto).
% 0.47/1.04 % set(auto) -> set(auto_inference).
% 0.47/1.04 % set(auto) -> set(auto_setup).
% 0.47/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.47/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.04 % set(auto) -> set(auto_limits).
% 0.47/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.04 % set(auto) -> set(auto_denials).
% 0.47/1.04 % set(auto) -> set(auto_process).
% 0.47/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.47/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.47/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.47/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.47/1.04 % set(auto2) -> assign(stats, some).
% 0.47/1.04 % set(auto2) -> clear(echo_input).
% 0.47/1.04 % set(auto2) -> set(quiet).
% 0.47/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.04 % set(auto2) -> clear(print_given).
% 0.47/1.04 assign(lrs_ticks,-1).
% 0.47/1.04 assign(sos_limit,10000).
% 0.47/1.04 assign(order,kbo).
% 0.47/1.04 set(lex_order_vars).
% 0.47/1.04 clear(print_given).
% 0.47/1.04
% 0.47/1.04 % formulas(sos). % not echoed (9 formulas)
% 0.47/1.04
% 0.47/1.04 ============================== end of input ==========================
% 0.47/1.04
% 0.47/1.04 % From the command line: assign(max_seconds, 300).
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.04
% 0.47/1.04 % Formulas that are not ordinary clauses:
% 0.47/1.04 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 2 (all B all C all D (subset(B,C) & subset(B,D) -> subset(B,intersection(C,D)))) # label(intersection_of_subsets) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 3 (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].
% 0.47/1.04 4 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 6 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.47/1.04 9 -(all B all C all D (B = intersection(C,D) <-> subset(B,C) & subset(B,D) & (all E (subset(E,C) & subset(E,D) -> subset(E,B))))) # label(prove_th57) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.47/1.04
% 0.47/1.04 ============================== end of process non-clausal formulas ===
% 0.47/1.04
% 0.47/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.04
% 0.47/1.04 ============================== PREDICATE ELIMINATION =================
% 0.47/1.04
% 0.47/1.04 ============================== end predicate elimination =============
% 0.47/1.04
% 0.47/1.04 Auto_denials: (non-Horn, no changes).
% 0.47/1.04
% 0.47/1.04 Term ordering decisions:
% 0.47/1.04 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. intersection=1. f1=1. f2=1.
% 0.47/1.04
% 0.47/1.04 ============================== end of process initial clauses ========
% 0.47/1.04
% 0.47/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.47/1.04
% 0.47/1.04 ============================== end of clauses for search =============
% 0.78/1.10
% 0.78/1.10 ============================== SEARCH ================================
% 0.78/1.10
% 0.78/1.10 % Starting search at 0.01 seconds.
% 0.78/1.10
% 0.78/1.10 ============================== PROOF =================================
% 0.78/1.10 % SZS status Theorem
% 0.78/1.10 % SZS output start Refutation
% 0.78/1.10
% 0.78/1.10 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.78/1.10 % Length of proof is 49.
% 0.78/1.10 % Level of proof is 15.
% 0.78/1.10 % Maximum clause weight is 15.000.
% 0.78/1.10 % Given clauses 164.
% 0.78/1.10
% 0.78/1.10 1 (all B all C subset(intersection(B,C),B)) # label(intersection_is_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 2 (all B all C all D (subset(B,C) & subset(B,D) -> subset(B,intersection(C,D)))) # label(intersection_of_subsets) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 6 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.10 9 -(all B all C all D (B = intersection(C,D) <-> subset(B,C) & subset(B,D) & (all E (subset(E,C) & subset(E,D) -> subset(E,B))))) # label(prove_th57) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.10 10 subset(A,A) # label(reflexivity_of_subset) # label(axiom). [clausify(7)].
% 0.78/1.10 11 subset(intersection(A,B),A) # label(intersection_is_subset) # label(axiom). [clausify(1)].
% 0.78/1.10 12 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(6)].
% 0.78/1.10 14 intersection(c2,c3) = c1 | subset(c1,c2) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 15 intersection(c2,c3) = c1 | subset(c1,c3) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 17 intersection(c2,c3) != c1 | -subset(c1,c2) | -subset(c1,c3) | -subset(c4,c1) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 24 A = B | -subset(B,A) | -subset(A,B) # label(equal_defn) # label(axiom). [clausify(5)].
% 0.78/1.10 27 -subset(A,B) | -subset(A,C) | subset(A,intersection(B,C)) # label(intersection_of_subsets) # label(axiom). [clausify(2)].
% 0.78/1.10 30 intersection(c2,c3) = c1 | -subset(A,c2) | -subset(A,c3) | subset(A,c1) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 31 intersection(c2,c3) != c1 | -subset(c1,c2) | -subset(c1,c3) | subset(c4,c2) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 32 intersection(c2,c3) != c1 | -subset(c1,c2) | -subset(c1,c3) | subset(c4,c3) # label(prove_th57) # label(negated_conjecture). [clausify(9)].
% 0.78/1.10 35 subset(intersection(A,B),B). [para(12(a,1),11(a,1))].
% 0.78/1.10 52 intersection(A,B) = A | -subset(A,intersection(A,B)). [resolve(24,b,11,a),flip(a)].
% 0.78/1.10 64 -subset(A,B) | subset(A,intersection(A,B)). [resolve(27,a,10,a)].
% 0.78/1.10 70 intersection(c2,c3) = c1 | -subset(intersection(A,c3),c2) | subset(intersection(A,c3),c1). [resolve(30,c,11,a),rewrite([12(7),12(11)])].
% 0.78/1.10 88 subset(c1,intersection(c1,c3)) | intersection(c2,c3) = c1. [resolve(64,a,15,b)].
% 0.78/1.10 89 subset(c1,intersection(c1,c2)) | intersection(c2,c3) = c1. [resolve(64,a,14,b)].
% 0.78/1.10 144 intersection(c2,c3) = c1 | intersection(c1,c3) = c1. [resolve(88,a,52,b)].
% 0.78/1.10 146 intersection(c2,c3) = c1 | intersection(c1,c2) = c1. [resolve(89,a,52,b)].
% 0.78/1.10 153 intersection(c1,c3) = c1 | subset(c1,c3). [para(144(a,1),35(a,1))].
% 0.78/1.10 172 intersection(c1,c3) = c1 | subset(c1,intersection(c1,c3)). [resolve(153,b,64,a)].
% 0.78/1.10 179 intersection(c1,c2) = c1 | subset(c1,c2). [para(146(a,1),11(a,1))].
% 0.78/1.10 192 intersection(c1,c2) = c1 | subset(c1,intersection(c1,c2)). [resolve(179,b,64,a)].
% 0.78/1.10 215 intersection(c1,c3) = c1. [resolve(172,b,52,b),merge(b)].
% 0.78/1.10 226 subset(c1,c3). [para(215(a,1),35(a,1))].
% 0.78/1.10 228 intersection(c2,c3) != c1 | -subset(c1,c2) | subset(c4,c3). [back_unit_del(32),unit_del(c,226)].
% 0.78/1.10 229 intersection(c2,c3) != c1 | -subset(c1,c2) | subset(c4,c2). [back_unit_del(31),unit_del(c,226)].
% 0.78/1.10 230 intersection(c2,c3) != c1 | -subset(c1,c2) | -subset(c4,c1). [back_unit_del(17),unit_del(c,226)].
% 0.78/1.10 231 -subset(c1,A) | subset(c1,intersection(A,c3)). [resolve(226,a,27,b)].
% 0.78/1.10 311 intersection(c1,c2) = c1. [resolve(192,b,52,b),merge(b)].
% 0.78/1.10 313 subset(c1,c2). [para(311(a,1),35(a,1))].
% 0.78/1.10 318 intersection(c2,c3) != c1 | -subset(c4,c1). [back_unit_del(230),unit_del(b,313)].
% 0.78/1.10 319 intersection(c2,c3) != c1 | subset(c4,c2). [back_unit_del(229),unit_del(b,313)].
% 0.78/1.10 320 intersection(c2,c3) != c1 | subset(c4,c3). [back_unit_del(228),unit_del(b,313)].
% 0.78/1.10 323 subset(c1,intersection(c2,c3)). [resolve(313,a,231,a)].
% 0.78/1.10 327 intersection(c2,c3) = c1 | -subset(intersection(c2,c3),c1). [resolve(323,a,24,c),flip(a)].
% 0.78/1.10 432 intersection(c2,c3) = c1 | subset(intersection(c2,c3),c1). [resolve(70,b,11,a)].
% 0.78/1.10 433 intersection(c2,c3) = c1. [resolve(432,b,327,b),merge(b)].
% 0.78/1.10 436 subset(c4,c3). [back_rewrite(320),rewrite([433(3)]),xx(a)].
% 0.78/1.10 437 subset(c4,c2). [back_rewrite(319),rewrite([433(3)]),xx(a)].
% 0.78/1.10 438 -subset(c4,c1). [back_rewrite(318),rewrite([433(3)]),xx(a)].
% 0.78/1.10 445 -subset(c4,A) | subset(c4,intersection(A,c3)). [resolve(436,a,27,b)].
% 0.78/1.10 523 $F. [resolve(445,a,437,a),rewrite([433(4)]),unit_del(a,438)].
% 0.78/1.10
% 0.78/1.10 % SZS output end Refutation
% 0.78/1.10 ============================== end of proof ==========================
% 0.78/1.10
% 0.78/1.10 ============================== STATISTICS ============================
% 0.78/1.10
% 0.78/1.10 Given=164. Generated=1808. Kept=513. proofs=1.
% 0.78/1.10 Usable=121. Sos=245. Demods=11. Limbo=0, Disabled=170. Hints=0.
% 0.78/1.10 Megabytes=0.38.
% 0.78/1.10 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.78/1.10
% 0.78/1.10 ============================== end of statistics =====================
% 0.78/1.10
% 0.78/1.10 ============================== end of search =========================
% 0.78/1.10
% 0.78/1.10 THEOREM PROVED
% 0.78/1.10 % SZS status Theorem
% 0.78/1.10
% 0.78/1.10 Exiting with 1 proof.
% 0.78/1.10
% 0.78/1.10 Process 31699 exit (max_proofs) Mon Jul 11 08:36:46 2022
% 0.78/1.10 Prover9 interrupted
%------------------------------------------------------------------------------