TSTP Solution File: SET596+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 04:30:34 EDT 2022
% Result : Theorem 1.41s 1.73s
% Output : Refutation 1.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET596+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n015.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 : Sun Jul 10 19:28:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.45/1.02 ============================== Prover9 ===============================
% 0.45/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.02 Process 12799 was started by sandbox2 on n015.cluster.edu,
% 0.45/1.02 Sun Jul 10 19:28:54 2022
% 0.45/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12646_n015.cluster.edu".
% 0.45/1.02 ============================== end of head ===========================
% 0.45/1.02
% 0.45/1.02 ============================== INPUT =================================
% 0.45/1.02
% 0.45/1.02 % Reading from file /tmp/Prover9_12646_n015.cluster.edu
% 0.45/1.02
% 0.45/1.02 set(prolog_style_variables).
% 0.45/1.02 set(auto2).
% 0.45/1.02 % set(auto2) -> set(auto).
% 0.45/1.02 % set(auto) -> set(auto_inference).
% 0.45/1.02 % set(auto) -> set(auto_setup).
% 0.45/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.02 % set(auto) -> set(auto_limits).
% 0.45/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.02 % set(auto) -> set(auto_denials).
% 0.45/1.02 % set(auto) -> set(auto_process).
% 0.45/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.02 % set(auto2) -> assign(stats, some).
% 0.45/1.02 % set(auto2) -> clear(echo_input).
% 0.45/1.02 % set(auto2) -> set(quiet).
% 0.45/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.02 % set(auto2) -> clear(print_given).
% 0.45/1.02 assign(lrs_ticks,-1).
% 0.45/1.02 assign(sos_limit,10000).
% 0.45/1.02 assign(order,kbo).
% 0.45/1.02 set(lex_order_vars).
% 0.45/1.02 clear(print_given).
% 0.45/1.02
% 0.45/1.02 % formulas(sos). % not echoed (11 formulas)
% 0.45/1.02
% 0.45/1.02 ============================== end of input ==========================
% 0.45/1.02
% 0.45/1.02 % From the command line: assign(max_seconds, 300).
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.02
% 0.45/1.02 % Formulas that are not ordinary clauses:
% 0.45/1.02 1 (all B (subset(B,empty_set) -> B = empty_set)) # label(subset_of_empty_set_is_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 2 (all B all C all D (subset(B,C) -> subset(intersection(B,D),intersection(C,D)))) # label(intersection_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 4 (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].
% 0.45/1.02 5 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 6 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 7 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 8 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 9 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 10 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.02 11 -(all B all C all D (subset(B,C) & intersection(C,D) = empty_set -> intersection(B,D) = empty_set)) # label(prove_th55) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.02
% 0.45/1.02 ============================== end of process non-clausal formulas ===
% 0.45/1.02
% 0.45/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.02
% 0.45/1.02 ============================== PREDICATE ELIMINATION =================
% 0.45/1.02 12 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(9)].
% 0.45/1.02 13 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(9)].
% 0.45/1.02 Derived: -member(A,B) | member(f2(B),B). [resolve(12,a,13,a)].
% 1.41/1.73
% 1.41/1.73 ============================== end predicate elimination =============
% 1.41/1.73
% 1.41/1.73 Auto_denials: (non-Horn, no changes).
% 1.41/1.73
% 1.41/1.73 Term ordering decisions:
% 1.41/1.73
% 1.41/1.73 % Assigning unary symbol f2 kb_weight 0 and highest precedence (11).
% 1.41/1.73 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. intersection=1. f1=1. f3=1. f2=0.
% 1.41/1.73
% 1.41/1.73 ============================== end of process initial clauses ========
% 1.41/1.73
% 1.41/1.73 ============================== CLAUSES FOR SEARCH ====================
% 1.41/1.73
% 1.41/1.73 ============================== end of clauses for search =============
% 1.41/1.73
% 1.41/1.73 ============================== SEARCH ================================
% 1.41/1.73
% 1.41/1.73 % Starting search at 0.01 seconds.
% 1.41/1.73
% 1.41/1.73 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 58 (0.00 of 0.30 sec).
% 1.41/1.73
% 1.41/1.73 ============================== PROOF =================================
% 1.41/1.73 % SZS status Theorem
% 1.41/1.73 % SZS output start Refutation
% 1.41/1.73
% 1.41/1.73 % Proof 1 at 0.71 (+ 0.01) seconds.
% 1.41/1.73 % Length of proof is 31.
% 1.41/1.73 % Level of proof is 10.
% 1.41/1.73 % Maximum clause weight is 16.000.
% 1.41/1.73 % Given clauses 1048.
% 1.41/1.73
% 1.41/1.73 1 (all B (subset(B,empty_set) -> B = empty_set)) # label(subset_of_empty_set_is_empty_set) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.73 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.73 4 (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].
% 1.41/1.73 5 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 1.41/1.73 11 -(all B all C all D (subset(B,C) & intersection(C,D) = empty_set -> intersection(B,D) = empty_set)) # label(prove_th55) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.41/1.73 15 subset(c1,c2) # label(prove_th55) # label(negated_conjecture). [clausify(11)].
% 1.41/1.73 16 intersection(c2,c3) = empty_set # label(prove_th55) # label(negated_conjecture). [clausify(11)].
% 1.41/1.73 17 empty_set = intersection(c2,c3). [copy(16),flip(a)].
% 1.41/1.73 19 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(5)].
% 1.41/1.73 21 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(3)].
% 1.41/1.73 22 -member(A,intersection(c2,c3)). [copy(21),rewrite([17(1)])].
% 1.41/1.73 23 intersection(c1,c3) != empty_set # label(prove_th55) # label(negated_conjecture). [clausify(11)].
% 1.41/1.73 24 intersection(c2,c3) != intersection(c1,c3). [copy(23),rewrite([17(4)]),flip(a)].
% 1.41/1.73 25 -subset(A,empty_set) | empty_set = A # label(subset_of_empty_set_is_empty_set) # label(axiom). [clausify(1)].
% 1.41/1.73 26 -subset(A,intersection(c2,c3)) | intersection(c2,c3) = A. [copy(25),rewrite([17(1),17(5)])].
% 1.41/1.73 29 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(4)].
% 1.41/1.73 30 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(4)].
% 1.41/1.73 32 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(5)].
% 1.41/1.73 37 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(4)].
% 1.41/1.73 40 intersection(c2,c3) = c_0. [new_symbol(24)].
% 1.41/1.73 42 -subset(A,c_0) | c_0 = A. [back_rewrite(26),rewrite([40(3),40(5)])].
% 1.41/1.73 43 intersection(c1,c3) != c_0. [back_rewrite(24),rewrite([40(3)]),flip(a)].
% 1.41/1.73 44 -member(A,c_0). [back_rewrite(22),rewrite([40(3)])].
% 1.41/1.73 54 -member(A,c1) | member(A,c2). [resolve(32,a,15,a)].
% 1.41/1.73 77 -subset(intersection(c1,c3),c_0). [ur(42,b,43,a(flip))].
% 1.41/1.73 109 member(f1(intersection(c1,c3),c_0),intersection(c1,c3)). [resolve(77,a,19,a)].
% 1.41/1.73 265 member(f1(intersection(c1,c3),c_0),c3). [resolve(109,a,30,a)].
% 1.41/1.73 266 member(f1(intersection(c1,c3),c_0),c1). [resolve(109,a,29,a)].
% 1.41/1.73 288 member(f1(intersection(c1,c3),c_0),intersection(A,c3)) | -member(f1(intersection(c1,c3),c_0),A). [resolve(265,a,37,c)].
% 1.41/1.73 301 member(f1(intersection(c1,c3),c_0),c2). [resolve(266,a,54,a)].
% 1.41/1.73 4383 $F. [resolve(288,b,301,a),rewrite([40(8)]),unit_del(a,44)].
% 1.41/1.73
% 1.41/1.73 % SZS output end Refutation
% 1.41/1.73 ============================== end of proof ==========================
% 1.41/1.73
% 1.41/1.73 ============================== STATISTICS ============================
% 1.41/1.73
% 1.41/1.73 Given=1048. Generated=23048. Kept=4365. proofs=1.
% 1.41/1.73 Usable=785. Sos=2207. Demods=5. Limbo=8, Disabled=1389. Hints=0.
% 1.41/1.73 Megabytes=3.06.
% 1.41/1.73 User_CPU=0.71, System_CPU=0.01, Wall_clock=0.
% 1.41/1.73
% 1.41/1.73 ============================== end of statistics =====================
% 1.41/1.73
% 1.41/1.73 ============================== end of search =========================
% 1.41/1.73
% 1.41/1.73 THEOREM PROVED
% 1.41/1.73 % SZS status Theorem
% 1.41/1.73
% 1.41/1.73 Exiting with 1 proof.
% 1.41/1.73
% 1.41/1.73 Process 12799 exit (max_proofs) Sun Jul 10 19:28:54 2022
% 1.41/1.73 Prover9 interrupted
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