TSTP Solution File: SET014+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET014+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n011.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 04:25:40 EDT 2022
% Result : Theorem 0.44s 1.02s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET014+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 : n011.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 13:10:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.44/1.02 ============================== Prover9 ===============================
% 0.44/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.02 Process 7358 was started by sandbox2 on n011.cluster.edu,
% 0.44/1.02 Sun Jul 10 13:10:27 2022
% 0.44/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7204_n011.cluster.edu".
% 0.44/1.02 ============================== end of head ===========================
% 0.44/1.02
% 0.44/1.02 ============================== INPUT =================================
% 0.44/1.02
% 0.44/1.02 % Reading from file /tmp/Prover9_7204_n011.cluster.edu
% 0.44/1.02
% 0.44/1.02 set(prolog_style_variables).
% 0.44/1.02 set(auto2).
% 0.44/1.02 % set(auto2) -> set(auto).
% 0.44/1.02 % set(auto) -> set(auto_inference).
% 0.44/1.02 % set(auto) -> set(auto_setup).
% 0.44/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.02 % set(auto) -> set(auto_limits).
% 0.44/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.02 % set(auto) -> set(auto_denials).
% 0.44/1.02 % set(auto) -> set(auto_process).
% 0.44/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.02 % set(auto2) -> assign(stats, some).
% 0.44/1.02 % set(auto2) -> clear(echo_input).
% 0.44/1.02 % set(auto2) -> set(quiet).
% 0.44/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.02 % set(auto2) -> clear(print_given).
% 0.44/1.02 assign(lrs_ticks,-1).
% 0.44/1.02 assign(sos_limit,10000).
% 0.44/1.02 assign(order,kbo).
% 0.44/1.02 set(lex_order_vars).
% 0.44/1.02 clear(print_given).
% 0.44/1.02
% 0.44/1.02 % formulas(sos). % not echoed (6 formulas)
% 0.44/1.02
% 0.44/1.02 ============================== end of input ==========================
% 0.44/1.02
% 0.44/1.02 % From the command line: assign(max_seconds, 300).
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.02
% 0.44/1.02 % Formulas that are not ordinary clauses:
% 0.44/1.02 1 (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].
% 0.44/1.02 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 3 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 4 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 5 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 6 -(all B all C all D (subset(B,C) & subset(D,C) -> subset(union(B,D),C))) # label(prove_union_subset) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02
% 0.44/1.02 ============================== end predicate elimination =============
% 0.44/1.02
% 0.44/1.02 Auto_denials: (non-Horn, no changes).
% 0.44/1.02
% 0.44/1.02 Term ordering decisions:
% 0.44/1.02 Function symbol KB weights: c1=1. c2=1. c3=1. union=1. f1=1. f2=1.
% 0.44/1.02
% 0.44/1.02 ============================== end of process initial clauses ========
% 0.44/1.02
% 0.44/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.02
% 0.44/1.02 ============================== end of clauses for search =============
% 0.44/1.02
% 0.44/1.02 ============================== SEARCH ================================
% 0.44/1.02
% 0.44/1.02 % Starting search at 0.01 seconds.
% 0.44/1.02
% 0.44/1.02 ============================== PROOF =================================
% 0.44/1.02 % SZS status Theorem
% 0.44/1.02 % SZS output start Refutation
% 0.44/1.02
% 0.44/1.02 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.44/1.02 % Length of proof is 16.
% 0.44/1.02 % Level of proof is 4.
% 0.44/1.02 % Maximum clause weight is 14.000.
% 0.44/1.02 % Given clauses 18.
% 0.44/1.02
% 0.44/1.02 1 (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].
% 0.44/1.02 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 6 -(all B all C all D (subset(B,C) & subset(D,C) -> subset(union(B,D),C))) # label(prove_union_subset) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.44/1.02 8 subset(c1,c2) # label(prove_union_subset) # label(negated_conjecture). [clausify(6)].
% 0.44/1.02 9 subset(c3,c2) # label(prove_union_subset) # label(negated_conjecture). [clausify(6)].
% 0.44/1.02 11 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.44/1.02 13 -subset(union(c1,c3),c2) # label(prove_union_subset) # label(negated_conjecture). [clausify(6)].
% 0.44/1.02 16 subset(A,B) | -member(f1(A,B),B) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.44/1.02 17 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.44/1.02 20 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.44/1.02 23 member(f1(union(c1,c3),c2),union(c1,c3)). [resolve(13,a,11,a)].
% 0.44/1.02 28 -member(f1(union(c1,c3),c2),c2). [ur(16,a,13,a)].
% 0.44/1.02 47 member(f1(union(c1,c3),c2),c1) | member(f1(union(c1,c3),c2),c3). [resolve(23,a,20,a)].
% 0.44/1.02 52 -member(f1(union(c1,c3),c2),c3). [ur(17,a,9,a,c,28,a)].
% 0.44/1.02 53 -member(f1(union(c1,c3),c2),c1). [ur(17,a,8,a,c,28,a)].
% 0.44/1.02 54 $F. [back_unit_del(47),unit_del(a,53),unit_del(b,52)].
% 0.44/1.02
% 0.44/1.02 % SZS output end Refutation
% 0.44/1.02 ============================== end of proof ==========================
% 0.44/1.02
% 0.44/1.02 ============================== STATISTICS ============================
% 0.44/1.02
% 0.44/1.02 Given=18. Generated=84. Kept=47. proofs=1.
% 0.44/1.02 Usable=18. Sos=26. Demods=1. Limbo=2, Disabled=16. Hints=0.
% 0.44/1.02 Megabytes=0.07.
% 0.44/1.02 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.44/1.02
% 0.44/1.02 ============================== end of statistics =====================
% 0.44/1.02
% 0.44/1.02 ============================== end of search =========================
% 0.44/1.02
% 0.44/1.02 THEOREM PROVED
% 0.44/1.02 % SZS status Theorem
% 0.44/1.02
% 0.44/1.02 Exiting with 1 proof.
% 0.44/1.02
% 0.44/1.02 Process 7358 exit (max_proofs) Sun Jul 10 13:10:27 2022
% 0.44/1.02 Prover9 interrupted
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