TSTP Solution File: SET578+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 04:30:22 EDT 2022
% Result : Theorem 0.75s 1.07s
% Output : Refutation 0.75s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET578+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 : n004.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 05:06:07 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.75/1.07 ============================== Prover9 ===============================
% 0.75/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.07 Process 31664 was started by sandbox2 on n004.cluster.edu,
% 0.75/1.07 Sun Jul 10 05:06:08 2022
% 0.75/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_31511_n004.cluster.edu".
% 0.75/1.07 ============================== end of head ===========================
% 0.75/1.07
% 0.75/1.07 ============================== INPUT =================================
% 0.75/1.07
% 0.75/1.07 % Reading from file /tmp/Prover9_31511_n004.cluster.edu
% 0.75/1.07
% 0.75/1.07 set(prolog_style_variables).
% 0.75/1.07 set(auto2).
% 0.75/1.07 % set(auto2) -> set(auto).
% 0.75/1.07 % set(auto) -> set(auto_inference).
% 0.75/1.07 % set(auto) -> set(auto_setup).
% 0.75/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.07 % set(auto) -> set(auto_limits).
% 0.75/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.07 % set(auto) -> set(auto_denials).
% 0.75/1.07 % set(auto) -> set(auto_process).
% 0.75/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.07 % set(auto2) -> assign(stats, some).
% 0.75/1.07 % set(auto2) -> clear(echo_input).
% 0.75/1.07 % set(auto2) -> set(quiet).
% 0.75/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.07 % set(auto2) -> clear(print_given).
% 0.75/1.07 assign(lrs_ticks,-1).
% 0.75/1.07 assign(sos_limit,10000).
% 0.75/1.07 assign(order,kbo).
% 0.75/1.07 set(lex_order_vars).
% 0.75/1.07 clear(print_given).
% 0.75/1.07
% 0.75/1.07 % formulas(sos). % not echoed (7 formulas)
% 0.75/1.07
% 0.75/1.07 ============================== end of input ==========================
% 0.75/1.07
% 0.75/1.07 % From the command line: assign(max_seconds, 300).
% 0.75/1.07
% 0.75/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.07
% 0.75/1.07 % Formulas that are not ordinary clauses:
% 0.75/1.07 1 (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].
% 0.75/1.07 2 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 3 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 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].
% 0.75/1.07 5 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 7 -(all B all C all D ((all E (member(E,B) <-> member(E,C) & member(E,D))) -> B = intersection(C,D))) # label(prove_th19) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.07
% 0.75/1.07 ============================== end of process non-clausal formulas ===
% 0.75/1.07
% 0.75/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.07
% 0.75/1.07 ============================== PREDICATE ELIMINATION =================
% 0.75/1.07
% 0.75/1.07 ============================== end predicate elimination =============
% 0.75/1.07
% 0.75/1.07 Auto_denials: (non-Horn, no changes).
% 0.75/1.07
% 0.75/1.07 Term ordering decisions:
% 0.75/1.07 Function symbol KB weights: c1=1. c2=1. c3=1. intersection=1. f1=1. f2=1.
% 0.75/1.07
% 0.75/1.07 ============================== end of process initial clauses ========
% 0.75/1.07
% 0.75/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.75/1.07
% 0.75/1.07 ============================== end of clauses for search =============
% 0.75/1.07
% 0.75/1.07 ============================== SEARCH ================================
% 0.75/1.07
% 0.75/1.07 % Starting search at 0.01 seconds.
% 0.75/1.07
% 0.75/1.07 ============================== PROOF =================================
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07 % SZS output start Refutation
% 0.75/1.07
% 0.75/1.07 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.75/1.07 % Length of proof is 25.
% 0.75/1.07 % Level of proof is 8.
% 0.75/1.07 % Maximum clause weight is 23.000.
% 0.75/1.07 % Given clauses 128.
% 0.75/1.07
% 0.75/1.07 1 (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].
% 0.75/1.07 3 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 6 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.75/1.07 7 -(all B all C all D ((all E (member(E,B) <-> member(E,C) & member(E,D))) -> B = intersection(C,D))) # label(prove_th19) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.75/1.07 9 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(3)].
% 0.75/1.07 11 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 0.75/1.07 12 intersection(c2,c3) != c1 # label(prove_th19) # label(negated_conjecture). [clausify(7)].
% 0.75/1.07 15 -member(A,c1) | member(A,c2) # label(prove_th19) # label(negated_conjecture). [clausify(7)].
% 0.75/1.07 16 -member(A,c1) | member(A,c3) # label(prove_th19) # label(negated_conjecture). [clausify(7)].
% 0.75/1.07 17 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(1)].
% 0.75/1.07 18 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 0.75/1.07 24 member(A,c1) | -member(A,c2) | -member(A,c3) # label(prove_th19) # label(negated_conjecture). [clausify(7)].
% 0.75/1.07 25 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 0.75/1.07 26 A = B | -member(f2(B,A),B) | -member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 0.75/1.07 28 member(f2(A,c1),c2) | c1 = A | member(f2(A,c1),A). [resolve(15,a,11,c)].
% 0.75/1.07 32 member(f2(A,c1),c3) | c1 = A | member(f2(A,c1),A). [resolve(16,a,11,c)].
% 0.75/1.07 65 c1 = A | member(f2(A,c1),A) | member(f2(A,c1),intersection(B,c2)) | -member(f2(A,c1),B). [resolve(28,a,25,c)].
% 0.75/1.07 115 member(f2(intersection(A,B),c1),c3) | intersection(A,B) = c1 | member(f2(intersection(A,B),c1),B). [resolve(32,c,18,a),flip(b)].
% 0.75/1.07 121 member(f2(intersection(A,c3),c1),c3) | intersection(A,c3) = c1. [factor(115,a,c)].
% 0.75/1.07 769 intersection(A,c3) = c1 | member(f2(intersection(A,c3),c1),intersection(A,c3)) | member(f2(intersection(A,c3),c1),intersection(c2,c3)). [resolve(65,d,121,a),rewrite([9(18)]),flip(a),merge(d)].
% 0.75/1.07 776 member(f2(intersection(c2,c3),c1),intersection(c2,c3)). [factor(769,b,c),unit_del(a,12)].
% 0.75/1.07 783 -member(f2(intersection(c2,c3),c1),c1). [resolve(776,a,26,b),flip(a),unit_del(a,12)].
% 0.75/1.07 786 member(f2(intersection(c2,c3),c1),c3). [resolve(776,a,18,a)].
% 0.75/1.07 787 member(f2(intersection(c2,c3),c1),c2). [resolve(776,a,17,a)].
% 0.75/1.07 792 $F. [resolve(786,a,24,c),unit_del(a,783),unit_del(b,787)].
% 0.75/1.07
% 0.75/1.07 % SZS output end Refutation
% 0.75/1.07 ============================== end of proof ==========================
% 0.75/1.07
% 0.75/1.07 ============================== STATISTICS ============================
% 0.75/1.07
% 0.75/1.07 Given=128. Generated=1588. Kept=784. proofs=1.
% 0.75/1.07 Usable=127. Sos=623. Demods=1. Limbo=4, Disabled=49. Hints=0.
% 0.75/1.07 Megabytes=0.59.
% 0.75/1.07 User_CPU=0.08, System_CPU=0.01, Wall_clock=0.
% 0.75/1.07
% 0.75/1.07 ============================== end of statistics =====================
% 0.75/1.07
% 0.75/1.07 ============================== end of search =========================
% 0.75/1.07
% 0.75/1.07 THEOREM PROVED
% 0.75/1.07 % SZS status Theorem
% 0.75/1.07
% 0.75/1.07 Exiting with 1 proof.
% 0.75/1.07
% 0.75/1.07 Process 31664 exit (max_proofs) Sun Jul 10 05:06:08 2022
% 0.75/1.07 Prover9 interrupted
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