TSTP Solution File: SET592+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 04:30:31 EDT 2022
% Result : Theorem 0.43s 0.99s
% Output : Refutation 0.43s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n024.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
% 0.12/0.34 % DateTime : Sun Jul 10 09:54:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.43/0.99 ============================== Prover9 ===============================
% 0.43/0.99 Prover9 (32) version 2009-11A, November 2009.
% 0.43/0.99 Process 26687 was started by sandbox2 on n024.cluster.edu,
% 0.43/0.99 Sun Jul 10 09:54:44 2022
% 0.43/0.99 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_26534_n024.cluster.edu".
% 0.43/0.99 ============================== end of head ===========================
% 0.43/0.99
% 0.43/0.99 ============================== INPUT =================================
% 0.43/0.99
% 0.43/0.99 % Reading from file /tmp/Prover9_26534_n024.cluster.edu
% 0.43/0.99
% 0.43/0.99 set(prolog_style_variables).
% 0.43/0.99 set(auto2).
% 0.43/0.99 % set(auto2) -> set(auto).
% 0.43/0.99 % set(auto) -> set(auto_inference).
% 0.43/0.99 % set(auto) -> set(auto_setup).
% 0.43/0.99 % set(auto_setup) -> set(predicate_elim).
% 0.43/0.99 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.43/0.99 % set(auto) -> set(auto_limits).
% 0.43/0.99 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.43/0.99 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.43/0.99 % set(auto) -> set(auto_denials).
% 0.43/0.99 % set(auto) -> set(auto_process).
% 0.43/0.99 % set(auto2) -> assign(new_constants, 1).
% 0.43/0.99 % set(auto2) -> assign(fold_denial_max, 3).
% 0.43/0.99 % set(auto2) -> assign(max_weight, "200.000").
% 0.43/0.99 % set(auto2) -> assign(max_hours, 1).
% 0.43/0.99 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.43/0.99 % set(auto2) -> assign(max_seconds, 0).
% 0.43/0.99 % set(auto2) -> assign(max_minutes, 5).
% 0.43/0.99 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.43/0.99 % set(auto2) -> set(sort_initial_sos).
% 0.43/0.99 % set(auto2) -> assign(sos_limit, -1).
% 0.43/0.99 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.43/0.99 % set(auto2) -> assign(max_megs, 400).
% 0.43/0.99 % set(auto2) -> assign(stats, some).
% 0.43/0.99 % set(auto2) -> clear(echo_input).
% 0.43/0.99 % set(auto2) -> set(quiet).
% 0.43/0.99 % set(auto2) -> clear(print_initial_clauses).
% 0.43/0.99 % set(auto2) -> clear(print_given).
% 0.43/0.99 assign(lrs_ticks,-1).
% 0.43/0.99 assign(sos_limit,10000).
% 0.43/0.99 assign(order,kbo).
% 0.43/0.99 set(lex_order_vars).
% 0.43/0.99 clear(print_given).
% 0.43/0.99
% 0.43/0.99 % formulas(sos). % not echoed (11 formulas)
% 0.43/0.99
% 0.43/0.99 ============================== end of input ==========================
% 0.43/0.99
% 0.43/0.99 % From the command line: assign(max_seconds, 300).
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.43/0.99
% 0.43/0.99 % Formulas that are not ordinary clauses:
% 0.43/0.99 1 (all B (subset(B,empty_set) -> B = empty_set)) # label(subset_of_empty_set_is_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 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].
% 0.43/0.99 6 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 7 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 8 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 9 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 11 -(all B all C all D (subset(B,C) & subset(B,D) & intersection(C,D) = empty_set -> B = empty_set)) # label(prove_th51) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99
% 0.43/0.99 ============================== end of process non-clausal formulas ===
% 0.43/0.99
% 0.43/0.99 ============================== PROCESS INITIAL CLAUSES ===============
% 0.43/0.99
% 0.43/0.99 ============================== PREDICATE ELIMINATION =================
% 0.43/0.99 12 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(9)].
% 0.43/0.99 13 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(9)].
% 0.43/0.99 Derived: -member(A,B) | member(f2(B),B). [resolve(12,a,13,a)].
% 0.43/0.99
% 0.43/0.99 ============================== end predicate elimination =============
% 0.43/0.99
% 0.43/0.99 Auto_denials: (non-Horn, no changes).
% 0.43/0.99
% 0.43/0.99 Term ordering decisions:
% 0.43/0.99
% 0.43/0.99 % Assigning unary symbol f2 kb_weight 0 and highest precedence (11).
% 0.43/0.99 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. intersection=1. f1=1. f3=1. f2=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of process initial clauses ========
% 0.43/0.99
% 0.43/0.99 ============================== CLAUSES FOR SEARCH ====================
% 0.43/0.99
% 0.43/0.99 ============================== end of clauses for search =============
% 0.43/0.99
% 0.43/0.99 ============================== SEARCH ================================
% 0.43/0.99
% 0.43/0.99 % Starting search at 0.01 seconds.
% 0.43/0.99
% 0.43/0.99 ============================== PROOF =================================
% 0.43/0.99 % SZS status Theorem
% 0.43/0.99 % SZS output start Refutation
% 0.43/0.99
% 0.43/0.99 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.43/0.99 % Length of proof is 14.
% 0.43/0.99 % Level of proof is 5.
% 0.43/0.99 % Maximum clause weight is 11.000.
% 0.43/0.99 % Given clauses 27.
% 0.43/0.99
% 0.43/0.99 1 (all B (subset(B,empty_set) -> B = empty_set)) # label(subset_of_empty_set_is_empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.43/0.99 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].
% 0.43/0.99 11 -(all B all C all D (subset(B,C) & subset(B,D) & intersection(C,D) = empty_set -> B = empty_set)) # label(prove_th51) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.43/0.99 15 subset(c1,c2) # label(prove_th51) # label(negated_conjecture). [clausify(11)].
% 0.43/0.99 16 subset(c1,c3) # label(prove_th51) # label(negated_conjecture). [clausify(11)].
% 0.43/0.99 17 intersection(c2,c3) = empty_set # label(prove_th51) # label(negated_conjecture). [clausify(11)].
% 0.43/0.99 18 empty_set = intersection(c2,c3). [copy(17),flip(a)].
% 0.43/0.99 24 empty_set != c1 # label(prove_th51) # label(negated_conjecture). [clausify(11)].
% 0.43/0.99 25 intersection(c2,c3) != c1. [copy(24),rewrite([18(1)])].
% 0.43/0.99 26 -subset(A,empty_set) | empty_set = A # label(subset_of_empty_set_is_empty_set) # label(axiom). [clausify(1)].
% 0.43/0.99 27 -subset(A,intersection(c2,c3)) | intersection(c2,c3) = A. [copy(26),rewrite([18(1),18(5)])].
% 0.43/0.99 37 -subset(A,B) | -subset(A,C) | subset(A,intersection(B,C)) # label(intersection_of_subsets) # label(axiom). [clausify(2)].
% 0.43/0.99 46 -subset(c1,intersection(c2,c3)). [ur(27,b,25,a)].
% 0.43/0.99 94 $F. [ur(37,b,16,a,c,46,a),unit_del(a,15)].
% 0.43/0.99
% 0.43/0.99 % SZS output end Refutation
% 0.43/0.99 ============================== end of proof ==========================
% 0.43/0.99
% 0.43/0.99 ============================== STATISTICS ============================
% 0.43/0.99
% 0.43/0.99 Given=27. Generated=136. Kept=76. proofs=1.
% 0.43/0.99 Usable=27. Sos=48. Demods=2. Limbo=1, Disabled=25. Hints=0.
% 0.43/0.99 Megabytes=0.10.
% 0.43/0.99 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.43/0.99
% 0.43/0.99 ============================== end of statistics =====================
% 0.43/0.99
% 0.43/0.99 ============================== end of search =========================
% 0.43/0.99
% 0.43/0.99 THEOREM PROVED
% 0.43/0.99 % SZS status Theorem
% 0.43/0.99
% 0.43/0.99 Exiting with 1 proof.
% 0.43/0.99
% 0.43/0.99 Process 26687 exit (max_proofs) Sun Jul 10 09:54:44 2022
% 0.43/0.99 Prover9 interrupted
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