TSTP Solution File: SET628+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n028.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 04:30:57 EDT 2022
% Result : Theorem 0.72s 0.97s
% Output : Refutation 0.72s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n028.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
% 0.12/0.33 % DateTime : Mon Jul 11 02:34:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/0.97 ============================== Prover9 ===============================
% 0.72/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.72/0.97 Process 7296 was started by sandbox on n028.cluster.edu,
% 0.72/0.97 Mon Jul 11 02:34:58 2022
% 0.72/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7113_n028.cluster.edu".
% 0.72/0.97 ============================== end of head ===========================
% 0.72/0.97
% 0.72/0.97 ============================== INPUT =================================
% 0.72/0.97
% 0.72/0.97 % Reading from file /tmp/Prover9_7113_n028.cluster.edu
% 0.72/0.97
% 0.72/0.97 set(prolog_style_variables).
% 0.72/0.97 set(auto2).
% 0.72/0.97 % set(auto2) -> set(auto).
% 0.72/0.97 % set(auto) -> set(auto_inference).
% 0.72/0.97 % set(auto) -> set(auto_setup).
% 0.72/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.72/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/0.97 % set(auto) -> set(auto_limits).
% 0.72/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/0.97 % set(auto) -> set(auto_denials).
% 0.72/0.97 % set(auto) -> set(auto_process).
% 0.72/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.72/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.72/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.72/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.72/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.72/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.72/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.72/0.97 % set(auto2) -> assign(stats, some).
% 0.72/0.97 % set(auto2) -> clear(echo_input).
% 0.72/0.97 % set(auto2) -> set(quiet).
% 0.72/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.72/0.97 % set(auto2) -> clear(print_given).
% 0.72/0.97 assign(lrs_ticks,-1).
% 0.72/0.97 assign(sos_limit,10000).
% 0.72/0.97 assign(order,kbo).
% 0.72/0.97 set(lex_order_vars).
% 0.72/0.97 clear(print_given).
% 0.72/0.97
% 0.72/0.97 % formulas(sos). % not echoed (7 formulas)
% 0.72/0.97
% 0.72/0.97 ============================== end of input ==========================
% 0.72/0.97
% 0.72/0.97 % From the command line: assign(max_seconds, 300).
% 0.72/0.97
% 0.72/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/0.97
% 0.72/0.97 % Formulas that are not ordinary clauses:
% 0.72/0.97 1 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 3 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 4 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 5 (all B all C (intersect(B,C) -> intersect(C,B))) # label(symmetry_of_intersect) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 6 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 7 -(all B (intersect(B,B) <-> not_equal(B,empty_set))) # label(prove_th110) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.97
% 0.72/0.97 ============================== end of process non-clausal formulas ===
% 0.72/0.97
% 0.72/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/0.97
% 0.72/0.97 ============================== PREDICATE ELIMINATION =================
% 0.72/0.97 8 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(6)].
% 0.72/0.97 9 empty(A) | member(f3(A),A) # label(empty_defn) # label(axiom). [clausify(6)].
% 0.72/0.97 Derived: -member(A,B) | member(f3(B),B). [resolve(8,a,9,a)].
% 0.72/0.97
% 0.72/0.97 ============================== end predicate elimination =============
% 0.72/0.97
% 0.72/0.97 Auto_denials: (non-Horn, no changes).
% 0.72/0.97
% 0.72/0.97 Term ordering decisions:
% 0.72/0.97
% 0.72/0.97 % Assigning unary symbol f3 kb_weight 0 and highest precedence (9).
% 0.72/0.97 Function symbol KB weights: empty_set=1. c1=1. f1=1. f2=1. f3=0.
% 0.72/0.97
% 0.72/0.97 ============================== end of process initial clauses ========
% 0.72/0.97
% 0.72/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.72/0.97
% 0.72/0.97 ============================== end of clauses for search =============
% 0.72/0.97
% 0.72/0.97 ============================== SEARCH ================================
% 0.72/0.97
% 0.72/0.97 % Starting search at 0.01 seconds.
% 0.72/0.97
% 0.72/0.97 ============================== PROOF =================================
% 0.72/0.97 % SZS status Theorem
% 0.72/0.97 % SZS output start Refutation
% 0.72/0.97
% 0.72/0.97 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.72/0.97 % Length of proof is 21.
% 0.72/0.97 % Level of proof is 5.
% 0.72/0.97 % Maximum clause weight is 13.000.
% 0.72/0.97 % Given clauses 22.
% 0.72/0.97
% 0.72/0.97 1 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 3 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 4 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.72/0.97 7 -(all B (intersect(B,B) <-> not_equal(B,empty_set))) # label(prove_th110) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/0.97 10 not_equal(A,B) | B = A # label(not_equal_defn) # label(axiom). [clausify(4)].
% 0.72/0.97 11 intersect(c1,c1) | not_equal(c1,empty_set) # label(prove_th110) # label(negated_conjecture). [clausify(7)].
% 0.72/0.97 12 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(3)].
% 0.72/0.97 13 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(2)].
% 0.72/0.97 14 -not_equal(A,B) | B != A # label(not_equal_defn) # label(axiom). [clausify(4)].
% 0.72/0.97 15 -intersect(c1,c1) | -not_equal(c1,empty_set) # label(prove_th110) # label(negated_conjecture). [clausify(7)].
% 0.72/0.97 18 -intersect(A,B) | member(f1(A,B),B) # label(intersect_defn) # label(axiom). [clausify(1)].
% 0.72/0.97 19 intersect(A,B) | -member(C,A) | -member(C,B) # label(intersect_defn) # label(axiom). [clausify(1)].
% 0.72/0.97 24 intersect(A,A) | -member(B,A). [factor(19,b,c)].
% 0.72/0.97 25 empty_set = A | member(f2(A,empty_set),A). [resolve(13,a,12,c)].
% 0.72/0.97 27 c1 != empty_set | intersect(c1,c1). [resolve(14,a,11,b),flip(a)].
% 0.72/0.97 29 -intersect(c1,c1) | c1 = empty_set. [resolve(15,b,10,a),flip(b)].
% 0.72/0.97 31 -intersect(A,empty_set). [ur(18,b,13,a)].
% 0.72/0.97 46 empty_set = A | intersect(A,A). [resolve(25,b,24,b)].
% 0.72/0.97 52 c1 = empty_set. [resolve(46,b,29,a),flip(a),merge(b)].
% 0.72/0.97 54 $F. [back_rewrite(27),rewrite([52(1),52(4),52(5)]),xx(a),unit_del(a,31)].
% 0.72/0.97
% 0.72/0.97 % SZS output end Refutation
% 0.72/0.97 ============================== end of proof ==========================
% 0.72/0.97
% 0.72/0.97 ============================== STATISTICS ============================
% 0.72/0.97
% 0.72/0.97 Given=22. Generated=70. Kept=44. proofs=1.
% 0.72/0.97 Usable=20. Sos=20. Demods=1. Limbo=2, Disabled=18. Hints=0.
% 0.72/0.97 Megabytes=0.06.
% 0.72/0.97 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.72/0.97
% 0.72/0.97 ============================== end of statistics =====================
% 0.72/0.97
% 0.72/0.97 ============================== end of search =========================
% 0.72/0.97
% 0.72/0.97 THEOREM PROVED
% 0.72/0.97 % SZS status Theorem
% 0.72/0.97
% 0.72/0.97 Exiting with 1 proof.
% 0.72/0.97
% 0.72/0.97 Process 7296 exit (max_proofs) Mon Jul 11 02:34:58 2022
% 0.72/0.97 Prover9 interrupted
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