TSTP Solution File: SET587+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET587+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n013.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 04:30:28 EDT 2022
% Result : Theorem 0.78s 1.07s
% Output : Refutation 0.78s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET587+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 : n013.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 : Sat Jul 9 18:23:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.78/1.04 ============================== Prover9 ===============================
% 0.78/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.78/1.04 Process 15413 was started by sandbox on n013.cluster.edu,
% 0.78/1.04 Sat Jul 9 18:24:00 2022
% 0.78/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_15259_n013.cluster.edu".
% 0.78/1.04 ============================== end of head ===========================
% 0.78/1.04
% 0.78/1.04 ============================== INPUT =================================
% 0.78/1.04
% 0.78/1.04 % Reading from file /tmp/Prover9_15259_n013.cluster.edu
% 0.78/1.04
% 0.78/1.04 set(prolog_style_variables).
% 0.78/1.04 set(auto2).
% 0.78/1.04 % set(auto2) -> set(auto).
% 0.78/1.04 % set(auto) -> set(auto_inference).
% 0.78/1.04 % set(auto) -> set(auto_setup).
% 0.78/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.78/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.78/1.04 % set(auto) -> set(auto_limits).
% 0.78/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.78/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.78/1.04 % set(auto) -> set(auto_denials).
% 0.78/1.04 % set(auto) -> set(auto_process).
% 0.78/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.78/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.78/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.78/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.78/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.78/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.78/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.78/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.78/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.78/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.78/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.78/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.78/1.04 % set(auto2) -> assign(stats, some).
% 0.78/1.04 % set(auto2) -> clear(echo_input).
% 0.78/1.04 % set(auto2) -> set(quiet).
% 0.78/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.78/1.04 % set(auto2) -> clear(print_given).
% 0.78/1.04 assign(lrs_ticks,-1).
% 0.78/1.04 assign(sos_limit,10000).
% 0.78/1.04 assign(order,kbo).
% 0.78/1.04 set(lex_order_vars).
% 0.78/1.04 clear(print_given).
% 0.78/1.04
% 0.78/1.04 % formulas(sos). % not echoed (9 formulas)
% 0.78/1.04
% 0.78/1.04 ============================== end of input ==========================
% 0.78/1.04
% 0.78/1.04 % From the command line: assign(max_seconds, 300).
% 0.78/1.04
% 0.78/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.78/1.04
% 0.78/1.04 % Formulas that are not ordinary clauses:
% 0.78/1.04 1 (all B all C ((all D (member(D,B) <-> member(D,C))) -> B = C)) # label(member_equal) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 2 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 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].
% 0.78/1.04 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 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].
% 0.78/1.04 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 8 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.04 9 -(all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(prove_difference_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.04
% 0.78/1.04 ============================== end of process non-clausal formulas ===
% 0.78/1.04
% 0.78/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.78/1.04
% 0.78/1.04 ============================== PREDICATE ELIMINATION =================
% 0.78/1.04 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.78/1.04 11 empty(A) | member(f4(A),A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.78/1.04 Derived: -member(A,B) | member(f4(B),B). [resolve(10,a,11,a)].
% 0.78/1.04
% 0.78/1.04 ============================== end predicate elimination =============
% 0.78/1.04
% 0.78/1.04 Auto_denials: (non-Horn, no changes).
% 0.78/1.04
% 0.78/1.04 Term ordering decisions:
% 0.78/1.04
% 0.78/1.04 % Assigning unary symbol f4 kb_weight 0 and highest precedence (11).
% 0.78/1.04 Function symbol KB weights: empty_set=1. c1=1. c2=1. difference=1. f1=1. f2=1. f3=1. f4=0.
% 0.78/1.04
% 0.78/1.04 ============================== end of process initial clauses ========
% 0.78/1.07
% 0.78/1.07 ============================== CLAUSES FOR SEARCH ====================
% 0.78/1.07
% 0.78/1.07 ============================== end of clauses for search =============
% 0.78/1.07
% 0.78/1.07 ============================== SEARCH ================================
% 0.78/1.07
% 0.78/1.07 % Starting search at 0.01 seconds.
% 0.78/1.07
% 0.78/1.07 ============================== PROOF =================================
% 0.78/1.07 % SZS status Theorem
% 0.78/1.07 % SZS output start Refutation
% 0.78/1.07
% 0.78/1.07 % Proof 1 at 0.04 (+ 0.00) seconds.
% 0.78/1.07 % Length of proof is 35.
% 0.78/1.07 % Level of proof is 11.
% 0.78/1.07 % Maximum clause weight is 17.000.
% 0.78/1.07 % Given clauses 96.
% 0.78/1.07
% 0.78/1.07 2 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 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].
% 0.78/1.07 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].
% 0.78/1.07 8 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.78/1.07 9 -(all B all C (difference(B,C) = empty_set <-> subset(B,C))) # label(prove_difference_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.78/1.07 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.78/1.07 11 empty(A) | member(f4(A),A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.78/1.07 13 subset(A,B) | member(f2(A,B),A) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.78/1.07 14 difference(c1,c2) = empty_set | subset(c1,c2) # label(prove_difference_empty_set) # label(negated_conjecture). [clausify(9)].
% 0.78/1.07 16 A = B | member(f3(B,A),B) | member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(6)].
% 0.78/1.07 17 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(3)].
% 0.78/1.07 18 -member(A,difference(B,C)) | -member(A,C) # label(difference_defn) # label(axiom). [clausify(2)].
% 0.78/1.07 19 difference(c1,c2) != empty_set | -subset(c1,c2) # label(prove_difference_empty_set) # label(negated_conjecture). [clausify(9)].
% 0.78/1.07 22 -member(A,difference(B,C)) | member(A,B) # label(difference_defn) # label(axiom). [clausify(2)].
% 0.78/1.07 23 subset(A,B) | -member(f2(A,B),B) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.78/1.07 24 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(4)].
% 0.78/1.07 28 member(A,difference(B,C)) | -member(A,B) | member(A,C) # label(difference_defn) # label(axiom). [clausify(2)].
% 0.78/1.07 31 -member(A,B) | member(f4(B),B). [resolve(10,a,11,a)].
% 0.78/1.07 32 empty_set = A | member(f3(A,empty_set),A). [resolve(17,a,16,c)].
% 0.78/1.07 40 difference(c1,c2) != empty_set | member(f2(c1,c2),c1). [resolve(19,b,13,a)].
% 0.78/1.07 50 -member(A,c1) | member(A,c2) | difference(c1,c2) = empty_set. [resolve(24,a,14,b)].
% 0.78/1.07 51 -member(A,B) | member(A,C) | member(f2(B,C),B). [resolve(24,a,13,a)].
% 0.78/1.07 83 empty_set = A | member(f4(A),A). [resolve(32,b,31,a)].
% 0.78/1.07 93 difference(A,B) = empty_set | member(f4(difference(A,B)),A). [resolve(83,b,22,a),flip(a)].
% 0.78/1.07 94 difference(A,B) = empty_set | -member(f4(difference(A,B)),B). [resolve(83,b,18,a),flip(a)].
% 0.78/1.07 140 difference(c1,A) = empty_set | member(f4(difference(c1,A)),c2) | difference(c1,c2) = empty_set. [resolve(93,b,50,a)].
% 0.78/1.07 147 difference(c1,c2) = empty_set | member(f4(difference(c1,c2)),c2). [factor(140,a,c)].
% 0.78/1.07 228 difference(c1,c2) = empty_set. [resolve(147,b,94,b),merge(b)].
% 0.78/1.07 229 member(f2(c1,c2),c1). [back_rewrite(40),rewrite([228(3)]),xx(a)].
% 0.78/1.07 230 -subset(c1,c2). [back_rewrite(19),rewrite([228(3)]),xx(a)].
% 0.78/1.07 257 -member(f2(c1,c2),c2). [ur(23,a,230,a)].
% 0.78/1.07 261 member(f2(c1,c2),A) | member(f2(c1,A),c1). [resolve(229,a,51,a)].
% 0.78/1.07 369 member(f2(c1,c2),A) | member(f2(c1,A),difference(c1,B)) | member(f2(c1,A),B). [resolve(261,b,28,b)].
% 0.78/1.07 371 $F. [factor(369,a,c),rewrite([228(11)]),unit_del(a,257),unit_del(b,17)].
% 0.78/1.07
% 0.78/1.07 % SZS output end Refutation
% 0.78/1.07 ============================== end of proof ==========================
% 0.78/1.07
% 0.78/1.07 ============================== STATISTICS ============================
% 0.78/1.07
% 0.78/1.07 Given=96. Generated=850. Kept=359. proofs=1.
% 0.78/1.07 Usable=87. Sos=224. Demods=3. Limbo=2, Disabled=68. Hints=0.
% 0.78/1.07 Megabytes=0.28.
% 0.78/1.07 User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.78/1.07
% 0.78/1.07 ============================== end of statistics =====================
% 0.78/1.07
% 0.78/1.07 ============================== end of search =========================
% 0.78/1.07
% 0.78/1.07 THEOREM PROVED
% 0.78/1.07 % SZS status Theorem
% 0.78/1.07
% 0.78/1.07 Exiting with 1 proof.
% 0.78/1.07
% 0.78/1.07 Process 15413 exit (max_proofs) Sat Jul 9 18:24:00 2022
% 0.78/1.07 Prover9 interrupted
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