TSTP Solution File: SET162+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 04:27:52 EDT 2022
% Result : Theorem 0.79s 1.09s
% Output : Refutation 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n010.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jul 11 02:38:45 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.79/1.03 ============================== Prover9 ===============================
% 0.79/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.03 Process 13767 was started by sandbox on n010.cluster.edu,
% 0.79/1.03 Mon Jul 11 02:38:46 2022
% 0.79/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13614_n010.cluster.edu".
% 0.79/1.03 ============================== end of head ===========================
% 0.79/1.03
% 0.79/1.03 ============================== INPUT =================================
% 0.79/1.03
% 0.79/1.03 % Reading from file /tmp/Prover9_13614_n010.cluster.edu
% 0.79/1.03
% 0.79/1.03 set(prolog_style_variables).
% 0.79/1.03 set(auto2).
% 0.79/1.03 % set(auto2) -> set(auto).
% 0.79/1.03 % set(auto) -> set(auto_inference).
% 0.79/1.03 % set(auto) -> set(auto_setup).
% 0.79/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.79/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.03 % set(auto) -> set(auto_limits).
% 0.79/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.03 % set(auto) -> set(auto_denials).
% 0.79/1.03 % set(auto) -> set(auto_process).
% 0.79/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.79/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.79/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.79/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.79/1.03 % set(auto2) -> assign(stats, some).
% 0.79/1.03 % set(auto2) -> clear(echo_input).
% 0.79/1.03 % set(auto2) -> set(quiet).
% 0.79/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.03 % set(auto2) -> clear(print_given).
% 0.79/1.03 assign(lrs_ticks,-1).
% 0.79/1.03 assign(sos_limit,10000).
% 0.79/1.03 assign(order,kbo).
% 0.79/1.03 set(lex_order_vars).
% 0.79/1.03 clear(print_given).
% 0.79/1.03
% 0.79/1.03 % formulas(sos). % not echoed (9 formulas)
% 0.79/1.03
% 0.79/1.03 ============================== end of input ==========================
% 0.79/1.03
% 0.79/1.03 % From the command line: assign(max_seconds, 300).
% 0.79/1.03
% 0.79/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.03
% 0.79/1.03 % Formulas that are not ordinary clauses:
% 0.79/1.03 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].
% 0.79/1.03 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 3 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 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].
% 0.79/1.03 6 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 7 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.03 9 -(all B union(B,empty_set) = B) # label(prove_union_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.79/1.03
% 0.79/1.03 ============================== end of process non-clausal formulas ===
% 0.79/1.03
% 0.79/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.03
% 0.79/1.03 ============================== PREDICATE ELIMINATION =================
% 0.79/1.03 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.79/1.03 11 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.79/1.03 Derived: -member(A,B) | member(f2(B),B). [resolve(10,a,11,a)].
% 0.79/1.03
% 0.79/1.03 ============================== end predicate elimination =============
% 0.79/1.03
% 0.79/1.03 Auto_denials: (non-Horn, no changes).
% 0.79/1.03
% 0.79/1.03 Term ordering decisions:
% 0.79/1.03
% 0.79/1.03 % Assigning unary symbol f2 kb_weight 0 and highest precedence (9).
% 0.79/1.03 Function symbol KB weights: empty_set=1. c1=1. union=1. f1=1. f3=1. f2=0.
% 0.79/1.03
% 0.79/1.03 ============================== end of process initial clauses ========
% 0.79/1.03
% 0.79/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.79/1.09
% 0.79/1.09 ============================== end of clauses for search =============
% 0.79/1.09
% 0.79/1.09 ============================== SEARCH ================================
% 0.79/1.09
% 0.79/1.09 % Starting search at 0.01 seconds.
% 0.79/1.09
% 0.79/1.09 ============================== PROOF =================================
% 0.79/1.09 % SZS status Theorem
% 0.79/1.09 % SZS output start Refutation
% 0.79/1.09
% 0.79/1.09 % Proof 1 at 0.07 (+ 0.00) seconds.
% 0.79/1.09 % Length of proof is 28.
% 0.79/1.09 % Level of proof is 9.
% 0.79/1.09 % Maximum clause weight is 26.000.
% 0.79/1.09 % Given clauses 89.
% 0.79/1.09
% 0.79/1.09 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].
% 0.79/1.09 2 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.09 4 (all B all C union(B,C) = union(C,B)) # label(commutativity_of_union) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.09 7 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.09 8 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.79/1.09 9 -(all B union(B,empty_set) = B) # label(prove_union_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.79/1.09 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.79/1.09 11 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(7)].
% 0.79/1.09 13 union(A,B) = union(B,A) # label(commutativity_of_union) # label(axiom). [clausify(4)].
% 0.79/1.09 15 A = B | member(f3(B,A),B) | member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.79/1.09 16 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(2)].
% 0.79/1.09 17 union(c1,empty_set) != c1 # label(prove_union_empty_set) # label(negated_conjecture). [clausify(9)].
% 0.79/1.09 18 union(empty_set,c1) != c1. [copy(17),rewrite([13(3)])].
% 0.79/1.09 21 member(A,union(B,C)) | -member(A,B) # label(union_defn) # label(axiom). [clausify(1)].
% 0.79/1.09 27 A != B | member(C,B) | -member(C,A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.79/1.09 28 -member(A,union(B,C)) | member(A,B) | member(A,C) # label(union_defn) # label(axiom). [clausify(1)].
% 0.79/1.09 29 A = B | -member(f3(B,A),B) | -member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(8)].
% 0.79/1.09 30 -member(A,B) | member(f2(B),B). [resolve(10,a,11,a)].
% 0.79/1.09 34 member(f3(A,B),union(B,C)) | B = A | member(f3(A,B),A). [resolve(21,b,15,c)].
% 0.79/1.09 36 member(f3(union(A,B),A),union(A,B)) | union(A,B) = A. [factor(34,a,c),flip(b)].
% 0.79/1.09 48 member(f3(union(A,B),C),A) | member(f3(union(A,B),C),B) | union(A,B) = C | member(f3(union(A,B),C),C). [resolve(28,a,15,b),flip(c)].
% 0.79/1.09 53 member(f3(union(A,B),A),A) | member(f3(union(A,B),A),B) | union(A,B) = A. [factor(48,a,d)].
% 0.79/1.09 132 union(A,B) = A | -member(f3(union(A,B),A),A). [resolve(36,a,29,b),flip(b),merge(b)].
% 0.79/1.09 440 member(f3(union(A,B),A),B) | union(A,B) = A. [resolve(53,a,132,b),merge(c)].
% 0.79/1.09 448 member(f3(union(A,B),B),A) | union(A,B) = B. [para(13(a,1),440(a,1,1)),rewrite([13(4)])].
% 0.79/1.09 450 union(A,B) = B | member(f2(A),A). [resolve(448,a,30,a)].
% 0.79/1.09 474 union(A,B) = B | A != C | member(f2(A),C). [resolve(450,b,27,c)].
% 0.79/1.09 481 $F. [ur(474,a,18,a,c,16,a),xx(a)].
% 0.79/1.09
% 0.79/1.09 % SZS output end Refutation
% 0.79/1.09 ============================== end of proof ==========================
% 0.79/1.09
% 0.79/1.09 ============================== STATISTICS ============================
% 0.79/1.09
% 0.79/1.09 Given=89. Generated=1352. Kept=468. proofs=1.
% 0.79/1.09 Usable=72. Sos=254. Demods=3. Limbo=0, Disabled=162. Hints=0.
% 0.79/1.09 Megabytes=0.33.
% 0.79/1.09 User_CPU=0.07, System_CPU=0.00, Wall_clock=0.
% 0.79/1.09
% 0.79/1.09 ============================== end of statistics =====================
% 0.79/1.09
% 0.79/1.09 ============================== end of search =========================
% 0.79/1.09
% 0.79/1.09 THEOREM PROVED
% 0.79/1.09 % SZS status Theorem
% 0.79/1.09
% 0.79/1.09 Exiting with 1 proof.
% 0.79/1.09
% 0.79/1.09 Process 13767 exit (max_proofs) Mon Jul 11 02:38:46 2022
% 0.79/1.09 Prover9 interrupted
%------------------------------------------------------------------------------