TSTP Solution File: SET062+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 04:26:34 EDT 2022
% Result : Theorem 0.42s 0.97s
% Output : Refutation 0.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET062+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n027.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 12:31:17 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.42/0.97 ============================== Prover9 ===============================
% 0.42/0.97 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.97 Process 8924 was started by sandbox on n027.cluster.edu,
% 0.42/0.97 Sun Jul 10 12:31:18 2022
% 0.42/0.97 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_8770_n027.cluster.edu".
% 0.42/0.97 ============================== end of head ===========================
% 0.42/0.97
% 0.42/0.97 ============================== INPUT =================================
% 0.42/0.97
% 0.42/0.97 % Reading from file /tmp/Prover9_8770_n027.cluster.edu
% 0.42/0.97
% 0.42/0.97 set(prolog_style_variables).
% 0.42/0.97 set(auto2).
% 0.42/0.97 % set(auto2) -> set(auto).
% 0.42/0.97 % set(auto) -> set(auto_inference).
% 0.42/0.97 % set(auto) -> set(auto_setup).
% 0.42/0.97 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.97 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.97 % set(auto) -> set(auto_limits).
% 0.42/0.97 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.97 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.97 % set(auto) -> set(auto_denials).
% 0.42/0.97 % set(auto) -> set(auto_process).
% 0.42/0.97 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.97 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.97 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.97 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.97 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.97 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.97 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.97 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.97 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.97 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.97 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.97 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.97 % set(auto2) -> assign(stats, some).
% 0.42/0.97 % set(auto2) -> clear(echo_input).
% 0.42/0.97 % set(auto2) -> set(quiet).
% 0.42/0.97 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.97 % set(auto2) -> clear(print_given).
% 0.42/0.97 assign(lrs_ticks,-1).
% 0.42/0.97 assign(sos_limit,10000).
% 0.42/0.97 assign(order,kbo).
% 0.42/0.97 set(lex_order_vars).
% 0.42/0.97 clear(print_given).
% 0.42/0.97
% 0.42/0.97 % formulas(sos). % not echoed (5 formulas)
% 0.42/0.97
% 0.42/0.97 ============================== end of input ==========================
% 0.42/0.97
% 0.42/0.97 % From the command line: assign(max_seconds, 300).
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.97
% 0.42/0.97 % Formulas that are not ordinary clauses:
% 0.42/0.97 1 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 3 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 4 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 5 -(all B subset(empty_set,B)) # label(prove_empty_set_subset) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.97
% 0.42/0.97 ============================== end of process non-clausal formulas ===
% 0.42/0.97
% 0.42/0.97 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.97
% 0.42/0.97 ============================== PREDICATE ELIMINATION =================
% 0.42/0.97 6 -subset(empty_set,c1) # label(prove_empty_set_subset) # label(negated_conjecture). [clausify(5)].
% 0.42/0.97 7 subset(A,A) # label(reflexivity_of_subset) # label(axiom). [clausify(3)].
% 0.42/0.97 8 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.42/0.97 Derived: member(f1(empty_set,c1),empty_set). [resolve(6,a,8,a)].
% 0.42/0.97 9 subset(A,B) | -member(f1(A,B),B) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.42/0.97 Derived: -member(f1(empty_set,c1),c1). [resolve(9,a,6,a)].
% 0.42/0.97 10 -subset(A,B) | -member(C,A) | member(C,B) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.42/0.97 Derived: -member(A,B) | member(A,C) | member(f1(B,C),B). [resolve(10,a,8,a)].
% 0.42/0.97 Derived: -member(A,B) | member(A,C) | -member(f1(B,C),C). [resolve(10,a,9,a)].
% 0.42/0.97 11 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(4)].
% 0.42/0.97 12 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(4)].
% 0.42/0.97 Derived: -member(A,B) | member(f2(B),B). [resolve(11,a,12,a)].
% 0.42/0.97
% 0.42/0.97 ============================== end predicate elimination =============
% 0.42/0.97
% 0.42/0.97 Auto_denials: (non-Horn, no changes).
% 0.42/0.97
% 0.42/0.97 Term ordering decisions:
% 0.42/0.97
% 0.42/0.97 % Assigning unary symbol f2 kb_weight 0 and highest precedence (5).
% 0.42/0.97 Function symbol KB weights: empty_set=1. c1=1. f1=1. f2=0.
% 0.42/0.97
% 0.42/0.97 ============================== PROOF =================================
% 0.42/0.97 % SZS status Theorem
% 0.42/0.97 % SZS output start Refutation
% 0.42/0.97
% 0.42/0.97 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.42/0.97 % Length of proof is 8.
% 0.42/0.97 % Level of proof is 3.
% 0.42/0.97 % Maximum clause weight is 3.000.
% 0.42/0.97 % Given clauses 0.
% 0.42/0.97
% 0.42/0.97 1 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 2 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.97 5 -(all B subset(empty_set,B)) # label(prove_empty_set_subset) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.97 6 -subset(empty_set,c1) # label(prove_empty_set_subset) # label(negated_conjecture). [clausify(5)].
% 0.42/0.97 8 subset(A,B) | member(f1(A,B),A) # label(subset_defn) # label(axiom). [clausify(2)].
% 0.42/0.97 13 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(1)].
% 0.42/0.97 14 member(f1(empty_set,c1),empty_set). [resolve(6,a,8,a)].
% 0.42/0.97 15 $F. [copy(14),unit_del(a,13)].
% 0.42/0.97
% 0.42/0.97 % SZS output end Refutation
% 0.42/0.97 ============================== end of proof ==========================
% 0.42/0.97
% 0.42/0.97 ============================== STATISTICS ============================
% 0.42/0.97
% 0.42/0.97 Given=0. Generated=2. Kept=1. proofs=1.
% 0.42/0.97 Usable=0. Sos=0. Demods=0. Limbo=1, Disabled=9. Hints=0.
% 0.42/0.97 Megabytes=0.02.
% 0.42/0.97 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.42/0.97
% 0.42/0.97 ============================== end of statistics =====================
% 0.42/0.97
% 0.42/0.97 ============================== end of search =========================
% 0.42/0.97
% 0.42/0.97 THEOREM PROVED
% 0.42/0.97 % SZS status Theorem
% 0.42/0.97
% 0.42/0.97 Exiting with 1 proof.
% 0.42/0.97
% 0.42/0.97 Process 8924 exit (max_proofs) Sun Jul 10 12:31:18 2022
% 0.42/0.97 Prover9 interrupted
%------------------------------------------------------------------------------