TSTP Solution File: SET008+3 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 04:25:32 EDT 2022
% Result : Theorem 1.06s 1.35s
% Output : Refutation 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET008+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n016.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 : Mon Jul 11 02:15:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.48/1.03 ============================== Prover9 ===============================
% 0.48/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.48/1.03 Process 8147 was started by sandbox2 on n016.cluster.edu,
% 0.48/1.03 Mon Jul 11 02:15:27 2022
% 0.48/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7993_n016.cluster.edu".
% 0.48/1.03 ============================== end of head ===========================
% 0.48/1.03
% 0.48/1.03 ============================== INPUT =================================
% 0.48/1.03
% 0.48/1.03 % Reading from file /tmp/Prover9_7993_n016.cluster.edu
% 0.48/1.03
% 0.48/1.03 set(prolog_style_variables).
% 0.48/1.03 set(auto2).
% 0.48/1.03 % set(auto2) -> set(auto).
% 0.48/1.03 % set(auto) -> set(auto_inference).
% 0.48/1.03 % set(auto) -> set(auto_setup).
% 0.48/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.48/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.48/1.03 % set(auto) -> set(auto_limits).
% 0.48/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.48/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.48/1.03 % set(auto) -> set(auto_denials).
% 0.48/1.03 % set(auto) -> set(auto_process).
% 0.48/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.48/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.48/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.48/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.48/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.48/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.48/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.48/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.48/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.48/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.48/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.48/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.48/1.03 % set(auto2) -> assign(stats, some).
% 0.48/1.03 % set(auto2) -> clear(echo_input).
% 0.48/1.03 % set(auto2) -> set(quiet).
% 0.48/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.48/1.03 % set(auto2) -> clear(print_given).
% 0.48/1.03 assign(lrs_ticks,-1).
% 0.48/1.03 assign(sos_limit,10000).
% 0.48/1.03 assign(order,kbo).
% 0.48/1.03 set(lex_order_vars).
% 0.48/1.03 clear(print_given).
% 0.48/1.03
% 0.48/1.03 % formulas(sos). % not echoed (10 formulas)
% 0.48/1.03
% 0.48/1.03 ============================== end of input ==========================
% 0.48/1.03
% 0.48/1.03 % From the command line: assign(max_seconds, 300).
% 0.48/1.03
% 0.48/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.48/1.03
% 0.48/1.03 % Formulas that are not ordinary clauses:
% 0.48/1.03 1 (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].
% 0.48/1.03 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].
% 0.48/1.03 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 4 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 5 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 6 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 7 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 8 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 9 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.48/1.03 10 -(all B all C intersection(difference(B,C),C) = empty_set) # label(prove_intersection_difference_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.48/1.03
% 0.48/1.03 ============================== end of process non-clausal formulas ===
% 0.48/1.03
% 0.48/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.48/1.03
% 0.48/1.03 ============================== PREDICATE ELIMINATION =================
% 0.48/1.03 11 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.48/1.03 12 empty(A) | member(f2(A),A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.48/1.03 Derived: -member(A,B) | member(f2(B),B). [resolve(11,a,12,a)].
% 0.48/1.03
% 0.48/1.03 ============================== end predicate elimination =============
% 0.48/1.03
% 0.48/1.03 Auto_denials: (non-Horn, no changes).
% 0.48/1.03
% 0.48/1.03 Term ordering decisions:
% 0.48/1.03
% 0.48/1.03 % Assigning unary symbol f2 kb_weight 0 and highest precedence (11).
% 1.06/1.35 Function symbol KB weights: empty_set=1. c1=1. c2=1. intersection=1. difference=1. f1=1. f3=1. f2=0.
% 1.06/1.35
% 1.06/1.35 ============================== end of process initial clauses ========
% 1.06/1.35
% 1.06/1.35 ============================== CLAUSES FOR SEARCH ====================
% 1.06/1.35
% 1.06/1.35 ============================== end of clauses for search =============
% 1.06/1.35
% 1.06/1.35 ============================== SEARCH ================================
% 1.06/1.35
% 1.06/1.35 % Starting search at 0.01 seconds.
% 1.06/1.35
% 1.06/1.35 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 114 (0.00 of 0.30 sec).
% 1.06/1.35
% 1.06/1.35 ============================== PROOF =================================
% 1.06/1.35 % SZS status Theorem
% 1.06/1.35 % SZS output start Refutation
% 1.06/1.35
% 1.06/1.35 % Proof 1 at 0.32 (+ 0.01) seconds.
% 1.06/1.35 % Length of proof is 19.
% 1.06/1.35 % Level of proof is 5.
% 1.06/1.35 % Maximum clause weight is 25.000.
% 1.06/1.35 % Given clauses 532.
% 1.06/1.35
% 1.06/1.35 1 (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].
% 1.06/1.35 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].
% 1.06/1.35 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.35 5 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.35 9 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 1.06/1.35 10 -(all B all C intersection(difference(B,C),C) = empty_set) # label(prove_intersection_difference_empty_set) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.06/1.35 14 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(5)].
% 1.06/1.35 16 A = B | member(f3(B,A),B) | member(f3(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(9)].
% 1.06/1.35 17 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(3)].
% 1.06/1.35 18 intersection(difference(c1,c2),c2) != empty_set # label(prove_intersection_difference_empty_set) # label(negated_conjecture). [clausify(10)].
% 1.06/1.35 19 intersection(c2,difference(c1,c2)) != empty_set. [copy(18),rewrite([14(5)])].
% 1.06/1.35 20 -member(A,difference(B,C)) | -member(A,C) # label(difference_defn) # label(axiom). [clausify(2)].
% 1.06/1.35 23 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(1)].
% 1.06/1.35 37 empty_set = A | member(f3(empty_set,A),A). [resolve(17,a,16,b),flip(a)].
% 1.06/1.35 40 member(f3(A,intersection(B,C)),B) | intersection(B,C) = A | member(f3(A,intersection(B,C)),A). [resolve(23,a,16,c)].
% 1.06/1.35 106 intersection(A,B) = empty_set | member(f3(empty_set,intersection(A,B)),A). [resolve(37,b,23,a),flip(a)].
% 1.06/1.35 146 intersection(A,difference(B,C)) = D | member(f3(D,intersection(A,difference(B,C))),D) | -member(f3(D,intersection(A,difference(B,C))),C). [resolve(40,a,20,a),rewrite([14(2),14(5),14(9)])].
% 1.06/1.35 3121 intersection(A,difference(B,A)) = empty_set. [resolve(146,c,106,b),merge(c),unit_del(b,17)].
% 1.06/1.35 3122 $F. [resolve(3121,a,19,a)].
% 1.06/1.35
% 1.06/1.35 % SZS output end Refutation
% 1.06/1.35 ============================== end of proof ==========================
% 1.06/1.35
% 1.06/1.35 ============================== STATISTICS ============================
% 1.06/1.35
% 1.06/1.35 Given=532. Generated=8843. Kept=3108. proofs=1.
% 1.06/1.35 Usable=527. Sos=2548. Demods=4. Limbo=5, Disabled=50. Hints=0.
% 1.06/1.35 Megabytes=2.38.
% 1.06/1.35 User_CPU=0.32, System_CPU=0.01, Wall_clock=1.
% 1.06/1.35
% 1.06/1.35 ============================== end of statistics =====================
% 1.06/1.35
% 1.06/1.35 ============================== end of search =========================
% 1.06/1.35
% 1.06/1.35 THEOREM PROVED
% 1.06/1.35 % SZS status Theorem
% 1.06/1.35
% 1.06/1.35 Exiting with 1 proof.
% 1.06/1.35
% 1.06/1.35 Process 8147 exit (max_proofs) Mon Jul 11 02:15:28 2022
% 1.06/1.35 Prover9 interrupted
%------------------------------------------------------------------------------