TSTP Solution File: SET355+4 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 04:29:07 EDT 2022
% Result : Theorem 0.76s 1.06s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET355+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.35 % Computer : n029.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 : Sun Jul 10 03:17:31 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.46/1.02 ============================== Prover9 ===============================
% 0.46/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.02 Process 2887 was started by sandbox2 on n029.cluster.edu,
% 0.46/1.02 Sun Jul 10 03:17:31 2022
% 0.46/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_2733_n029.cluster.edu".
% 0.46/1.02 ============================== end of head ===========================
% 0.46/1.02
% 0.46/1.02 ============================== INPUT =================================
% 0.46/1.02
% 0.46/1.02 % Reading from file /tmp/Prover9_2733_n029.cluster.edu
% 0.46/1.02
% 0.46/1.02 set(prolog_style_variables).
% 0.46/1.02 set(auto2).
% 0.46/1.02 % set(auto2) -> set(auto).
% 0.46/1.02 % set(auto) -> set(auto_inference).
% 0.46/1.02 % set(auto) -> set(auto_setup).
% 0.46/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.02 % set(auto) -> set(auto_limits).
% 0.46/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.02 % set(auto) -> set(auto_denials).
% 0.46/1.02 % set(auto) -> set(auto_process).
% 0.46/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.02 % set(auto2) -> assign(stats, some).
% 0.46/1.02 % set(auto2) -> clear(echo_input).
% 0.46/1.02 % set(auto2) -> set(quiet).
% 0.46/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.02 % set(auto2) -> clear(print_given).
% 0.46/1.02 assign(lrs_ticks,-1).
% 0.46/1.02 assign(sos_limit,10000).
% 0.46/1.02 assign(order,kbo).
% 0.46/1.02 set(lex_order_vars).
% 0.46/1.02 clear(print_given).
% 0.46/1.02
% 0.46/1.02 % formulas(sos). % not echoed (12 formulas)
% 0.46/1.02
% 0.46/1.02 ============================== end of input ==========================
% 0.46/1.02
% 0.46/1.02 % From the command line: assign(max_seconds, 300).
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.02
% 0.46/1.02 % Formulas that are not ordinary clauses:
% 0.46/1.02 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 4 (all X all A all B (member(X,intersection(A,B)) <-> member(X,A) & member(X,B))) # label(intersection) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 5 (all X all A all B (member(X,union(A,B)) <-> member(X,A) | member(X,B))) # label(union) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 7 (all B all A all E (member(B,difference(E,A)) <-> member(B,E) & -member(B,A))) # label(difference) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 9 (all X all A all B (member(X,unordered_pair(A,B)) <-> X = A | X = B)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 10 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 11 (all X all A (member(X,product(A)) <-> (all Y (member(Y,A) -> member(X,Y))))) # label(product) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.02 12 -(all A all X (member(X,A) -> subset(X,sum(A)))) # label(thI43) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.02
% 0.46/1.02 ============================== end of process non-clausal formulas ===
% 0.46/1.02
% 0.46/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.02
% 0.46/1.02 ============================== PREDICATE ELIMINATION =================
% 0.46/1.02 13 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.46/1.02 14 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom). [clausify(2)].
% 0.76/1.06 15 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.76/1.06
% 0.76/1.06 ============================== end predicate elimination =============
% 0.76/1.06
% 0.76/1.06 Auto_denials: (non-Horn, no changes).
% 0.76/1.06
% 0.76/1.06 Term ordering decisions:
% 0.76/1.06 Function symbol KB weights: empty_set=1. c1=1. c2=1. intersection=1. union=1. unordered_pair=1. difference=1. f1=1. f2=1. f3=1. product=1. sum=1. power_set=1. singleton=1.
% 0.76/1.06
% 0.76/1.06 ============================== end of process initial clauses ========
% 0.76/1.06
% 0.76/1.06 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.06
% 0.76/1.06 ============================== end of clauses for search =============
% 0.76/1.06
% 0.76/1.06 ============================== SEARCH ================================
% 0.76/1.06
% 0.76/1.06 % Starting search at 0.01 seconds.
% 0.76/1.06
% 0.76/1.06 ============================== PROOF =================================
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06 % SZS output start Refutation
% 0.76/1.06
% 0.76/1.06 % Proof 1 at 0.05 (+ 0.00) seconds.
% 0.76/1.06 % Length of proof is 11.
% 0.76/1.06 % Level of proof is 3.
% 0.76/1.06 % Maximum clause weight is 10.000.
% 0.76/1.06 % Given clauses 87.
% 0.76/1.06
% 0.76/1.06 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 10 (all X all A (member(X,sum(A)) <-> (exists Y (member(Y,A) & member(X,Y))))) # label(sum) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.06 12 -(all A all X (member(X,A) -> subset(X,sum(A)))) # label(thI43) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.06 16 member(c2,c1) # label(thI43) # label(negated_conjecture). [clausify(12)].
% 0.76/1.06 17 subset(A,B) | member(f1(A,B),A) # label(subset) # label(axiom). [clausify(1)].
% 0.76/1.06 20 -subset(c2,sum(c1)) # label(thI43) # label(negated_conjecture). [clausify(12)].
% 0.76/1.06 26 subset(A,B) | -member(f1(A,B),B) # label(subset) # label(axiom). [clausify(1)].
% 0.76/1.06 38 member(A,sum(B)) | -member(C,B) | -member(A,C) # label(sum) # label(axiom). [clausify(10)].
% 0.76/1.06 49 member(f1(c2,sum(c1)),c2). [resolve(20,a,17,a)].
% 0.76/1.06 57 -member(f1(c2,sum(c1)),sum(c1)). [ur(26,a,20,a)].
% 0.76/1.06 945 $F. [ur(38,a,57,a,c,49,a),unit_del(a,16)].
% 0.76/1.06
% 0.76/1.06 % SZS output end Refutation
% 0.76/1.06 ============================== end of proof ==========================
% 0.76/1.06
% 0.76/1.06 ============================== STATISTICS ============================
% 0.76/1.06
% 0.76/1.06 Given=87. Generated=1308. Kept=929. proofs=1.
% 0.76/1.06 Usable=86. Sos=782. Demods=1. Limbo=33, Disabled=59. Hints=0.
% 0.76/1.06 Megabytes=0.64.
% 0.76/1.06 User_CPU=0.05, System_CPU=0.00, Wall_clock=0.
% 0.76/1.06
% 0.76/1.06 ============================== end of statistics =====================
% 0.76/1.06
% 0.76/1.06 ============================== end of search =========================
% 0.76/1.06
% 0.76/1.06 THEOREM PROVED
% 0.76/1.06 % SZS status Theorem
% 0.76/1.06
% 0.76/1.06 Exiting with 1 proof.
% 0.76/1.06
% 0.76/1.06 Process 2887 exit (max_proofs) Sun Jul 10 03:17:31 2022
% 0.76/1.06 Prover9 interrupted
%------------------------------------------------------------------------------