TSTP Solution File: SET366+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET366+4 : 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 04:29:11 EDT 2022
% Result : Theorem 0.74s 1.01s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 02:34:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.00 ============================== Prover9 ===============================
% 0.74/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.00 Process 31633 was started by sandbox on n016.cluster.edu,
% 0.74/1.00 Mon Jul 11 02:34:43 2022
% 0.74/1.00 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_31467_n016.cluster.edu".
% 0.74/1.00 ============================== end of head ===========================
% 0.74/1.00
% 0.74/1.00 ============================== INPUT =================================
% 0.74/1.00
% 0.74/1.00 % Reading from file /tmp/Prover9_31467_n016.cluster.edu
% 0.74/1.00
% 0.74/1.00 set(prolog_style_variables).
% 0.74/1.00 set(auto2).
% 0.74/1.00 % set(auto2) -> set(auto).
% 0.74/1.00 % set(auto) -> set(auto_inference).
% 0.74/1.00 % set(auto) -> set(auto_setup).
% 0.74/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.00 % set(auto) -> set(auto_limits).
% 0.74/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.00 % set(auto) -> set(auto_denials).
% 0.74/1.00 % set(auto) -> set(auto_process).
% 0.74/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.00 % set(auto2) -> assign(stats, some).
% 0.74/1.00 % set(auto2) -> clear(echo_input).
% 0.74/1.00 % set(auto2) -> set(quiet).
% 0.74/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.00 % set(auto2) -> clear(print_given).
% 0.74/1.00 assign(lrs_ticks,-1).
% 0.74/1.00 assign(sos_limit,10000).
% 0.74/1.00 assign(order,kbo).
% 0.74/1.00 set(lex_order_vars).
% 0.74/1.00 clear(print_given).
% 0.74/1.00
% 0.74/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.74/1.00
% 0.74/1.00 ============================== end of input ==========================
% 0.74/1.00
% 0.74/1.00 % From the command line: assign(max_seconds, 300).
% 0.74/1.00
% 0.74/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.00
% 0.74/1.00 % Formulas that are not ordinary clauses:
% 0.74/1.00 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 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].
% 0.74/1.00 12 -(all A member(empty_set,power_set(A))) # label(thI47) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.00
% 0.74/1.00 ============================== end of process non-clausal formulas ===
% 0.74/1.00
% 0.74/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.00
% 0.74/1.00 ============================== PREDICATE ELIMINATION =================
% 0.74/1.00 13 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.74/1.00 14 -equal_set(A,B) | subset(A,B) # label(equal_set) # label(axiom). [clausify(2)].
% 0.74/1.01 15 -equal_set(A,B) | subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 0.74/1.01 16 member(A,power_set(B)) | -subset(A,B) # label(power_set) # label(axiom). [clausify(3)].
% 0.74/1.01 17 subset(A,B) | member(f1(A,B),A) # label(subset) # label(axiom). [clausify(1)].
% 0.74/1.01 18 -member(A,power_set(B)) | subset(A,B) # label(power_set) # label(axiom). [clausify(3)].
% 0.74/1.01 Derived: member(A,power_set(B)) | member(f1(A,B),A). [resolve(16,b,17,a)].
% 0.74/1.01 19 subset(A,B) | -member(f1(A,B),B) # label(subset) # label(axiom). [clausify(1)].
% 0.74/1.01 Derived: -member(f1(A,B),B) | member(A,power_set(B)). [resolve(19,a,16,b)].
% 0.74/1.01 20 -subset(A,B) | -member(C,A) | member(C,B) # label(subset) # label(axiom). [clausify(1)].
% 0.74/1.01 Derived: -member(A,B) | member(A,C) | member(f1(B,C),B). [resolve(20,a,17,a)].
% 0.74/1.01 Derived: -member(A,B) | member(A,C) | -member(B,power_set(C)). [resolve(20,a,18,b)].
% 0.74/1.01 Derived: -member(A,B) | member(A,C) | -member(f1(B,C),C). [resolve(20,a,19,a)].
% 0.74/1.01
% 0.74/1.01 ============================== end predicate elimination =============
% 0.74/1.01
% 0.74/1.01 Auto_denials: (non-Horn, no changes).
% 0.74/1.01
% 0.74/1.01 Term ordering decisions:
% 0.74/1.01 Function symbol KB weights: empty_set=1. c1=1. intersection=1. union=1. unordered_pair=1. difference=1. f1=1. f2=1. f3=1. power_set=1. product=1. sum=1. singleton=1.
% 0.74/1.01
% 0.74/1.01 ============================== end of process initial clauses ========
% 0.74/1.01
% 0.74/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.01
% 0.74/1.01 ============================== end of clauses for search =============
% 0.74/1.01
% 0.74/1.01 ============================== SEARCH ================================
% 0.74/1.01
% 0.74/1.01 % Starting search at 0.01 seconds.
% 0.74/1.01
% 0.74/1.01 ============================== PROOF =================================
% 0.74/1.01 % SZS status Theorem
% 0.74/1.01 % SZS output start Refutation
% 0.74/1.01
% 0.74/1.01 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.74/1.01 % Length of proof is 11.
% 0.74/1.01 % Level of proof is 4.
% 0.74/1.01 % Maximum clause weight is 9.000.
% 0.74/1.01 % Given clauses 23.
% 0.74/1.01
% 0.74/1.01 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 12 -(all A member(empty_set,power_set(A))) # label(thI47) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.01 16 member(A,power_set(B)) | -subset(A,B) # label(power_set) # label(axiom). [clausify(3)].
% 0.74/1.01 17 subset(A,B) | member(f1(A,B),A) # label(subset) # label(axiom). [clausify(1)].
% 0.74/1.01 22 -member(A,empty_set) # label(empty_set) # label(axiom). [clausify(6)].
% 0.74/1.01 23 -member(empty_set,power_set(c1)) # label(thI47) # label(negated_conjecture). [clausify(12)].
% 0.74/1.01 43 member(A,power_set(B)) | member(f1(A,B),A). [resolve(16,b,17,a)].
% 0.74/1.01 106 member(empty_set,power_set(A)). [resolve(43,b,22,a)].
% 0.74/1.01 107 $F. [resolve(106,a,23,a)].
% 0.74/1.01
% 0.74/1.01 % SZS output end Refutation
% 0.74/1.01 ============================== end of proof ==========================
% 0.74/1.01
% 0.74/1.01 ============================== STATISTICS ============================
% 0.74/1.01
% 0.74/1.01 Given=23. Generated=88. Kept=86. proofs=1.
% 0.74/1.01 Usable=23. Sos=44. Demods=0. Limbo=18, Disabled=35. Hints=0.
% 0.74/1.01 Megabytes=0.12.
% 0.74/1.01 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.74/1.01
% 0.74/1.01 ============================== end of statistics =====================
% 0.74/1.01
% 0.74/1.01 ============================== end of search =========================
% 0.74/1.01
% 0.74/1.01 THEOREM PROVED
% 0.74/1.01 % SZS status Theorem
% 0.74/1.01
% 0.74/1.01 Exiting with 1 proof.
% 0.74/1.01
% 0.74/1.01 Process 31633 exit (max_proofs) Mon Jul 11 02:34:43 2022
% 0.74/1.01 Prover9 interrupted
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