TSTP Solution File: SET602+4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 04:30:38 EDT 2022
% Result : Theorem 3.00s 3.35s
% Output : Refutation 3.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET602+4 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 20:13:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.01 ============================== Prover9 ===============================
% 0.45/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.01 Process 24571 was started by sandbox2 on n004.cluster.edu,
% 0.45/1.01 Sat Jul 9 20:13:08 2022
% 0.45/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24417_n004.cluster.edu".
% 0.45/1.01 ============================== end of head ===========================
% 0.45/1.01
% 0.45/1.01 ============================== INPUT =================================
% 0.45/1.01
% 0.45/1.01 % Reading from file /tmp/Prover9_24417_n004.cluster.edu
% 0.45/1.01
% 0.45/1.01 set(prolog_style_variables).
% 0.45/1.01 set(auto2).
% 0.45/1.01 % set(auto2) -> set(auto).
% 0.45/1.01 % set(auto) -> set(auto_inference).
% 0.45/1.01 % set(auto) -> set(auto_setup).
% 0.45/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.01 % set(auto) -> set(auto_limits).
% 0.45/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.01 % set(auto) -> set(auto_denials).
% 0.45/1.01 % set(auto) -> set(auto_process).
% 0.45/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.01 % set(auto2) -> assign(stats, some).
% 0.45/1.01 % set(auto2) -> clear(echo_input).
% 0.45/1.01 % set(auto2) -> set(quiet).
% 0.45/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.01 % set(auto2) -> clear(print_given).
% 0.45/1.01 assign(lrs_ticks,-1).
% 0.45/1.01 assign(sos_limit,10000).
% 0.45/1.01 assign(order,kbo).
% 0.45/1.01 set(lex_order_vars).
% 0.45/1.01 clear(print_given).
% 0.45/1.01
% 0.45/1.01 % formulas(sos). % not echoed (12 formulas)
% 0.45/1.01
% 0.45/1.01 ============================== end of input ==========================
% 0.45/1.01
% 0.45/1.01 % From the command line: assign(max_seconds, 300).
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.01
% 0.45/1.01 % Formulas that are not ordinary clauses:
% 0.45/1.01 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 8 (all X all A (member(X,singleton(A)) <-> X = A)) # label(singleton) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 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].
% 0.45/1.01 12 -(all E equal_set(difference(E,E),empty_set)) # label(thI29) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.01
% 0.45/1.01 ============================== end of process non-clausal formulas ===
% 0.45/1.01
% 0.45/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.01
% 0.45/1.01 ============================== PREDICATE ELIMINATION =================
% 0.45/1.01
% 0.45/1.01 ============================== end predicate elimination =============
% 0.45/1.01
% 0.45/1.01 Auto_denials: (non-Horn, no changes).
% 3.00/3.35
% 3.00/3.35 Term ordering decisions:
% 3.00/3.35 Function symbol KB weights: empty_set=1. c1=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.
% 3.00/3.35
% 3.00/3.35 ============================== end of process initial clauses ========
% 3.00/3.35
% 3.00/3.35 ============================== CLAUSES FOR SEARCH ====================
% 3.00/3.35
% 3.00/3.35 ============================== end of clauses for search =============
% 3.00/3.35
% 3.00/3.35 ============================== SEARCH ================================
% 3.00/3.35
% 3.00/3.35 % Starting search at 0.01 seconds.
% 3.00/3.35
% 3.00/3.35 Low Water (keep): wt=11.000, iters=3376
% 3.00/3.35
% 3.00/3.35 Low Water (keep): wt=10.000, iters=3359
% 3.00/3.35
% 3.00/3.35 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 0.45 sec).
% 3.00/3.35
% 3.00/3.35 Low Water (keep): wt=9.000, iters=3337
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4344, wt=37.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=3380, wt=35.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4339, wt=32.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4341, wt=31.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4356, wt=30.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=7538, wt=29.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=7363, wt=28.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=6360, wt=27.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=6429, wt=26.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4119, wt=14.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4512, wt=13.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4545, wt=12.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=4532, wt=11.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=5549, wt=10.000
% 3.00/3.35
% 3.00/3.35 Low Water (displace): id=13425, wt=8.000
% 3.00/3.35
% 3.00/3.35 ============================== PROOF =================================
% 3.00/3.35 % SZS status Theorem
% 3.00/3.35 % SZS output start Refutation
% 3.00/3.35
% 3.00/3.35 % Proof 1 at 2.13 (+ 0.22) seconds.
% 3.00/3.35 % Length of proof is 23.
% 3.00/3.35 % Level of proof is 7.
% 3.00/3.35 % Maximum clause weight is 13.000.
% 3.00/3.35 % Given clauses 1566.
% 3.00/3.35
% 3.00/3.35 1 (all A all B (subset(A,B) <-> (all X (member(X,A) -> member(X,B))))) # label(subset) # label(axiom) # label(non_clause). [assumption].
% 3.00/3.35 2 (all A all B (equal_set(A,B) <-> subset(A,B) & subset(B,A))) # label(equal_set) # label(axiom) # label(non_clause). [assumption].
% 3.00/3.35 3 (all X all A (member(X,power_set(A)) <-> subset(X,A))) # label(power_set) # label(axiom) # label(non_clause). [assumption].
% 3.00/3.35 6 (all X -member(X,empty_set)) # label(empty_set) # label(axiom) # label(non_clause). [assumption].
% 3.00/3.35 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].
% 3.00/3.35 12 -(all E equal_set(difference(E,E),empty_set)) # label(thI29) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.00/3.35 13 subset(A,B) | member(f1(A,B),A) # label(subset) # label(axiom). [clausify(1)].
% 3.00/3.35 15 -member(A,empty_set) # label(empty_set) # label(axiom). [clausify(6)].
% 3.00/3.35 16 -equal_set(difference(c1,c1),empty_set) # label(thI29) # label(negated_conjecture). [clausify(12)].
% 3.00/3.35 17 -member(A,difference(B,C)) | -member(A,C) # label(difference) # label(axiom). [clausify(7)].
% 3.00/3.35 20 -member(A,power_set(B)) | subset(A,B) # label(power_set) # label(axiom). [clausify(3)].
% 3.00/3.35 21 member(A,power_set(B)) | -subset(A,B) # label(power_set) # label(axiom). [clausify(3)].
% 3.00/3.35 29 -member(A,difference(B,C)) | member(A,B) # label(difference) # label(axiom). [clausify(7)].
% 3.00/3.35 33 equal_set(A,B) | -subset(A,B) | -subset(B,A) # label(equal_set) # label(axiom). [clausify(2)].
% 3.00/3.35 51 member(A,power_set(B)) | member(f1(A,B),A). [resolve(21,b,13,a)].
% 3.00/3.35 395 member(difference(A,B),power_set(C)) | member(f1(difference(A,B),C),A). [resolve(51,b,29,a)].
% 3.00/3.35 403 member(difference(A,B),power_set(C)) | -member(f1(difference(A,B),C),B). [resolve(51,b,17,a)].
% 3.00/3.35 404 member(empty_set,power_set(A)). [resolve(51,b,15,a)].
% 3.00/3.35 517 subset(empty_set,A). [resolve(404,a,20,a)].
% 3.00/3.35 535 -subset(difference(c1,c1),empty_set). [ur(33,a,16,a,c,517,a)].
% 3.00/3.35 980 -member(difference(c1,c1),power_set(empty_set)). [ur(20,b,535,a)].
% 3.00/3.35 14245 member(difference(A,A),power_set(B)). [resolve(403,b,395,b),merge(b)].
% 3.00/3.35 14246 $F. [resolve(14245,a,980,a)].
% 3.00/3.35
% 3.00/3.35 % SZS output end Refutation
% 3.00/3.35 ============================== end of proof ==========================
% 3.00/3.35
% 3.00/3.35 ============================== STATISTICS ============================
% 3.00/3.35
% 3.00/3.35 Given=1566. Generated=434944. Kept=14233. proofs=1.
% 3.00/3.35 Usable=1553. Sos=9999. Demods=31. Limbo=8, Disabled=2702. Hints=0.
% 3.00/3.35 Megabytes=8.65.
% 3.00/3.35 User_CPU=2.13, System_CPU=0.22, Wall_clock=2.
% 3.00/3.35
% 3.00/3.35 ============================== end of statistics =====================
% 3.00/3.35
% 3.00/3.35 ============================== end of search =========================
% 3.00/3.35
% 3.00/3.35 THEOREM PROVED
% 3.00/3.35 % SZS status Theorem
% 3.00/3.35
% 3.00/3.35 Exiting with 1 proof.
% 3.00/3.35
% 3.00/3.35 Process 24571 exit (max_proofs) Sat Jul 9 20:13:10 2022
% 3.00/3.35 Prover9 interrupted
%------------------------------------------------------------------------------