TSTP Solution File: SET985+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 04:33:51 EDT 2022
% Result : Theorem 0.46s 1.00s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET985+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n005.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 : Mon Jul 11 06:23:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.46/1.00 ============================== Prover9 ===============================
% 0.46/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.46/1.00 Process 5866 was started by sandbox2 on n005.cluster.edu,
% 0.46/1.00 Mon Jul 11 06:23:52 2022
% 0.46/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_5713_n005.cluster.edu".
% 0.46/1.00 ============================== end of head ===========================
% 0.46/1.00
% 0.46/1.00 ============================== INPUT =================================
% 0.46/1.00
% 0.46/1.00 % Reading from file /tmp/Prover9_5713_n005.cluster.edu
% 0.46/1.00
% 0.46/1.00 set(prolog_style_variables).
% 0.46/1.00 set(auto2).
% 0.46/1.00 % set(auto2) -> set(auto).
% 0.46/1.00 % set(auto) -> set(auto_inference).
% 0.46/1.00 % set(auto) -> set(auto_setup).
% 0.46/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.46/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.46/1.00 % set(auto) -> set(auto_limits).
% 0.46/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.46/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.46/1.00 % set(auto) -> set(auto_denials).
% 0.46/1.00 % set(auto) -> set(auto_process).
% 0.46/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.46/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.46/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.46/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.46/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.46/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.46/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.46/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.46/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.46/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.46/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.46/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.46/1.00 % set(auto2) -> assign(stats, some).
% 0.46/1.00 % set(auto2) -> clear(echo_input).
% 0.46/1.00 % set(auto2) -> set(quiet).
% 0.46/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.46/1.00 % set(auto2) -> clear(print_given).
% 0.46/1.00 assign(lrs_ticks,-1).
% 0.46/1.00 assign(sos_limit,10000).
% 0.46/1.00 assign(order,kbo).
% 0.46/1.00 set(lex_order_vars).
% 0.46/1.00 clear(print_given).
% 0.46/1.00
% 0.46/1.00 % formulas(sos). % not echoed (8 formulas)
% 0.46/1.00
% 0.46/1.00 ============================== end of input ==========================
% 0.46/1.00
% 0.46/1.00 % From the command line: assign(max_seconds, 300).
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.46/1.00
% 0.46/1.00 % Formulas that are not ordinary clauses:
% 0.46/1.00 1 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 2 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 3 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 4 (all A all B (cartesian_product2(A,B) = empty_set <-> A = empty_set | B = empty_set)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 5 (all A all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) -> cartesian_product2(A,B) = empty_set | subset(A,C) & subset(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 6 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.00 7 -(all A (-empty(A) -> (all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) | subset(cartesian_product2(B,A),cartesian_product2(D,C)) -> subset(B,D))))) # label(t139_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.00
% 0.46/1.00 ============================== end of process non-clausal formulas ===
% 0.46/1.00
% 0.46/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.46/1.00
% 0.46/1.00 ============================== PREDICATE ELIMINATION =================
% 0.46/1.00
% 0.46/1.00 ============================== end predicate elimination =============
% 0.46/1.00
% 0.46/1.00 Auto_denials: (non-Horn, no changes).
% 0.46/1.00
% 0.46/1.00 Term ordering decisions:
% 0.46/1.00 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cartesian_product2=1.
% 0.46/1.00
% 0.46/1.00 ============================== end of process initial clauses ========
% 0.46/1.00
% 0.46/1.00 ============================== CLAUSES FOR SEARCH ====================
% 0.46/1.00
% 0.46/1.00 ============================== end of clauses for search =============
% 0.46/1.00
% 0.46/1.00 ============================== SEARCH ================================
% 0.46/1.00
% 0.46/1.00 % Starting search at 0.01 seconds.
% 0.46/1.00
% 0.46/1.00 ============================== PROOF =================================
% 0.46/1.00 % SZS status Theorem
% 0.46/1.00 % SZS output start Refutation
% 0.46/1.00
% 0.46/1.00 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.46/1.01 % Length of proof is 19.
% 0.46/1.01 % Level of proof is 7.
% 0.46/1.01 % Maximum clause weight is 15.000.
% 0.46/1.01 % Given clauses 21.
% 0.46/1.01
% 0.46/1.01 4 (all A all B (cartesian_product2(A,B) = empty_set <-> A = empty_set | B = empty_set)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 5 (all A all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) -> cartesian_product2(A,B) = empty_set | subset(A,C) & subset(B,D))) # label(t138_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 6 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.46/1.01 7 -(all A (-empty(A) -> (all B all C all D (subset(cartesian_product2(A,B),cartesian_product2(C,D)) | subset(cartesian_product2(B,A),cartesian_product2(D,C)) -> subset(B,D))))) # label(t139_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.46/1.01 8 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 0.46/1.01 11 subset(empty_set,A) # label(t2_xboole_1) # label(axiom). [clausify(6)].
% 0.46/1.01 12 subset(cartesian_product2(c3,c4),cartesian_product2(c5,c6)) | subset(cartesian_product2(c4,c3),cartesian_product2(c6,c5)) # label(t139_zfmisc_1) # label(negated_conjecture). [clausify(7)].
% 0.46/1.01 14 -empty(c3) # label(t139_zfmisc_1) # label(negated_conjecture). [clausify(7)].
% 0.46/1.01 15 -subset(c4,c6) # label(t139_zfmisc_1) # label(negated_conjecture). [clausify(7)].
% 0.46/1.01 20 cartesian_product2(A,B) != empty_set | A = empty_set | B = empty_set # label(t113_zfmisc_1) # label(axiom). [clausify(4)].
% 0.46/1.01 21 cartesian_product2(A,B) != empty_set | empty_set = A | empty_set = B. [copy(20),flip(b),flip(c)].
% 0.46/1.01 22 -subset(cartesian_product2(A,B),cartesian_product2(C,D)) | cartesian_product2(A,B) = empty_set | subset(A,C) # label(t138_zfmisc_1) # label(axiom). [clausify(5)].
% 0.46/1.01 23 -subset(cartesian_product2(A,B),cartesian_product2(C,D)) | cartesian_product2(A,B) = empty_set | subset(B,D) # label(t138_zfmisc_1) # label(axiom). [clausify(5)].
% 0.46/1.01 27 cartesian_product2(c4,c3) = empty_set | subset(cartesian_product2(c3,c4),cartesian_product2(c5,c6)). [resolve(22,a,12,b),unit_del(b,15)].
% 0.46/1.01 31 cartesian_product2(c4,c3) = empty_set | cartesian_product2(c3,c4) = empty_set. [resolve(27,b,23,a),unit_del(c,15)].
% 0.46/1.01 32 cartesian_product2(c3,c4) = empty_set | c4 = empty_set | c3 = empty_set. [resolve(31,a,21,a),flip(b),flip(c)].
% 0.46/1.01 35 c4 = empty_set | c3 = empty_set. [resolve(32,a,21,a),flip(c),flip(d),merge(c),merge(d)].
% 0.46/1.01 38 c3 = empty_set. [para(35(a,1),15(a,1)),unit_del(b,11)].
% 0.46/1.01 39 $F. [back_rewrite(14),rewrite([38(1)]),unit_del(a,8)].
% 0.46/1.01
% 0.46/1.01 % SZS output end Refutation
% 0.46/1.01 ============================== end of proof ==========================
% 0.46/1.01
% 0.46/1.01 ============================== STATISTICS ============================
% 0.46/1.01
% 0.46/1.01 Given=21. Generated=80. Kept=28. proofs=1.
% 0.46/1.01 Usable=16. Sos=1. Demods=3. Limbo=1, Disabled=23. Hints=0.
% 0.46/1.01 Megabytes=0.05.
% 0.46/1.01 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.46/1.01
% 0.46/1.01 ============================== end of statistics =====================
% 0.46/1.01
% 0.46/1.01 ============================== end of search =========================
% 0.46/1.01
% 0.46/1.01 THEOREM PROVED
% 0.46/1.01 % SZS status Theorem
% 0.46/1.01
% 0.46/1.01 Exiting with 1 proof.
% 0.46/1.01
% 0.46/1.01 Process 5866 exit (max_proofs) Mon Jul 11 06:23:52 2022
% 0.46/1.01 Prover9 interrupted
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