TSTP Solution File: SEU165+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU165+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 13:29:33 EDT 2022
% Result : Theorem 0.66s 0.96s
% Output : Refutation 0.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU165+3 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 20 06:58:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.66/0.96 ============================== Prover9 ===============================
% 0.66/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.66/0.96 Process 23251 was started by sandbox on n017.cluster.edu,
% 0.66/0.96 Mon Jun 20 06:58:59 2022
% 0.66/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23098_n017.cluster.edu".
% 0.66/0.96 ============================== end of head ===========================
% 0.66/0.96
% 0.66/0.96 ============================== INPUT =================================
% 0.66/0.96
% 0.66/0.96 % Reading from file /tmp/Prover9_23098_n017.cluster.edu
% 0.66/0.96
% 0.66/0.96 set(prolog_style_variables).
% 0.66/0.96 set(auto2).
% 0.66/0.96 % set(auto2) -> set(auto).
% 0.66/0.96 % set(auto) -> set(auto_inference).
% 0.66/0.96 % set(auto) -> set(auto_setup).
% 0.66/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.66/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.66/0.96 % set(auto) -> set(auto_limits).
% 0.66/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.66/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.66/0.96 % set(auto) -> set(auto_denials).
% 0.66/0.96 % set(auto) -> set(auto_process).
% 0.66/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.66/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.66/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.66/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.66/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.66/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.66/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.66/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.66/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.66/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.66/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.66/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.66/0.96 % set(auto2) -> assign(stats, some).
% 0.66/0.96 % set(auto2) -> clear(echo_input).
% 0.66/0.96 % set(auto2) -> set(quiet).
% 0.66/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.66/0.96 % set(auto2) -> clear(print_given).
% 0.66/0.96 assign(lrs_ticks,-1).
% 0.66/0.96 assign(sos_limit,10000).
% 0.66/0.96 assign(order,kbo).
% 0.66/0.96 set(lex_order_vars).
% 0.66/0.96 clear(print_given).
% 0.66/0.96
% 0.66/0.96 % formulas(sos). % not echoed (8 formulas)
% 0.66/0.96
% 0.66/0.96 ============================== end of input ==========================
% 0.66/0.96
% 0.66/0.96 % From the command line: assign(max_seconds, 300).
% 0.66/0.96
% 0.66/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.66/0.96
% 0.66/0.96 % Formulas that are not ordinary clauses:
% 0.66/0.96 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 3 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 4 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 5 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 6 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 7 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 8 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.66/0.96
% 0.66/0.96 ============================== end of process non-clausal formulas ===
% 0.66/0.96
% 0.66/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.66/0.96
% 0.66/0.96 ============================== PREDICATE ELIMINATION =================
% 0.66/0.96
% 0.66/0.96 ============================== end predicate elimination =============
% 0.66/0.96
% 0.66/0.96 Auto_denials: (non-Horn, no changes).
% 0.66/0.96
% 0.66/0.96 Term ordering decisions:
% 0.66/0.96
% 0.66/0.96 % Assigning unary symbol singleton kb_weight 0 and highest precedence (13).
% 0.66/0.96 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. cartesian_product2=1. unordered_pair=1. singleton=0.
% 0.66/0.96
% 0.66/0.96 ============================== end of process initial clauses ========
% 0.66/0.96
% 0.66/0.96 ============================== CLAUSES FOR SEARCH ====================
% 0.66/0.96
% 0.66/0.96 ============================== end of clauses for search =============
% 0.66/0.96
% 0.66/0.96 ============================== SEARCH ================================
% 0.66/0.96
% 0.66/0.96 % Starting search at 0.01 seconds.
% 0.66/0.96
% 0.66/0.96 ============================== PROOF =================================
% 0.66/0.96 % SZS status Theorem
% 0.66/0.96 % SZS output start Refutation
% 0.66/0.96
% 0.66/0.96 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.66/0.96 % Length of proof is 24.
% 0.66/0.96 % Level of proof is 7.
% 0.66/0.96 % Maximum clause weight is 16.000.
% 0.66/0.96 % Given clauses 17.
% 0.66/0.96
% 0.66/0.96 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 6 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 7 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.66/0.96 8 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(t106_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.66/0.96 10 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(1)].
% 0.66/0.96 11 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(6)].
% 0.66/0.96 12 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(11),rewrite([10(4)])].
% 0.66/0.96 13 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c3,c5) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.66/0.96 14 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c3,c5). [copy(13),rewrite([12(3)])].
% 0.66/0.96 15 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.66/0.96 16 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c4,c6). [copy(15),rewrite([12(3)])].
% 0.66/0.96 21 -in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.66/0.96 22 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6). [copy(21),rewrite([12(3)])].
% 0.66/0.96 23 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(axiom). [clausify(7)].
% 0.66/0.96 24 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(23),rewrite([12(1)])].
% 0.66/0.96 25 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(7)].
% 0.66/0.96 26 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(25),rewrite([12(1)])].
% 0.66/0.96 27 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(7)].
% 0.66/0.96 28 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(27),rewrite([12(1)])].
% 0.66/0.96 34 in(c3,c5). [resolve(24,a,14,a),merge(b)].
% 0.66/0.96 35 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c4,c6). [back_unit_del(22),unit_del(b,34)].
% 0.66/0.96 36 in(c4,c6). [resolve(26,a,16,a),merge(b)].
% 0.66/0.96 37 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)). [back_unit_del(35),unit_del(b,36)].
% 0.66/0.96 46 $F. [ur(28,a,37,a,b,34,a),unit_del(a,36)].
% 0.66/0.96
% 0.66/0.96 % SZS output end Refutation
% 0.66/0.96 ============================== end of proof ==========================
% 0.66/0.96
% 0.66/0.96 ============================== STATISTICS ============================
% 0.66/0.96
% 0.66/0.96 Given=17. Generated=55. Kept=29. proofs=1.
% 0.66/0.96 Usable=14. Sos=8. Demods=2. Limbo=0, Disabled=19. Hints=0.
% 0.66/0.96 Megabytes=0.06.
% 0.66/0.96 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.66/0.96
% 0.66/0.96 ============================== end of statistics =====================
% 0.66/0.96
% 0.66/0.96 ============================== end of search =========================
% 0.66/0.96
% 0.66/0.96 THEOREM PROVED
% 0.66/0.96 % SZS status Theorem
% 0.66/0.96
% 0.66/0.96 Exiting with 1 proof.
% 0.66/0.96
% 0.66/0.96 Process 23251 exit (max_proofs) Mon Jun 20 06:58:59 2022
% 0.66/0.96 Prover9 interrupted
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