TSTP Solution File: SEU165+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n020.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 0.71s 1.02s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU165+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n020.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 Jun 20 08:27:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.71/1.02 ============================== Prover9 ===============================
% 0.71/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.71/1.02 Process 4064 was started by sandbox2 on n020.cluster.edu,
% 0.71/1.02 Mon Jun 20 08:27:19 2022
% 0.71/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_3911_n020.cluster.edu".
% 0.71/1.02 ============================== end of head ===========================
% 0.71/1.02
% 0.71/1.02 ============================== INPUT =================================
% 0.71/1.02
% 0.71/1.02 % Reading from file /tmp/Prover9_3911_n020.cluster.edu
% 0.71/1.02
% 0.71/1.02 set(prolog_style_variables).
% 0.71/1.02 set(auto2).
% 0.71/1.02 % set(auto2) -> set(auto).
% 0.71/1.02 % set(auto) -> set(auto_inference).
% 0.71/1.02 % set(auto) -> set(auto_setup).
% 0.71/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.71/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.71/1.02 % set(auto) -> set(auto_limits).
% 0.71/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.71/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.71/1.02 % set(auto) -> set(auto_denials).
% 0.71/1.02 % set(auto) -> set(auto_process).
% 0.71/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.71/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.71/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.71/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.71/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.71/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.71/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.71/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.71/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.71/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.71/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.71/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.71/1.02 % set(auto2) -> assign(stats, some).
% 0.71/1.02 % set(auto2) -> clear(echo_input).
% 0.71/1.02 % set(auto2) -> set(quiet).
% 0.71/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.71/1.02 % set(auto2) -> clear(print_given).
% 0.71/1.02 assign(lrs_ticks,-1).
% 0.71/1.02 assign(sos_limit,10000).
% 0.71/1.02 assign(order,kbo).
% 0.71/1.02 set(lex_order_vars).
% 0.71/1.02 clear(print_given).
% 0.71/1.02
% 0.71/1.02 % formulas(sos). % not echoed (12 formulas)
% 0.71/1.02
% 0.71/1.02 ============================== end of input ==========================
% 0.71/1.02
% 0.71/1.02 % From the command line: assign(max_seconds, 300).
% 0.71/1.02
% 0.71/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.71/1.02
% 0.71/1.02 % Formulas that are not ordinary clauses:
% 0.71/1.02 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 2 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 3 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 4 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 5 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 6 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 7 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 8 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 9 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 10 (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].
% 0.71/1.02 11 (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].
% 0.71/1.02 12 -(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].
% 0.71/1.02
% 0.71/1.02 ============================== end of process non-clausal formulas ===
% 0.71/1.02
% 0.71/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.71/1.02
% 0.71/1.02 ============================== PREDICATE ELIMINATION =================
% 0.71/1.02
% 0.71/1.02 ============================== end predicate elimination =============
% 0.71/1.02
% 0.71/1.02 Auto_denials: (non-Horn, no changes).
% 0.71/1.02
% 0.71/1.02 Term ordering decisions:
% 0.71/1.02
% 0.71/1.02 % Assigning unary symbol singleton kb_weight 0 and highest precedence (13).
% 0.71/1.02 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.
% 0.71/1.02
% 0.71/1.02 ============================== end of process initial clauses ========
% 0.71/1.02
% 0.71/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.71/1.02
% 0.71/1.02 ============================== end of clauses for search =============
% 0.71/1.02
% 0.71/1.02 ============================== SEARCH ================================
% 0.71/1.02
% 0.71/1.02 % Starting search at 0.01 seconds.
% 0.71/1.02
% 0.71/1.02 ============================== PROOF =================================
% 0.71/1.02 % SZS status Theorem
% 0.71/1.02 % SZS output start Refutation
% 0.71/1.02
% 0.71/1.02 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.71/1.02 % Length of proof is 24.
% 0.71/1.02 % Level of proof is 7.
% 0.71/1.02 % Maximum clause weight is 16.000.
% 0.71/1.02 % Given clauses 17.
% 0.71/1.02
% 0.71/1.02 1 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.71/1.02 10 (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].
% 0.71/1.02 11 (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].
% 0.71/1.02 12 -(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].
% 0.71/1.02 14 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(1)].
% 0.71/1.02 15 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(10)].
% 0.71/1.02 16 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(15),rewrite([14(4)])].
% 0.71/1.02 17 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c3,c5) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.71/1.02 18 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c3,c5). [copy(17),rewrite([16(3)])].
% 0.71/1.02 19 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.71/1.02 20 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | in(c4,c6). [copy(19),rewrite([16(3)])].
% 0.71/1.02 25 -in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6) # label(t106_zfmisc_1) # label(negated_conjecture). [clausify(12)].
% 0.71/1.02 26 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c3,c5) | -in(c4,c6). [copy(25),rewrite([16(3)])].
% 0.71/1.02 27 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(axiom). [clausify(11)].
% 0.71/1.02 28 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(27),rewrite([16(1)])].
% 0.71/1.02 29 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(11)].
% 0.71/1.02 30 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(29),rewrite([16(1)])].
% 0.71/1.02 31 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(11)].
% 0.71/1.02 32 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(31),rewrite([16(1)])].
% 0.71/1.02 38 in(c3,c5). [resolve(28,a,18,a),merge(b)].
% 0.71/1.02 39 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)) | -in(c4,c6). [back_unit_del(26),unit_del(b,38)].
% 0.71/1.02 40 in(c4,c6). [resolve(30,a,20,a),merge(b)].
% 0.71/1.02 41 -in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)). [back_unit_del(39),unit_del(b,40)].
% 0.71/1.02 50 $F. [ur(32,a,41,a,b,38,a),unit_del(a,40)].
% 0.71/1.02
% 0.71/1.02 % SZS output end Refutation
% 0.71/1.02 ============================== end of proof ==========================
% 0.71/1.02
% 0.71/1.02 ============================== STATISTICS ============================
% 0.71/1.02
% 0.71/1.02 Given=17. Generated=55. Kept=29. proofs=1.
% 0.71/1.02 Usable=14. Sos=8. Demods=2. Limbo=0, Disabled=19. Hints=0.
% 0.71/1.02 Megabytes=0.06.
% 0.71/1.02 User_CPU=0.01, System_CPU=0.00, Wall_clock=0.
% 0.71/1.02
% 0.71/1.02 ============================== end of statistics =====================
% 0.71/1.02
% 0.71/1.02 ============================== end of search =========================
% 0.71/1.02
% 0.71/1.02 THEOREM PROVED
% 0.71/1.02 % SZS status Theorem
% 0.71/1.02
% 0.71/1.02 Exiting with 1 proof.
% 0.71/1.02
% 0.71/1.02 Process 4064 exit (max_proofs) Mon Jun 20 08:27:19 2022
% 0.71/1.02 Prover9 interrupted
%------------------------------------------------------------------------------