TSTP Solution File: SET954+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET954+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 04:33:40 EDT 2022
% Result : Theorem 132.14s 132.48s
% Output : Refutation 132.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET954+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % 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 : Sat Jul 9 17:36:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 13576 was started by sandbox on n005.cluster.edu,
% 0.74/1.01 Sat Jul 9 17:36:22 2022
% 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13396_n005.cluster.edu".
% 0.74/1.01 ============================== end of head ===========================
% 0.74/1.01
% 0.74/1.01 ============================== INPUT =================================
% 0.74/1.01
% 0.74/1.01 % Reading from file /tmp/Prover9_13396_n005.cluster.edu
% 0.74/1.01
% 0.74/1.01 set(prolog_style_variables).
% 0.74/1.01 set(auto2).
% 0.74/1.01 % set(auto2) -> set(auto).
% 0.74/1.01 % set(auto) -> set(auto_inference).
% 0.74/1.01 % set(auto) -> set(auto_setup).
% 0.74/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.74/1.01 % set(auto) -> set(auto_limits).
% 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.74/1.01 % set(auto) -> set(auto_denials).
% 0.74/1.01 % set(auto) -> set(auto_process).
% 0.74/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.74/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.74/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.74/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.74/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.74/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.74/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.74/1.01 % set(auto2) -> assign(stats, some).
% 0.74/1.01 % set(auto2) -> clear(echo_input).
% 0.74/1.01 % set(auto2) -> set(quiet).
% 0.74/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.74/1.01 % set(auto2) -> clear(print_given).
% 0.74/1.01 assign(lrs_ticks,-1).
% 0.74/1.01 assign(sos_limit,10000).
% 0.74/1.01 assign(order,kbo).
% 0.74/1.01 set(lex_order_vars).
% 0.74/1.01 clear(print_given).
% 0.74/1.01
% 0.74/1.01 % formulas(sos). % not echoed (8 formulas)
% 0.74/1.01
% 0.74/1.01 ============================== end of input ==========================
% 0.74/1.01
% 0.74/1.01 % From the command line: assign(max_seconds, 300).
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.74/1.01
% 0.74/1.01 % Formulas that are not ordinary clauses:
% 0.74/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 3 (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].
% 0.74/1.01 4 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 5 (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].
% 0.74/1.01 6 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 7 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 8 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) -> in(ordered_pair(B,A),cartesian_product2(D,C)))) # label(t107_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.01
% 0.74/1.01 ============================== end of process non-clausal formulas ===
% 0.74/1.01
% 0.74/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.74/1.01
% 0.74/1.01 ============================== PREDICATE ELIMINATION =================
% 0.74/1.01
% 0.74/1.01 ============================== end predicate elimination =============
% 0.74/1.01
% 0.74/1.01 Auto_denials:
% 0.74/1.01 % copying label rc2_xboole_0 to answer in negative clause
% 0.74/1.01 % copying label fc1_zfmisc_1 to answer in negative clause
% 0.74/1.01 % copying label antisymmetry_r2_hidden to answer in negative clause
% 0.74/1.01 % copying label t107_zfmisc_1 to answer in negative clause
% 0.74/1.01 % assign(max_proofs, 4). % (Horn set with more than one neg. clause)
% 0.74/1.01
% 0.74/1.01 Term ordering decisions:
% 0.74/1.01
% 0.74/1.01 % Assigning unary symbol singleton kb_weight 0 and highest precedence (13).
% 0.74/1.01 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.
% 132.14/132.48
% 132.14/132.48 ============================== end of process initial clauses ========
% 132.14/132.48
% 132.14/132.48 ============================== CLAUSES FOR SEARCH ====================
% 132.14/132.48
% 132.14/132.48 ============================== end of clauses for search =============
% 132.14/132.48
% 132.14/132.48 ============================== SEARCH ================================
% 132.14/132.48
% 132.14/132.48 % Starting search at 0.01 seconds.
% 132.14/132.48
% 132.14/132.48 ============================== PROOF =================================
% 132.14/132.48 % SZS status Theorem
% 132.14/132.48 % SZS output start Refutation
% 132.14/132.48
% 132.14/132.48 % Proof 1 at 0.01 (+ 0.00) seconds: t107_zfmisc_1.
% 132.14/132.48 % Length of proof is 20.
% 132.14/132.48 % Level of proof is 5.
% 132.14/132.48 % Maximum clause weight is 16.000.
% 132.14/132.48 % Given clauses 18.
% 132.14/132.48
% 132.14/132.48 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 132.14/132.48 3 (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].
% 132.14/132.48 5 (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].
% 132.14/132.48 8 -(all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) -> in(ordered_pair(B,A),cartesian_product2(D,C)))) # label(t107_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 132.14/132.48 10 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 132.14/132.48 11 in(ordered_pair(c3,c4),cartesian_product2(c5,c6)) # label(t107_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 132.14/132.48 12 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(3)].
% 132.14/132.48 13 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(12),rewrite([10(4)])].
% 132.14/132.48 18 -in(ordered_pair(c4,c3),cartesian_product2(c6,c5)) # label(t107_zfmisc_1) # label(negated_conjecture) # answer(t107_zfmisc_1). [clausify(8)].
% 132.14/132.48 19 -in(unordered_pair(singleton(c4),unordered_pair(c3,c4)),cartesian_product2(c6,c5)) # answer(t107_zfmisc_1). [copy(18),rewrite([13(3),10(5)])].
% 132.14/132.48 20 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(axiom). [clausify(5)].
% 132.14/132.48 21 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(20),rewrite([13(1)])].
% 132.14/132.48 22 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(5)].
% 132.14/132.48 23 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(22),rewrite([13(1)])].
% 132.14/132.48 24 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(5)].
% 132.14/132.48 25 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(24),rewrite([13(1)])].
% 132.14/132.48 26 in(unordered_pair(singleton(c3),unordered_pair(c3,c4)),cartesian_product2(c5,c6)). [back_rewrite(11),rewrite([13(3)])].
% 132.14/132.48 30 in(c4,c6). [hyper(23,a,26,a)].
% 132.14/132.48 31 in(c3,c5). [hyper(21,a,26,a)].
% 132.14/132.48 48 $F # answer(t107_zfmisc_1). [hyper(25,b,30,a,c,31,a),rewrite([10(5)]),unit_del(a,19)].
% 132.14/132.48
% 132.14/132.48 % SZS output end Refutation
% 132.14/132.48 ============================== end of proof ==========================
% 132.14/132.48
% 132.14/132.48 % Disable descendants (x means already disabled):
% 132.14/132.48 18x 19 27 28 33 34 37 38
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=96.000, iters=3529
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=91.000, iters=3472
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=86.000, iters=3452
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=84.000, iters=3424
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=82.000, iters=3839
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=79.000, iters=3396
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=77.000, iters=3336
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=75.000, iters=3350
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=72.000, iters=3359
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=70.000, iters=3339
% 132.14/132.48
% 132.14/132.48 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 4.95 sec).
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=67.000, iters=3339
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=65.000, iters=3345
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=63.000, iters=3339
% 132.14/132.48
% 132.14/132.48 Low Water (keep): wt=62.000, iters=3334
% 132.14/132.48
% 132.14/132.48 Low Water (displace): id=2348, wt=135.000
% 132.14/132.48
% 132.14/132.48 Low Water (displace): id=3358, wt=123.000
% 132.14/132.48
% 132.14/132.48 Low Water (displace): id=3481, wt=118.000
% 132.14/132.48
% 132.14/132.48 Low Water (displace): id=2918, wt=116.000
% 132.14/132.48
% 132.14/132.48 Low Water (displCputime limit exceeded (core dumped)
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