TSTP Solution File: SET959+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 04:33:42 EDT 2022
% Result : Theorem 0.76s 1.03s
% Output : Refutation 0.76s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 17:22:33 EDT 2022
% 0.21/0.36 % CPUTime :
% 0.76/1.03 ============================== Prover9 ===============================
% 0.76/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03 Process 2457 was started by sandbox on n027.cluster.edu,
% 0.76/1.03 Sun Jul 10 17:22:33 2022
% 0.76/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2304_n027.cluster.edu".
% 0.76/1.03 ============================== end of head ===========================
% 0.76/1.03
% 0.76/1.03 ============================== INPUT =================================
% 0.76/1.03
% 0.76/1.03 % Reading from file /tmp/Prover9_2304_n027.cluster.edu
% 0.76/1.03
% 0.76/1.03 set(prolog_style_variables).
% 0.76/1.03 set(auto2).
% 0.76/1.03 % set(auto2) -> set(auto).
% 0.76/1.03 % set(auto) -> set(auto_inference).
% 0.76/1.03 % set(auto) -> set(auto_setup).
% 0.76/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.03 % set(auto) -> set(auto_limits).
% 0.76/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.03 % set(auto) -> set(auto_denials).
% 0.76/1.03 % set(auto) -> set(auto_process).
% 0.76/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.03 % set(auto2) -> assign(stats, some).
% 0.76/1.03 % set(auto2) -> clear(echo_input).
% 0.76/1.03 % set(auto2) -> set(quiet).
% 0.76/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.03 % set(auto2) -> clear(print_given).
% 0.76/1.03 assign(lrs_ticks,-1).
% 0.76/1.03 assign(sos_limit,10000).
% 0.76/1.03 assign(order,kbo).
% 0.76/1.03 set(lex_order_vars).
% 0.76/1.03 clear(print_given).
% 0.76/1.03
% 0.76/1.03 % formulas(sos). % not echoed (8 formulas)
% 0.76/1.03
% 0.76/1.03 ============================== end of input ==========================
% 0.76/1.03
% 0.76/1.03 % From the command line: assign(max_seconds, 300).
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.03
% 0.76/1.03 % Formulas that are not ordinary clauses:
% 0.76/1.03 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 4 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 5 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 6 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 7 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 -(all A all B ((all C -(in(C,A) & (all D all E C != ordered_pair(D,E)))) & (all C -(in(C,B) & (all D all E C != ordered_pair(D,E)))) & (all C all D (in(ordered_pair(C,D),A) <-> in(ordered_pair(C,D),B))) -> A = B)) # label(t112_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03
% 0.76/1.03 ============================== end of process non-clausal formulas ===
% 0.76/1.03
% 0.76/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.03
% 0.76/1.03 ============================== PREDICATE ELIMINATION =================
% 0.76/1.03
% 0.76/1.03 ============================== end predicate elimination =============
% 0.76/1.03
% 0.76/1.03 Auto_denials: (non-Horn, no changes).
% 0.76/1.03
% 0.76/1.03 Term ordering decisions:
% 0.76/1.03 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. ordered_pair=1. unordered_pair=1. f1=1. singleton=1. f2=1. f3=1. f4=1. f5=1.
% 0.76/1.03
% 0.76/1.03 ============================== end of process initial clauses ========
% 0.76/1.03
% 0.76/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.76/1.03
% 0.76/1.03 ============================== end of clauses for search =============
% 0.76/1.03
% 0.76/1.03 ============================== SEARCH ================================
% 0.76/1.03
% 0.76/1.03 % Starting search at 0.01 seconds.
% 0.76/1.03
% 0.76/1.03 ============================== PROOF =================================
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03 % SZS output start Refutation
% 0.76/1.03
% 0.76/1.03 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.76/1.03 % Length of proof is 29.
% 0.76/1.03 % Level of proof is 13.
% 0.76/1.03 % Maximum clause weight is 41.000.
% 0.76/1.03 % Given clauses 39.
% 0.76/1.03
% 0.76/1.03 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 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].
% 0.76/1.03 7 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.76/1.03 8 -(all A all B ((all C -(in(C,A) & (all D all E C != ordered_pair(D,E)))) & (all C -(in(C,B) & (all D all E C != ordered_pair(D,E)))) & (all C all D (in(ordered_pair(C,D),A) <-> in(ordered_pair(C,D),B))) -> A = B)) # label(t112_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.76/1.03 10 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.76/1.03 11 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(3)].
% 0.76/1.03 12 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(11),rewrite([10(4)])].
% 0.76/1.03 13 in(f1(A,B),A) | in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(7)].
% 0.76/1.03 15 c4 != c3 # label(t112_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.76/1.03 19 -in(A,c3) | ordered_pair(f2(A),f3(A)) = A # label(t112_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.76/1.03 20 -in(A,c3) | unordered_pair(singleton(f2(A)),unordered_pair(f2(A),f3(A))) = A. [copy(19),rewrite([12(5)])].
% 0.76/1.03 21 -in(A,c4) | ordered_pair(f4(A),f5(A)) = A # label(t112_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.76/1.03 22 -in(A,c4) | unordered_pair(singleton(f4(A)),unordered_pair(f4(A),f5(A))) = A. [copy(21),rewrite([12(5)])].
% 0.76/1.03 23 -in(ordered_pair(A,B),c3) | in(ordered_pair(A,B),c4) # label(t112_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.76/1.03 24 -in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | in(unordered_pair(singleton(A),unordered_pair(A,B)),c4). [copy(23),rewrite([12(1),12(6)])].
% 0.76/1.03 25 in(ordered_pair(A,B),c3) | -in(ordered_pair(A,B),c4) # label(t112_zfmisc_1) # label(negated_conjecture). [clausify(8)].
% 0.76/1.03 26 in(unordered_pair(singleton(A),unordered_pair(A,B)),c3) | -in(unordered_pair(singleton(A),unordered_pair(A,B)),c4). [copy(25),rewrite([12(1),12(6)])].
% 0.76/1.03 27 -in(f1(A,B),A) | -in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(7)].
% 0.76/1.03 31 unordered_pair(singleton(f2(f1(A,c3))),unordered_pair(f2(f1(A,c3)),f3(f1(A,c3)))) = f1(A,c3) | in(f1(A,c3),A) | c3 = A. [resolve(20,a,13,b)].
% 0.76/1.03 35 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))) = f1(c4,c3). [resolve(31,b,22,a),flip(b),unit_del(b,15)].
% 0.76/1.03 46 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))),c3) | -in(f1(c4,c3),c4). [para(35(b,1),26(b,1))].
% 0.76/1.03 57 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(unordered_pair(singleton(f4(f1(c4,c3))),unordered_pair(f4(f1(c4,c3)),f5(f1(c4,c3)))),c3). [resolve(46,c,31,b),flip(d),merge(c),unit_del(c,15)].
% 0.76/1.03 61 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3) | in(f1(c4,c3),c3). [para(35(b,1),57(b,1)),merge(b)].
% 0.76/1.03 63 unordered_pair(singleton(f2(f1(c4,c3))),unordered_pair(f2(f1(c4,c3)),f3(f1(c4,c3)))) = f1(c4,c3). [resolve(61,b,20,a),merge(b)].
% 0.76/1.03 67 -in(f1(c4,c3),c3) | in(f1(c4,c3),c4). [para(63(a,1),24(a,1)),rewrite([63(20)])].
% 0.76/1.03 69 in(f1(c4,c3),c3) | -in(f1(c4,c3),c4). [para(63(a,1),26(b,1)),rewrite([63(15)])].
% 0.76/1.03 71 in(f1(c4,c3),c4). [resolve(67,a,13,b),flip(c),merge(b),unit_del(b,15)].
% 0.76/1.03 72 in(f1(c4,c3),c3). [back_unit_del(69),unit_del(b,71)].
% 0.76/1.03 73 $F. [resolve(71,a,27,a),flip(b),unit_del(a,72),unit_del(b,15)].
% 0.76/1.03
% 0.76/1.03 % SZS output end Refutation
% 0.76/1.03 ============================== end of proof ==========================
% 0.76/1.03
% 0.76/1.03 ============================== STATISTICS ============================
% 0.76/1.03
% 0.76/1.03 Given=39. Generated=137. Kept=58. proofs=1.
% 0.76/1.03 Usable=29. Sos=9. Demods=3. Limbo=0, Disabled=33. Hints=0.
% 0.76/1.03 Megabytes=0.18.
% 0.76/1.03 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.76/1.03
% 0.76/1.03 ============================== end of statistics =====================
% 0.76/1.03
% 0.76/1.03 ============================== end of search =========================
% 0.76/1.03
% 0.76/1.03 THEOREM PROVED
% 0.76/1.03 % SZS status Theorem
% 0.76/1.03
% 0.76/1.03 Exiting with 1 proof.
% 0.76/1.03
% 0.76/1.03 Process 2457 exit (max_proofs) Sun Jul 10 17:22:33 2022
% 0.76/1.03 Prover9 interrupted
%------------------------------------------------------------------------------