TSTP Solution File: SET962+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.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 04:33:43 EDT 2022
% Result : Theorem 0.74s 1.02s
% Output : Refutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET962+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.12/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 19:01:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.74/1.01 ============================== Prover9 ===============================
% 0.74/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.74/1.01 Process 28486 was started by sandbox2 on n023.cluster.edu,
% 0.74/1.01 Sat Jul 9 19:01:41 2022
% 0.74/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28333_n023.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_28333_n023.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 (9 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 (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.01 9 -(all A all B (cartesian_product2(A,A) = cartesian_product2(B,B) -> A = B)) # label(t115_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: (non-Horn, no changes).
% 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 (12).
% 0.74/1.01 Function symbol KB weights: c1=1. c2=1. c3=1. c4=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. f1=1. singleton=0.
% 0.74/1.01
% 0.74/1.01 ============================== end of process initial clauses ========
% 0.74/1.01
% 0.74/1.01 ============================== CLAUSES FOR SEARCH ====================
% 0.74/1.01
% 0.74/1.01 ============================== end of clauses for search =============
% 0.74/1.02
% 0.74/1.02 ============================== SEARCH ================================
% 0.74/1.02
% 0.74/1.02 % Starting search at 0.01 seconds.
% 0.74/1.02
% 0.74/1.02 ============================== PROOF =================================
% 0.74/1.02 % SZS status Theorem
% 0.74/1.02 % SZS output start Refutation
% 0.74/1.02
% 0.74/1.02 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.74/1.02 % Length of proof is 25.
% 0.74/1.02 % Level of proof is 10.
% 0.74/1.02 % Maximum clause weight is 24.000.
% 0.74/1.02 % Given clauses 35.
% 0.74/1.02
% 0.74/1.02 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 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].
% 0.74/1.02 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].
% 0.74/1.02 8 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.74/1.02 9 -(all A all B (cartesian_product2(A,A) = cartesian_product2(B,B) -> A = B)) # label(t115_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.74/1.02 11 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 0.74/1.02 12 cartesian_product2(c4,c4) = cartesian_product2(c3,c3) # label(t115_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.74/1.02 13 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(3)].
% 0.74/1.02 14 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(13),rewrite([11(4)])].
% 0.74/1.02 15 in(f1(A,B),A) | in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(8)].
% 0.74/1.02 17 c4 != c3 # label(t115_zfmisc_1) # label(negated_conjecture). [clausify(9)].
% 0.74/1.02 23 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(5)].
% 0.74/1.02 24 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(23),rewrite([14(1)])].
% 0.74/1.02 25 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(5)].
% 0.74/1.02 26 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(25),rewrite([14(1)])].
% 0.74/1.02 27 -in(f1(A,B),A) | -in(f1(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(8)].
% 0.74/1.02 29 in(unordered_pair(singleton(A),unordered_pair(A,A)),cartesian_product2(B,B)) | -in(A,B). [factor(26,b,c)].
% 0.74/1.02 33 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(c3,c3)) | in(B,c4). [para(12(a,1),24(a,2))].
% 0.74/1.02 40 in(unordered_pair(singleton(f1(A,B)),unordered_pair(f1(A,B),f1(A,B))),cartesian_product2(B,B)) | in(f1(A,B),A) | B = A. [resolve(29,b,15,b)].
% 0.74/1.02 70 in(f1(A,c3),A) | c3 = A | in(f1(A,c3),c4). [resolve(40,a,33,a)].
% 0.74/1.02 78 in(f1(c4,c3),c4). [factor(70,a,c),flip(b),unit_del(b,17)].
% 0.74/1.02 82 in(unordered_pair(singleton(f1(c4,c3)),unordered_pair(f1(c4,c3),f1(c4,c3))),cartesian_product2(c3,c3)). [resolve(78,a,29,b),rewrite([12(15)])].
% 0.74/1.02 83 -in(f1(c4,c3),c3). [resolve(78,a,27,a),flip(b),unit_del(b,17)].
% 0.74/1.02 109 -in(unordered_pair(singleton(A),unordered_pair(A,f1(c4,c3))),cartesian_product2(B,c3)). [ur(24,b,83,a)].
% 0.74/1.02 110 $F. [resolve(109,a,82,a)].
% 0.74/1.02
% 0.74/1.02 % SZS output end Refutation
% 0.74/1.02 ============================== end of proof ==========================
% 0.74/1.02
% 0.74/1.02 ============================== STATISTICS ============================
% 0.74/1.02
% 0.74/1.02 Given=35. Generated=206. Kept=95. proofs=1.
% 0.74/1.02 Usable=34. Sos=56. Demods=3. Limbo=0, Disabled=17. Hints=0.
% 0.74/1.02 Megabytes=0.15.
% 0.74/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.74/1.02
% 0.74/1.02 ============================== end of statistics =====================
% 0.74/1.02
% 0.74/1.02 ============================== end of search =========================
% 0.74/1.02
% 0.74/1.02 THEOREM PROVED
% 0.74/1.02 % SZS status Theorem
% 0.74/1.02
% 0.74/1.02 Exiting with 1 proof.
% 0.74/1.02
% 0.74/1.02 Process 28486 exit (max_proofs) Sat Jul 9 19:01:41 2022
% 0.74/1.02 Prover9 interrupted
%------------------------------------------------------------------------------