TSTP Solution File: SET908+1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n021.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 04:33:19 EDT 2022

% Result   : Theorem 0.76s 1.05s
% Output   : Refutation 0.76s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13  % Problem  : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 600
% 0.13/0.36  % DateTime : Sun Jul 10 19:14:22 EDT 2022
% 0.13/0.36  % CPUTime  : 
% 0.76/1.03  ============================== Prover9 ===============================
% 0.76/1.03  Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.03  Process 29137 was started by sandbox2 on n021.cluster.edu,
% 0.76/1.03  Sun Jul 10 19:14:23 2022
% 0.76/1.03  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28984_n021.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_28984_n021.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 (12 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 set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  6 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  7 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  8 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  9 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  10 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.03  11 -(all A all B set_union2(singleton(A),B) != empty_set) # label(t49_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:  empty_set=1. c1=1. c2=1. c3=1. c4=1. set_union2=1. f1=1. singleton=1. f2=1. f3=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 ====================
% 0.76/1.05  
% 0.76/1.05  ============================== end of clauses for search =============
% 0.76/1.05  
% 0.76/1.05  ============================== SEARCH ================================
% 0.76/1.05  
% 0.76/1.05  % Starting search at 0.01 seconds.
% 0.76/1.05  
% 0.76/1.05  ============================== PROOF =================================
% 0.76/1.05  % SZS status Theorem
% 0.76/1.05  % SZS output start Refutation
% 0.76/1.05  
% 0.76/1.05  % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.76/1.05  % Length of proof is 18.
% 0.76/1.05  % Level of proof is 5.
% 0.76/1.05  % Maximum clause weight is 11.000.
% 0.76/1.05  % Given clauses 41.
% 0.76/1.05  
% 0.76/1.05  2 (all A all B set_union2(A,B) = set_union2(B,A)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.05  3 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.05  4 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.05  5 (all A all B all C (C = set_union2(A,B) <-> (all D (in(D,C) <-> in(D,A) | in(D,B))))) # label(d2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.05  8 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
% 0.76/1.05  11 -(all A all B set_union2(singleton(A),B) != empty_set) # label(t49_zfmisc_1) # label(negated_conjecture) # label(non_clause).  [assumption].
% 0.76/1.05  14 set_union2(A,A) = A # label(idempotence_k2_xboole_0) # label(axiom).  [clausify(8)].
% 0.76/1.05  15 set_union2(singleton(c3),c4) = empty_set # label(t49_zfmisc_1) # label(negated_conjecture).  [clausify(11)].
% 0.76/1.05  16 empty_set = set_union2(singleton(c3),c4).  [copy(15),flip(a)].
% 0.76/1.05  17 set_union2(A,B) = set_union2(B,A) # label(commutativity_k2_xboole_0) # label(axiom).  [clausify(2)].
% 0.76/1.05  24 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom).  [clausify(4)].
% 0.76/1.05  25 set_union2(c4,singleton(c3)) != A | -in(B,A).  [copy(24),rewrite([16(1),17(4)])].
% 0.76/1.05  29 singleton(A) != B | in(C,B) | C != A # label(d1_tarski) # label(axiom).  [clausify(3)].
% 0.76/1.05  31 set_union2(A,B) != C | in(D,C) | -in(D,B) # label(d2_xboole_0) # label(axiom).  [clausify(5)].
% 0.76/1.05  58 -in(A,set_union2(c4,singleton(c3))).  [ur(25,a,17,a),rewrite([17(4)])].
% 0.76/1.05  71 in(A,singleton(B)) | A != B.  [resolve(29,a,14,a(flip)),rewrite([14(3)])].
% 0.76/1.05  211 in(A,singleton(A)).  [resolve(71,b,14,a),rewrite([14(1)])].
% 0.76/1.05  250 $F.  [ur(31,b,58,a,c,211,a),flip(a),xx(a)].
% 0.76/1.05  
% 0.76/1.05  % SZS output end Refutation
% 0.76/1.05  ============================== end of proof ==========================
% 0.76/1.05  
% 0.76/1.05  ============================== STATISTICS ============================
% 0.76/1.05  
% 0.76/1.05  Given=41. Generated=773. Kept=234. proofs=1.
% 0.76/1.05  Usable=39. Sos=146. Demods=4. Limbo=16, Disabled=54. Hints=0.
% 0.76/1.05  Megabytes=0.21.
% 0.76/1.05  User_CPU=0.04, System_CPU=0.00, Wall_clock=0.
% 0.76/1.05  
% 0.76/1.05  ============================== end of statistics =====================
% 0.76/1.05  
% 0.76/1.05  ============================== end of search =========================
% 0.76/1.05  
% 0.76/1.05  THEOREM PROVED
% 0.76/1.05  % SZS status Theorem
% 0.76/1.05  
% 0.76/1.05  Exiting with 1 proof.
% 0.76/1.05  
% 0.76/1.05  Process 29137 exit (max_proofs) Sun Jul 10 19:14:23 2022
% 0.76/1.05  Prover9 interrupted
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