TSTP Solution File: SET847-2 by Prover9---1109a

View Problem - Process Solution

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% File     : Prover9---1109a
% Problem  : SET847-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n017.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 04:32:46 EDT 2022

% Result   : Unsatisfiable 0.47s 1.01s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET847-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n017.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jul  9 21:09:17 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.47/1.01  ============================== Prover9 ===============================
% 0.47/1.01  Prover9 (32) version 2009-11A, November 2009.
% 0.47/1.01  Process 21960 was started by sandbox on n017.cluster.edu,
% 0.47/1.01  Sat Jul  9 21:09:18 2022
% 0.47/1.01  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21804_n017.cluster.edu".
% 0.47/1.01  ============================== end of head ===========================
% 0.47/1.01  
% 0.47/1.01  ============================== INPUT =================================
% 0.47/1.01  
% 0.47/1.01  % Reading from file /tmp/Prover9_21804_n017.cluster.edu
% 0.47/1.01  
% 0.47/1.01  set(prolog_style_variables).
% 0.47/1.01  set(auto2).
% 0.47/1.01      % set(auto2) -> set(auto).
% 0.47/1.01      % set(auto) -> set(auto_inference).
% 0.47/1.01      % set(auto) -> set(auto_setup).
% 0.47/1.01      % set(auto_setup) -> set(predicate_elim).
% 0.47/1.01      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.47/1.01      % set(auto) -> set(auto_limits).
% 0.47/1.01      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.47/1.01      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.47/1.01      % set(auto) -> set(auto_denials).
% 0.47/1.01      % set(auto) -> set(auto_process).
% 0.47/1.01      % set(auto2) -> assign(new_constants, 1).
% 0.47/1.01      % set(auto2) -> assign(fold_denial_max, 3).
% 0.47/1.01      % set(auto2) -> assign(max_weight, "200.000").
% 0.47/1.01      % set(auto2) -> assign(max_hours, 1).
% 0.47/1.01      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.47/1.01      % set(auto2) -> assign(max_seconds, 0).
% 0.47/1.01      % set(auto2) -> assign(max_minutes, 5).
% 0.47/1.01      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.47/1.01      % set(auto2) -> set(sort_initial_sos).
% 0.47/1.01      % set(auto2) -> assign(sos_limit, -1).
% 0.47/1.01      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.47/1.01      % set(auto2) -> assign(max_megs, 400).
% 0.47/1.01      % set(auto2) -> assign(stats, some).
% 0.47/1.01      % set(auto2) -> clear(echo_input).
% 0.47/1.01      % set(auto2) -> set(quiet).
% 0.47/1.01      % set(auto2) -> clear(print_initial_clauses).
% 0.47/1.01      % set(auto2) -> clear(print_given).
% 0.47/1.01  assign(lrs_ticks,-1).
% 0.47/1.01  assign(sos_limit,10000).
% 0.47/1.01  assign(order,kbo).
% 0.47/1.01  set(lex_order_vars).
% 0.47/1.01  clear(print_given).
% 0.47/1.01  
% 0.47/1.01  % formulas(sos).  % not echoed (11 formulas)
% 0.47/1.01  
% 0.47/1.01  ============================== end of input ==========================
% 0.47/1.01  
% 0.47/1.01  % From the command line: assign(max_seconds, 300).
% 0.47/1.01  
% 0.47/1.01  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.47/1.01  
% 0.47/1.01  % Formulas that are not ordinary clauses:
% 0.47/1.01  
% 0.47/1.01  ============================== end of process non-clausal formulas ===
% 0.47/1.01  
% 0.47/1.01  ============================== PROCESS INITIAL CLAUSES ===============
% 0.47/1.01  
% 0.47/1.01  ============================== PREDICATE ELIMINATION =================
% 0.47/1.01  
% 0.47/1.01  ============================== end predicate elimination =============
% 0.47/1.01  
% 0.47/1.01  Auto_denials:  (non-Horn, no changes).
% 0.47/1.01  
% 0.47/1.01  Term ordering decisions:
% 0.47/1.01  
% 0.47/1.01  % Assigning unary symbol tc_set kb_weight 0 and highest precedence (14).
% 0.47/1.01  Function symbol KB weights:  c_emptyset=1. t_a=1. v_S=1. c_Zorn_OTFin=1. c_Union=1. c_Zorn_Ochain=1. c_Zorn_Omaxchain=1. c_Main_OsubsetI__1=1. c_Zorn_Osucc=1. c_minus=1. tc_set=0.
% 0.47/1.01  
% 0.47/1.01  ============================== end of process initial clauses ========
% 0.47/1.01  
% 0.47/1.01  ============================== CLAUSES FOR SEARCH ====================
% 0.47/1.01  
% 0.47/1.01  ============================== end of clauses for search =============
% 0.47/1.01  
% 0.47/1.01  ============================== SEARCH ================================
% 0.47/1.01  
% 0.47/1.01  % Starting search at 0.01 seconds.
% 0.47/1.01  
% 0.47/1.01  ============================== PROOF =================================
% 0.47/1.01  % SZS status Unsatisfiable
% 0.47/1.01  % SZS output start Refutation
% 0.47/1.01  
% 0.47/1.01  % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.47/1.01  % Length of proof is 21.
% 0.47/1.01  % Level of proof is 6.
% 0.47/1.01  % Maximum clause weight is 29.000.
% 0.47/1.01  % Given clauses 23.
% 0.47/1.01  
% 0.47/1.01  1 c_lessequals(c_emptyset,A,tc_set(B)) # label(cls_Set_Oempty__subsetI_0) # label(axiom).  [assumption].
% 0.47/1.01  2 c_lessequals(A,A,tc_set(B)) # label(cls_Set_Osubset__refl_0) # label(axiom).  [assumption].
% 0.47/1.01  3 c_in(c_Main_OsubsetI__1(A,B,C),A,C) | c_lessequals(A,B,tc_set(C)) # label(cls_Set_OsubsetI_0) # label(axiom).  [assumption].
% 0.47/1.01  4 -c_in(A,c_emptyset,B) # label(cls_Set_OemptyE_0) # label(axiom).  [assumption].
% 0.47/1.01  5 -c_in(A,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))) # label(cls_conjecture_0) # label(negated_conjecture).  [assumption].
% 0.47/1.01  6 -c_in(A,c_minus(c_Zorn_Ochain(B,C),c_Zorn_Omaxchain(B,C),tc_set(tc_set(tc_set(C)))),tc_set(tc_set(C))) | c_Zorn_Osucc(B,A,C) != A # label(cls_Zorn_Osucc__not__equals_0) # label(axiom).  [assumption].
% 0.47/1.01  7 -c_lessequals(A,B,tc_set(C)) | -c_lessequals(B,A,tc_set(C)) | B = A # label(cls_Set_Osubset__antisym_0) # label(axiom).  [assumption].
% 0.47/1.01  8 -c_in(A,B,C) | c_in(A,D,C) | c_in(A,c_minus(B,D,tc_set(C)),C) # label(cls_Set_ODiffI_0) # label(axiom).  [assumption].
% 0.47/1.01  9 -c_in(A,c_Zorn_OTFin(B,C),tc_set(tc_set(C))) | c_in(A,c_Zorn_Ochain(B,C),tc_set(tc_set(C))) # label(cls_Zorn_OTFin__chain__lemma4_0) # label(axiom).  [assumption].
% 0.47/1.01  10 -c_lessequals(A,c_Zorn_OTFin(B,C),tc_set(tc_set(tc_set(C)))) | c_in(c_Union(A,tc_set(C)),c_Zorn_OTFin(B,C),tc_set(tc_set(C))) # label(cls_Zorn_OTFin__UnionI_0) # label(axiom).  [assumption].
% 0.47/1.01  11 -c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))) | c_Union(c_Zorn_OTFin(A,B),tc_set(B)) = c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) # label(cls_Zorn_Oequal__succ__Union_1) # label(axiom).  [assumption].
% 0.47/1.01  12 -c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))) | c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B)).  [copy(11),flip(b)].
% 0.47/1.01  13 -c_lessequals(A,B,tc_set(C)) | A = B | c_in(c_Main_OsubsetI__1(B,A,C),B,C).  [resolve(7,a,3,b)].
% 0.47/1.01  17 c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_OTFin(A,B),tc_set(tc_set(B))).  [resolve(10,a,2,a)].
% 0.47/1.01  19 c_Zorn_Osucc(A,c_Union(c_Zorn_OTFin(A,B),tc_set(B)),B) = c_Union(c_Zorn_OTFin(A,B),tc_set(B)).  [back_unit_del(12),unit_del(a,17)].
% 0.47/1.01  21 c_emptyset = A | c_in(c_Main_OsubsetI__1(A,c_emptyset,B),A,B).  [resolve(13,a,1,a)].
% 0.47/1.01  25 c_Zorn_Omaxchain(v_S,t_a) = c_emptyset.  [resolve(21,b,5,a),flip(a)].
% 0.47/1.01  26 -c_in(A,c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))) | c_Zorn_Osucc(v_S,A,t_a) != A.  [para(25(a,1),6(a,2,2))].
% 0.47/1.01  31 c_in(c_Union(c_Zorn_OTFin(A,B),tc_set(B)),c_Zorn_Ochain(A,B),tc_set(tc_set(B))).  [resolve(17,a,9,a)].
% 0.47/1.01  34 -c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_minus(c_Zorn_Ochain(v_S,t_a),c_emptyset,tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))).  [ur(26,b,19,a)].
% 0.47/1.01  40 $F.  [ur(8,b,4,a,c,34,a),unit_del(a,31)].
% 0.47/1.01  
% 0.47/1.01  % SZS output end Refutation
% 0.47/1.01  ============================== end of proof ==========================
% 0.47/1.01  
% 0.47/1.01  ============================== STATISTICS ============================
% 0.47/1.01  
% 0.47/1.01  Given=23. Generated=56. Kept=38. proofs=1.
% 0.47/1.01  Usable=22. Sos=14. Demods=2. Limbo=0, Disabled=13. Hints=0.
% 0.47/1.01  Megabytes=0.10.
% 0.47/1.01  User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.47/1.01  
% 0.47/1.01  ============================== end of statistics =====================
% 0.47/1.01  
% 0.47/1.01  ============================== end of search =========================
% 0.47/1.01  
% 0.47/1.01  THEOREM PROVED
% 0.47/1.01  % SZS status Unsatisfiable
% 0.47/1.01  
% 0.47/1.01  Exiting with 1 proof.
% 0.47/1.01  
% 0.47/1.01  Process 21960 exit (max_proofs) Sat Jul  9 21:09:18 2022
% 0.47/1.01  Prover9 interrupted
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