TSTP Solution File: COL044-8 by Prover9---1109a

View Problem - Process Solution

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% File     : Prover9---1109a
% Problem  : COL044-8 : TPTP v8.1.0. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n024.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 : Fri Jul 15 00:39:49 EDT 2022

% Result   : Unsatisfiable 0.86s 1.15s
% Output   : Refutation 0.86s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : COL044-8 : TPTP v8.1.0. Released v2.1.0.
% 0.07/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n024.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue May 31 09:17:51 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.86/1.15  ============================== Prover9 ===============================
% 0.86/1.15  Prover9 (32) version 2009-11A, November 2009.
% 0.86/1.15  Process 5609 was started by sandbox on n024.cluster.edu,
% 0.86/1.15  Tue May 31 09:17:52 2022
% 0.86/1.15  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5456_n024.cluster.edu".
% 0.86/1.15  ============================== end of head ===========================
% 0.86/1.15  
% 0.86/1.15  ============================== INPUT =================================
% 0.86/1.15  
% 0.86/1.15  % Reading from file /tmp/Prover9_5456_n024.cluster.edu
% 0.86/1.15  
% 0.86/1.15  set(prolog_style_variables).
% 0.86/1.15  set(auto2).
% 0.86/1.15      % set(auto2) -> set(auto).
% 0.86/1.15      % set(auto) -> set(auto_inference).
% 0.86/1.15      % set(auto) -> set(auto_setup).
% 0.86/1.15      % set(auto_setup) -> set(predicate_elim).
% 0.86/1.15      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.86/1.15      % set(auto) -> set(auto_limits).
% 0.86/1.15      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.86/1.15      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.86/1.15      % set(auto) -> set(auto_denials).
% 0.86/1.15      % set(auto) -> set(auto_process).
% 0.86/1.15      % set(auto2) -> assign(new_constants, 1).
% 0.86/1.15      % set(auto2) -> assign(fold_denial_max, 3).
% 0.86/1.15      % set(auto2) -> assign(max_weight, "200.000").
% 0.86/1.15      % set(auto2) -> assign(max_hours, 1).
% 0.86/1.15      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.86/1.15      % set(auto2) -> assign(max_seconds, 0).
% 0.86/1.15      % set(auto2) -> assign(max_minutes, 5).
% 0.86/1.15      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.86/1.15      % set(auto2) -> set(sort_initial_sos).
% 0.86/1.15      % set(auto2) -> assign(sos_limit, -1).
% 0.86/1.15      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.86/1.15      % set(auto2) -> assign(max_megs, 400).
% 0.86/1.15      % set(auto2) -> assign(stats, some).
% 0.86/1.15      % set(auto2) -> clear(echo_input).
% 0.86/1.15      % set(auto2) -> set(quiet).
% 0.86/1.15      % set(auto2) -> clear(print_initial_clauses).
% 0.86/1.15      % set(auto2) -> clear(print_given).
% 0.86/1.15  assign(lrs_ticks,-1).
% 0.86/1.15  assign(sos_limit,10000).
% 0.86/1.15  assign(order,kbo).
% 0.86/1.15  set(lex_order_vars).
% 0.86/1.15  clear(print_given).
% 0.86/1.15  
% 0.86/1.15  % formulas(sos).  % not echoed (4 formulas)
% 0.86/1.15  
% 0.86/1.15  ============================== end of input ==========================
% 0.86/1.15  
% 0.86/1.15  % From the command line: assign(max_seconds, 300).
% 0.86/1.15  
% 0.86/1.15  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.86/1.15  
% 0.86/1.15  % Formulas that are not ordinary clauses:
% 0.86/1.15  
% 0.86/1.15  ============================== end of process non-clausal formulas ===
% 0.86/1.15  
% 0.86/1.15  ============================== PROCESS INITIAL CLAUSES ===============
% 0.86/1.15  
% 0.86/1.15  ============================== PREDICATE ELIMINATION =================
% 0.86/1.15  
% 0.86/1.15  ============================== end predicate elimination =============
% 0.86/1.15  
% 0.86/1.15  Auto_denials:
% 0.86/1.15    % copying label prove_strong_fixed_point to answer in negative clause
% 0.86/1.15  
% 0.86/1.15  Term ordering decisions:
% 0.86/1.15  Function symbol KB weights:  b=1. n=1. strong_fixed_point=1. fixed_pt=1. apply=1.
% 0.86/1.15  
% 0.86/1.15  ============================== end of process initial clauses ========
% 0.86/1.15  
% 0.86/1.15  ============================== CLAUSES FOR SEARCH ====================
% 0.86/1.15  
% 0.86/1.15  ============================== end of clauses for search =============
% 0.86/1.15  
% 0.86/1.15  ============================== SEARCH ================================
% 0.86/1.15  
% 0.86/1.15  % Starting search at 0.01 seconds.
% 0.86/1.15  
% 0.86/1.15  ============================== PROOF =================================
% 0.86/1.15  % SZS status Unsatisfiable
% 0.86/1.15  % SZS output start Refutation
% 0.86/1.15  
% 0.86/1.15  % Proof 1 at 0.15 (+ 0.00) seconds: prove_strong_fixed_point.
% 0.86/1.15  % Length of proof is 13.
% 0.86/1.15  % Level of proof is 6.
% 0.86/1.15  % Maximum clause weight is 53.000.
% 0.86/1.15  % Given clauses 31.
% 0.86/1.15  
% 0.86/1.15  1 apply(apply(apply(b,A),B),C) = apply(A,apply(B,C)) # label(b_definition) # label(axiom).  [assumption].
% 0.86/1.15  2 apply(apply(apply(n,A),B),C) = apply(apply(apply(A,C),B),C) # label(n_definition) # label(axiom).  [assumption].
% 0.86/1.15  3 strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n)),b)),b) # label(strong_fixed_point) # label(axiom).  [assumption].
% 0.86/1.15  4 apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) # label(prove_strong_fixed_point) # label(negated_conjecture) # answer(prove_strong_fixed_point).  [assumption].
% 0.86/1.15  5 apply(fixed_pt,apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt)))) != apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))) # answer(prove_strong_fixed_point).  [copy(4),rewrite([3(1),1(29),1(27),3(27),1(55),1(53)]),flip(a)].
% 0.86/1.15  10 apply(apply(apply(n,apply(b,A)),B),C) = apply(apply(A,apply(C,B)),C).  [para(1(a,1),2(a,2,1))].
% 0.86/1.15  12 apply(apply(apply(apply(A,B),C),B),C) = apply(apply(apply(n,apply(n,A)),B),C).  [para(2(a,1),2(a,2,1)),flip(a)].
% 0.86/1.15  99 apply(apply(apply(n,apply(b,apply(b,A))),B),C) = apply(A,apply(apply(C,B),C)).  [para(10(a,2),1(a,1))].
% 0.86/1.15  428 apply(apply(apply(n,apply(n,apply(apply(b,apply(b,b)),apply(n,apply(apply(b,b),n))))),n),apply(b,apply(b,fixed_pt))) != apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))) # answer(prove_strong_fixed_point).  [para(12(a,2),5(a,1,2)),rewrite([1(16),1(20),1(26)]),flip(a)].
% 0.86/1.15  778 apply(fixed_pt,apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point).  [para(12(a,2),428(a,1)),rewrite([1(15),1(19),1(25)]),flip(a)].
% 0.86/1.15  780 apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point).  [para(2(a,1),778(a,1,2,1)),rewrite([1(12),1(18)])].
% 0.86/1.15  785 apply(fixed_pt,apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt))))) != apply(apply(apply(n,apply(b,apply(b,fixed_pt))),apply(n,apply(b,apply(b,fixed_pt)))),apply(n,apply(b,apply(b,fixed_pt)))) # answer(prove_strong_fixed_point).  [para(2(a,1),780(a,2,1)),rewrite([1(36),1(42)])].
% 0.86/1.15  786 $F # answer(prove_strong_fixed_point).  [resolve(785,a,99,a(flip))].
% 0.86/1.15  
% 0.86/1.15  % SZS output end Refutation
% 0.86/1.15  ============================== end of proof ==========================
% 0.86/1.15  
% 0.86/1.15  ============================== STATISTICS ============================
% 0.86/1.15  
% 0.86/1.15  Given=31. Generated=2162. Kept=784. proofs=1.
% 0.86/1.15  Usable=30. Sos=704. Demods=165. Limbo=1, Disabled=52. Hints=0.
% 0.86/1.15  Megabytes=1.31.
% 0.86/1.15  User_CPU=0.15, System_CPU=0.00, Wall_clock=0.
% 0.86/1.15  
% 0.86/1.15  ============================== end of statistics =====================
% 0.86/1.15  
% 0.86/1.15  ============================== end of search =========================
% 0.86/1.15  
% 0.86/1.15  THEOREM PROVED
% 0.86/1.15  % SZS status Unsatisfiable
% 0.86/1.15  
% 0.86/1.15  Exiting with 1 proof.
% 0.86/1.15  
% 0.86/1.15  Process 5609 exit (max_proofs) Tue May 31 09:17:52 2022
% 0.86/1.15  Prover9 interrupted
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