TSTP Solution File: SEU850^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SEU850^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n029.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  : 300s
% DateTime : Tue May 21 03:44:04 EDT 2024

% Result   : Theorem 4.28s 2.50s
% Output   : Refutation 4.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   41 (  10 unt;   8 typ;   0 def)
%            Number of atoms       :   84 (  14 equ;   0 cnn)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :  134 (  24   ~;  32   |;   9   &;  57   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   20 (   0   ^  20   !;   0   ?;  20   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(sk1_type,type,
    sk1: a > $o ).

thf(sk2_type,type,
    sk2: a > $o ).

thf(sk3_type,type,
    sk3: a > $o ).

thf(sk4_type,type,
    sk4: $o ).

thf(sk5_type,type,
    sk5: a ).

thf(sk6_type,type,
    sk6: a ).

thf(sk7_type,type,
    sk7: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ( ( A = B )
        & ( B = C ) )
     => ( ! [D: a] :
            ( ( A @ D )
           => ( B @ D ) )
        & ! [D: a] :
            ( ( B @ D )
           => ( C @ D ) )
        & ! [D: a] :
            ( ( C @ D )
           => ( A @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGAZING_THM9_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ( A = B )
          & ( B = C ) )
       => ( ! [D: a] :
              ( ( A @ D )
             => ( B @ D ) )
          & ! [D: a] :
              ( ( B @ D )
             => ( C @ D ) )
          & ! [D: a] :
              ( ( C @ D )
             => ( A @ D ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > $o,B: a > $o,C: a > $o] :
        ( ( ( A = B )
          & ( B = C ) )
       => ( ! [D: a] :
              ( ( A @ D )
             => ( B @ D ) )
          & ! [D: a] :
              ( ( B @ D )
             => ( C @ D ) )
          & ! [D: a] :
              ( ( C @ D )
             => ( A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(6,plain,
    ( sk4
    | ~ ( sk3 @ sk6 )
    | ( sk3 @ sk7 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    sk2 = sk3,
    inference(cnf,[status(esa)],[3]) ).

thf(12,plain,
    sk3 = sk2,
    inference(lifteq,[status(thm)],[5]) ).

thf(14,plain,
    ! [A: a] :
      ( ( sk3 @ A )
      = ( sk2 @ A ) ),
    inference(func_ext,[status(esa)],[12]) ).

thf(30,plain,
    ( sk4
    | ~ ( sk2 @ sk6 )
    | ( sk2 @ sk7 ) ),
    inference(rewrite,[status(thm)],[6,14]) ).

thf(8,plain,
    sk1 = sk2,
    inference(cnf,[status(esa)],[3]) ).

thf(13,plain,
    sk2 = sk1,
    inference(lifteq,[status(thm)],[8]) ).

thf(16,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      = ( sk1 @ A ) ),
    inference(func_ext,[status(esa)],[13]) ).

thf(51,plain,
    ( sk4
    | ~ ( sk1 @ sk6 )
    | ( sk1 @ sk7 ) ),
    inference(rewrite,[status(thm)],[30,16]) ).

thf(11,plain,
    ( sk4
    | ( sk2 @ sk6 )
    | ( sk3 @ sk7 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(22,plain,
    ( sk4
    | ( sk2 @ sk6 )
    | ( sk2 @ sk7 ) ),
    inference(rewrite,[status(thm)],[11,14]) ).

thf(49,plain,
    ( sk4
    | ( sk1 @ sk6 )
    | ( sk1 @ sk7 ) ),
    inference(rewrite,[status(thm)],[22,16]) ).

thf(9,plain,
    ( ( sk1 @ sk5 )
    | ~ sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(10,plain,
    ( ~ ( sk2 @ sk5 )
    | ~ sk4 ),
    inference(cnf,[status(esa)],[3]) ).

thf(44,plain,
    ( ~ ( sk1 @ sk5 )
    | ~ sk4 ),
    inference(rewrite,[status(thm)],[10,16]) ).

thf(59,plain,
    ( ~ sk4
    | ( ( sk1 @ sk5 )
     != ( sk1 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[9,44]) ).

thf(60,plain,
    ~ sk4,
    inference(pattern_uni,[status(thm)],[59:[]]) ).

thf(63,plain,
    ( $false
    | ( sk1 @ sk6 )
    | ( sk1 @ sk7 ) ),
    inference(rewrite,[status(thm)],[49,60]) ).

thf(64,plain,
    ( ( sk1 @ sk6 )
    | ( sk1 @ sk7 ) ),
    inference(simp,[status(thm)],[63]) ).

thf(7,plain,
    ( sk4
    | ( sk2 @ sk6 )
    | ~ ( sk1 @ sk7 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(4,plain,
    ( sk4
    | ~ ( sk3 @ sk6 )
    | ~ ( sk1 @ sk7 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(21,plain,
    ( sk4
    | ~ ( sk2 @ sk6 )
    | ~ ( sk1 @ sk7 ) ),
    inference(rewrite,[status(thm)],[4,14]) ).

thf(39,plain,
    ( sk4
    | ~ ( sk1 @ sk7 )
    | ( ( sk2 @ sk6 )
     != ( sk2 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[7,21]) ).

thf(40,plain,
    ( sk4
    | ~ ( sk1 @ sk7 ) ),
    inference(pattern_uni,[status(thm)],[39:[]]) ).

thf(61,plain,
    ( $false
    | ~ ( sk1 @ sk7 ) ),
    inference(rewrite,[status(thm)],[40,60]) ).

thf(62,plain,
    ~ ( sk1 @ sk7 ),
    inference(simp,[status(thm)],[61]) ).

thf(68,plain,
    ( ( sk1 @ sk6 )
    | $false ),
    inference(rewrite,[status(thm)],[64,62]) ).

thf(69,plain,
    sk1 @ sk6,
    inference(simp,[status(thm)],[68]) ).

thf(97,plain,
    ( $false
    | ~ $true
    | $false ),
    inference(rewrite,[status(thm)],[51,69,60,62]) ).

thf(98,plain,
    $false,
    inference(simp,[status(thm)],[97]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : SEU850^5 : TPTP v8.2.0. Released v4.0.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 17:00:39 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.02/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.13  % [INFO] 	 Parsing done (164ms). 
% 1.30/1.15  % [INFO] 	 Running in sequential loop mode. 
% 1.94/1.52  % [INFO] 	 nitpick registered as external prover. 
% 1.94/1.53  % [INFO] 	 Scanning for conjecture ... 
% 2.12/1.61  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.12/1.65  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.12/1.65  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.12/1.65  % [INFO] 	 Type checking passed. 
% 2.12/1.66  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 4.28/2.49  % [INFO] 	 Killing All external provers ... 
% 4.28/2.49  % Time passed: 2016ms (effective reasoning time: 1337ms)
% 4.28/2.49  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.28/2.49  % Axioms used in derivation (0): 
% 4.28/2.49  % No. of inferences in proof: 33
% 4.28/2.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2016 ms resp. 1337 ms w/o parsing
% 4.28/2.54  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.28/2.54  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------