TSTP Solution File: SET593^5 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SET593^5 : 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 03:06:22 EDT 2024

% Result   : Theorem 4.70s 1.99s
% Output   : Refutation 4.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   53 (   8 unt;   6 typ;   0 def)
%            Number of atoms       :  119 (  11 equ;   0 cnn)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  258 (  53   ~;  56   |;   9   &; 128   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   12 (  12   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   0   ^  24   !;   0   ?;  24   :)

% 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: a ).

thf(sk5_type,type,
    sk5: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o,C: a > $o] :
      ( ! [D: a] :
          ( ( A @ D )
         => ( ( B @ D )
            | ( C @ D ) ) )
     => ( ! [D: a] :
            ( ( ( A @ D )
              & ~ ( B @ D ) )
           => ( C @ D ) )
        & ! [D: a] :
            ( ( ( A @ D )
              & ~ ( C @ D ) )
           => ( B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBOOL_PROP_52_pme) ).

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

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

thf(5,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ( sk3 @ A ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(11,plain,
    ( ~ ( sk3 @ sk4 )
    | ~ ( sk3 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(33,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ( sk3 @ sk4 )
      | ( ( sk3 @ A )
       != ( sk3 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[5,11]) ).

thf(34,plain,
    ( ~ ( sk1 @ sk5 )
    | ( sk2 @ sk5 )
    | ~ ( sk3 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( sk5 ))]]) ).

thf(13,plain,
    ( ( sk1 @ sk4 )
    | ( sk1 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(27,plain,
    ! [A: a] :
      ( ( sk1 @ sk4 )
      | ( sk2 @ A )
      | ( sk3 @ A )
      | ( ( sk1 @ sk5 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[13,5]) ).

thf(28,plain,
    ( ( sk1 @ sk4 )
    | ( sk2 @ sk5 )
    | ( sk3 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk5 ))]]) ).

thf(7,plain,
    ( ( sk1 @ sk4 )
    | ~ ( sk3 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(59,plain,
    ( ( sk1 @ sk4 )
    | ( sk2 @ sk5 )
    | ( ( sk3 @ sk5 )
     != ( sk3 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[28,7]) ).

thf(60,plain,
    ( ( sk1 @ sk4 )
    | ( sk2 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[59:[]]) ).

thf(12,plain,
    ( ( sk1 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(82,plain,
    ( ( sk1 @ sk4 )
    | ( ( sk2 @ sk5 )
     != ( sk2 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[60,12]) ).

thf(83,plain,
    sk1 @ sk4,
    inference(pattern_uni,[status(thm)],[82:[]]) ).

thf(104,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ( sk3 @ A )
      | ( ( sk1 @ sk4 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[83,5]) ).

thf(105,plain,
    ( ( sk2 @ sk4 )
    | ( sk3 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk4 ))]]) ).

thf(9,plain,
    ( ~ ( sk3 @ sk4 )
    | ( sk1 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(120,plain,
    ( ( sk2 @ sk4 )
    | ( sk1 @ sk5 )
    | ( ( sk3 @ sk4 )
     != ( sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[105,9]) ).

thf(121,plain,
    ( ( sk2 @ sk4 )
    | ( sk1 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[120:[]]) ).

thf(4,plain,
    ( ~ ( sk2 @ sk4 )
    | ( sk1 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(146,plain,
    ( ( sk1 @ sk5 )
    | ( ( sk2 @ sk4 )
     != ( sk2 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[121,4]) ).

thf(147,plain,
    sk1 @ sk5,
    inference(pattern_uni,[status(thm)],[146:[]]) ).

thf(155,plain,
    ( ~ $true
    | ( sk2 @ sk5 )
    | ~ ( sk3 @ sk4 ) ),
    inference(rewrite,[status(thm)],[34,147]) ).

thf(156,plain,
    ( ( sk2 @ sk5 )
    | ~ ( sk3 @ sk4 ) ),
    inference(simp,[status(thm)],[155]) ).

thf(157,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ( sk3 @ A )
      | ( ( sk1 @ sk5 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[147,5]) ).

thf(158,plain,
    ( ( sk2 @ sk5 )
    | ( sk3 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( sk5 ))]]) ).

thf(8,plain,
    ( ~ ( sk2 @ sk4 )
    | ~ ( sk3 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(189,plain,
    ( ( sk2 @ sk5 )
    | ~ ( sk2 @ sk4 )
    | ( ( sk3 @ sk5 )
     != ( sk3 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[158,8]) ).

thf(190,plain,
    ( ( sk2 @ sk5 )
    | ~ ( sk2 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[189:[]]) ).

thf(6,plain,
    ( ~ ( sk2 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(211,plain,
    ( ~ ( sk2 @ sk4 )
    | ( ( sk2 @ sk5 )
     != ( sk2 @ sk5 ) ) ),
    inference(paramod_ordered,[status(thm)],[190,6]) ).

thf(212,plain,
    ~ ( sk2 @ sk4 ),
    inference(pattern_uni,[status(thm)],[211:[]]) ).

thf(227,plain,
    ( $false
    | ( sk3 @ sk4 ) ),
    inference(rewrite,[status(thm)],[105,212]) ).

thf(228,plain,
    sk3 @ sk4,
    inference(simp,[status(thm)],[227]) ).

thf(236,plain,
    ( ( sk2 @ sk5 )
    | ~ $true ),
    inference(rewrite,[status(thm)],[156,228]) ).

thf(237,plain,
    sk2 @ sk5,
    inference(simp,[status(thm)],[236]) ).

thf(10,plain,
    ( ~ ( sk3 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(23,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ( sk2 @ sk5 )
      | ( ( sk3 @ A )
       != ( sk3 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[5,10]) ).

thf(24,plain,
    ( ~ ( sk1 @ sk4 )
    | ( sk2 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( sk4 ))]]) ).

thf(102,plain,
    ( ~ $true
    | ( sk2 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(rewrite,[status(thm)],[24,83]) ).

thf(103,plain,
    ( ( sk2 @ sk4 )
    | ~ ( sk2 @ sk5 ) ),
    inference(simp,[status(thm)],[102]) ).

thf(229,plain,
    ( $false
    | ~ ( sk2 @ sk5 ) ),
    inference(rewrite,[status(thm)],[103,212]) ).

thf(230,plain,
    ~ ( sk2 @ sk5 ),
    inference(simp,[status(thm)],[229]) ).

thf(251,plain,
    $false,
    inference(rewrite,[status(thm)],[237,230]) ).

thf(252,plain,
    $false,
    inference(simp,[status(thm)],[251]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET593^5 : TPTP v8.2.0. Released v4.0.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n029.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Mon May 20 12:08:54 EDT 2024
% 0.15/0.37  % CPUTime  : 
% 0.98/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.14/0.97  % [INFO] 	 Parsing done (103ms). 
% 1.25/0.97  % [INFO] 	 Running in sequential loop mode. 
% 1.54/1.17  % [INFO] 	 nitpick registered as external prover. 
% 1.54/1.17  % [INFO] 	 Scanning for conjecture ... 
% 1.64/1.22  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.80/1.24  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.80/1.24  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.80/1.24  % [INFO] 	 Type checking passed. 
% 1.80/1.24  % [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 ... 
% 4.70/1.99  % [INFO] 	 Killing All external provers ... 
% 4.70/1.99  % Time passed: 1460ms (effective reasoning time: 1012ms)
% 4.70/1.99  % 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)>
% 4.70/1.99  % Axioms used in derivation (0): 
% 4.70/1.99  % No. of inferences in proof: 47
% 4.70/1.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1460 ms resp. 1012 ms w/o parsing
% 4.70/2.03  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.70/2.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------