TSTP Solution File: SEV398^5 by Leo-III-SAT---1.7.15

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.15
% Problem  : SEV398^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d SAT

% Computer : n001.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 : Mon Jun 24 16:00:10 EDT 2024

% Result   : Theorem 207.29s 43.52s
% Output   : Refutation 207.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   35 (   4 unt;   0 typ;   0 def)
%            Number of atoms       :  211 (  12 equ;   0 cnn)
%            Maximal formula atoms :    9 (   6 avg)
%            Number of connectives :  389 (  38   ~;  34   |;   8   &; 285   @)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :   40 (  40   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   70 (   0   ^  70   !;   0   ?;  70   :)

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

thf(cF_type,type,
    cF: ( a > $o ) > a > $o ).

thf(cG_type,type,
    cG: ( a > $o ) > a > $o ).

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

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

thf(sk3_type,type,
    sk3: a ).

thf(1,conjecture,
    ( ( ! [A: a > $o,B: a > $o] :
          ( ! [C: a] :
              ( ( A @ C )
             => ( B @ C ) )
         => ! [C: a] :
              ( ( cF @ B @ C )
             => ( cF @ A @ C ) ) )
      & ! [A: a > $o] :
          ( ! [B: a] :
              ( ( A @ B )
             => ( cF @ ( cG @ A ) @ B ) )
          & ! [B: a] :
              ( ( A @ B )
             => ( cG @ ( cF @ A ) @ B ) ) ) )
   => ! [A: a > $o,B: a] :
        ( ( cF @ ( cG @ ( cF @ A ) ) @ B )
        = ( cF @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM67A_pme) ).

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

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

thf(4,plain,
    ~ ( ( ! [A: a > $o,B: a > $o] :
            ( ! [C: a] :
                ( ( A @ C )
               => ( B @ C ) )
           => ! [C: a] :
                ( ( cF @ B @ C )
               => ( cF @ A @ C ) ) )
        & ! [A: a > $o,B: a] :
            ( ( A @ B )
           => ( cF @ ( cG @ A ) @ B ) )
        & ! [A: a > $o,B: a] :
            ( ( A @ B )
           => ( cG @ ( cF @ A ) @ B ) ) )
     => ! [A: a > $o,B: a] :
          ( ( cF @ ( cG @ ( cF @ A ) ) @ B )
          = ( cF @ A @ B ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(6,plain,
    ( ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
   != ( cF @ sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(10,plain,
    ( ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
   != ( cF @ sk2 @ sk3 ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(7,plain,
    ! [B: a,A: a > $o] :
      ( ~ ( A @ B )
      | ( cF @ ( cG @ A ) @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(12,plain,
    ! [B: a,A: a > $o] :
      ( ~ ( A @ B )
      | ( cF @ ( cG @ A ) @ B ) ),
    inference(simp,[status(thm)],[7]) ).

thf(1044,plain,
    ! [B: a,A: a > $o] :
      ( ~ ( A @ B )
      | ~ ( cF @ sk2 @ sk3 )
      | ( ( cF @ ( cG @ A ) @ B )
       != ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[12,10]) ).

thf(1045,plain,
    ( ~ ( cF @ sk2 @ sk3 )
    | ~ ( cF @ sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( cF @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(1150,plain,
    ~ ( cF @ sk2 @ sk3 ),
    inference(simp,[status(thm)],[1045]) ).

thf(1174,plain,
    cF @ ( cG @ ( cF @ sk2 ) ) @ sk3,
    inference(rewrite,[status(thm)],[10,1150]) ).

thf(8,plain,
    ! [C: a,B: a > $o,A: a > $o] :
      ( ( A @ ( sk1 @ B @ A ) )
      | ~ ( cF @ B @ C )
      | ( cF @ A @ C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    ( ~ ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
    | ~ ( cF @ sk2 @ sk3 ) ),
    inference(bool_ext,[status(thm)],[10]) ).

thf(149,plain,
    ! [C: a,B: a > $o,A: a > $o] :
      ( ( A @ ( sk1 @ B @ A ) )
      | ~ ( cF @ B @ C )
      | ~ ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
      | ( ( cF @ A @ C )
       != ( cF @ sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[8,14]) ).

thf(150,plain,
    ! [A: a > $o] :
      ( ( sk2 @ ( sk1 @ A @ sk2 ) )
      | ~ ( cF @ A @ sk3 )
      | ~ ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).

thf(184,plain,
    ! [A: a > $o] :
      ( ( sk2 @ ( sk1 @ A @ sk2 ) )
      | ~ ( cF @ A @ sk3 )
      | ~ ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 ) ),
    inference(simp,[status(thm)],[150]) ).

thf(12469,plain,
    ! [A: a > $o] :
      ( ( sk2 @ ( sk1 @ A @ sk2 ) )
      | ~ ( cF @ A @ sk3 )
      | ~ $true ),
    inference(rewrite,[status(thm)],[184,1174]) ).

thf(12470,plain,
    ! [A: a > $o] :
      ( ( sk2 @ ( sk1 @ A @ sk2 ) )
      | ~ ( cF @ A @ sk3 ) ),
    inference(simp,[status(thm)],[12469]) ).

thf(12496,plain,
    ! [A: a > $o] :
      ( ( sk2 @ ( sk1 @ A @ sk2 ) )
      | ( ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
       != ( cF @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1174,12470]) ).

thf(12497,plain,
    sk2 @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ sk2 ),
    inference(pattern_uni,[status(thm)],[12496:[bind(A,$thf( cG @ ( cF @ sk2 ) ))]]) ).

thf(9,plain,
    ! [B: a,A: a > $o] :
      ( ~ ( A @ B )
      | ( cG @ ( cF @ A ) @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(11,plain,
    ! [B: a,A: a > $o] :
      ( ~ ( A @ B )
      | ( cG @ ( cF @ A ) @ B ) ),
    inference(simp,[status(thm)],[9]) ).

thf(13920,plain,
    ! [B: a,A: a > $o] :
      ( ( cG @ ( cF @ A ) @ B )
      | ( ( sk2 @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ sk2 ) )
       != ( A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[12497,11]) ).

thf(13931,plain,
    cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ sk2 ),
    inference(pre_uni,[status(thm)],[13920:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ ( cG @ ( cF @ sk2 ) ) @ sk2 ))]]) ).

thf(15,plain,
    ( ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
    | ( cF @ sk2 @ sk3 ) ),
    inference(bool_ext,[status(thm)],[10]) ).

thf(5,plain,
    ! [C: a,B: a > $o,A: a > $o] :
      ( ~ ( B @ ( sk1 @ B @ A ) )
      | ~ ( cF @ B @ C )
      | ( cF @ A @ C ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(47,plain,
    ! [C: a,B: a > $o,A: a > $o] :
      ( ( cF @ sk2 @ sk3 )
      | ~ ( B @ ( sk1 @ B @ A ) )
      | ( cF @ A @ C )
      | ( ( cF @ ( cG @ ( cF @ sk2 ) ) @ sk3 )
       != ( cF @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[15,5]) ).

thf(48,plain,
    ! [A: a > $o] :
      ( ( cF @ sk2 @ sk3 )
      | ~ ( cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ A ) )
      | ( cF @ A @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( A )),bind(B,$thf( cG @ ( cF @ sk2 ) )),bind(C,$thf( sk3 ))]]) ).

thf(1407,plain,
    ! [A: a > $o] :
      ( $false
      | ~ ( cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ A ) )
      | ( cF @ A @ sk3 ) ),
    inference(rewrite,[status(thm)],[48,1150]) ).

thf(1408,plain,
    ! [A: a > $o] :
      ( ~ ( cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ A ) )
      | ( cF @ A @ sk3 ) ),
    inference(simp,[status(thm)],[1407]) ).

thf(42673,plain,
    ! [A: a > $o] :
      ( ( cF @ A @ sk3 )
      | ( ( cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ sk2 ) )
       != ( cG @ ( cF @ sk2 ) @ ( sk1 @ ( cG @ ( cF @ sk2 ) ) @ A ) ) ) ),
    inference(paramod_ordered,[status(thm)],[13931,1408]) ).

thf(42674,plain,
    cF @ sk2 @ sk3,
    inference(pattern_uni,[status(thm)],[42673:[bind(A,$thf( sk2 ))]]) ).

thf(42792,plain,
    $false,
    inference(rewrite,[status(thm)],[42674,1150]) ).

thf(42793,plain,
    $false,
    inference(simp,[status(thm)],[42792]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SEV398^5 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12  % Command  : run_Leo-III %s %d SAT
% 0.11/0.33  % Computer : n001.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Fri Jun 21 19:41:40 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 1.09/0.93  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.30/1.05  % [INFO] 	 Parsing done (118ms). 
% 1.30/1.06  % [INFO] 	 Running in sequential loop mode. 
% 1.67/1.29  % [INFO] 	 nitpick registered as external prover. 
% 1.67/1.29  % [INFO] 	 Scanning for conjecture ... 
% 1.85/1.35  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.00/1.37  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.00/1.37  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 2.00/1.38  % [INFO] 	 Type checking passed. 
% 2.00/1.38  % [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 ... 
% 207.29/43.52  % [INFO] 	 Killing All external provers ... 
% 207.29/43.52  % Time passed: 42981ms (effective reasoning time: 42451ms)
% 207.29/43.52  % 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)>
% 207.29/43.52  % Axioms used in derivation (0): 
% 207.29/43.52  % No. of inferences in proof: 35
% 207.29/43.52  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 42981 ms resp. 42451 ms w/o parsing
% 207.29/43.57  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 207.29/43.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------