TSTP Solution File: SYN918+1 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : SYN918+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n012.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 08:19:59 EDT 2024

% Result   : Theorem 3.69s 2.19s
% Output   : Refutation 3.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   35 (   6 unt;   4 typ;   0 def)
%            Number of atoms       :  135 (   6 equ;   0 cnn)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  265 (  49   ~;  40   |;  24   &; 124   @)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    3 (   3   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    7 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   47 (   0   ^  38   !;   9   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
thf(f_type,type,
    f: $i > $o ).

thf(g_type,type,
    g: $i > $o ).

thf(h_type,type,
    h: $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(1,conjecture,
    ( ( ! [A: $i] :
          ( ( ( ( f @ A )
              & ( g @ A ) )
           => ( h @ A ) )
         => ? [B: $i] :
              ( ( f @ B )
              & ~ ( g @ B ) ) )
      & ( ! [A: $i] :
            ( ( f @ A )
           => ( g @ A ) )
        | ! [A: $i] :
            ( ( f @ A )
           => ( h @ A ) ) ) )
   => ( ! [A: $i] :
          ( ( ( f @ A )
            & ( h @ A ) )
         => ( g @ A ) )
     => ? [A: $i] :
          ( ( f @ A )
          & ( g @ A )
          & ~ ( h @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).

thf(2,negated_conjecture,
    ~ ( ( ! [A: $i] :
            ( ( ( ( f @ A )
                & ( g @ A ) )
             => ( h @ A ) )
           => ? [B: $i] :
                ( ( f @ B )
                & ~ ( g @ B ) ) )
        & ( ! [A: $i] :
              ( ( f @ A )
             => ( g @ A ) )
          | ! [A: $i] :
              ( ( f @ A )
             => ( h @ A ) ) ) )
     => ( ! [A: $i] :
            ( ( ( f @ A )
              & ( h @ A ) )
           => ( g @ A ) )
       => ? [A: $i] :
            ( ( f @ A )
            & ( g @ A )
            & ~ ( h @ A ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ( ( ! [A: $i] :
            ( ( ( ( f @ A )
                & ( g @ A ) )
             => ( h @ A ) )
           => ? [B: $i] :
                ( ( f @ B )
                & ~ ( g @ B ) ) )
        & ( ! [A: $i] :
              ( ( f @ A )
             => ( g @ A ) )
          | ! [A: $i] :
              ( ( f @ A )
             => ( h @ A ) ) ) )
     => ( ! [A: $i] :
            ( ( ( f @ A )
              & ( h @ A ) )
           => ( g @ A ) )
       => ? [A: $i] :
            ( ( f @ A )
            & ( g @ A )
            & ~ ( h @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ~ ( ( ( ( ( ! [A: $i] : ( f @ A )
              & ! [A: $i] : ( g @ A ) )
           => ? [A: $i] : ( h @ A ) )
         => ? [A: $i] :
              ( ( f @ A )
              & ~ ( g @ A ) ) )
        & ( ! [A: $i] :
              ( ( f @ A )
             => ( g @ A ) )
          | ! [A: $i] :
              ( ( f @ A )
             => ( h @ A ) ) ) )
     => ( ! [A: $i] :
            ( ( ( f @ A )
              & ( h @ A ) )
           => ( g @ A ) )
       => ? [A: $i] :
            ( ( f @ A )
            & ( g @ A )
            & ~ ( h @ A ) ) ) ),
    inference(miniscope,[status(thm)],[3]) ).

thf(6,plain,
    ! [A: $i] :
      ( ( f @ A )
      | ( f @ sk1 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(21,plain,
    ! [A: $i] :
      ( ( f @ A )
      | ( ( f @ sk1 )
       != ( f @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[6]) ).

thf(22,plain,
    f @ sk1,
    inference(pattern_uni,[status(thm)],[21:[bind(A,$thf( sk1 ))]]) ).

thf(5,plain,
    ! [B: $i,A: $i] :
      ( ~ ( f @ A )
      | ( g @ A )
      | ~ ( f @ B )
      | ( h @ B ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(14,plain,
    ! [B: $i,A: $i] :
      ( ~ ( f @ A )
      | ( g @ A )
      | ~ ( f @ B )
      | ( h @ B ) ),
    inference(simp,[status(thm)],[5]) ).

thf(43,plain,
    ! [B: $i,A: $i] :
      ( ~ ( f @ A )
      | ( g @ A )
      | ( h @ B )
      | ( ( f @ sk1 )
       != ( f @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[22,14]) ).

thf(44,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ( g @ A )
      | ( h @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).

thf(8,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ~ ( h @ A )
      | ( g @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(20,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ~ ( h @ A )
      | ( g @ A ) ),
    inference(simp,[status(thm)],[8]) ).

thf(53,plain,
    ! [A: $i] :
      ( ~ ( h @ A )
      | ( g @ A )
      | ( ( f @ sk1 )
       != ( f @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,20]) ).

thf(54,plain,
    ( ~ ( h @ sk1 )
    | ( g @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[53:[bind(A,$thf( sk1 ))]]) ).

thf(9,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ~ ( g @ A )
      | ( h @ A ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(16,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ~ ( g @ A )
      | ( h @ A ) ),
    inference(simp,[status(thm)],[9]) ).

thf(26,plain,
    ! [A: $i] :
      ( ~ ( g @ A )
      | ( h @ A )
      | ( ( f @ sk1 )
       != ( f @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22,16]) ).

thf(27,plain,
    ( ~ ( g @ sk1 )
    | ( h @ sk1 ) ),
    inference(pattern_uni,[status(thm)],[26:[bind(A,$thf( sk1 ))]]) ).

thf(11,plain,
    ! [A: $i] :
      ( ~ ( h @ A )
      | ~ ( g @ sk1 ) ),
    inference(cnf,[status(esa)],[4]) ).

thf(19,plain,
    ! [A: $i] :
      ( ~ ( h @ A )
      | ~ ( g @ sk1 ) ),
    inference(simp,[status(thm)],[11]) ).

thf(35,plain,
    ! [A: $i] :
      ( ~ ( g @ sk1 )
      | ( ( h @ sk1 )
       != ( h @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[27,19]) ).

thf(36,plain,
    ~ ( g @ sk1 ),
    inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( sk1 ))]]) ).

thf(58,plain,
    ( ~ ( h @ sk1 )
    | $false ),
    inference(rewrite,[status(thm)],[54,36]) ).

thf(59,plain,
    ~ ( h @ sk1 ),
    inference(simp,[status(thm)],[58]) ).

thf(64,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ( g @ A )
      | $false ),
    inference(rewrite,[status(thm)],[44,59]) ).

thf(65,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ( g @ A ) ),
    inference(simp,[status(thm)],[64]) ).

thf(68,plain,
    ! [A: $i] :
      ( ~ ( f @ A )
      | ( ( g @ A )
       != ( g @ sk1 ) ) ),
    inference(paramod_ordered,[status(thm)],[65,36]) ).

thf(69,plain,
    ~ ( f @ sk1 ),
    inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( sk1 ))]]) ).

thf(73,plain,
    ~ $true,
    inference(rewrite,[status(thm)],[69,22]) ).

thf(74,plain,
    $false,
    inference(simp,[status(thm)],[73]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09  % Problem  : SYN918+1 : TPTP v8.2.0. Released v3.1.0.
% 0.09/0.11  % Command  : run_Leo-III %s %d
% 0.11/0.31  % Computer : n012.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit : 300
% 0.11/0.31  % WCLimit  : 300
% 0.11/0.31  % DateTime : Mon May 20 14:27:24 EDT 2024
% 0.11/0.31  % CPUTime  : 
% 0.87/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.12/1.06  % [INFO] 	 Parsing done (146ms). 
% 1.28/1.08  % [INFO] 	 Running in sequential loop mode. 
% 1.78/1.42  % [INFO] 	 nitpick registered as external prover. 
% 1.78/1.43  % [INFO] 	 Scanning for conjecture ... 
% 1.87/1.51  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 2.01/1.54  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 2.01/1.54  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.01/1.55  % [INFO] 	 Type checking passed. 
% 2.01/1.55  % [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 ... 
% 3.69/2.18  % [INFO] 	 Killing All external provers ... 
% 3.69/2.18  % Time passed: 1725ms (effective reasoning time: 1100ms)
% 3.69/2.18  % 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)>
% 3.69/2.19  % Axioms used in derivation (0): 
% 3.69/2.19  % No. of inferences in proof: 31
% 3.69/2.19  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1725 ms resp. 1100 ms w/o parsing
% 3.69/2.24  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.69/2.24  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------