%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SYN979+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 : Thu Jul 21 09:12:35 EDT 2022

% Result   : Theorem 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   14 (   8 unt;   0 def)
%            Number of atoms       :   70 (   0 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :   68 (  12   ~;   7   |;  37   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   30 (   2 sgn  20   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
    ! [A,B] :
    ? [X,Y] :
      ( ( ( q(X)
         => p(X,A) )
        & q(A)
        & q(B)
        & ( r(Y)
         => p(B,Y) )
        & r(A)
        & r(B)
        & ( s(A)
         => p(X,Y) )
        & s(A) )
     => p(A,B) ) ).

fof(subgoal_0,plain,
    ! [A,B] :
    ? [X,Y] :
      ( ( ( q(X)
         => p(X,A) )
        & q(A)
        & q(B)
        & ( r(Y)
         => p(B,Y) )
        & r(A)
        & r(B)
        & ( s(A)
         => p(X,Y) )
        & s(A) )
     => p(A,B) ),
    inference(strip,[],[prove_this]) ).

fof(negate_0_0,plain,
    ~ ! [A,B] :
      ? [X,Y] :
        ( ( ( q(X)
           => p(X,A) )
          & q(A)
          & q(B)
          & ( r(Y)
           => p(B,Y) )
          & r(A)
          & r(B)
          & ( s(A)
           => p(X,Y) )
          & s(A) )
       => p(A,B) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B] :
      ( ~ p(A,B)
      & q(A)
      & q(B)
      & r(A)
      & r(B)
      & s(A)
      & ( ~ s(A)
        | ! [X,Y] : p(X,Y) )
      & ! [X] :
          ( ~ q(X)
          | p(X,A) )
      & ! [Y] :
          ( ~ r(Y)
          | p(B,Y) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ p(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
    & q(skolemFOFtoCNF_A)
    & q(skolemFOFtoCNF_B)
    & r(skolemFOFtoCNF_A)
    & r(skolemFOFtoCNF_B)
    & s(skolemFOFtoCNF_A)
    & ( ~ s(skolemFOFtoCNF_A)
      | ! [X,Y] : p(X,Y) )
    & ! [X] :
        ( ~ q(X)
        | p(X,skolemFOFtoCNF_A) )
    & ! [Y] :
        ( ~ r(Y)
        | p(skolemFOFtoCNF_B,Y) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ p(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ~ s(skolemFOFtoCNF_A)
    | ! [X,Y] : p(X,Y) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_4,plain,
    s(skolemFOFtoCNF_A),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_5,plain,
    ! [X,Y] : p(X,Y),
    inference(simplify,[],[normalize_0_3,normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] : p(X,Y),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ~ p(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    p(X,Y),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    p(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_A)),bind(Y,$fot(skolemFOFtoCNF_B))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( p(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_2,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN979+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jul 12 01:37:09 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------