%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 : Sat Jul 16 23:58:30 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    1
% Syntax   : Number of formulae    :    9 (   4 unt;   0 def)
%            Number of atoms       :   34 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   37 (  12   ~;   0   |;   4   &)
%                                         (   1 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-2 aty)
%            Number of variables   :   20 (   0 sgn  20   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0s] :
              ( mem(V0s,arr(A_27a,bool))
             => ! [V1t] :
                  ( mem(V1t,arr(A_27b,bool))
                 => ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
                  <=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ) ) ).

fof(subgoal_0,plain,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0s] :
              ( mem(V0s,arr(A_27a,bool))
             => ! [V1t] :
                  ( ( mem(V1t,arr(A_27b,bool))
                    & ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
                 => ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ),
    inference(strip,[],[conj_thm_2Ecardinal_2ECARD__NOT__LE]) ).

fof(subgoal_1,plain,
    ! [A_27a] :
      ( ne(A_27a)
     => ! [A_27b] :
          ( ne(A_27b)
         => ! [V0s] :
              ( mem(V0s,arr(A_27a,bool))
             => ! [V1t] :
                  ( ( mem(V1t,arr(A_27b,bool))
                    & ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
                 => ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ),
    inference(strip,[],[conj_thm_2Ecardinal_2ECARD__NOT__LE]) ).

fof(negate_0_0,plain,
    ~ ! [A_27a] :
        ( ne(A_27a)
       => ! [A_27b] :
            ( ne(A_27b)
           => ! [V0s] :
                ( mem(V0s,arr(A_27a,bool))
               => ! [V1t] :
                    ( ( mem(V1t,arr(A_27b,bool))
                      & ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
                   => ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    $false,
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_0]) ).

fof(negate_1_0,plain,
    ~ ! [A_27a] :
        ( ne(A_27a)
       => ! [A_27b] :
            ( ne(A_27b)
           => ! [V0s] :
                ( mem(V0s,arr(A_27a,bool))
               => ! [V1t] :
                    ( ( mem(V1t,arr(A_27b,bool))
                      & ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) )
                   => ~ p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t)) ) ) ) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    $false,
    inference(canonicalize,[],[negate_1_0]) ).

cnf(refute_1_0,plain,
    $false,
    inference(canonicalize,[],[normalize_1_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.11/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n017.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jun  3 02:31:28 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43  
% 0.19/0.43  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.43  
%------------------------------------------------------------------------------