%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV405+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 : Wed Jul 20 20:31:31 EDT 2022

% Result   : Theorem 0.22s 0.45s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   24 (  15 unt;   0 def)
%            Number of atoms       :   40 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   28 (  12   ~;   1   |;   5   &)
%                                         (   1 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-3 aty)
%            Number of variables   :   48 (   2 sgn  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax22,axiom,
    ! [U,V] : ~ pair_in_list(create_slb,U,V) ).

fof(ax36,axiom,
    ! [U,V] : check_cpq(triple(U,create_slb,V)) ).

fof(l41_co,conjecture,
    ! [U,V] :
      ( check_cpq(triple(U,create_slb,V))
    <=> ! [W,X] :
          ( pair_in_list(create_slb,W,X)
         => less_than(X,W) ) ) ).

fof(subgoal_0,plain,
    ! [U,V] :
      ( check_cpq(triple(U,create_slb,V))
     => ! [W,X] :
          ( pair_in_list(create_slb,W,X)
         => less_than(X,W) ) ),
    inference(strip,[],[l41_co]) ).

fof(subgoal_1,plain,
    ! [U,V] :
      ( ! [W,X] :
          ( pair_in_list(create_slb,W,X)
         => less_than(X,W) )
     => check_cpq(triple(U,create_slb,V)) ),
    inference(strip,[],[l41_co]) ).

fof(negate_0_0,plain,
    ~ ! [U,V] :
        ( check_cpq(triple(U,create_slb,V))
       => ! [W,X] :
            ( pair_in_list(create_slb,W,X)
           => less_than(X,W) ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ? [U,V] : check_cpq(triple(U,create_slb,V))
    & ? [W,X] :
        ( ~ less_than(X,W)
        & pair_in_list(create_slb,W,X) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [U,V] : check_cpq(triple(U,create_slb,V)),
    inference(canonicalize,[],[ax36]) ).

fof(normalize_0_2,plain,
    ! [U,V] : check_cpq(triple(U,create_slb,V)),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ? [W,X] :
      ( ~ less_than(X,W)
      & pair_in_list(create_slb,W,X) ),
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( ~ less_than(skolemFOFtoCNF_X,skolemFOFtoCNF_W)
    & pair_in_list(create_slb,skolemFOFtoCNF_W,skolemFOFtoCNF_X) ),
    inference(skolemize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    pair_in_list(create_slb,skolemFOFtoCNF_W,skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [U,V] : ~ pair_in_list(create_slb,U,V),
    inference(canonicalize,[],[ax22]) ).

fof(normalize_0_7,plain,
    ! [U,V] : ~ pair_in_list(create_slb,U,V),
    inference(specialize,[],[normalize_0_6]) ).

cnf(refute_0_0,plain,
    pair_in_list(create_slb,skolemFOFtoCNF_W,skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_1,plain,
    ~ pair_in_list(create_slb,U,V),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    ~ pair_in_list(create_slb,skolemFOFtoCNF_W,skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_1:[bind(U,$fot(skolemFOFtoCNF_W)),bind(V,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( pair_in_list(create_slb,skolemFOFtoCNF_W,skolemFOFtoCNF_X) )],[refute_0_0,refute_0_2]) ).

fof(negate_1_0,plain,
    ~ ! [U,V] :
        ( ! [W,X] :
            ( pair_in_list(create_slb,W,X)
           => less_than(X,W) )
       => check_cpq(triple(U,create_slb,V)) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ( ? [U,V] : ~ check_cpq(triple(U,create_slb,V))
    & ! [W,X] :
        ( ~ pair_in_list(create_slb,W,X)
        | less_than(X,W) ) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ! [U,V] : check_cpq(triple(U,create_slb,V)),
    inference(canonicalize,[],[ax36]) ).

fof(normalize_1_2,plain,
    ! [U,V] : check_cpq(triple(U,create_slb,V)),
    inference(specialize,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    $false,
    inference(simplify,[],[normalize_1_0,normalize_1_2]) ).

cnf(refute_1_0,plain,
    $false,
    inference(canonicalize,[],[normalize_1_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV405+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n013.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Wed Jun 15 11:48:59 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.45  
% 0.22/0.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.22/0.45  
%------------------------------------------------------------------------------