%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV412+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : Wed Jul 20 20:31:32 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    9 (   2 unt;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    4 (   3 avg)
%            Number of connectives :   24 (   6   ~;   4   |;  10   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 2-2 aty)
%            Number of variables   :   28 (   0 sgn  24   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(l48_li3839,lemma,
    ! [U,V,W,X] :
      ( ( pair_in_list(U,V,W)
        & strictly_less_than(W,X) )
     => pair_in_list(update_slb(U,X),V,X) ) ).

fof(l48_co,conjecture,
    ! [U,V,W,X] :
      ( ( pair_in_list(U,V,W)
        & strictly_less_than(V,X)
        & strictly_less_than(W,X) )
     => pair_in_list(update_slb(U,X),V,X) ) ).

fof(subgoal_0,plain,
    ! [U,V,W,X] :
      ( ( pair_in_list(U,V,W)
        & strictly_less_than(V,X)
        & strictly_less_than(W,X) )
     => pair_in_list(update_slb(U,X),V,X) ),
    inference(strip,[],[l48_co]) ).

fof(negate_0_0,plain,
    ~ ! [U,V,W,X] :
        ( ( pair_in_list(U,V,W)
          & strictly_less_than(V,X)
          & strictly_less_than(W,X) )
       => pair_in_list(update_slb(U,X),V,X) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [U,V,W,X] :
      ( ~ pair_in_list(update_slb(U,X),V,X)
      & pair_in_list(U,V,W)
      & strictly_less_than(V,X)
      & strictly_less_than(W,X) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ! [U,V,W,X] :
      ( ~ pair_in_list(U,V,W)
      | ~ strictly_less_than(W,X)
      | pair_in_list(update_slb(U,X),V,X) ),
    inference(canonicalize,[],[l48_li3839]) ).

fof(normalize_0_2,plain,
    ! [U,V,W,X] :
      ( ~ pair_in_list(U,V,W)
      | ~ strictly_less_than(W,X)
      | pair_in_list(update_slb(U,X),V,X) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_2]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWV412+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n017.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 20:41:10 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38  
% 0.14/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38  
%------------------------------------------------------------------------------