%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWV121+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 20:30:11 EDT 2022

% Result   : Theorem 0.42s 0.58s
% Output   : CNFRefutation 0.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    2
% Syntax   : Number of formulae    :    8 (   4 unt;   0 def)
%            Number of atoms       :   68 (  12 equ)
%            Maximal formula atoms :   16 (   8 avg)
%            Number of connectives :   74 (  14   ~;  12   |;  36   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-3 aty)
%            Number of variables   :   24 (   0 sgn  24   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ttrue,axiom,
    true ).

fof(quaternion_ds1_symm_0014,conjecture,
    ( ( ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,minus(n6,n1))
            & leq(B,minus(n6,n1)) )
         => a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,minus(n3,n1))
            & leq(D,minus(n3,n1)) )
         => a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
      & ! [E,F] :
          ( ( leq(n0,E)
            & leq(n0,F)
            & leq(E,minus(n6,n1))
            & leq(F,minus(n6,n1)) )
         => a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) ) )
   => true ) ).

fof(subgoal_0,plain,
    ( ( ! [A,B] :
          ( ( leq(n0,A)
            & leq(n0,B)
            & leq(A,minus(n6,n1))
            & leq(B,minus(n6,n1)) )
         => a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
      & ! [C,D] :
          ( ( leq(n0,C)
            & leq(n0,D)
            & leq(C,minus(n3,n1))
            & leq(D,minus(n3,n1)) )
         => a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
      & ! [E,F] :
          ( ( leq(n0,E)
            & leq(n0,F)
            & leq(E,minus(n6,n1))
            & leq(F,minus(n6,n1)) )
         => a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) ) )
   => true ),
    inference(strip,[],[quaternion_ds1_symm_0014]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [A,B] :
            ( ( leq(n0,A)
              & leq(n0,B)
              & leq(A,minus(n6,n1))
              & leq(B,minus(n6,n1)) )
           => a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
        & ! [C,D] :
            ( ( leq(n0,C)
              & leq(n0,D)
              & leq(C,minus(n3,n1))
              & leq(D,minus(n3,n1)) )
           => a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
        & ! [E,F] :
            ( ( leq(n0,E)
              & leq(n0,F)
              & leq(E,minus(n6,n1))
              & leq(F,minus(n6,n1)) )
           => a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) ) )
     => true ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ true
    & ! [A,B] :
        ( ~ leq(A,minus(n6,n1))
        | ~ leq(B,minus(n6,n1))
        | ~ leq(n0,A)
        | ~ leq(n0,B)
        | a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) )
    & ! [C,D] :
        ( ~ leq(C,minus(n3,n1))
        | ~ leq(D,minus(n3,n1))
        | ~ leq(n0,C)
        | ~ leq(n0,D)
        | a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
    & ! [E,F] :
        ( ~ leq(E,minus(n6,n1))
        | ~ leq(F,minus(n6,n1))
        | ~ leq(n0,E)
        | ~ leq(n0,F)
        | a_select3(pminus_ds1_filter,E,F) = a_select3(pminus_ds1_filter,F,E) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    true,
    inference(canonicalize,[],[ttrue]) ).

fof(normalize_0_2,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_1]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWV121+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n005.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 : Tue Jun 14 18:29:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.42/0.58  
% 0.42/0.58  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.42/0.58  
%------------------------------------------------------------------------------