TSTP Solution File: MSC010+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : MSC010+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 : Sun Jul 17 22:51:31 EDT 2022

% Result   : Theorem 0.14s 0.41s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   35 (   2 unt;   9 def)
%            Number of atoms       :  784 ( 163 equ)
%            Maximal formula atoms :   68 (  22 avg)
%            Number of connectives :  988 ( 239   ~; 200   |; 464   &)
%                                         (  23 <=>;  62  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (  13 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   4 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  16 con; 0-3 aty)
%            Number of variables   :  254 (   0 sgn 173   !;  81   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(n1,axiom,
    ( ( pv63 != pv64
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ! [X1,X2] :
          ( ( leq(n0,X1)
            & leq(n0,X2)
            & leq(X1,n2)
            & leq(X2,n5) )
         => a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X3,X4] :
          ( ( leq(n0,X3)
            & leq(n0,X4)
            & leq(X3,n5)
            & leq(X4,n5) )
         => a_select3(phi_ds1_filter_init,X3,X4) = init )
      & ! [X5,X6] :
          ( ( leq(n0,X5)
            & leq(n0,X6)
            & leq(X5,n5)
            & leq(X6,n0) )
         => a_select3(dv_ds1_filter_init,X5,X6) = init )
      & ! [X7,X8] :
          ( ( leq(n0,X7)
            & leq(n0,X8)
            & leq(X7,n5)
            & leq(X8,n5) )
         => a_select3(q_ds1_filter_init,X7,X8) = init )
      & ! [X9,X10] :
          ( ( leq(n0,X9)
            & leq(n0,X10)
            & leq(X9,n2)
            & leq(X10,n2) )
         => a_select3(r_ds1_filter_init,X9,X10) = init )
      & ! [X11,X12] :
          ( ( leq(n0,X11)
            & leq(n0,X12)
            & leq(X11,n5)
            & leq(X12,n0) )
         => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ( leq(n0,X13)
            & leq(n0,X14)
            & leq(X13,n5)
            & leq(X14,n5) )
         => a_select3(pminus_ds1_filter_init,X13,X14) = init )
      & ! [X15,X16] :
          ( ( leq(n0,X15)
            & leq(n0,X16)
            & leq(X15,n5)
            & leq(X16,n5) )
         => ( ( X15 = pv63
              & gt(pv64,X16) )
           => a_select3(id_ds1_filter_init,X15,X16) = init ) )
      & ! [X17,X18] :
          ( ( leq(n0,X17)
            & leq(n0,X18)
            & leq(X17,n5)
            & leq(X18,n5) )
         => ( gt(pv63,X17)
           => a_select3(id_ds1_filter_init,X17,X18) = init ) )
      & ! [X19] :
          ( ( leq(n0,X19)
            & leq(X19,pred(pv63)) )
         => ! [X20] :
              ( ( leq(n0,X20)
                & leq(X20,n5) )
             => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
   => ! [X21,X22] :
        ( ( leq(n0,X21)
          & leq(n0,X22)
          & leq(X21,n5)
          & leq(X22,n5) )
       => ( ( pv64 != X22
            & X21 = pv63
            & leq(X22,pv64) )
         => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) ).

fof(n91,conjecture,
    ~ ~ ( ( pv63 != pv64
          & leq(n0,pv5)
          & leq(n0,pv63)
          & leq(n0,pv64)
          & leq(pv5,n998)
          & leq(pv63,n5)
          & leq(pv64,n5)
          & ! [X1,X2] :
              ( ( leq(n0,X1)
                & leq(n0,X2)
                & leq(X1,n2)
                & leq(X2,n5) )
             => a_select3(h_ds1_filter_init,X1,X2) = init )
          & ! [X3,X4] :
              ( ( leq(n0,X3)
                & leq(n0,X4)
                & leq(X3,n5)
                & leq(X4,n5) )
             => a_select3(phi_ds1_filter_init,X3,X4) = init )
          & ! [X5,X6] :
              ( ( leq(n0,X5)
                & leq(n0,X6)
                & leq(X5,n5)
                & leq(X6,n0) )
             => a_select3(dv_ds1_filter_init,X5,X6) = init )
          & ! [X7,X8] :
              ( ( leq(n0,X7)
                & leq(n0,X8)
                & leq(X7,n5)
                & leq(X8,n5) )
             => a_select3(q_ds1_filter_init,X7,X8) = init )
          & ! [X9,X10] :
              ( ( leq(n0,X9)
                & leq(n0,X10)
                & leq(X9,n2)
                & leq(X10,n2) )
             => a_select3(r_ds1_filter_init,X9,X10) = init )
          & ! [X11,X12] :
              ( ( leq(n0,X11)
                & leq(n0,X12)
                & leq(X11,n5)
                & leq(X12,n0) )
             => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
          & ! [X13,X14] :
              ( ( leq(n0,X13)
                & leq(n0,X14)
                & leq(X13,n5)
                & leq(X14,n5) )
             => a_select3(pminus_ds1_filter_init,X13,X14) = init )
          & ! [X15,X16] :
              ( ( leq(n0,X15)
                & leq(n0,X16)
                & leq(X15,n5)
                & leq(X16,n5) )
             => ( ( X15 = pv63
                  & gt(pv64,X16) )
               => a_select3(id_ds1_filter_init,X15,X16) = init ) )
          & ! [X17,X18] :
              ( ( leq(n0,X17)
                & leq(n0,X18)
                & leq(X17,n5)
                & leq(X18,n5) )
             => ( gt(pv63,X17)
               => a_select3(id_ds1_filter_init,X17,X18) = init ) )
          & ! [X19] :
              ( ( leq(n0,X19)
                & leq(X19,pred(pv63)) )
             => ! [X20] :
                  ( ( leq(n0,X20)
                    & leq(X20,n5) )
                 => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
       => ! [X21,X22] :
            ( ( leq(n0,X21)
              & leq(n0,X22)
              & leq(X21,n5)
              & leq(X22,n5) )
           => ( ( pv64 != X22
                & X21 = pv63
                & leq(X22,pv64) )
             => a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) ).

fof(definition_0,definition,
    ( definitionFOFtoCNF_0
  <=> ( ~ leq(n0,pv5)
      | ~ leq(n0,pv63)
      | ~ leq(n0,pv64)
      | ~ leq(pv5,n998)
      | ~ leq(pv63,n5)
      | ~ leq(pv64,n5)
      | pv63 = pv64
      | ? [X19] :
          ( leq(X19,pred(pv63))
          & leq(n0,X19)
          & ? [X20] :
              ( a_select3(id_ds1_filter_init,X19,X20) != init
              & leq(X20,n5)
              & leq(n0,X20) ) )
      | ? [X1,X2] :
          ( a_select3(h_ds1_filter_init,X1,X2) != init
          & leq(X1,n2)
          & leq(X2,n5)
          & leq(n0,X1)
          & leq(n0,X2) )
      | ? [X10,X9] :
          ( a_select3(r_ds1_filter_init,X9,X10) != init
          & leq(X10,n2)
          & leq(X9,n2)
          & leq(n0,X10)
          & leq(n0,X9) )
      | ? [X11,X12] :
          ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
          & leq(X11,n5)
          & leq(X12,n0)
          & leq(n0,X11)
          & leq(n0,X12) )
      | ? [X13,X14] :
          ( a_select3(pminus_ds1_filter_init,X13,X14) != init
          & leq(X13,n5)
          & leq(X14,n5)
          & leq(n0,X13)
          & leq(n0,X14) )
      | ! [X21,X22] :
          ( X21 != pv63
          | ~ leq(X21,n5)
          | ~ leq(X22,n5)
          | ~ leq(X22,pv64)
          | ~ leq(n0,X21)
          | ~ leq(n0,X22)
          | a_select3(id_ds1_filter_init,X21,X22) = init
          | pv64 = X22 ) ) ) ).

fof(definition_1,definition,
    ( definitionFOFtoCNF_1
  <=> ( ! [X11,X12] :
          ( ~ leq(X11,n5)
          | ~ leq(X12,n0)
          | ~ leq(n0,X11)
          | ~ leq(n0,X12)
          | a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ~ leq(X13,n5)
          | ~ leq(X14,n5)
          | ~ leq(n0,X13)
          | ~ leq(n0,X14)
          | a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ) ).

fof(definition_2,definition,
    ! [X11,X12] :
      ( definitionFOFtoCNF_2(X11,X12)
    <=> ( ~ leq(X11,n5)
        | ~ leq(X12,n0)
        | ~ leq(n0,X11)
        | ~ leq(n0,X12)
        | a_select3(xhatmin_ds1_filter_init,X11,X12) = init ) ) ).

fof(definition_3,definition,
    ! [X19] :
      ( definitionFOFtoCNF_3(X19)
    <=> ( ~ leq(X19,pred(pv63))
        | ~ leq(n0,X19)
        | ! [X20] :
            ( ~ leq(X20,n5)
            | ~ leq(n0,X20)
            | a_select3(id_ds1_filter_init,X19,X20) = init ) ) ) ).

fof(definition_4,definition,
    ! [X1,X2] :
      ( definitionFOFtoCNF_4(X1,X2)
    <=> ( ~ leq(X1,n2)
        | ~ leq(X2,n5)
        | ~ leq(n0,X1)
        | ~ leq(n0,X2)
        | a_select3(h_ds1_filter_init,X1,X2) = init ) ) ).

fof(definition_5,definition,
    ( definitionFOFtoCNF_5
  <=> ( ? [X15,X16] :
          ( a_select3(id_ds1_filter_init,X15,X16) != init
          & X15 = pv63
          & gt(pv64,X16)
          & leq(X15,n5)
          & leq(X16,n5)
          & leq(n0,X15)
          & leq(n0,X16) )
      | ? [X17,X18] :
          ( a_select3(id_ds1_filter_init,X17,X18) != init
          & gt(pv63,X17)
          & leq(X17,n5)
          & leq(X18,n5)
          & leq(n0,X17)
          & leq(n0,X18) ) ) ) ).

fof(definition_6,definition,
    ! [X17,X18] :
      ( definitionFOFtoCNF_6(X17,X18)
    <=> ( ~ gt(pv63,X17)
        | ~ leq(X17,n5)
        | ~ leq(X18,n5)
        | ~ leq(n0,X17)
        | ~ leq(n0,X18)
        | a_select3(id_ds1_filter_init,X17,X18) = init ) ) ).

fof(definition_7,definition,
    ! [X3,X4] :
      ( definitionFOFtoCNF_7(X3,X4)
    <=> ( a_select3(phi_ds1_filter_init,X3,X4) != init
        & leq(X3,n5)
        & leq(X4,n5)
        & leq(n0,X3)
        & leq(n0,X4) ) ) ).

fof(definition_8,definition,
    ! [X5,X6] :
      ( definitionFOFtoCNF_8(X5,X6)
    <=> ( a_select3(dv_ds1_filter_init,X5,X6) != init
        & leq(X5,n5)
        & leq(X6,n0)
        & leq(n0,X5)
        & leq(n0,X6) ) ) ).

fof(subgoal_0,plain,
    ( ( pv63 != pv64
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ! [X1,X2] :
          ( ( leq(n0,X1)
            & leq(n0,X2)
            & leq(X1,n2)
            & leq(X2,n5) )
         => a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X3,X4] :
          ( ( leq(n0,X3)
            & leq(n0,X4)
            & leq(X3,n5)
            & leq(X4,n5) )
         => a_select3(phi_ds1_filter_init,X3,X4) = init )
      & ! [X5,X6] :
          ( ( leq(n0,X5)
            & leq(n0,X6)
            & leq(X5,n5)
            & leq(X6,n0) )
         => a_select3(dv_ds1_filter_init,X5,X6) = init )
      & ! [X7,X8] :
          ( ( leq(n0,X7)
            & leq(n0,X8)
            & leq(X7,n5)
            & leq(X8,n5) )
         => a_select3(q_ds1_filter_init,X7,X8) = init )
      & ! [X9,X10] :
          ( ( leq(n0,X9)
            & leq(n0,X10)
            & leq(X9,n2)
            & leq(X10,n2) )
         => a_select3(r_ds1_filter_init,X9,X10) = init )
      & ! [X11,X12] :
          ( ( leq(n0,X11)
            & leq(n0,X12)
            & leq(X11,n5)
            & leq(X12,n0) )
         => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ( leq(n0,X13)
            & leq(n0,X14)
            & leq(X13,n5)
            & leq(X14,n5) )
         => a_select3(pminus_ds1_filter_init,X13,X14) = init )
      & ! [X15,X16] :
          ( ( leq(n0,X15)
            & leq(n0,X16)
            & leq(X15,n5)
            & leq(X16,n5) )
         => ( ( X15 = pv63
              & gt(pv64,X16) )
           => a_select3(id_ds1_filter_init,X15,X16) = init ) )
      & ! [X17,X18] :
          ( ( leq(n0,X17)
            & leq(n0,X18)
            & leq(X17,n5)
            & leq(X18,n5) )
         => ( gt(pv63,X17)
           => a_select3(id_ds1_filter_init,X17,X18) = init ) )
      & ! [X19] :
          ( ( leq(n0,X19)
            & leq(X19,pred(pv63)) )
         => ! [X20] :
              ( ( leq(n0,X20)
                & leq(X20,n5) )
             => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
   => ! [X21,X22] :
        ( ( leq(n0,X21)
          & leq(n0,X22)
          & leq(X21,n5)
          & leq(X22,n5)
          & pv64 != X22
          & X21 = pv63
          & leq(X22,pv64) )
       => a_select3(id_ds1_filter_init,X21,X22) = init ) ),
    inference(strip,[],[n91]) ).

fof(negate_0_0,plain,
    ~ ( ( pv63 != pv64
        & leq(n0,pv5)
        & leq(n0,pv63)
        & leq(n0,pv64)
        & leq(pv5,n998)
        & leq(pv63,n5)
        & leq(pv64,n5)
        & ! [X1,X2] :
            ( ( leq(n0,X1)
              & leq(n0,X2)
              & leq(X1,n2)
              & leq(X2,n5) )
           => a_select3(h_ds1_filter_init,X1,X2) = init )
        & ! [X3,X4] :
            ( ( leq(n0,X3)
              & leq(n0,X4)
              & leq(X3,n5)
              & leq(X4,n5) )
           => a_select3(phi_ds1_filter_init,X3,X4) = init )
        & ! [X5,X6] :
            ( ( leq(n0,X5)
              & leq(n0,X6)
              & leq(X5,n5)
              & leq(X6,n0) )
           => a_select3(dv_ds1_filter_init,X5,X6) = init )
        & ! [X7,X8] :
            ( ( leq(n0,X7)
              & leq(n0,X8)
              & leq(X7,n5)
              & leq(X8,n5) )
           => a_select3(q_ds1_filter_init,X7,X8) = init )
        & ! [X9,X10] :
            ( ( leq(n0,X9)
              & leq(n0,X10)
              & leq(X9,n2)
              & leq(X10,n2) )
           => a_select3(r_ds1_filter_init,X9,X10) = init )
        & ! [X11,X12] :
            ( ( leq(n0,X11)
              & leq(n0,X12)
              & leq(X11,n5)
              & leq(X12,n0) )
           => a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
        & ! [X13,X14] :
            ( ( leq(n0,X13)
              & leq(n0,X14)
              & leq(X13,n5)
              & leq(X14,n5) )
           => a_select3(pminus_ds1_filter_init,X13,X14) = init )
        & ! [X15,X16] :
            ( ( leq(n0,X15)
              & leq(n0,X16)
              & leq(X15,n5)
              & leq(X16,n5) )
           => ( ( X15 = pv63
                & gt(pv64,X16) )
             => a_select3(id_ds1_filter_init,X15,X16) = init ) )
        & ! [X17,X18] :
            ( ( leq(n0,X17)
              & leq(n0,X18)
              & leq(X17,n5)
              & leq(X18,n5) )
           => ( gt(pv63,X17)
             => a_select3(id_ds1_filter_init,X17,X18) = init ) )
        & ! [X19] :
            ( ( leq(n0,X19)
              & leq(X19,pred(pv63)) )
           => ! [X20] :
                ( ( leq(n0,X20)
                  & leq(X20,n5) )
               => a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
     => ! [X21,X22] :
          ( ( leq(n0,X21)
            & leq(n0,X22)
            & leq(X21,n5)
            & leq(X22,n5)
            & pv64 != X22
            & X21 = pv63
            & leq(X22,pv64) )
         => a_select3(id_ds1_filter_init,X21,X22) = init ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( pv63 != pv64
    & leq(n0,pv5)
    & leq(n0,pv63)
    & leq(n0,pv64)
    & leq(pv5,n998)
    & leq(pv63,n5)
    & leq(pv64,n5)
    & ? [X21,X22] :
        ( a_select3(id_ds1_filter_init,X21,X22) != init
        & pv64 != X22
        & X21 = pv63
        & leq(X21,n5)
        & leq(X22,n5)
        & leq(X22,pv64)
        & leq(n0,X21)
        & leq(n0,X22) )
    & ! [X19] :
        ( ~ leq(X19,pred(pv63))
        | ~ leq(n0,X19)
        | ! [X20] :
            ( ~ leq(X20,n5)
            | ~ leq(n0,X20)
            | a_select3(id_ds1_filter_init,X19,X20) = init ) )
    & ! [X1,X2] :
        ( ~ leq(X1,n2)
        | ~ leq(X2,n5)
        | ~ leq(n0,X1)
        | ~ leq(n0,X2)
        | a_select3(h_ds1_filter_init,X1,X2) = init )
    & ! [X10,X9] :
        ( ~ leq(X10,n2)
        | ~ leq(X9,n2)
        | ~ leq(n0,X10)
        | ~ leq(n0,X9)
        | a_select3(r_ds1_filter_init,X9,X10) = init )
    & ! [X11,X12] :
        ( ~ leq(X11,n5)
        | ~ leq(X12,n0)
        | ~ leq(n0,X11)
        | ~ leq(n0,X12)
        | a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
    & ! [X13,X14] :
        ( ~ leq(X13,n5)
        | ~ leq(X14,n5)
        | ~ leq(n0,X13)
        | ~ leq(n0,X14)
        | a_select3(pminus_ds1_filter_init,X13,X14) = init )
    & ! [X15,X16] :
        ( X15 != pv63
        | ~ gt(pv64,X16)
        | ~ leq(X15,n5)
        | ~ leq(X16,n5)
        | ~ leq(n0,X15)
        | ~ leq(n0,X16)
        | a_select3(id_ds1_filter_init,X15,X16) = init )
    & ! [X17,X18] :
        ( ~ gt(pv63,X17)
        | ~ leq(X17,n5)
        | ~ leq(X18,n5)
        | ~ leq(n0,X17)
        | ~ leq(n0,X18)
        | a_select3(id_ds1_filter_init,X17,X18) = init )
    & ! [X3,X4] :
        ( ~ leq(X3,n5)
        | ~ leq(X4,n5)
        | ~ leq(n0,X3)
        | ~ leq(n0,X4)
        | a_select3(phi_ds1_filter_init,X3,X4) = init )
    & ! [X5,X6] :
        ( ~ leq(X5,n5)
        | ~ leq(X6,n0)
        | ~ leq(n0,X5)
        | ~ leq(n0,X6)
        | a_select3(dv_ds1_filter_init,X5,X6) = init )
    & ! [X7,X8] :
        ( ~ leq(X7,n5)
        | ~ leq(X8,n5)
        | ~ leq(n0,X7)
        | ~ leq(n0,X8)
        | a_select3(q_ds1_filter_init,X7,X8) = init ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ leq(n0,pv5)
    | ~ leq(n0,pv63)
    | ~ leq(n0,pv64)
    | ~ leq(pv5,n998)
    | ~ leq(pv63,n5)
    | ~ leq(pv64,n5)
    | pv63 = pv64
    | ? [X19] :
        ( leq(X19,pred(pv63))
        & leq(n0,X19)
        & ? [X20] :
            ( a_select3(id_ds1_filter_init,X19,X20) != init
            & leq(X20,n5)
            & leq(n0,X20) ) )
    | ? [X1,X2] :
        ( a_select3(h_ds1_filter_init,X1,X2) != init
        & leq(X1,n2)
        & leq(X2,n5)
        & leq(n0,X1)
        & leq(n0,X2) )
    | ? [X10,X9] :
        ( a_select3(r_ds1_filter_init,X9,X10) != init
        & leq(X10,n2)
        & leq(X9,n2)
        & leq(n0,X10)
        & leq(n0,X9) )
    | ? [X11,X12] :
        ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
        & leq(X11,n5)
        & leq(X12,n0)
        & leq(n0,X11)
        & leq(n0,X12) )
    | ? [X13,X14] :
        ( a_select3(pminus_ds1_filter_init,X13,X14) != init
        & leq(X13,n5)
        & leq(X14,n5)
        & leq(n0,X13)
        & leq(n0,X14) )
    | ? [X15,X16] :
        ( a_select3(id_ds1_filter_init,X15,X16) != init
        & X15 = pv63
        & gt(pv64,X16)
        & leq(X15,n5)
        & leq(X16,n5)
        & leq(n0,X15)
        & leq(n0,X16) )
    | ? [X17,X18] :
        ( a_select3(id_ds1_filter_init,X17,X18) != init
        & gt(pv63,X17)
        & leq(X17,n5)
        & leq(X18,n5)
        & leq(n0,X17)
        & leq(n0,X18) )
    | ? [X3,X4] :
        ( a_select3(phi_ds1_filter_init,X3,X4) != init
        & leq(X3,n5)
        & leq(X4,n5)
        & leq(n0,X3)
        & leq(n0,X4) )
    | ? [X5,X6] :
        ( a_select3(dv_ds1_filter_init,X5,X6) != init
        & leq(X5,n5)
        & leq(X6,n0)
        & leq(n0,X5)
        & leq(n0,X6) )
    | ? [X7,X8] :
        ( a_select3(q_ds1_filter_init,X7,X8) != init
        & leq(X7,n5)
        & leq(X8,n5)
        & leq(n0,X7)
        & leq(n0,X8) )
    | ! [X21,X22] :
        ( X21 != pv63
        | ~ leq(X21,n5)
        | ~ leq(X22,n5)
        | ~ leq(X22,pv64)
        | ~ leq(n0,X21)
        | ~ leq(n0,X22)
        | a_select3(id_ds1_filter_init,X21,X22) = init
        | pv64 = X22 ) ),
    inference(canonicalize,[],[n1]) ).

fof(normalize_0_2,plain,
    ( ~ definitionFOFtoCNF_0
  <=> ( pv63 != pv64
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ? [X21,X22] :
          ( a_select3(id_ds1_filter_init,X21,X22) != init
          & pv64 != X22
          & X21 = pv63
          & leq(X21,n5)
          & leq(X22,n5)
          & leq(X22,pv64)
          & leq(n0,X21)
          & leq(n0,X22) )
      & ! [X19] :
          ( ~ leq(X19,pred(pv63))
          | ~ leq(n0,X19)
          | ! [X20] :
              ( ~ leq(X20,n5)
              | ~ leq(n0,X20)
              | a_select3(id_ds1_filter_init,X19,X20) = init ) )
      & ! [X1,X2] :
          ( ~ leq(X1,n2)
          | ~ leq(X2,n5)
          | ~ leq(n0,X1)
          | ~ leq(n0,X2)
          | a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X10,X9] :
          ( ~ leq(X10,n2)
          | ~ leq(X9,n2)
          | ~ leq(n0,X10)
          | ~ leq(n0,X9)
          | a_select3(r_ds1_filter_init,X9,X10) = init )
      & ! [X11,X12] :
          ( ~ leq(X11,n5)
          | ~ leq(X12,n0)
          | ~ leq(n0,X11)
          | ~ leq(n0,X12)
          | a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
      & ! [X13,X14] :
          ( ~ leq(X13,n5)
          | ~ leq(X14,n5)
          | ~ leq(n0,X13)
          | ~ leq(n0,X14)
          | a_select3(pminus_ds1_filter_init,X13,X14) = init ) ) ),
    inference(canonicalize,[],[definition_0]) ).

fof(normalize_0_3,plain,
    ( ~ definitionFOFtoCNF_1
  <=> ( ? [X11,X12] :
          ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
          & leq(X11,n5)
          & leq(X12,n0)
          & leq(n0,X11)
          & leq(n0,X12) )
      | ? [X13,X14] :
          ( a_select3(pminus_ds1_filter_init,X13,X14) != init
          & leq(X13,n5)
          & leq(X14,n5)
          & leq(n0,X13)
          & leq(n0,X14) ) ) ),
    inference(canonicalize,[],[definition_1]) ).

fof(normalize_0_4,plain,
    ! [X11,X12] :
      ( ~ definitionFOFtoCNF_2(X11,X12)
    <=> ( a_select3(xhatmin_ds1_filter_init,X11,X12) != init
        & leq(X11,n5)
        & leq(X12,n0)
        & leq(n0,X11)
        & leq(n0,X12) ) ),
    inference(canonicalize,[],[definition_2]) ).

fof(normalize_0_5,plain,
    ( ~ definitionFOFtoCNF_1
  <=> ( ? [X11,X12] : ~ definitionFOFtoCNF_2(X11,X12)
      | ? [X13,X14] :
          ( a_select3(pminus_ds1_filter_init,X13,X14) != init
          & leq(X13,n5)
          & leq(X14,n5)
          & leq(n0,X13)
          & leq(n0,X14) ) ) ),
    inference(simplify,[],[normalize_0_3,normalize_0_4]) ).

fof(normalize_0_6,plain,
    ( ~ definitionFOFtoCNF_0
  <=> ( pv63 != pv64
      & definitionFOFtoCNF_1
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ? [X21,X22] :
          ( a_select3(id_ds1_filter_init,X21,X22) != init
          & pv64 != X22
          & X21 = pv63
          & leq(X21,n5)
          & leq(X22,n5)
          & leq(X22,pv64)
          & leq(n0,X21)
          & leq(n0,X22) )
      & ! [X19] :
          ( ~ leq(X19,pred(pv63))
          | ~ leq(n0,X19)
          | ! [X20] :
              ( ~ leq(X20,n5)
              | ~ leq(n0,X20)
              | a_select3(id_ds1_filter_init,X19,X20) = init ) )
      & ! [X1,X2] :
          ( ~ leq(X1,n2)
          | ~ leq(X2,n5)
          | ~ leq(n0,X1)
          | ~ leq(n0,X2)
          | a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X10,X9] :
          ( ~ leq(X10,n2)
          | ~ leq(X9,n2)
          | ~ leq(n0,X10)
          | ~ leq(n0,X9)
          | a_select3(r_ds1_filter_init,X9,X10) = init ) ) ),
    inference(simplify,[],[normalize_0_2,normalize_0_5,normalize_0_4]) ).

fof(normalize_0_7,plain,
    ! [X19] :
      ( ~ definitionFOFtoCNF_3(X19)
    <=> ( leq(X19,pred(pv63))
        & leq(n0,X19)
        & ? [X20] :
            ( a_select3(id_ds1_filter_init,X19,X20) != init
            & leq(X20,n5)
            & leq(n0,X20) ) ) ),
    inference(canonicalize,[],[definition_3]) ).

fof(normalize_0_8,plain,
    ( ~ definitionFOFtoCNF_0
  <=> ( pv63 != pv64
      & definitionFOFtoCNF_1
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ? [X21,X22] :
          ( a_select3(id_ds1_filter_init,X21,X22) != init
          & pv64 != X22
          & X21 = pv63
          & leq(X21,n5)
          & leq(X22,n5)
          & leq(X22,pv64)
          & leq(n0,X21)
          & leq(n0,X22) )
      & ! [X19] : definitionFOFtoCNF_3(X19)
      & ! [X1,X2] :
          ( ~ leq(X1,n2)
          | ~ leq(X2,n5)
          | ~ leq(n0,X1)
          | ~ leq(n0,X2)
          | a_select3(h_ds1_filter_init,X1,X2) = init )
      & ! [X10,X9] :
          ( ~ leq(X10,n2)
          | ~ leq(X9,n2)
          | ~ leq(n0,X10)
          | ~ leq(n0,X9)
          | a_select3(r_ds1_filter_init,X9,X10) = init ) ) ),
    inference(simplify,[],[normalize_0_6,normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X1,X2] :
      ( ~ definitionFOFtoCNF_4(X1,X2)
    <=> ( a_select3(h_ds1_filter_init,X1,X2) != init
        & leq(X1,n2)
        & leq(X2,n5)
        & leq(n0,X1)
        & leq(n0,X2) ) ),
    inference(canonicalize,[],[definition_4]) ).

fof(normalize_0_10,plain,
    ( ~ definitionFOFtoCNF_0
  <=> ( pv63 != pv64
      & definitionFOFtoCNF_1
      & leq(n0,pv5)
      & leq(n0,pv63)
      & leq(n0,pv64)
      & leq(pv5,n998)
      & leq(pv63,n5)
      & leq(pv64,n5)
      & ? [X21,X22] :
          ( a_select3(id_ds1_filter_init,X21,X22) != init
          & pv64 != X22
          & X21 = pv63
          & leq(X21,n5)
          & leq(X22,n5)
          & leq(X22,pv64)
          & leq(n0,X21)
          & leq(n0,X22) )
      & ! [X19] : definitionFOFtoCNF_3(X19)
      & ! [X1,X2] : definitionFOFtoCNF_4(X1,X2)
      & ! [X10,X9] :
          ( ~ leq(X10,n2)
          | ~ leq(X9,n2)
          | ~ leq(n0,X10)
          | ~ leq(n0,X9)
          | a_select3(r_ds1_filter_init,X9,X10) = init ) ) ),
    inference(simplify,[],[normalize_0_8,normalize_0_9]) ).

fof(normalize_0_11,plain,
    ( definitionFOFtoCNF_0
    | ? [X15,X16] :
        ( a_select3(id_ds1_filter_init,X15,X16) != init
        & X15 = pv63
        & gt(pv64,X16)
        & leq(X15,n5)
        & leq(X16,n5)
        & leq(n0,X15)
        & leq(n0,X16) )
    | ? [X17,X18] :
        ( a_select3(id_ds1_filter_init,X17,X18) != init
        & gt(pv63,X17)
        & leq(X17,n5)
        & leq(X18,n5)
        & leq(n0,X17)
        & leq(n0,X18) )
    | ? [X3,X4] :
        ( a_select3(phi_ds1_filter_init,X3,X4) != init
        & leq(X3,n5)
        & leq(X4,n5)
        & leq(n0,X3)
        & leq(n0,X4) )
    | ? [X5,X6] :
        ( a_select3(dv_ds1_filter_init,X5,X6) != init
        & leq(X5,n5)
        & leq(X6,n0)
        & leq(n0,X5)
        & leq(n0,X6) )
    | ? [X7,X8] :
        ( a_select3(q_ds1_filter_init,X7,X8) != init
        & leq(X7,n5)
        & leq(X8,n5)
        & leq(n0,X7)
        & leq(n0,X8) ) ),
    inference(simplify,[],[normalize_0_1,normalize_0_10,normalize_0_5,normalize_0_7,normalize_0_9,normalize_0_4]) ).

fof(normalize_0_12,plain,
    ( ~ definitionFOFtoCNF_5
  <=> ( ! [X15,X16] :
          ( X15 != pv63
          | ~ gt(pv64,X16)
          | ~ leq(X15,n5)
          | ~ leq(X16,n5)
          | ~ leq(n0,X15)
          | ~ leq(n0,X16)
          | a_select3(id_ds1_filter_init,X15,X16) = init )
      & ! [X17,X18] :
          ( ~ gt(pv63,X17)
          | ~ leq(X17,n5)
          | ~ leq(X18,n5)
          | ~ leq(n0,X17)
          | ~ leq(n0,X18)
          | a_select3(id_ds1_filter_init,X17,X18) = init ) ) ),
    inference(canonicalize,[],[definition_5]) ).

fof(normalize_0_13,plain,
    ! [X17,X18] :
      ( ~ definitionFOFtoCNF_6(X17,X18)
    <=> ( a_select3(id_ds1_filter_init,X17,X18) != init
        & gt(pv63,X17)
        & leq(X17,n5)
        & leq(X18,n5)
        & leq(n0,X17)
        & leq(n0,X18) ) ),
    inference(canonicalize,[],[definition_6]) ).

fof(normalize_0_14,plain,
    ( ~ definitionFOFtoCNF_5
  <=> ( ! [X15,X16] :
          ( X15 != pv63
          | ~ gt(pv64,X16)
          | ~ leq(X15,n5)
          | ~ leq(X16,n5)
          | ~ leq(n0,X15)
          | ~ leq(n0,X16)
          | a_select3(id_ds1_filter_init,X15,X16) = init )
      & ! [X17,X18] : definitionFOFtoCNF_6(X17,X18) ) ),
    inference(simplify,[],[normalize_0_12,normalize_0_13]) ).

fof(normalize_0_15,plain,
    ( definitionFOFtoCNF_0
    | definitionFOFtoCNF_5
    | ? [X3,X4] :
        ( a_select3(phi_ds1_filter_init,X3,X4) != init
        & leq(X3,n5)
        & leq(X4,n5)
        & leq(n0,X3)
        & leq(n0,X4) )
    | ? [X5,X6] :
        ( a_select3(dv_ds1_filter_init,X5,X6) != init
        & leq(X5,n5)
        & leq(X6,n0)
        & leq(n0,X5)
        & leq(n0,X6) )
    | ? [X7,X8] :
        ( a_select3(q_ds1_filter_init,X7,X8) != init
        & leq(X7,n5)
        & leq(X8,n5)
        & leq(n0,X7)
        & leq(n0,X8) ) ),
    inference(simplify,[],[normalize_0_11,normalize_0_14,normalize_0_13]) ).

fof(normalize_0_16,plain,
    ! [X3,X4] :
      ( ~ definitionFOFtoCNF_7(X3,X4)
    <=> ( ~ leq(X3,n5)
        | ~ leq(X4,n5)
        | ~ leq(n0,X3)
        | ~ leq(n0,X4)
        | a_select3(phi_ds1_filter_init,X3,X4) = init ) ),
    inference(canonicalize,[],[definition_7]) ).

fof(normalize_0_17,plain,
    ( definitionFOFtoCNF_0
    | definitionFOFtoCNF_5
    | ? [X3,X4] : definitionFOFtoCNF_7(X3,X4)
    | ? [X5,X6] :
        ( a_select3(dv_ds1_filter_init,X5,X6) != init
        & leq(X5,n5)
        & leq(X6,n0)
        & leq(n0,X5)
        & leq(n0,X6) )
    | ? [X7,X8] :
        ( a_select3(q_ds1_filter_init,X7,X8) != init
        & leq(X7,n5)
        & leq(X8,n5)
        & leq(n0,X7)
        & leq(n0,X8) ) ),
    inference(simplify,[],[normalize_0_15,normalize_0_16]) ).

fof(normalize_0_18,plain,
    ! [X5,X6] :
      ( ~ definitionFOFtoCNF_8(X5,X6)
    <=> ( ~ leq(X5,n5)
        | ~ leq(X6,n0)
        | ~ leq(n0,X5)
        | ~ leq(n0,X6)
        | a_select3(dv_ds1_filter_init,X5,X6) = init ) ),
    inference(canonicalize,[],[definition_8]) ).

fof(normalize_0_19,plain,
    ( definitionFOFtoCNF_0
    | definitionFOFtoCNF_5
    | ? [X3,X4] : definitionFOFtoCNF_7(X3,X4)
    | ? [X5,X6] : definitionFOFtoCNF_8(X5,X6)
    | ? [X7,X8] :
        ( a_select3(q_ds1_filter_init,X7,X8) != init
        & leq(X7,n5)
        & leq(X8,n5)
        & leq(n0,X7)
        & leq(n0,X8) ) ),
    inference(simplify,[],[normalize_0_17,normalize_0_18]) ).

fof(normalize_0_20,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_19,normalize_0_14,normalize_0_10,normalize_0_5,normalize_0_7,normalize_0_9,normalize_0_4,normalize_0_13,normalize_0_16,normalize_0_18]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : MSC010+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.36  % Computer : n008.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 : Fri Jul  1 15:54:38 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41  
% 0.14/0.41  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.43  
%------------------------------------------------------------------------------