TSTP Solution File: ALG069+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : ALG069+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 : Thu Jul 14 17:34:59 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   69 (  17 unt;   0 def)
%            Number of atoms       :  188 (  83 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  198 (  79   ~;  66   |;  24   &)
%                                         (   0 <=>;  29  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   79 (   0 sgn  55   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(ax3,axiom,
    ! [U] :
      ( sorti1(U)
     => ? [V] :
          ( sorti1(V)
          & op1(V,V) = U ) ) ).

fof(ax4,axiom,
    ~ ! [U] :
        ( sorti2(U)
       => ? [V] :
            ( sorti2(V)
            & op2(V,V) = U ) ) ).

fof(co1,conjecture,
    ( ( ! [U] :
          ( sorti1(U)
         => sorti2(h(U)) )
      & ! [V] :
          ( sorti2(V)
         => sorti1(j(V)) ) )
   => ~ ( ! [W] :
            ( sorti1(W)
           => ! [X] :
                ( sorti1(X)
               => h(op1(W,X)) = op2(h(W),h(X)) ) )
        & ! [Y0] :
            ( sorti2(Y0)
           => ! [Z0] :
                ( sorti2(Z0)
               => j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
        & ! [X1] :
            ( sorti2(X1)
           => h(j(X1)) = X1 )
        & ! [X2] :
            ( sorti1(X2)
           => j(h(X2)) = X2 ) ) ) ).

fof(subgoal_0,plain,
    ( ( ! [U] :
          ( sorti1(U)
         => sorti2(h(U)) )
      & ! [V] :
          ( sorti2(V)
         => sorti1(j(V)) )
      & ! [W] :
          ( sorti1(W)
         => ! [X] :
              ( sorti1(X)
             => h(op1(W,X)) = op2(h(W),h(X)) ) )
      & ! [Y0] :
          ( sorti2(Y0)
         => ! [Z0] :
              ( sorti2(Z0)
             => j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
      & ! [X1] :
          ( sorti2(X1)
         => h(j(X1)) = X1 ) )
   => ~ ! [X2] :
          ( sorti1(X2)
         => j(h(X2)) = X2 ) ),
    inference(strip,[],[co1]) ).

fof(negate_0_0,plain,
    ~ ( ( ! [U] :
            ( sorti1(U)
           => sorti2(h(U)) )
        & ! [V] :
            ( sorti2(V)
           => sorti1(j(V)) )
        & ! [W] :
            ( sorti1(W)
           => ! [X] :
                ( sorti1(X)
               => h(op1(W,X)) = op2(h(W),h(X)) ) )
        & ! [Y0] :
            ( sorti2(Y0)
           => ! [Z0] :
                ( sorti2(Z0)
               => j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) )
        & ! [X1] :
            ( sorti2(X1)
           => h(j(X1)) = X1 ) )
     => ~ ! [X2] :
            ( sorti1(X2)
           => j(h(X2)) = X2 ) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [U] :
      ( sorti2(U)
      & ! [V] :
          ( op2(V,V) != U
          | ~ sorti2(V) ) ),
    inference(canonicalize,[],[ax4]) ).

fof(normalize_0_1,plain,
    ( sorti2(skolemFOFtoCNF_U)
    & ! [V] :
        ( op2(V,V) != skolemFOFtoCNF_U
        | ~ sorti2(V) ) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [V] :
      ( op2(V,V) != skolemFOFtoCNF_U
      | ~ sorti2(V) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [V] :
      ( op2(V,V) != skolemFOFtoCNF_U
      | ~ sorti2(V) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [U] :
      ( ~ sorti1(U)
      | ? [V] :
          ( op1(V,V) = U
          & sorti1(V) ) ),
    inference(canonicalize,[],[ax3]) ).

fof(normalize_0_5,plain,
    ! [U] :
      ( ~ sorti1(U)
      | ? [V] :
          ( op1(V,V) = U
          & sorti1(V) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [U] :
      ( ( ~ sorti1(U)
        | op1(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) = U )
      & ( ~ sorti1(U)
        | sorti1(skolemFOFtoCNF_V(U)) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [U] :
      ( ~ sorti1(U)
      | sorti1(skolemFOFtoCNF_V(U)) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    sorti2(skolemFOFtoCNF_U),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_9,plain,
    ( ! [U] :
        ( ~ sorti1(U)
        | sorti2(h(U)) )
    & ! [V] :
        ( ~ sorti2(V)
        | sorti1(j(V)) )
    & ! [W] :
        ( ~ sorti1(W)
        | ! [X] :
            ( ~ sorti1(X)
            | h(op1(W,X)) = op2(h(W),h(X)) ) )
    & ! [X1] :
        ( ~ sorti2(X1)
        | h(j(X1)) = X1 )
    & ! [X2] :
        ( ~ sorti1(X2)
        | j(h(X2)) = X2 )
    & ! [Y0] :
        ( ~ sorti2(Y0)
        | ! [Z0] :
            ( ~ sorti2(Z0)
            | j(op2(Y0,Z0)) = op1(j(Y0),j(Z0)) ) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_10,plain,
    ! [V] :
      ( ~ sorti2(V)
      | sorti1(j(V)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [V] :
      ( ~ sorti2(V)
      | sorti1(j(V)) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [W] :
      ( ~ sorti1(W)
      | ! [X] :
          ( ~ sorti1(X)
          | h(op1(W,X)) = op2(h(W),h(X)) ) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_13,plain,
    ! [W] :
      ( ~ sorti1(W)
      | ! [X] :
          ( ~ sorti1(X)
          | h(op1(W,X)) = op2(h(W),h(X)) ) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [W,X] :
      ( ~ sorti1(W)
      | ~ sorti1(X)
      | h(op1(W,X)) = op2(h(W),h(X)) ),
    inference(clausify,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | h(j(X1)) = X1 ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_16,plain,
    ! [X1] :
      ( ~ sorti2(X1)
      | h(j(X1)) = X1 ),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [U] :
      ( ~ sorti1(U)
      | op1(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) = U ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_18,plain,
    ! [U] :
      ( ~ sorti1(U)
      | sorti2(h(U)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_19,plain,
    ! [U] :
      ( ~ sorti1(U)
      | sorti2(h(U)) ),
    inference(specialize,[],[normalize_0_18]) ).

cnf(refute_0_0,plain,
    ( op2(V,V) != skolemFOFtoCNF_U
    | ~ sorti2(V) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_U
    | ~ sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    inference(subst,[],[refute_0_0:[bind(V,$fot(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))))]]) ).

cnf(refute_0_2,plain,
    ( ~ sorti1(U)
    | sorti1(skolemFOFtoCNF_V(U)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( ~ sorti1(j(skolemFOFtoCNF_U))
    | sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) ),
    inference(subst,[],[refute_0_2:[bind(U,$fot(j(skolemFOFtoCNF_U)))]]) ).

cnf(refute_0_4,plain,
    sorti2(skolemFOFtoCNF_U),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ sorti2(V)
    | sorti1(j(V)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_6,plain,
    ( ~ sorti2(skolemFOFtoCNF_U)
    | sorti1(j(skolemFOFtoCNF_U)) ),
    inference(subst,[],[refute_0_5:[bind(V,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_7,plain,
    sorti1(j(skolemFOFtoCNF_U)),
    inference(resolve,[$cnf( sorti2(skolemFOFtoCNF_U) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),
    inference(resolve,[$cnf( sorti1(j(skolemFOFtoCNF_U)) )],[refute_0_7,refute_0_3]) ).

cnf(refute_0_9,plain,
    ( ~ sorti1(W)
    | ~ sorti1(X)
    | h(op1(W,X)) = op2(h(W),h(X)) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_10,plain,
    ( ~ sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    inference(subst,[],[refute_0_9:[bind(W,$fot(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),bind(X,$fot(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))]]) ).

cnf(refute_0_11,plain,
    h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),
    inference(resolve,[$cnf( sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) )],[refute_0_8,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ sorti2(X1)
    | h(j(X1)) = X1 ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_13,plain,
    ( ~ sorti2(skolemFOFtoCNF_U)
    | h(j(skolemFOFtoCNF_U)) = skolemFOFtoCNF_U ),
    inference(subst,[],[refute_0_12:[bind(X1,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_14,plain,
    h(j(skolemFOFtoCNF_U)) = skolemFOFtoCNF_U,
    inference(resolve,[$cnf( sorti2(skolemFOFtoCNF_U) )],[refute_0_4,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ sorti1(U)
    | op1(skolemFOFtoCNF_V(U),skolemFOFtoCNF_V(U)) = U ),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_16,plain,
    ( ~ sorti1(j(skolemFOFtoCNF_U))
    | op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) = j(skolemFOFtoCNF_U) ),
    inference(subst,[],[refute_0_15:[bind(U,$fot(j(skolemFOFtoCNF_U)))]]) ).

cnf(refute_0_17,plain,
    op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) = j(skolemFOFtoCNF_U),
    inference(resolve,[$cnf( sorti1(j(skolemFOFtoCNF_U)) )],[refute_0_7,refute_0_16]) ).

cnf(refute_0_18,plain,
    h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),
    introduced(tautology,[refl,[$fot(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))))]]) ).

cnf(refute_0_19,plain,
    ( h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))
    | op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) != j(skolemFOFtoCNF_U)
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = h(j(skolemFOFtoCNF_U)) ),
    introduced(tautology,[equality,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))) ),[1,0],$fot(j(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_20,plain,
    ( op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) != j(skolemFOFtoCNF_U)
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = h(j(skolemFOFtoCNF_U)) ),
    inference(resolve,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = h(j(skolemFOFtoCNF_U)),
    inference(resolve,[$cnf( $equal(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),j(skolemFOFtoCNF_U)) )],[refute_0_17,refute_0_20]) ).

cnf(refute_0_22,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_23,plain,
    ( X0 != X0
    | X0 != Y
    | Y = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).

cnf(refute_0_24,plain,
    ( X0 != Y
    | Y = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( Y != X0
    | Y != Z
    | X0 = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).

cnf(refute_0_26,plain,
    ( X0 != Y
    | Y != Z
    | X0 = Z ),
    inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( h(j(skolemFOFtoCNF_U)) != skolemFOFtoCNF_U
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != h(j(skolemFOFtoCNF_U))
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
    inference(subst,[],[refute_0_26:[bind(X0,$fot(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))))),bind(Y,$fot(h(j(skolemFOFtoCNF_U)))),bind(Z,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_28,plain,
    ( h(j(skolemFOFtoCNF_U)) != skolemFOFtoCNF_U
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
    inference(resolve,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),h(j(skolemFOFtoCNF_U))) )],[refute_0_21,refute_0_27]) ).

cnf(refute_0_29,plain,
    h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U,
    inference(resolve,[$cnf( $equal(h(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_U) )],[refute_0_14,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))
    | h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_U
    | skolemFOFtoCNF_U = op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    introduced(tautology,[equality,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))) ),[0],$fot(skolemFOFtoCNF_U)]]) ).

cnf(refute_0_31,plain,
    ( h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))
    | skolemFOFtoCNF_U = op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    inference(resolve,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),skolemFOFtoCNF_U) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    skolemFOFtoCNF_U = op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),
    inference(resolve,[$cnf( $equal(h(op1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)),skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))) )],[refute_0_11,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( skolemFOFtoCNF_U != op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))
    | op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
    inference(subst,[],[refute_0_24:[bind(X0,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))))]]) ).

cnf(refute_0_34,plain,
    op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U,op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))) )],[refute_0_32,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) != skolemFOFtoCNF_U
    | skolemFOFtoCNF_U != skolemFOFtoCNF_U
    | op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
    introduced(tautology,[equality,[$cnf( ~ $equal(op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),skolemFOFtoCNF_U) ),[0],$fot(skolemFOFtoCNF_U)]]) ).

cnf(refute_0_36,plain,
    ( skolemFOFtoCNF_U != skolemFOFtoCNF_U
    | op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) = skolemFOFtoCNF_U ),
    inference(resolve,[$cnf( $equal(op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),skolemFOFtoCNF_U) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ( skolemFOFtoCNF_U != skolemFOFtoCNF_U
    | ~ sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    inference(resolve,[$cnf( $equal(op2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))),h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),skolemFOFtoCNF_U) )],[refute_0_36,refute_0_1]) ).

cnf(refute_0_38,plain,
    skolemFOFtoCNF_U = skolemFOFtoCNF_U,
    introduced(tautology,[refl,[$fot(skolemFOFtoCNF_U)]]) ).

cnf(refute_0_39,plain,
    ~ sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_38,refute_0_37]) ).

cnf(refute_0_40,plain,
    ( ~ sorti1(U)
    | sorti2(h(U)) ),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_41,plain,
    ( ~ sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))
    | sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) ),
    inference(subst,[],[refute_0_40:[bind(U,$fot(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))))]]) ).

cnf(refute_0_42,plain,
    sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))),
    inference(resolve,[$cnf( sorti1(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U))) )],[refute_0_8,refute_0_41]) ).

cnf(refute_0_43,plain,
    $false,
    inference(resolve,[$cnf( sorti2(h(skolemFOFtoCNF_V(j(skolemFOFtoCNF_U)))) )],[refute_0_42,refute_0_39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : ALG069+1 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n028.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Wed Jun  8 16:54:46 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.54  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.54  
% 0.20/0.54  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.54  
%------------------------------------------------------------------------------