TSTP Solution File: KRS172+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS172+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 03:19:04 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :  175 (  65 unt;   0 def)
%            Number of atoms       :  351 (  36 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  348 ( 172   ~;  74   |;  53   &)
%                                         (  27 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   7 con; 0-0 aty)
%            Number of variables   :  186 (   2 sgn 142   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_0,axiom,
    ! [X] :
      ( cowlThing(X)
      & ~ cowlNothing(X) ) ).

fof(axiom_1,axiom,
    ! [X] :
      ( xsd_string(X)
    <=> ~ xsd_integer(X) ) ).

fof(axiom_2,axiom,
    ! [X] :
      ( cd(X)
    <=> rq(X,iv) ) ).

fof(axiom_3,axiom,
    ! [X] :
      ( cd(X)
    <=> rp(X,iv) ) ).

fof(axiom_4,axiom,
    ! [X,Y,Z] :
      ( ( rp(X,Y)
        & rp(X,Z) )
     => Y = Z ) ).

fof(axiom_5,axiom,
    ! [X,Y] :
      ( rp(X,Y)
     => cd(X) ) ).

fof(axiom_6,axiom,
    ! [X,Y,Z] :
      ( ( rq(X,Y)
        & rq(X,Z) )
     => Y = Z ) ).

fof(axiom_7,axiom,
    ! [X,Y] :
      ( rq(X,Y)
     => cd(X) ) ).

fof(the_axiom,conjecture,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
    & ! [X] :
        ( xsd_string(X)
      <=> ~ xsd_integer(X) )
    & ! [X,Y] :
        ( rq(X,Y)
      <=> rp(X,Y) ) ) ).

fof(subgoal_0,plain,
    ! [X] : cowlThing(X),
    inference(strip,[],[the_axiom]) ).

fof(subgoal_1,plain,
    ! [X] :
      ( cowlThing(X)
     => ~ cowlNothing(X) ),
    inference(strip,[],[the_axiom]) ).

fof(subgoal_2,plain,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
   => ! [X] :
        ( xsd_string(X)
       => ~ xsd_integer(X) ) ),
    inference(strip,[],[the_axiom]) ).

fof(subgoal_3,plain,
    ( ! [X] :
        ( cowlThing(X)
        & ~ cowlNothing(X) )
   => ! [X] :
        ( ~ xsd_integer(X)
       => xsd_string(X) ) ),
    inference(strip,[],[the_axiom]) ).

fof(subgoal_4,plain,
    ( ( ! [X] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) ) )
   => ! [X,Y] :
        ( rq(X,Y)
       => rp(X,Y) ) ),
    inference(strip,[],[the_axiom]) ).

fof(subgoal_5,plain,
    ( ( ! [X] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
      & ! [X] :
          ( xsd_string(X)
        <=> ~ xsd_integer(X) ) )
   => ! [X,Y] :
        ( rp(X,Y)
       => rq(X,Y) ) ),
    inference(strip,[],[the_axiom]) ).

fof(negate_0_0,plain,
    ~ ! [X] : cowlThing(X),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X] : ~ cowlThing(X),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_0_2,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    $false,
    inference(simplify,[],[normalize_0_0,normalize_0_3]) ).

cnf(refute_0_0,plain,
    $false,
    inference(canonicalize,[],[normalize_0_4]) ).

fof(negate_1_0,plain,
    ~ ! [X] :
        ( cowlThing(X)
       => ~ cowlNothing(X) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ? [X] :
      ( cowlNothing(X)
      & cowlThing(X) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_1_2,plain,
    ! [X] : ~ cowlNothing(X),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [X] : ~ cowlNothing(X),
    inference(specialize,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_1_1]) ).

fof(normalize_1_5,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    $false,
    inference(simplify,[],[normalize_1_0,normalize_1_3,normalize_1_5]) ).

cnf(refute_1_0,plain,
    $false,
    inference(canonicalize,[],[normalize_1_6]) ).

fof(negate_2_0,plain,
    ~ ( ! [X] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
     => ! [X] :
          ( xsd_string(X)
         => ~ xsd_integer(X) ) ),
    inference(negate,[],[subgoal_2]) ).

fof(normalize_2_0,plain,
    ( ? [X] :
        ( xsd_integer(X)
        & xsd_string(X) )
    & ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[negate_2_0]) ).

fof(normalize_2_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_2_2,plain,
    ! [X] : ~ cowlNothing(X),
    inference(conjunct,[],[normalize_2_1]) ).

fof(normalize_2_3,plain,
    ! [X] : ~ cowlNothing(X),
    inference(specialize,[],[normalize_2_2]) ).

fof(normalize_2_4,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_2_1]) ).

fof(normalize_2_5,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_2_4]) ).

fof(normalize_2_6,plain,
    ? [X] :
      ( xsd_integer(X)
      & xsd_string(X) ),
    inference(simplify,[],[normalize_2_0,normalize_2_3,normalize_2_5]) ).

fof(normalize_2_7,plain,
    ( xsd_integer(skolemFOFtoCNF_X)
    & xsd_string(skolemFOFtoCNF_X) ),
    inference(skolemize,[],[normalize_2_6]) ).

fof(normalize_2_8,plain,
    xsd_string(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_2_7]) ).

fof(normalize_2_9,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_2_10,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(specialize,[],[normalize_2_9]) ).

fof(normalize_2_11,plain,
    ! [X] :
      ( ( ~ xsd_integer(X)
        | ~ xsd_string(X) )
      & ( xsd_integer(X)
        | xsd_string(X) ) ),
    inference(clausify,[],[normalize_2_10]) ).

fof(normalize_2_12,plain,
    ! [X] :
      ( ~ xsd_integer(X)
      | ~ xsd_string(X) ),
    inference(conjunct,[],[normalize_2_11]) ).

fof(normalize_2_13,plain,
    xsd_integer(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_2_7]) ).

cnf(refute_2_0,plain,
    xsd_string(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_2_8]) ).

cnf(refute_2_1,plain,
    ( ~ xsd_integer(X)
    | ~ xsd_string(X) ),
    inference(canonicalize,[],[normalize_2_12]) ).

cnf(refute_2_2,plain,
    ( ~ xsd_integer(skolemFOFtoCNF_X)
    | ~ xsd_string(skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_2_1:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_2_3,plain,
    ~ xsd_integer(skolemFOFtoCNF_X),
    inference(resolve,[$cnf( xsd_string(skolemFOFtoCNF_X) )],[refute_2_0,refute_2_2]) ).

cnf(refute_2_4,plain,
    xsd_integer(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_2_13]) ).

cnf(refute_2_5,plain,
    $false,
    inference(resolve,[$cnf( xsd_integer(skolemFOFtoCNF_X) )],[refute_2_4,refute_2_3]) ).

fof(negate_3_0,plain,
    ~ ( ! [X] :
          ( cowlThing(X)
          & ~ cowlNothing(X) )
     => ! [X] :
          ( ~ xsd_integer(X)
         => xsd_string(X) ) ),
    inference(negate,[],[subgoal_3]) ).

fof(normalize_3_0,plain,
    ( ? [X] :
        ( ~ xsd_integer(X)
        & ~ xsd_string(X) )
    & ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[negate_3_0]) ).

fof(normalize_3_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_3_2,plain,
    ! [X] : ~ cowlNothing(X),
    inference(conjunct,[],[normalize_3_1]) ).

fof(normalize_3_3,plain,
    ! [X] : ~ cowlNothing(X),
    inference(specialize,[],[normalize_3_2]) ).

fof(normalize_3_4,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_3_1]) ).

fof(normalize_3_5,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_3_4]) ).

fof(normalize_3_6,plain,
    ? [X] :
      ( ~ xsd_integer(X)
      & ~ xsd_string(X) ),
    inference(simplify,[],[normalize_3_0,normalize_3_3,normalize_3_5]) ).

fof(normalize_3_7,plain,
    ( ~ xsd_integer(skolemFOFtoCNF_X_1)
    & ~ xsd_string(skolemFOFtoCNF_X_1) ),
    inference(skolemize,[],[normalize_3_6]) ).

fof(normalize_3_8,plain,
    ~ xsd_string(skolemFOFtoCNF_X_1),
    inference(conjunct,[],[normalize_3_7]) ).

fof(normalize_3_9,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_3_10,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(specialize,[],[normalize_3_9]) ).

fof(normalize_3_11,plain,
    ! [X] :
      ( ( ~ xsd_integer(X)
        | ~ xsd_string(X) )
      & ( xsd_integer(X)
        | xsd_string(X) ) ),
    inference(clausify,[],[normalize_3_10]) ).

fof(normalize_3_12,plain,
    ! [X] :
      ( xsd_integer(X)
      | xsd_string(X) ),
    inference(conjunct,[],[normalize_3_11]) ).

fof(normalize_3_13,plain,
    ~ xsd_integer(skolemFOFtoCNF_X_1),
    inference(conjunct,[],[normalize_3_7]) ).

cnf(refute_3_0,plain,
    ~ xsd_string(skolemFOFtoCNF_X_1),
    inference(canonicalize,[],[normalize_3_8]) ).

cnf(refute_3_1,plain,
    ( xsd_integer(X)
    | xsd_string(X) ),
    inference(canonicalize,[],[normalize_3_12]) ).

cnf(refute_3_2,plain,
    ( xsd_integer(skolemFOFtoCNF_X_1)
    | xsd_string(skolemFOFtoCNF_X_1) ),
    inference(subst,[],[refute_3_1:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_3_3,plain,
    xsd_integer(skolemFOFtoCNF_X_1),
    inference(resolve,[$cnf( xsd_string(skolemFOFtoCNF_X_1) )],[refute_3_2,refute_3_0]) ).

cnf(refute_3_4,plain,
    ~ xsd_integer(skolemFOFtoCNF_X_1),
    inference(canonicalize,[],[normalize_3_13]) ).

cnf(refute_3_5,plain,
    $false,
    inference(resolve,[$cnf( xsd_integer(skolemFOFtoCNF_X_1) )],[refute_3_3,refute_3_4]) ).

fof(negate_4_0,plain,
    ~ ( ( ! [X] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) ) )
     => ! [X,Y] :
          ( rq(X,Y)
         => rp(X,Y) ) ),
    inference(negate,[],[subgoal_4]) ).

fof(normalize_4_0,plain,
    ( ? [X,Y] :
        ( ~ rp(X,Y)
        & rq(X,Y) )
    & ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X)
    & ! [X] :
        ( ~ xsd_integer(X)
      <=> xsd_string(X) ) ),
    inference(canonicalize,[],[negate_4_0]) ).

fof(normalize_4_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_4_2,plain,
    ! [X] : ~ cowlNothing(X),
    inference(conjunct,[],[normalize_4_1]) ).

fof(normalize_4_3,plain,
    ! [X] : ~ cowlNothing(X),
    inference(specialize,[],[normalize_4_2]) ).

fof(normalize_4_4,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_4_1]) ).

fof(normalize_4_5,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_4_4]) ).

fof(normalize_4_6,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_4_7,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(specialize,[],[normalize_4_6]) ).

fof(normalize_4_8,plain,
    ? [X,Y] :
      ( ~ rp(X,Y)
      & rq(X,Y) ),
    inference(simplify,[],[normalize_4_0,normalize_4_3,normalize_4_5,normalize_4_7]) ).

fof(normalize_4_9,plain,
    ( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
    & rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),
    inference(skolemize,[],[normalize_4_8]) ).

fof(normalize_4_10,plain,
    ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_4_9]) ).

fof(normalize_4_11,plain,
    rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_4_9]) ).

fof(normalize_4_12,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rq(X,iv) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_4_13,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rq(X,iv) ),
    inference(specialize,[],[normalize_4_12]) ).

fof(normalize_4_14,plain,
    ! [X] :
      ( ( ~ cd(X)
        | rq(X,iv) )
      & ( ~ rq(X,iv)
        | cd(X) ) ),
    inference(clausify,[],[normalize_4_13]) ).

fof(normalize_4_15,plain,
    ! [X] :
      ( ~ cd(X)
      | rq(X,iv) ),
    inference(conjunct,[],[normalize_4_14]) ).

fof(normalize_4_16,plain,
    ! [X] :
      ( cd(X)
      | ! [Y] : ~ rq(X,Y) ),
    inference(canonicalize,[],[axiom_7]) ).

fof(normalize_4_17,plain,
    ! [X] :
      ( cd(X)
      | ! [Y] : ~ rq(X,Y) ),
    inference(specialize,[],[normalize_4_16]) ).

fof(normalize_4_18,plain,
    ! [X,Y] :
      ( ~ rq(X,Y)
      | cd(X) ),
    inference(clausify,[],[normalize_4_17]) ).

fof(normalize_4_19,plain,
    ! [X,Y,Z] :
      ( ~ rq(X,Y)
      | ~ rq(X,Z)
      | Y = Z ),
    inference(canonicalize,[],[axiom_6]) ).

fof(normalize_4_20,plain,
    ! [X,Y,Z] :
      ( ~ rq(X,Y)
      | ~ rq(X,Z)
      | Y = Z ),
    inference(specialize,[],[normalize_4_19]) ).

fof(normalize_4_21,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rp(X,iv) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_4_22,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rp(X,iv) ),
    inference(specialize,[],[normalize_4_21]) ).

fof(normalize_4_23,plain,
    ! [X] :
      ( ( ~ cd(X)
        | rp(X,iv) )
      & ( ~ rp(X,iv)
        | cd(X) ) ),
    inference(clausify,[],[normalize_4_22]) ).

fof(normalize_4_24,plain,
    ! [X] :
      ( ~ cd(X)
      | rp(X,iv) ),
    inference(conjunct,[],[normalize_4_23]) ).

cnf(refute_4_0,plain,
    ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_4_10]) ).

cnf(refute_4_1,plain,
    rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_4_11]) ).

cnf(refute_4_2,plain,
    ( ~ cd(X)
    | rq(X,iv) ),
    inference(canonicalize,[],[normalize_4_15]) ).

cnf(refute_4_3,plain,
    ( ~ cd(skolemFOFtoCNF_X_2)
    | rq(skolemFOFtoCNF_X_2,iv) ),
    inference(subst,[],[refute_4_2:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).

cnf(refute_4_4,plain,
    ( ~ rq(X,Y)
    | cd(X) ),
    inference(canonicalize,[],[normalize_4_18]) ).

cnf(refute_4_5,plain,
    ( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
    | cd(skolemFOFtoCNF_X_2) ),
    inference(subst,[],[refute_4_4:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_4_6,plain,
    cd(skolemFOFtoCNF_X_2),
    inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_5]) ).

cnf(refute_4_7,plain,
    rq(skolemFOFtoCNF_X_2,iv),
    inference(resolve,[$cnf( cd(skolemFOFtoCNF_X_2) )],[refute_4_6,refute_4_3]) ).

cnf(refute_4_8,plain,
    ( ~ rq(X,Y)
    | ~ rq(X,Z)
    | Y = Z ),
    inference(canonicalize,[],[normalize_4_20]) ).

cnf(refute_4_9,plain,
    ( ~ rq(skolemFOFtoCNF_X_2,X_25)
    | ~ rq(skolemFOFtoCNF_X_2,iv)
    | iv = X_25 ),
    inference(subst,[],[refute_4_8:[bind(X,$fot(skolemFOFtoCNF_X_2)),bind(Y,$fot(iv)),bind(Z,$fot(X_25))]]) ).

cnf(refute_4_10,plain,
    ( ~ rq(skolemFOFtoCNF_X_2,X_25)
    | iv = X_25 ),
    inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,iv) )],[refute_4_7,refute_4_9]) ).

cnf(refute_4_11,plain,
    ( ~ rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y)
    | iv = skolemFOFtoCNF_Y ),
    inference(subst,[],[refute_4_10:[bind(X_25,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_4_12,plain,
    iv = skolemFOFtoCNF_Y,
    inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_1,refute_4_11]) ).

cnf(refute_4_13,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_4_14,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_4_15,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_4_13,refute_4_14]) ).

cnf(refute_4_16,plain,
    ( iv != skolemFOFtoCNF_Y
    | skolemFOFtoCNF_Y = iv ),
    inference(subst,[],[refute_4_15:[bind(X0,$fot(iv)),bind(Y0,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_4_17,plain,
    skolemFOFtoCNF_Y = iv,
    inference(resolve,[$cnf( $equal(iv,skolemFOFtoCNF_Y) )],[refute_4_12,refute_4_16]) ).

cnf(refute_4_18,plain,
    ( skolemFOFtoCNF_Y != iv
    | ~ rp(skolemFOFtoCNF_X_2,iv)
    | rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),
    introduced(tautology,[equality,[$cnf( ~ rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),[1],$fot(iv)]]) ).

cnf(refute_4_19,plain,
    ( ~ rp(skolemFOFtoCNF_X_2,iv)
    | rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y,iv) )],[refute_4_17,refute_4_18]) ).

cnf(refute_4_20,plain,
    ~ rp(skolemFOFtoCNF_X_2,iv),
    inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,skolemFOFtoCNF_Y) )],[refute_4_19,refute_4_0]) ).

cnf(refute_4_21,plain,
    ( ~ cd(X)
    | rp(X,iv) ),
    inference(canonicalize,[],[normalize_4_24]) ).

cnf(refute_4_22,plain,
    ( ~ cd(skolemFOFtoCNF_X_2)
    | rp(skolemFOFtoCNF_X_2,iv) ),
    inference(subst,[],[refute_4_21:[bind(X,$fot(skolemFOFtoCNF_X_2))]]) ).

cnf(refute_4_23,plain,
    rp(skolemFOFtoCNF_X_2,iv),
    inference(resolve,[$cnf( cd(skolemFOFtoCNF_X_2) )],[refute_4_6,refute_4_22]) ).

cnf(refute_4_24,plain,
    $false,
    inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_2,iv) )],[refute_4_23,refute_4_20]) ).

fof(negate_5_0,plain,
    ~ ( ( ! [X] :
            ( cowlThing(X)
            & ~ cowlNothing(X) )
        & ! [X] :
            ( xsd_string(X)
          <=> ~ xsd_integer(X) ) )
     => ! [X,Y] :
          ( rp(X,Y)
         => rq(X,Y) ) ),
    inference(negate,[],[subgoal_5]) ).

fof(normalize_5_0,plain,
    ( ? [X,Y] :
        ( ~ rq(X,Y)
        & rp(X,Y) )
    & ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X)
    & ! [X] :
        ( ~ xsd_integer(X)
      <=> xsd_string(X) ) ),
    inference(canonicalize,[],[negate_5_0]) ).

fof(normalize_5_1,plain,
    ( ! [X] : ~ cowlNothing(X)
    & ! [X] : cowlThing(X) ),
    inference(canonicalize,[],[axiom_0]) ).

fof(normalize_5_2,plain,
    ! [X] : ~ cowlNothing(X),
    inference(conjunct,[],[normalize_5_1]) ).

fof(normalize_5_3,plain,
    ! [X] : ~ cowlNothing(X),
    inference(specialize,[],[normalize_5_2]) ).

fof(normalize_5_4,plain,
    ! [X] : cowlThing(X),
    inference(conjunct,[],[normalize_5_1]) ).

fof(normalize_5_5,plain,
    ! [X] : cowlThing(X),
    inference(specialize,[],[normalize_5_4]) ).

fof(normalize_5_6,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(canonicalize,[],[axiom_1]) ).

fof(normalize_5_7,plain,
    ! [X] :
      ( ~ xsd_integer(X)
    <=> xsd_string(X) ),
    inference(specialize,[],[normalize_5_6]) ).

fof(normalize_5_8,plain,
    ? [X,Y] :
      ( ~ rq(X,Y)
      & rp(X,Y) ),
    inference(simplify,[],[normalize_5_0,normalize_5_3,normalize_5_5,normalize_5_7]) ).

fof(normalize_5_9,plain,
    ( ~ rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
    & rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),
    inference(skolemize,[],[normalize_5_8]) ).

fof(normalize_5_10,plain,
    ~ rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
    inference(conjunct,[],[normalize_5_9]) ).

fof(normalize_5_11,plain,
    rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
    inference(conjunct,[],[normalize_5_9]) ).

fof(normalize_5_12,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rp(X,iv) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_5_13,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rp(X,iv) ),
    inference(specialize,[],[normalize_5_12]) ).

fof(normalize_5_14,plain,
    ! [X] :
      ( ( ~ cd(X)
        | rp(X,iv) )
      & ( ~ rp(X,iv)
        | cd(X) ) ),
    inference(clausify,[],[normalize_5_13]) ).

fof(normalize_5_15,plain,
    ! [X] :
      ( ~ cd(X)
      | rp(X,iv) ),
    inference(conjunct,[],[normalize_5_14]) ).

fof(normalize_5_16,plain,
    ! [X] :
      ( cd(X)
      | ! [Y] : ~ rp(X,Y) ),
    inference(canonicalize,[],[axiom_5]) ).

fof(normalize_5_17,plain,
    ! [X] :
      ( cd(X)
      | ! [Y] : ~ rp(X,Y) ),
    inference(specialize,[],[normalize_5_16]) ).

fof(normalize_5_18,plain,
    ! [X,Y] :
      ( ~ rp(X,Y)
      | cd(X) ),
    inference(clausify,[],[normalize_5_17]) ).

fof(normalize_5_19,plain,
    ! [X,Y,Z] :
      ( ~ rp(X,Y)
      | ~ rp(X,Z)
      | Y = Z ),
    inference(canonicalize,[],[axiom_4]) ).

fof(normalize_5_20,plain,
    ! [X,Y,Z] :
      ( ~ rp(X,Y)
      | ~ rp(X,Z)
      | Y = Z ),
    inference(specialize,[],[normalize_5_19]) ).

fof(normalize_5_21,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rq(X,iv) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_5_22,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ~ rq(X,iv) ),
    inference(specialize,[],[normalize_5_21]) ).

fof(normalize_5_23,plain,
    ! [X] :
      ( ( ~ cd(X)
        | rq(X,iv) )
      & ( ~ rq(X,iv)
        | cd(X) ) ),
    inference(clausify,[],[normalize_5_22]) ).

fof(normalize_5_24,plain,
    ! [X] :
      ( ~ cd(X)
      | rq(X,iv) ),
    inference(conjunct,[],[normalize_5_23]) ).

cnf(refute_5_0,plain,
    ~ rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
    inference(canonicalize,[],[normalize_5_10]) ).

cnf(refute_5_1,plain,
    rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1),
    inference(canonicalize,[],[normalize_5_11]) ).

cnf(refute_5_2,plain,
    ( ~ cd(X)
    | rp(X,iv) ),
    inference(canonicalize,[],[normalize_5_15]) ).

cnf(refute_5_3,plain,
    ( ~ cd(skolemFOFtoCNF_X_3)
    | rp(skolemFOFtoCNF_X_3,iv) ),
    inference(subst,[],[refute_5_2:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).

cnf(refute_5_4,plain,
    ( ~ rp(X,Y)
    | cd(X) ),
    inference(canonicalize,[],[normalize_5_18]) ).

cnf(refute_5_5,plain,
    ( ~ rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
    | cd(skolemFOFtoCNF_X_3) ),
    inference(subst,[],[refute_5_4:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_5_6,plain,
    cd(skolemFOFtoCNF_X_3),
    inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_5]) ).

cnf(refute_5_7,plain,
    rp(skolemFOFtoCNF_X_3,iv),
    inference(resolve,[$cnf( cd(skolemFOFtoCNF_X_3) )],[refute_5_6,refute_5_3]) ).

cnf(refute_5_8,plain,
    ( ~ rp(X,Y)
    | ~ rp(X,Z)
    | Y = Z ),
    inference(canonicalize,[],[normalize_5_20]) ).

cnf(refute_5_9,plain,
    ( ~ rp(skolemFOFtoCNF_X_3,X_41)
    | ~ rp(skolemFOFtoCNF_X_3,iv)
    | iv = X_41 ),
    inference(subst,[],[refute_5_8:[bind(X,$fot(skolemFOFtoCNF_X_3)),bind(Y,$fot(iv)),bind(Z,$fot(X_41))]]) ).

cnf(refute_5_10,plain,
    ( ~ rp(skolemFOFtoCNF_X_3,X_41)
    | iv = X_41 ),
    inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_3,iv) )],[refute_5_7,refute_5_9]) ).

cnf(refute_5_11,plain,
    ( ~ rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1)
    | iv = skolemFOFtoCNF_Y_1 ),
    inference(subst,[],[refute_5_10:[bind(X_41,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_5_12,plain,
    iv = skolemFOFtoCNF_Y_1,
    inference(resolve,[$cnf( rp(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_1,refute_5_11]) ).

cnf(refute_5_13,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_5_14,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_5_15,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_5_13,refute_5_14]) ).

cnf(refute_5_16,plain,
    ( iv != skolemFOFtoCNF_Y_1
    | skolemFOFtoCNF_Y_1 = iv ),
    inference(subst,[],[refute_5_15:[bind(X0,$fot(iv)),bind(Y0,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_5_17,plain,
    skolemFOFtoCNF_Y_1 = iv,
    inference(resolve,[$cnf( $equal(iv,skolemFOFtoCNF_Y_1) )],[refute_5_12,refute_5_16]) ).

cnf(refute_5_18,plain,
    ( skolemFOFtoCNF_Y_1 != iv
    | ~ rq(skolemFOFtoCNF_X_3,iv)
    | rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),
    introduced(tautology,[equality,[$cnf( ~ rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),[1],$fot(iv)]]) ).

cnf(refute_5_19,plain,
    ( ~ rq(skolemFOFtoCNF_X_3,iv)
    | rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1,iv) )],[refute_5_17,refute_5_18]) ).

cnf(refute_5_20,plain,
    ~ rq(skolemFOFtoCNF_X_3,iv),
    inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_3,skolemFOFtoCNF_Y_1) )],[refute_5_19,refute_5_0]) ).

cnf(refute_5_21,plain,
    ( ~ cd(X)
    | rq(X,iv) ),
    inference(canonicalize,[],[normalize_5_24]) ).

cnf(refute_5_22,plain,
    ( ~ cd(skolemFOFtoCNF_X_3)
    | rq(skolemFOFtoCNF_X_3,iv) ),
    inference(subst,[],[refute_5_21:[bind(X,$fot(skolemFOFtoCNF_X_3))]]) ).

cnf(refute_5_23,plain,
    rq(skolemFOFtoCNF_X_3,iv),
    inference(resolve,[$cnf( cd(skolemFOFtoCNF_X_3) )],[refute_5_6,refute_5_22]) ).

cnf(refute_5_24,plain,
    $false,
    inference(resolve,[$cnf( rq(skolemFOFtoCNF_X_3,iv) )],[refute_5_23,refute_5_20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : KRS172+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n023.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Tue Jun  7 09:06:38 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36  
% 0.12/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37  
%------------------------------------------------------------------------------