TSTP Solution File: SEU187+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU187+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 : Tue Jul 19 12:39:08 EDT 2022

% Result   : Theorem 2.13s 2.34s
% Output   : CNFRefutation 2.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   98 (  34 unt;   0 def)
%            Number of atoms       :  231 (  47 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  237 ( 104   ~; 103   |;  12   &)
%                                         (  12 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   1 con; 0-2 aty)
%            Number of variables   :  115 (   2 sgn  60   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d4_relat_1,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ) ).

fof(d5_relat_1,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ) ).

fof(existence_m1_subset_1,axiom,
    ! [A] :
    ? [B] : element(B,A) ).

fof(fc1_xboole_0,axiom,
    empty(empty_set) ).

fof(fc4_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set) ) ).

fof(t2_subset,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ) ).

fof(t60_relat_1,conjecture,
    ( relation_dom(empty_set) = empty_set
    & relation_rng(empty_set) = empty_set ) ).

fof(t6_boole,axiom,
    ! [A] :
      ( empty(A)
     => A = empty_set ) ).

fof(t7_boole,axiom,
    ! [A,B] :
      ~ ( in(A,B)
        & empty(B) ) ).

fof(subgoal_0,plain,
    relation_dom(empty_set) = empty_set,
    inference(strip,[],[t60_relat_1]) ).

fof(subgoal_1,plain,
    ( relation_dom(empty_set) = empty_set
   => relation_rng(empty_set) = empty_set ),
    inference(strip,[],[t60_relat_1]) ).

fof(negate_0_0,plain,
    relation_dom(empty_set) != empty_set,
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(canonicalize,[],[t6_boole]) ).

fof(normalize_0_1,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ~ empty(B)
      | ~ in(A,B) ),
    inference(canonicalize,[],[t7_boole]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( ~ empty(B)
      | ~ in(A,B) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( empty(empty_set)
    & relation(empty_set) ),
    inference(canonicalize,[],[fc4_relat_1]) ).

fof(normalize_0_5,plain,
    empty(empty_set),
    inference(canonicalize,[],[fc1_xboole_0]) ).

fof(normalize_0_6,plain,
    relation(empty_set),
    inference(simplify,[],[normalize_0_4,normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [A] :
    ? [B] : element(B,A),
    inference(canonicalize,[],[existence_m1_subset_1]) ).

fof(normalize_0_8,plain,
    ! [A] :
    ? [B] : element(B,A),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A] : element(skolemFOFtoCNF_B(A),A),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A,B] :
      ( ~ element(A,B)
      | empty(B)
      | in(A,B) ),
    inference(canonicalize,[],[t2_subset]) ).

fof(normalize_0_11,plain,
    ! [A,B] :
      ( ~ element(A,B)
      | empty(B)
      | in(A,B) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B != relation_dom(A)
        <=> ? [C] :
              ( ~ in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    inference(canonicalize,[],[d4_relat_1]) ).

fof(normalize_0_13,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B != relation_dom(A)
        <=> ? [C] :
              ( ~ in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [A,B,C,D] :
      ( ( B != relation_dom(A)
        | ~ in(C,B)
        | ~ relation(A)
        | in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) )
      & ( B != relation_dom(A)
        | ~ in(ordered_pair(C,D),A)
        | ~ relation(A)
        | in(C,B) )
      & ( ~ in(ordered_pair(skolemFOFtoCNF_C(A,B),D),A)
        | ~ in(skolemFOFtoCNF_C(A,B),B)
        | ~ relation(A)
        | B = relation_dom(A) )
      & ( ~ relation(A)
        | B = relation_dom(A)
        | in(ordered_pair(skolemFOFtoCNF_C(A,B),skolemFOFtoCNF_D(A,B)),A)
        | in(skolemFOFtoCNF_C(A,B),B) ) ),
    inference(clausify,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [A,B,C] :
      ( B != relation_dom(A)
      | ~ in(C,B)
      | ~ relation(A)
      | in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
    inference(conjunct,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    relation_dom(empty_set) != empty_set,
    inference(canonicalize,[],[negate_0_0]) ).

cnf(refute_0_0,plain,
    ( ~ empty(A)
    | A = empty_set ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ empty(relation_dom(empty_set))
    | relation_dom(empty_set) = empty_set ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(relation_dom(empty_set)))]]) ).

cnf(refute_0_2,plain,
    ( ~ empty(B)
    | ~ in(A,B) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ empty(empty_set)
    | ~ in(ordered_pair(skolemFOFtoCNF_B(relation_dom(empty_set)),skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(relation_dom(empty_set)))),empty_set) ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(ordered_pair(skolemFOFtoCNF_B(relation_dom(empty_set)),skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(relation_dom(empty_set)))))),bind(B,$fot(empty_set))]]) ).

cnf(refute_0_4,plain,
    relation(empty_set),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    element(skolemFOFtoCNF_B(A),A),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_6,plain,
    element(skolemFOFtoCNF_B(X_40),X_40),
    inference(subst,[],[refute_0_5:[bind(A,$fot(X_40))]]) ).

cnf(refute_0_7,plain,
    ( ~ element(A,B)
    | empty(B)
    | in(A,B) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( ~ element(skolemFOFtoCNF_B(X_40),X_40)
    | empty(X_40)
    | in(skolemFOFtoCNF_B(X_40),X_40) ),
    inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_B(X_40))),bind(B,$fot(X_40))]]) ).

cnf(refute_0_9,plain,
    ( empty(X_40)
    | in(skolemFOFtoCNF_B(X_40),X_40) ),
    inference(resolve,[$cnf( element(skolemFOFtoCNF_B(X_40),X_40) )],[refute_0_6,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( empty(relation_dom(X_73))
    | in(skolemFOFtoCNF_B(relation_dom(X_73)),relation_dom(X_73)) ),
    inference(subst,[],[refute_0_9:[bind(X_40,$fot(relation_dom(X_73)))]]) ).

cnf(refute_0_11,plain,
    ( B != relation_dom(A)
    | ~ in(C,B)
    | ~ relation(A)
    | in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_12,plain,
    ( relation_dom(A) != relation_dom(A)
    | ~ in(C,relation_dom(A))
    | ~ relation(A)
    | in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
    inference(subst,[],[refute_0_11:[bind(B,$fot(relation_dom(A)))]]) ).

cnf(refute_0_13,plain,
    relation_dom(A) = relation_dom(A),
    introduced(tautology,[refl,[$fot(relation_dom(A))]]) ).

cnf(refute_0_14,plain,
    ( ~ in(C,relation_dom(A))
    | ~ relation(A)
    | in(ordered_pair(C,skolemFOFtoCNF_D_1(A,C)),A) ),
    inference(resolve,[$cnf( $equal(relation_dom(A),relation_dom(A)) )],[refute_0_13,refute_0_12]) ).

cnf(refute_0_15,plain,
    ( ~ in(skolemFOFtoCNF_B(relation_dom(X_73)),relation_dom(X_73))
    | ~ relation(X_73)
    | in(ordered_pair(skolemFOFtoCNF_B(relation_dom(X_73)),skolemFOFtoCNF_D_1(X_73,skolemFOFtoCNF_B(relation_dom(X_73)))),X_73) ),
    inference(subst,[],[refute_0_14:[bind(A,$fot(X_73)),bind(C,$fot(skolemFOFtoCNF_B(relation_dom(X_73))))]]) ).

cnf(refute_0_16,plain,
    ( ~ relation(X_73)
    | empty(relation_dom(X_73))
    | in(ordered_pair(skolemFOFtoCNF_B(relation_dom(X_73)),skolemFOFtoCNF_D_1(X_73,skolemFOFtoCNF_B(relation_dom(X_73)))),X_73) ),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_B(relation_dom(X_73)),relation_dom(X_73)) )],[refute_0_10,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ relation(empty_set)
    | empty(relation_dom(empty_set))
    | in(ordered_pair(skolemFOFtoCNF_B(relation_dom(empty_set)),skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(relation_dom(empty_set)))),empty_set) ),
    inference(subst,[],[refute_0_16:[bind(X_73,$fot(empty_set))]]) ).

cnf(refute_0_18,plain,
    ( empty(relation_dom(empty_set))
    | in(ordered_pair(skolemFOFtoCNF_B(relation_dom(empty_set)),skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(relation_dom(empty_set)))),empty_set) ),
    inference(resolve,[$cnf( relation(empty_set) )],[refute_0_4,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( ~ empty(empty_set)
    | empty(relation_dom(empty_set)) ),
    inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_B(relation_dom(empty_set)),skolemFOFtoCNF_D_1(empty_set,skolemFOFtoCNF_B(relation_dom(empty_set)))),empty_set) )],[refute_0_18,refute_0_3]) ).

cnf(refute_0_20,plain,
    empty(empty_set),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_21,plain,
    empty(relation_dom(empty_set)),
    inference(resolve,[$cnf( empty(empty_set) )],[refute_0_20,refute_0_19]) ).

cnf(refute_0_22,plain,
    relation_dom(empty_set) = empty_set,
    inference(resolve,[$cnf( empty(relation_dom(empty_set)) )],[refute_0_21,refute_0_1]) ).

cnf(refute_0_23,plain,
    relation_dom(empty_set) != empty_set,
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_24,plain,
    $false,
    inference(resolve,[$cnf( $equal(relation_dom(empty_set),empty_set) )],[refute_0_22,refute_0_23]) ).

fof(negate_1_0,plain,
    ~ ( relation_dom(empty_set) = empty_set
     => relation_rng(empty_set) = empty_set ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(canonicalize,[],[t6_boole]) ).

fof(normalize_1_1,plain,
    ! [A] :
      ( ~ empty(A)
      | A = empty_set ),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [A,B] :
      ( ~ empty(B)
      | ~ in(A,B) ),
    inference(canonicalize,[],[t7_boole]) ).

fof(normalize_1_3,plain,
    ! [A,B] :
      ( ~ empty(B)
      | ~ in(A,B) ),
    inference(specialize,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ( empty(empty_set)
    & relation(empty_set) ),
    inference(canonicalize,[],[fc4_relat_1]) ).

fof(normalize_1_5,plain,
    empty(empty_set),
    inference(canonicalize,[],[fc1_xboole_0]) ).

fof(normalize_1_6,plain,
    relation(empty_set),
    inference(simplify,[],[normalize_1_4,normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [A] :
    ? [B] : element(B,A),
    inference(canonicalize,[],[existence_m1_subset_1]) ).

fof(normalize_1_8,plain,
    ! [A] :
    ? [B] : element(B,A),
    inference(specialize,[],[normalize_1_7]) ).

fof(normalize_1_9,plain,
    ! [A] : element(skolemFOFtoCNF_B(A),A),
    inference(skolemize,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    ! [A,B] :
      ( ~ element(A,B)
      | empty(B)
      | in(A,B) ),
    inference(canonicalize,[],[t2_subset]) ).

fof(normalize_1_11,plain,
    ! [A,B] :
      ( ~ element(A,B)
      | empty(B)
      | in(A,B) ),
    inference(specialize,[],[normalize_1_10]) ).

fof(normalize_1_12,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B != relation_rng(A)
        <=> ? [C] :
              ( ~ in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(canonicalize,[],[d5_relat_1]) ).

fof(normalize_1_13,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B != relation_rng(A)
        <=> ? [C] :
              ( ~ in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(specialize,[],[normalize_1_12]) ).

fof(normalize_1_14,plain,
    ! [A,B,C,D] :
      ( ( B != relation_rng(A)
        | ~ in(C,B)
        | ~ relation(A)
        | in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) )
      & ( B != relation_rng(A)
        | ~ in(ordered_pair(D,C),A)
        | ~ relation(A)
        | in(C,B) )
      & ( ~ in(ordered_pair(D,skolemFOFtoCNF_C_1(A,B)),A)
        | ~ in(skolemFOFtoCNF_C_1(A,B),B)
        | ~ relation(A)
        | B = relation_rng(A) )
      & ( ~ relation(A)
        | B = relation_rng(A)
        | in(ordered_pair(skolemFOFtoCNF_D_2(A,B),skolemFOFtoCNF_C_1(A,B)),A)
        | in(skolemFOFtoCNF_C_1(A,B),B) ) ),
    inference(clausify,[],[normalize_1_13]) ).

fof(normalize_1_15,plain,
    ! [A,B,C] :
      ( B != relation_rng(A)
      | ~ in(C,B)
      | ~ relation(A)
      | in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
    inference(conjunct,[],[normalize_1_14]) ).

fof(normalize_1_16,plain,
    ( relation_rng(empty_set) != empty_set
    & relation_dom(empty_set) = empty_set ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_17,plain,
    relation_rng(empty_set) != empty_set,
    inference(conjunct,[],[normalize_1_16]) ).

cnf(refute_1_0,plain,
    ( ~ empty(A)
    | A = empty_set ),
    inference(canonicalize,[],[normalize_1_1]) ).

cnf(refute_1_1,plain,
    ( ~ empty(relation_rng(empty_set))
    | relation_rng(empty_set) = empty_set ),
    inference(subst,[],[refute_1_0:[bind(A,$fot(relation_rng(empty_set)))]]) ).

cnf(refute_1_2,plain,
    ( ~ empty(B)
    | ~ in(A,B) ),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_3,plain,
    ( ~ empty(empty_set)
    | ~ in(ordered_pair(skolemFOFtoCNF_D_3(empty_set,skolemFOFtoCNF_B(relation_rng(empty_set))),skolemFOFtoCNF_B(relation_rng(empty_set))),empty_set) ),
    inference(subst,[],[refute_1_2:[bind(A,$fot(ordered_pair(skolemFOFtoCNF_D_3(empty_set,skolemFOFtoCNF_B(relation_rng(empty_set))),skolemFOFtoCNF_B(relation_rng(empty_set))))),bind(B,$fot(empty_set))]]) ).

cnf(refute_1_4,plain,
    relation(empty_set),
    inference(canonicalize,[],[normalize_1_6]) ).

cnf(refute_1_5,plain,
    element(skolemFOFtoCNF_B(A),A),
    inference(canonicalize,[],[normalize_1_9]) ).

cnf(refute_1_6,plain,
    element(skolemFOFtoCNF_B(X_118),X_118),
    inference(subst,[],[refute_1_5:[bind(A,$fot(X_118))]]) ).

cnf(refute_1_7,plain,
    ( ~ element(A,B)
    | empty(B)
    | in(A,B) ),
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_8,plain,
    ( ~ element(skolemFOFtoCNF_B(X_118),X_118)
    | empty(X_118)
    | in(skolemFOFtoCNF_B(X_118),X_118) ),
    inference(subst,[],[refute_1_7:[bind(A,$fot(skolemFOFtoCNF_B(X_118))),bind(B,$fot(X_118))]]) ).

cnf(refute_1_9,plain,
    ( empty(X_118)
    | in(skolemFOFtoCNF_B(X_118),X_118) ),
    inference(resolve,[$cnf( element(skolemFOFtoCNF_B(X_118),X_118) )],[refute_1_6,refute_1_8]) ).

cnf(refute_1_10,plain,
    ( empty(relation_rng(X_151))
    | in(skolemFOFtoCNF_B(relation_rng(X_151)),relation_rng(X_151)) ),
    inference(subst,[],[refute_1_9:[bind(X_118,$fot(relation_rng(X_151)))]]) ).

cnf(refute_1_11,plain,
    ( B != relation_rng(A)
    | ~ in(C,B)
    | ~ relation(A)
    | in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
    inference(canonicalize,[],[normalize_1_15]) ).

cnf(refute_1_12,plain,
    ( relation_rng(A) != relation_rng(A)
    | ~ in(C,relation_rng(A))
    | ~ relation(A)
    | in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
    inference(subst,[],[refute_1_11:[bind(B,$fot(relation_rng(A)))]]) ).

cnf(refute_1_13,plain,
    relation_rng(A) = relation_rng(A),
    introduced(tautology,[refl,[$fot(relation_rng(A))]]) ).

cnf(refute_1_14,plain,
    ( ~ in(C,relation_rng(A))
    | ~ relation(A)
    | in(ordered_pair(skolemFOFtoCNF_D_3(A,C),C),A) ),
    inference(resolve,[$cnf( $equal(relation_rng(A),relation_rng(A)) )],[refute_1_13,refute_1_12]) ).

cnf(refute_1_15,plain,
    ( ~ in(skolemFOFtoCNF_B(relation_rng(X_151)),relation_rng(X_151))
    | ~ relation(X_151)
    | in(ordered_pair(skolemFOFtoCNF_D_3(X_151,skolemFOFtoCNF_B(relation_rng(X_151))),skolemFOFtoCNF_B(relation_rng(X_151))),X_151) ),
    inference(subst,[],[refute_1_14:[bind(A,$fot(X_151)),bind(C,$fot(skolemFOFtoCNF_B(relation_rng(X_151))))]]) ).

cnf(refute_1_16,plain,
    ( ~ relation(X_151)
    | empty(relation_rng(X_151))
    | in(ordered_pair(skolemFOFtoCNF_D_3(X_151,skolemFOFtoCNF_B(relation_rng(X_151))),skolemFOFtoCNF_B(relation_rng(X_151))),X_151) ),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_B(relation_rng(X_151)),relation_rng(X_151)) )],[refute_1_10,refute_1_15]) ).

cnf(refute_1_17,plain,
    ( ~ relation(empty_set)
    | empty(relation_rng(empty_set))
    | in(ordered_pair(skolemFOFtoCNF_D_3(empty_set,skolemFOFtoCNF_B(relation_rng(empty_set))),skolemFOFtoCNF_B(relation_rng(empty_set))),empty_set) ),
    inference(subst,[],[refute_1_16:[bind(X_151,$fot(empty_set))]]) ).

cnf(refute_1_18,plain,
    ( empty(relation_rng(empty_set))
    | in(ordered_pair(skolemFOFtoCNF_D_3(empty_set,skolemFOFtoCNF_B(relation_rng(empty_set))),skolemFOFtoCNF_B(relation_rng(empty_set))),empty_set) ),
    inference(resolve,[$cnf( relation(empty_set) )],[refute_1_4,refute_1_17]) ).

cnf(refute_1_19,plain,
    ( ~ empty(empty_set)
    | empty(relation_rng(empty_set)) ),
    inference(resolve,[$cnf( in(ordered_pair(skolemFOFtoCNF_D_3(empty_set,skolemFOFtoCNF_B(relation_rng(empty_set))),skolemFOFtoCNF_B(relation_rng(empty_set))),empty_set) )],[refute_1_18,refute_1_3]) ).

cnf(refute_1_20,plain,
    empty(empty_set),
    inference(canonicalize,[],[normalize_1_5]) ).

cnf(refute_1_21,plain,
    empty(relation_rng(empty_set)),
    inference(resolve,[$cnf( empty(empty_set) )],[refute_1_20,refute_1_19]) ).

cnf(refute_1_22,plain,
    relation_rng(empty_set) = empty_set,
    inference(resolve,[$cnf( empty(relation_rng(empty_set)) )],[refute_1_21,refute_1_1]) ).

cnf(refute_1_23,plain,
    relation_rng(empty_set) != empty_set,
    inference(canonicalize,[],[normalize_1_17]) ).

cnf(refute_1_24,plain,
    $false,
    inference(resolve,[$cnf( $equal(relation_rng(empty_set),empty_set) )],[refute_1_22,refute_1_23]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SEU187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 21:11:43 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.13/2.34  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.13/2.34  
% 2.13/2.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.13/2.34  
%------------------------------------------------------------------------------