TSTP Solution File: SEU127+2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU127+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 12:38:34 EDT 2022

% Result   : Theorem 0.20s 0.44s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  10 unt;   0 def)
%            Number of atoms       :   87 (  13 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :   92 (  36   ~;  34   |;  12   &)
%                                         (   9 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   75 (   3 sgn  38   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ) ).

fof(d3_xboole_0,axiom,
    ! [A,B,C] :
      ( C = set_intersection2(A,B)
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ) ).

fof(t17_xboole_1,conjecture,
    ! [A,B] : subset(set_intersection2(A,B),A) ).

fof(subgoal_0,plain,
    ! [A,B] : subset(set_intersection2(A,B),A),
    inference(strip,[],[t17_xboole_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B] : subset(set_intersection2(A,B),A),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B] : ~ subset(set_intersection2(A,B),A),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ~ subset(A,B)
    <=> ? [C] :
          ( ~ in(C,B)
          & in(C,A) ) ),
    inference(canonicalize,[],[d3_tarski]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( ~ subset(A,B)
    <=> ? [C] :
          ( ~ in(C,B)
          & in(C,A) ) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A,B,C] :
      ( ( ~ in(skolemFOFtoCNF_C(A,B),B)
        | subset(A,B) )
      & ( in(skolemFOFtoCNF_C(A,B),A)
        | subset(A,B) )
      & ( ~ in(C,A)
        | ~ subset(A,B)
        | in(C,B) ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A,B] :
      ( ~ in(skolemFOFtoCNF_C(A,B),B)
      | subset(A,B) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,B] :
      ( in(skolemFOFtoCNF_C(A,B),A)
      | subset(A,B) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_7,plain,
    ! [A,B,C] :
      ( C != set_intersection2(A,B)
    <=> ? [D] :
          ( ~ in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    inference(canonicalize,[],[d3_xboole_0]) ).

fof(normalize_0_8,plain,
    ! [A,B,C] :
      ( C != set_intersection2(A,B)
    <=> ? [D] :
          ( ~ in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A,B,C,D] :
      ( ( C != set_intersection2(A,B)
        | ~ in(D,C)
        | in(D,A) )
      & ( C != set_intersection2(A,B)
        | ~ in(D,C)
        | in(D,B) )
      & ( C = set_intersection2(A,B)
        | in(skolemFOFtoCNF_D_1(A,B,C),A)
        | in(skolemFOFtoCNF_D_1(A,B,C),C) )
      & ( C = set_intersection2(A,B)
        | in(skolemFOFtoCNF_D_1(A,B,C),B)
        | in(skolemFOFtoCNF_D_1(A,B,C),C) )
      & ( C != set_intersection2(A,B)
        | ~ in(D,A)
        | ~ in(D,B)
        | in(D,C) )
      & ( ~ in(skolemFOFtoCNF_D_1(A,B,C),A)
        | ~ in(skolemFOFtoCNF_D_1(A,B,C),B)
        | ~ in(skolemFOFtoCNF_D_1(A,B,C),C)
        | C = set_intersection2(A,B) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [A,B,C,D] :
      ( C != set_intersection2(A,B)
      | ~ in(D,C)
      | in(D,A) ),
    inference(conjunct,[],[normalize_0_9]) ).

cnf(refute_0_0,plain,
    ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ in(skolemFOFtoCNF_C(A,B),B)
    | subset(A,B) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ( ~ in(skolemFOFtoCNF_C(set_intersection2(X_204,X_205),X_204),X_204)
    | subset(set_intersection2(X_204,X_205),X_204) ),
    inference(subst,[],[refute_0_1:[bind(A,$fot(set_intersection2(X_204,X_205))),bind(B,$fot(X_204))]]) ).

cnf(refute_0_3,plain,
    ( in(skolemFOFtoCNF_C(A,B),A)
    | subset(A,B) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
    ( in(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B),set_intersection2(X_81,X_82))
    | subset(set_intersection2(X_81,X_82),B) ),
    inference(subst,[],[refute_0_3:[bind(A,$fot(set_intersection2(X_81,X_82)))]]) ).

cnf(refute_0_5,plain,
    ( C != set_intersection2(A,B)
    | ~ in(D,C)
    | in(D,A) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_6,plain,
    ( set_intersection2(A,B) != set_intersection2(A,B)
    | ~ in(D,set_intersection2(A,B))
    | in(D,A) ),
    inference(subst,[],[refute_0_5:[bind(C,$fot(set_intersection2(A,B)))]]) ).

cnf(refute_0_7,plain,
    set_intersection2(A,B) = set_intersection2(A,B),
    introduced(tautology,[refl,[$fot(set_intersection2(A,B))]]) ).

cnf(refute_0_8,plain,
    ( ~ in(D,set_intersection2(A,B))
    | in(D,A) ),
    inference(resolve,[$cnf( $equal(set_intersection2(A,B),set_intersection2(A,B)) )],[refute_0_7,refute_0_6]) ).

cnf(refute_0_9,plain,
    ( ~ in(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B),set_intersection2(X_81,X_82))
    | in(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B),X_81) ),
    inference(subst,[],[refute_0_8:[bind(A,$fot(X_81)),bind(B,$fot(X_82)),bind(D,$fot(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B)))]]) ).

cnf(refute_0_10,plain,
    ( in(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B),X_81)
    | subset(set_intersection2(X_81,X_82),B) ),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_C(set_intersection2(X_81,X_82),B),set_intersection2(X_81,X_82)) )],[refute_0_4,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( in(skolemFOFtoCNF_C(set_intersection2(X_204,X_205),X_204),X_204)
    | subset(set_intersection2(X_204,X_205),X_204) ),
    inference(subst,[],[refute_0_10:[bind(B,$fot(X_204)),bind(X_81,$fot(X_204)),bind(X_82,$fot(X_205))]]) ).

cnf(refute_0_12,plain,
    subset(set_intersection2(X_204,X_205),X_204),
    inference(resolve,[$cnf( in(skolemFOFtoCNF_C(set_intersection2(X_204,X_205),X_204),X_204) )],[refute_0_11,refute_0_2]) ).

cnf(refute_0_13,plain,
    subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2),
    inference(subst,[],[refute_0_12:[bind(X_204,$fot(skolemFOFtoCNF_A_2)),bind(X_205,$fot(skolemFOFtoCNF_B_1))]]) ).

cnf(refute_0_14,plain,
    $false,
    inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B_1),skolemFOFtoCNF_A_2) )],[refute_0_13,refute_0_0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU127+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n026.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jun 19 13:47:55 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44  
% 0.20/0.44  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.45  
%------------------------------------------------------------------------------