TSTP Solution File: GEO082+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 : Sat Jul 16 05:24:09 EDT 2022

% Result   : Theorem 2.43s 2.59s
% Output   : CNFRefutation 2.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   45 (  12 unt;   0 def)
%            Number of atoms       :  110 (  31 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  105 (  40   ~;  42   |;  12   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   57 (   0 sgn  32   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(part_of_defn,axiom,
    ! [C,C1] :
      ( part_of(C1,C)
    <=> ! [P] :
          ( incident_c(P,C1)
         => incident_c(P,C) ) ) ).

fof(c9,axiom,
    ! [C,C1] :
      ( ! [P] :
          ( incident_c(P,C)
        <=> incident_c(P,C1) )
     => C = C1 ) ).

fof(part_of_antisymmetry,conjecture,
    ! [C1,C2] :
      ( ( part_of(C1,C2)
        & part_of(C2,C1) )
     => C1 = C2 ) ).

fof(subgoal_0,plain,
    ! [C1,C2] :
      ( ( part_of(C1,C2)
        & part_of(C2,C1) )
     => C1 = C2 ),
    inference(strip,[],[part_of_antisymmetry]) ).

fof(negate_0_0,plain,
    ~ ! [C1,C2] :
        ( ( part_of(C1,C2)
          & part_of(C2,C1) )
       => C1 = C2 ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [C,C1] :
      ( C = C1
      | ? [P] :
          ( ~ incident_c(P,C)
        <=> incident_c(P,C1) ) ),
    inference(canonicalize,[],[c9]) ).

fof(normalize_0_1,plain,
    ! [C,C1] :
      ( C = C1
      | ? [P] :
          ( ~ incident_c(P,C)
        <=> incident_c(P,C1) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [C,C1] :
      ( ( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
        | ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
        | C = C1 )
      & ( C = C1
        | incident_c(skolemFOFtoCNF_P_3(C,C1),C)
        | incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [C,C1] :
      ( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
      | ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
      | C = C1 ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [C1,C2] :
      ( C1 != C2
      & part_of(C1,C2)
      & part_of(C2,C1) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2
    & part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
    & part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [C,C1] :
      ( ~ part_of(C1,C)
    <=> ? [P] :
          ( ~ incident_c(P,C)
          & incident_c(P,C1) ) ),
    inference(canonicalize,[],[part_of_defn]) ).

fof(normalize_0_8,plain,
    ! [C,C1] :
      ( ~ part_of(C1,C)
    <=> ? [P] :
          ( ~ incident_c(P,C)
          & incident_c(P,C1) ) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [C,C1,P] :
      ( ( ~ incident_c(skolemFOFtoCNF_P(C,C1),C)
        | part_of(C1,C) )
      & ( incident_c(skolemFOFtoCNF_P(C,C1),C1)
        | part_of(C1,C) )
      & ( ~ incident_c(P,C1)
        | ~ part_of(C1,C)
        | incident_c(P,C) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [C,C1,P] :
      ( ~ incident_c(P,C1)
      | ~ part_of(C1,C)
      | incident_c(P,C) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [C,C1] :
      ( C = C1
      | incident_c(skolemFOFtoCNF_P_3(C,C1),C)
      | incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_12,plain,
    skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2,
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_13,plain,
    part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C)
    | ~ incident_c(skolemFOFtoCNF_P_3(C,C1),C1)
    | C = C1 ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
    | ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
    | skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2 ),
    inference(subst,[],[refute_0_0:[bind(C,$fot(skolemFOFtoCNF_C2_2)),bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).

cnf(refute_0_2,plain,
    part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ incident_c(P,C1)
    | ~ part_of(C1,C)
    | incident_c(P,C) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_4,plain,
    ( ~ incident_c(X_501,skolemFOFtoCNF_C1_2)
    | ~ part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2)
    | incident_c(X_501,skolemFOFtoCNF_C2_2) ),
    inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C2_2)),bind(C1,$fot(skolemFOFtoCNF_C1_2)),bind(P,$fot(X_501))]]) ).

cnf(refute_0_5,plain,
    ( ~ incident_c(X_501,skolemFOFtoCNF_C1_2)
    | incident_c(X_501,skolemFOFtoCNF_C2_2) ),
    inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    ( ~ incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
    | incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
    inference(subst,[],[refute_0_5:[bind(X_501,$fot(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2)))]]) ).

cnf(refute_0_7,plain,
    ( C = C1
    | incident_c(skolemFOFtoCNF_P_3(C,C1),C)
    | incident_c(skolemFOFtoCNF_P_3(C,C1),C1) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( X_1233 = skolemFOFtoCNF_C1_2
    | incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),X_1233)
    | incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) ),
    inference(subst,[],[refute_0_7:[bind(C,$fot(X_1233)),bind(C1,$fot(skolemFOFtoCNF_C1_2))]]) ).

cnf(refute_0_9,plain,
    ( X_1233 = skolemFOFtoCNF_C1_2
    | incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),X_1233)
    | incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
    inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(X_1233,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) )],[refute_0_8,refute_0_6]) ).

cnf(refute_0_10,plain,
    ( skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2
    | incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) ),
    inference(subst,[],[refute_0_9:[bind(X_1233,$fot(skolemFOFtoCNF_C2_2))]]) ).

cnf(refute_0_11,plain,
    skolemFOFtoCNF_C1_2 != skolemFOFtoCNF_C2_2,
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_12,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_13,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_14,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( skolemFOFtoCNF_C2_2 != skolemFOFtoCNF_C1_2
    | skolemFOFtoCNF_C1_2 = skolemFOFtoCNF_C2_2 ),
    inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_C2_2)),bind(Y,$fot(skolemFOFtoCNF_C1_2))]]) ).

cnf(refute_0_16,plain,
    skolemFOFtoCNF_C2_2 != skolemFOFtoCNF_C1_2,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C1_2,skolemFOFtoCNF_C2_2) )],[refute_0_15,refute_0_11]) ).

cnf(refute_0_17,plain,
    incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_10,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2)
    | skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2 ),
    inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) )],[refute_0_17,refute_0_1]) ).

cnf(refute_0_19,plain,
    part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_20,plain,
    ( ~ incident_c(X_501,skolemFOFtoCNF_C2_2)
    | ~ part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2)
    | incident_c(X_501,skolemFOFtoCNF_C1_2) ),
    inference(subst,[],[refute_0_3:[bind(C,$fot(skolemFOFtoCNF_C1_2)),bind(C1,$fot(skolemFOFtoCNF_C2_2)),bind(P,$fot(X_501))]]) ).

cnf(refute_0_21,plain,
    ( ~ incident_c(X_501,skolemFOFtoCNF_C2_2)
    | incident_c(X_501,skolemFOFtoCNF_C1_2) ),
    inference(resolve,[$cnf( part_of(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( ~ incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2)
    | incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) ),
    inference(subst,[],[refute_0_21:[bind(X_501,$fot(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2)))]]) ).

cnf(refute_0_23,plain,
    incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2),
    inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C2_2) )],[refute_0_17,refute_0_22]) ).

cnf(refute_0_24,plain,
    skolemFOFtoCNF_C2_2 = skolemFOFtoCNF_C1_2,
    inference(resolve,[$cnf( incident_c(skolemFOFtoCNF_P_3(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2),skolemFOFtoCNF_C1_2) )],[refute_0_23,refute_0_18]) ).

cnf(refute_0_25,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C2_2,skolemFOFtoCNF_C1_2) )],[refute_0_24,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n015.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
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jun 17 21:38:12 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.43/2.59  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.43/2.59  
% 2.43/2.59  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.43/2.60  
%------------------------------------------------------------------------------