TSTP Solution File: GEO146+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO146+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 05:24:39 EDT 2022

% Result   : Theorem 0.67s 0.85s
% Output   : CNFRefutation 0.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   57 (  16 unt;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  101 (  52   ~;  26   |;   8   &)
%                                         (  11 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   88 (   0 sgn  66   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(connect_defn,axiom,
    ! [X,Y,P] :
      ( connect(X,Y,P)
    <=> once(at_the_same_time(at(X,P),at(Y,P))) ) ).

fof(symmetry_of_at_the_same_time,axiom,
    ! [A,B] :
      ( once(at_the_same_time(A,B))
    <=> once(at_the_same_time(B,A)) ) ).

fof(t12,conjecture,
    ! [X,Y,P] :
      ( connect(X,Y,P)
    <=> connect(Y,X,P) ) ).

fof(subgoal_0,plain,
    ! [X,Y,P] :
      ( connect(X,Y,P)
     => connect(Y,X,P) ),
    inference(strip,[],[t12]) ).

fof(subgoal_1,plain,
    ! [X,Y,P] :
      ( connect(Y,X,P)
     => connect(X,Y,P) ),
    inference(strip,[],[t12]) ).

fof(negate_0_0,plain,
    ~ ! [X,Y,P] :
        ( connect(X,Y,P)
       => connect(Y,X,P) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
    <=> ~ once(at_the_same_time(B,A)) ),
    inference(canonicalize,[],[symmetry_of_at_the_same_time]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
    <=> ~ once(at_the_same_time(B,A)) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ( ~ once(at_the_same_time(A,B))
        | once(at_the_same_time(B,A)) )
      & ( ~ once(at_the_same_time(B,A))
        | once(at_the_same_time(A,B)) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
      | once(at_the_same_time(B,A)) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [P,X,Y] :
      ( ~ connect(Y,X,P)
      & connect(X,Y,P) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( ~ connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9)
    & connect(skolemFOFtoCNF_X,skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    connect(skolemFOFtoCNF_X,skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
    <=> ~ once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(canonicalize,[],[connect_defn]) ).

fof(normalize_0_8,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
    <=> ~ once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [P,X,Y] :
      ( ( ~ connect(X,Y,P)
        | once(at_the_same_time(at(X,P),at(Y,P))) )
      & ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
        | connect(X,Y,P) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
      | once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [P,X,Y] :
      ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
      | connect(X,Y,P) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_12,plain,
    ~ connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ once(at_the_same_time(A,B))
    | once(at_the_same_time(B,A)) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ once(at_the_same_time(at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9)))
    | once(at_the_same_time(at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9))) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9))),bind(B,$fot(at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9)))]]) ).

cnf(refute_0_2,plain,
    connect(skolemFOFtoCNF_X,skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ connect(X,Y,P)
    | once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_4,plain,
    ( ~ connect(skolemFOFtoCNF_X,skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9)
    | once(at_the_same_time(at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9))) ),
    inference(subst,[],[refute_0_3:[bind(P,$fot(skolemFOFtoCNF_P_9)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_5,plain,
    once(at_the_same_time(at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9))),
    inference(resolve,[$cnf( connect(skolemFOFtoCNF_X,skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9) )],[refute_0_2,refute_0_4]) ).

cnf(refute_0_6,plain,
    once(at_the_same_time(at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9))),
    inference(resolve,[$cnf( once(at_the_same_time(at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9))) )],[refute_0_5,refute_0_1]) ).

cnf(refute_0_7,plain,
    ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
    | connect(X,Y,P) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( ~ once(at_the_same_time(at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9)))
    | connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9) ),
    inference(subst,[],[refute_0_7:[bind(P,$fot(skolemFOFtoCNF_P_9)),bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_9,plain,
    connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),
    inference(resolve,[$cnf( once(at_the_same_time(at(skolemFOFtoCNF_Y,skolemFOFtoCNF_P_9),at(skolemFOFtoCNF_X,skolemFOFtoCNF_P_9))) )],[refute_0_6,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_11,plain,
    $false,
    inference(resolve,[$cnf( connect(skolemFOFtoCNF_Y,skolemFOFtoCNF_X,skolemFOFtoCNF_P_9) )],[refute_0_9,refute_0_10]) ).

fof(negate_1_0,plain,
    ~ ! [X,Y,P] :
        ( connect(Y,X,P)
       => connect(X,Y,P) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
    <=> ~ once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(canonicalize,[],[connect_defn]) ).

fof(normalize_1_1,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
    <=> ~ once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ! [P,X,Y] :
      ( ( ~ connect(X,Y,P)
        | once(at_the_same_time(at(X,P),at(Y,P))) )
      & ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
        | connect(X,Y,P) ) ),
    inference(clausify,[],[normalize_1_1]) ).

fof(normalize_1_3,plain,
    ! [P,X,Y] :
      ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
      | connect(X,Y,P) ),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
    <=> ~ once(at_the_same_time(B,A)) ),
    inference(canonicalize,[],[symmetry_of_at_the_same_time]) ).

fof(normalize_1_5,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
    <=> ~ once(at_the_same_time(B,A)) ),
    inference(specialize,[],[normalize_1_4]) ).

fof(normalize_1_6,plain,
    ! [A,B] :
      ( ( ~ once(at_the_same_time(A,B))
        | once(at_the_same_time(B,A)) )
      & ( ~ once(at_the_same_time(B,A))
        | once(at_the_same_time(A,B)) ) ),
    inference(clausify,[],[normalize_1_5]) ).

fof(normalize_1_7,plain,
    ! [A,B] :
      ( ~ once(at_the_same_time(A,B))
      | once(at_the_same_time(B,A)) ),
    inference(conjunct,[],[normalize_1_6]) ).

fof(normalize_1_8,plain,
    ? [P,X,Y] :
      ( ~ connect(X,Y,P)
      & connect(Y,X,P) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_9,plain,
    ( ~ connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10)
    & connect(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10) ),
    inference(skolemize,[],[normalize_1_8]) ).

fof(normalize_1_10,plain,
    connect(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),
    inference(conjunct,[],[normalize_1_9]) ).

fof(normalize_1_11,plain,
    ! [P,X,Y] :
      ( ~ connect(X,Y,P)
      | once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(conjunct,[],[normalize_1_2]) ).

fof(normalize_1_12,plain,
    ~ connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),
    inference(conjunct,[],[normalize_1_9]) ).

cnf(refute_1_0,plain,
    ( ~ once(at_the_same_time(at(X,P),at(Y,P)))
    | connect(X,Y,P) ),
    inference(canonicalize,[],[normalize_1_3]) ).

cnf(refute_1_1,plain,
    ( ~ once(at_the_same_time(at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10)))
    | connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10) ),
    inference(subst,[],[refute_1_0:[bind(P,$fot(skolemFOFtoCNF_P_10)),bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_1_2,plain,
    ( ~ once(at_the_same_time(A,B))
    | once(at_the_same_time(B,A)) ),
    inference(canonicalize,[],[normalize_1_7]) ).

cnf(refute_1_3,plain,
    ( ~ once(at_the_same_time(at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10)))
    | once(at_the_same_time(at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10))) ),
    inference(subst,[],[refute_1_2:[bind(A,$fot(at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10))),bind(B,$fot(at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10)))]]) ).

cnf(refute_1_4,plain,
    connect(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),
    inference(canonicalize,[],[normalize_1_10]) ).

cnf(refute_1_5,plain,
    ( ~ connect(X,Y,P)
    | once(at_the_same_time(at(X,P),at(Y,P))) ),
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_6,plain,
    ( ~ connect(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10)
    | once(at_the_same_time(at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10))) ),
    inference(subst,[],[refute_1_5:[bind(P,$fot(skolemFOFtoCNF_P_10)),bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(Y,$fot(skolemFOFtoCNF_X_1))]]) ).

cnf(refute_1_7,plain,
    once(at_the_same_time(at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10))),
    inference(resolve,[$cnf( connect(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10) )],[refute_1_4,refute_1_6]) ).

cnf(refute_1_8,plain,
    once(at_the_same_time(at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10))),
    inference(resolve,[$cnf( once(at_the_same_time(at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10))) )],[refute_1_7,refute_1_3]) ).

cnf(refute_1_9,plain,
    connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),
    inference(resolve,[$cnf( once(at_the_same_time(at(skolemFOFtoCNF_X_1,skolemFOFtoCNF_P_10),at(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10))) )],[refute_1_8,refute_1_1]) ).

cnf(refute_1_10,plain,
    ~ connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10),
    inference(canonicalize,[],[normalize_1_12]) ).

cnf(refute_1_11,plain,
    $false,
    inference(resolve,[$cnf( connect(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1,skolemFOFtoCNF_P_10) )],[refute_1_9,refute_1_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO146+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 : Sat Jun 18 05:52:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.67/0.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.67/0.85  
% 0.67/0.85  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.67/0.85  
%------------------------------------------------------------------------------