TSTP Solution File: GEO219+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO219+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n005.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 05:25:32 EDT 2022

% Result   : Theorem 0.20s 0.41s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   57 (  17 unt;   0 def)
%            Number of atoms       :  147 (   0 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  149 (  59   ~;  69   |;  16   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   75 (   0 sgn  42   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(apart3,axiom,
    ! [X] : ~ convergent_lines(X,X) ).

fof(ax6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ) ).

fof(coipo1,axiom,
    ! [L,M] :
      ~ ( ~ convergent_lines(L,M)
        & ~ unorthogonal_lines(L,M) ) ).

fof(cotno1,axiom,
    ! [L,M,N] :
      ( ( ( ~ convergent_lines(L,M)
          | ~ unorthogonal_lines(L,M) )
        & ( ~ convergent_lines(L,N)
          | ~ unorthogonal_lines(L,N) ) )
     => ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N) ) ) ).

fof(con,conjecture,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ convergent_lines(L,N) )
     => ~ unorthogonal_lines(M,N) ) ).

fof(subgoal_0,plain,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ convergent_lines(L,N) )
     => ~ unorthogonal_lines(M,N) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [L,M,N] :
        ( ( ~ unorthogonal_lines(L,M)
          & ~ convergent_lines(L,N) )
       => ~ unorthogonal_lines(M,N) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [L,M,N] :
      ( ~ convergent_lines(L,N)
      & ~ unorthogonal_lines(L,M)
      & unorthogonal_lines(M,N) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
    & ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    & unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_4,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N)
      | ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) ) ),
    inference(canonicalize,[],[cotno1]) ).

fof(normalize_0_5,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N)
      | ( convergent_lines(L,M)
        & unorthogonal_lines(L,M) )
      | ( convergent_lines(L,N)
        & unorthogonal_lines(L,N) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [L,M,N] :
      ( ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N)
        | convergent_lines(L,M)
        | convergent_lines(L,N) )
      & ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N)
        | convergent_lines(L,M)
        | unorthogonal_lines(L,N) )
      & ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N)
        | convergent_lines(L,N)
        | unorthogonal_lines(L,M) )
      & ( ~ convergent_lines(M,N)
        | ~ unorthogonal_lines(M,N)
        | unorthogonal_lines(L,M)
        | unorthogonal_lines(L,N) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(M,N)
      | ~ unorthogonal_lines(M,N)
      | convergent_lines(L,N)
      | unorthogonal_lines(L,M) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(canonicalize,[],[apart3]) ).

fof(normalize_0_9,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(canonicalize,[],[ax6]) ).

fof(normalize_0_11,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_13,plain,
    ! [L,M] :
      ( convergent_lines(L,M)
      | unorthogonal_lines(L,M) ),
    inference(canonicalize,[],[coipo1]) ).

fof(normalize_0_14,plain,
    ! [L,M] :
      ( convergent_lines(L,M)
      | unorthogonal_lines(L,M) ),
    inference(specialize,[],[normalize_0_13]) ).

cnf(refute_0_0,plain,
    ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ( ~ convergent_lines(M,N)
    | ~ unorthogonal_lines(M,N)
    | convergent_lines(L,N)
    | unorthogonal_lines(L,M) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | ~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | convergent_lines(X_107,skolemFOFtoCNF_N)
    | unorthogonal_lines(X_107,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_2:[bind(L,$fot(X_107)),bind(M,$fot(skolemFOFtoCNF_M)),bind(N,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_4,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | convergent_lines(X_107,skolemFOFtoCNF_N)
    | unorthogonal_lines(X_107,skolemFOFtoCNF_M) ),
    inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_1,refute_0_3]) ).

cnf(refute_0_5,plain,
    ~ convergent_lines(X,X),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_6,plain,
    ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_7,plain,
    ( ~ convergent_lines(X,Y)
    | convergent_lines(X,Z)
    | convergent_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_8,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_M,Z)
    | convergent_lines(skolemFOFtoCNF_N,Z) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_9,plain,
    ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_10,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,X_25)
    | convergent_lines(X_25,Z)
    | convergent_lines(skolemFOFtoCNF_L,Z) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(X_25))]]) ).

cnf(refute_0_11,plain,
    ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_12,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_M,X_22)
    | convergent_lines(X_22,Z)
    | convergent_lines(skolemFOFtoCNF_M,Z) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(X_22))]]) ).

cnf(refute_0_13,plain,
    ( convergent_lines(L,M)
    | unorthogonal_lines(L,M) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_14,plain,
    ( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_13:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_15,plain,
    convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_0]) ).

cnf(refute_0_16,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,X_21)
    | convergent_lines(skolemFOFtoCNF_M,X_21) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M)),bind(Z,$fot(X_21))]]) ).

cnf(refute_0_17,plain,
    ( convergent_lines(skolemFOFtoCNF_L,X_21)
    | convergent_lines(skolemFOFtoCNF_M,X_21) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( convergent_lines(skolemFOFtoCNF_L,X_22)
    | convergent_lines(skolemFOFtoCNF_M,X_22) ),
    inference(subst,[],[refute_0_17:[bind(X_21,$fot(X_22))]]) ).

cnf(refute_0_19,plain,
    ( convergent_lines(X_22,Z)
    | convergent_lines(skolemFOFtoCNF_L,X_22)
    | convergent_lines(skolemFOFtoCNF_M,Z) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,X_22) )],[refute_0_18,refute_0_12]) ).

cnf(refute_0_20,plain,
    ( convergent_lines(X_24,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,X_24)
    | convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_19:[bind(Z,$fot(skolemFOFtoCNF_M)),bind(X_22,$fot(X_24))]]) ).

cnf(refute_0_21,plain,
    ( convergent_lines(X_24,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,X_24) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_20,refute_0_11]) ).

cnf(refute_0_22,plain,
    ( convergent_lines(X_25,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,X_25) ),
    inference(subst,[],[refute_0_21:[bind(X_24,$fot(X_25))]]) ).

cnf(refute_0_23,plain,
    ( convergent_lines(X_25,Z)
    | convergent_lines(X_25,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,Z) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,X_25) )],[refute_0_22,refute_0_10]) ).

cnf(refute_0_24,plain,
    ( convergent_lines(X_67,skolemFOFtoCNF_M)
    | convergent_lines(X_67,skolemFOFtoCNF_N)
    | convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_N)),bind(X_25,$fot(X_67))]]) ).

cnf(refute_0_25,plain,
    ( convergent_lines(X_67,skolemFOFtoCNF_M)
    | convergent_lines(X_67,skolemFOFtoCNF_N) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_24,refute_0_9]) ).

cnf(refute_0_26,plain,
    ( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_25:[bind(X_67,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_27,plain,
    convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_26,refute_0_6]) ).

cnf(refute_0_28,plain,
    ( convergent_lines(skolemFOFtoCNF_M,Z)
    | convergent_lines(skolemFOFtoCNF_N,Z) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_M) )],[refute_0_27,refute_0_8]) ).

cnf(refute_0_29,plain,
    ( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_28:[bind(Z,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_30,plain,
    convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_29,refute_0_6]) ).

cnf(refute_0_31,plain,
    ( convergent_lines(X_107,skolemFOFtoCNF_N)
    | unorthogonal_lines(X_107,skolemFOFtoCNF_M) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_30,refute_0_4]) ).

cnf(refute_0_32,plain,
    ( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
    | unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_31:[bind(X_107,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_33,plain,
    convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_32,refute_0_0]) ).

cnf(refute_0_34,plain,
    $false,
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_33,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO219+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n005.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 13:31:53 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.41  
% 0.20/0.41  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.42  
%------------------------------------------------------------------------------