TSTP Solution File: GEO220+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n016.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 05:25:33 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   39 (  10 unt;   0 def)
%            Number of atoms       :   82 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   76 (  33   ~;  23   |;  10   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   53 (   0 sgn  38   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(couo1,axiom,
    ! [L,M,N] :
      ( ( ~ unorthogonal_lines(L,M)
        & ~ unorthogonal_lines(L,N) )
     => ~ convergent_lines(M,N) ) ).

fof(a3,axiom,
    ! [X,Y] :
      ( parallel_lines(X,Y)
    <=> ~ convergent_lines(X,Y) ) ).

fof(a5,axiom,
    ! [X,Y] :
      ( orthogonal_lines(X,Y)
    <=> ~ unorthogonal_lines(X,Y) ) ).

fof(con,conjecture,
    ! [L,M,N] :
      ( ( orthogonal_lines(L,M)
        & orthogonal_lines(L,N) )
     => parallel_lines(M,N) ) ).

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

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

fof(normalize_0_0,plain,
    ! [X,Y] :
      ( ~ orthogonal_lines(X,Y)
    <=> unorthogonal_lines(X,Y) ),
    inference(canonicalize,[],[a5]) ).

fof(normalize_0_1,plain,
    ! [X,Y] :
      ( ~ orthogonal_lines(X,Y)
    <=> unorthogonal_lines(X,Y) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ( ~ orthogonal_lines(X,Y)
        | ~ unorthogonal_lines(X,Y) )
      & ( orthogonal_lines(X,Y)
        | unorthogonal_lines(X,Y) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( ~ orthogonal_lines(X,Y)
      | ~ unorthogonal_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [L,M,N] :
      ( ~ parallel_lines(M,N)
      & orthogonal_lines(L,M)
      & orthogonal_lines(L,N) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    & orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    & orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
    <=> parallel_lines(X,Y) ),
    inference(canonicalize,[],[a3]) ).

fof(normalize_0_9,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
    <=> parallel_lines(X,Y) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ( ~ convergent_lines(X,Y)
        | ~ parallel_lines(X,Y) )
      & ( convergent_lines(X,Y)
        | parallel_lines(X,Y) ) ),
    inference(clausify,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y] :
      ( convergent_lines(X,Y)
      | parallel_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(M,N)
      | unorthogonal_lines(L,M)
      | unorthogonal_lines(L,N) ),
    inference(canonicalize,[],[couo1]) ).

fof(normalize_0_13,plain,
    ! [L,M,N] :
      ( ~ convergent_lines(M,N)
      | unorthogonal_lines(L,M)
      | unorthogonal_lines(L,N) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ orthogonal_lines(X,Y)
    | ~ unorthogonal_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_2,plain,
    orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ orthogonal_lines(X_113,skolemFOFtoCNF_N)
    | ~ unorthogonal_lines(X_113,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(X_113)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_4,plain,
    ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_5,plain,
    ( convergent_lines(X,Y)
    | parallel_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_6,plain,
    ( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_7,plain,
    convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_6,refute_0_4]) ).

cnf(refute_0_8,plain,
    ( ~ convergent_lines(M,N)
    | unorthogonal_lines(L,M)
    | unorthogonal_lines(L,N) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_9,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | unorthogonal_lines(X_104,skolemFOFtoCNF_M)
    | unorthogonal_lines(X_104,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_8:[bind(L,$fot(X_104)),bind(M,$fot(skolemFOFtoCNF_M)),bind(N,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_10,plain,
    ( unorthogonal_lines(X_104,skolemFOFtoCNF_M)
    | unorthogonal_lines(X_104,skolemFOFtoCNF_N) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( unorthogonal_lines(X_113,skolemFOFtoCNF_M)
    | unorthogonal_lines(X_113,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_10:[bind(X_104,$fot(X_113))]]) ).

cnf(refute_0_12,plain,
    ( ~ orthogonal_lines(X_113,skolemFOFtoCNF_N)
    | unorthogonal_lines(X_113,skolemFOFtoCNF_M) ),
    inference(resolve,[$cnf( unorthogonal_lines(X_113,skolemFOFtoCNF_N) )],[refute_0_11,refute_0_3]) ).

cnf(refute_0_13,plain,
    ( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
    | unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_12:[bind(X_113,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_14,plain,
    unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_2,refute_0_13]) ).

cnf(refute_0_15,plain,
    ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_1]) ).

cnf(refute_0_16,plain,
    orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_16,refute_0_15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n016.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 : Fri Jun 17 20:18:51 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.39  
% 0.20/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39  
%------------------------------------------------------------------------------