TSTP Solution File: GEO217+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO217+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 05:25:31 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   74 (  21 unt;   0 def)
%            Number of atoms       :  155 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  127 (  46   ~;  64   |;   8   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :  104 (   0 sgn  51   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(apart2,axiom,
    ! [X] : ~ distinct_lines(X,X) ).

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

fof(apart5,axiom,
    ! [X,Y,Z] :
      ( distinct_lines(X,Y)
     => ( distinct_lines(X,Z)
        | distinct_lines(Y,Z) ) ) ).

fof(ceq3,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( distinct_lines(Y,Z)
        | convergent_lines(X,Z) ) ) ).

fof(p1,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,Y) ) ).

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

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

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

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

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

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

fof(normalize_0_2,plain,
    parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
    <=> parallel_lines(X,Y) ),
    inference(canonicalize,[],[a3]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
    <=> parallel_lines(X,Y) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ( ~ convergent_lines(X,Y)
        | ~ parallel_lines(X,Y) )
      & ( convergent_lines(X,Y)
        | parallel_lines(X,Y) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | ~ parallel_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(canonicalize,[],[p1]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] : ~ distinct_lines(X,X),
    inference(canonicalize,[],[apart2]) ).

fof(normalize_0_10,plain,
    ! [X] : ~ distinct_lines(X,X),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(X,Y)
      | distinct_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[apart5]) ).

fof(normalize_0_12,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(X,Y)
      | distinct_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[ceq3]) ).

fof(normalize_0_14,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_16,plain,
    ! [X,Y] :
      ( convergent_lines(X,Y)
      | parallel_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_17,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(canonicalize,[],[apart3]) ).

fof(normalize_0_18,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(conjunct,[],[normalize_0_1]) ).

cnf(refute_0_0,plain,
    parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ convergent_lines(X,Y)
    | ~ parallel_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
    | ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_3,plain,
    ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
    inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ distinct_lines(X,Y)
    | convergent_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ distinct_lines(X_213,skolemFOFtoCNF_M)
    | convergent_lines(X_213,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_213)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_6,plain,
    ( ~ distinct_lines(X_212,skolemFOFtoCNF_N)
    | convergent_lines(X_212,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_212)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_7,plain,
    ~ distinct_lines(X,X),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_8,plain,
    ~ distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_9,plain,
    ( ~ distinct_lines(X,Y)
    | distinct_lines(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_10,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_N,X_187)
    | distinct_lines(X_187,Z)
    | distinct_lines(skolemFOFtoCNF_N,Z) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_187))]]) ).

cnf(refute_0_11,plain,
    ( ~ convergent_lines(X,Y)
    | convergent_lines(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_12,plain,
    ( ~ convergent_lines(X_186,X_185)
    | convergent_lines(X_186,Z)
    | distinct_lines(X_185,Z) ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(X_186)),bind(Y,$fot(X_185))]]) ).

cnf(refute_0_13,plain,
    ( ~ distinct_lines(X_144,X_143)
    | convergent_lines(X_144,X_143) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_144)),bind(Y,$fot(X_143))]]) ).

cnf(refute_0_14,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_N,X_77)
    | distinct_lines(X_77,Z)
    | distinct_lines(skolemFOFtoCNF_N,Z) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_N)),bind(Y,$fot(X_77))]]) ).

cnf(refute_0_15,plain,
    ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_16,plain,
    ( convergent_lines(X,Y)
    | parallel_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_17,plain,
    ( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).

cnf(refute_0_18,plain,
    convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
    inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_17,refute_0_15]) ).

cnf(refute_0_19,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
    | convergent_lines(skolemFOFtoCNF_M,X_76)
    | distinct_lines(skolemFOFtoCNF_N,X_76) ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N)),bind(Z,$fot(X_76))]]) ).

cnf(refute_0_20,plain,
    ( convergent_lines(skolemFOFtoCNF_M,X_76)
    | distinct_lines(skolemFOFtoCNF_N,X_76) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( convergent_lines(skolemFOFtoCNF_M,X_77)
    | distinct_lines(skolemFOFtoCNF_N,X_77) ),
    inference(subst,[],[refute_0_20:[bind(X_76,$fot(X_77))]]) ).

cnf(refute_0_22,plain,
    ( convergent_lines(skolemFOFtoCNF_M,X_77)
    | distinct_lines(X_77,Z)
    | distinct_lines(skolemFOFtoCNF_N,Z) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_77) )],[refute_0_21,refute_0_14]) ).

cnf(refute_0_23,plain,
    ( convergent_lines(skolemFOFtoCNF_M,X_144)
    | distinct_lines(X_144,X_143)
    | distinct_lines(skolemFOFtoCNF_N,X_143) ),
    inference(subst,[],[refute_0_22:[bind(Z,$fot(X_143)),bind(X_77,$fot(X_144))]]) ).

cnf(refute_0_24,plain,
    ( convergent_lines(X_144,X_143)
    | convergent_lines(skolemFOFtoCNF_M,X_144)
    | distinct_lines(skolemFOFtoCNF_N,X_143) ),
    inference(resolve,[$cnf( distinct_lines(X_144,X_143) )],[refute_0_23,refute_0_13]) ).

cnf(refute_0_25,plain,
    ( convergent_lines(X_186,X_185)
    | convergent_lines(skolemFOFtoCNF_M,X_186)
    | distinct_lines(skolemFOFtoCNF_N,X_185) ),
    inference(subst,[],[refute_0_24:[bind(X_143,$fot(X_185)),bind(X_144,$fot(X_186))]]) ).

cnf(refute_0_26,plain,
    ( convergent_lines(X_186,Z)
    | convergent_lines(skolemFOFtoCNF_M,X_186)
    | distinct_lines(X_185,Z)
    | distinct_lines(skolemFOFtoCNF_N,X_185) ),
    inference(resolve,[$cnf( convergent_lines(X_186,X_185) )],[refute_0_25,refute_0_12]) ).

cnf(refute_0_27,plain,
    ( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M)
    | distinct_lines(X_185,skolemFOFtoCNF_M)
    | distinct_lines(skolemFOFtoCNF_N,X_185) ),
    inference(subst,[],[refute_0_26:[bind(Z,$fot(skolemFOFtoCNF_M)),bind(X_186,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_28,plain,
    ~ convergent_lines(X,X),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_29,plain,
    ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
    inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_30,plain,
    ( distinct_lines(X_185,skolemFOFtoCNF_M)
    | distinct_lines(skolemFOFtoCNF_N,X_185) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_27,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( distinct_lines(X_187,skolemFOFtoCNF_M)
    | distinct_lines(skolemFOFtoCNF_N,X_187) ),
    inference(subst,[],[refute_0_30:[bind(X_185,$fot(X_187))]]) ).

cnf(refute_0_32,plain,
    ( distinct_lines(X_187,Z)
    | distinct_lines(X_187,skolemFOFtoCNF_M)
    | distinct_lines(skolemFOFtoCNF_N,Z) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,X_187) )],[refute_0_31,refute_0_10]) ).

cnf(refute_0_33,plain,
    ( distinct_lines(X_211,skolemFOFtoCNF_M)
    | distinct_lines(X_211,skolemFOFtoCNF_N)
    | distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_32:[bind(Z,$fot(skolemFOFtoCNF_N)),bind(X_187,$fot(X_211))]]) ).

cnf(refute_0_34,plain,
    ( distinct_lines(X_211,skolemFOFtoCNF_M)
    | distinct_lines(X_211,skolemFOFtoCNF_N) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_N) )],[refute_0_33,refute_0_8]) ).

cnf(refute_0_35,plain,
    ( distinct_lines(X_212,skolemFOFtoCNF_M)
    | distinct_lines(X_212,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_34:[bind(X_211,$fot(X_212))]]) ).

cnf(refute_0_36,plain,
    ( convergent_lines(X_212,skolemFOFtoCNF_N)
    | distinct_lines(X_212,skolemFOFtoCNF_M) ),
    inference(resolve,[$cnf( distinct_lines(X_212,skolemFOFtoCNF_N) )],[refute_0_35,refute_0_6]) ).

cnf(refute_0_37,plain,
    ( convergent_lines(X_213,skolemFOFtoCNF_N)
    | distinct_lines(X_213,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_36:[bind(X_212,$fot(X_213))]]) ).

cnf(refute_0_38,plain,
    ( convergent_lines(X_213,skolemFOFtoCNF_M)
    | convergent_lines(X_213,skolemFOFtoCNF_N) ),
    inference(resolve,[$cnf( distinct_lines(X_213,skolemFOFtoCNF_M) )],[refute_0_37,refute_0_5]) ).

cnf(refute_0_39,plain,
    ( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
    inference(subst,[],[refute_0_38:[bind(X_213,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_40,plain,
    convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_39,refute_0_3]) ).

cnf(refute_0_41,plain,
    parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_42,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | ~ parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_43,plain,
    ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_41,refute_0_42]) ).

cnf(refute_0_44,plain,
    $false,
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_40,refute_0_43]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO217+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : metis --show proof --show saturation %s
% 0.12/0.34  % Computer : n029.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 08:50:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.43  
% 0.19/0.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.43  
%------------------------------------------------------------------------------