TSTP Solution File: GEO269+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO269+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 05:26:03 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   79 (  19 unt;   0 def)
%            Number of atoms       :  154 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  141 (  66   ~;  60   |;   5   &)
%                                         (   9 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :  132 (   4 sgn  64   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
    ! [X,Y] :
      ( unequally_directed_opposite_lines(X,Y)
    <=> unequally_directed_lines(X,reverse_line(Y)) ) ).

fof(a4_defns,axiom,
    ! [X,Y] :
      ( equally_directed_lines(X,Y)
    <=> ~ unequally_directed_lines(X,Y) ) ).

fof(a5_defns,axiom,
    ! [X,Y] :
      ( equally_directed_opposite_lines(X,Y)
    <=> ~ unequally_directed_opposite_lines(X,Y) ) ).

fof(ax5_basics,axiom,
    ! [L] : equally_directed_lines(L,L) ).

fof(ax8_basics,axiom,
    ! [L,M] :
      ( unequally_directed_lines(L,M)
      | unequally_directed_lines(L,reverse_line(M)) ) ).

fof(ax9_basics,axiom,
    ! [L,M] :
      ( ( unequally_directed_lines(L,M)
        & unequally_directed_lines(L,reverse_line(M)) )
     => ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ) ).

fof(ax11_basics,axiom,
    ! [L,M] :
      ~ ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ).

fof(con,conjecture,
    ! [L] : equally_directed_opposite_lines(L,reverse_line(L)) ).

fof(subgoal_0,plain,
    ! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [L] : equally_directed_opposite_lines(L,reverse_line(L)),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X,Y] :
      ( ~ equally_directed_lines(X,Y)
    <=> unequally_directed_lines(X,Y) ),
    inference(canonicalize,[],[a4_defns]) ).

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

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

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

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ equally_directed_opposite_lines(X,Y)
    <=> unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[a5_defns]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ~ equally_directed_opposite_lines(X,Y)
    <=> unequally_directed_opposite_lines(X,Y) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y] :
      ( ( ~ equally_directed_opposite_lines(X,Y)
        | ~ unequally_directed_opposite_lines(X,Y) )
      & ( equally_directed_opposite_lines(X,Y)
        | unequally_directed_opposite_lines(X,Y) ) ),
    inference(clausify,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ equally_directed_opposite_lines(X,Y)
      | ~ unequally_directed_opposite_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( equally_directed_lines(X,Y)
      | unequally_directed_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_9,plain,
    ! [X,Y] :
      ( ~ unequally_directed_lines(X,reverse_line(Y))
    <=> ~ unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[a1_defns]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ~ unequally_directed_lines(X,reverse_line(Y))
    <=> ~ unequally_directed_opposite_lines(X,Y) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y] :
      ( ( ~ unequally_directed_lines(X,reverse_line(Y))
        | unequally_directed_opposite_lines(X,Y) )
      & ( ~ unequally_directed_opposite_lines(X,Y)
        | unequally_directed_lines(X,reverse_line(Y)) ) ),
    inference(clausify,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ unequally_directed_lines(X,reverse_line(Y))
      | unequally_directed_opposite_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [L,M] :
      ( unequally_directed_lines(L,M)
      | unequally_directed_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[ax8_basics]) ).

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

fof(normalize_0_15,plain,
    ? [L] : ~ equally_directed_opposite_lines(L,reverse_line(L)),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_16,plain,
    ~ equally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_L)),
    inference(skolemize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [X,Y] :
      ( equally_directed_opposite_lines(X,Y)
      | unequally_directed_opposite_lines(X,Y) ),
    inference(conjunct,[],[normalize_0_6]) ).

fof(normalize_0_18,plain,
    ! [X,Y] :
      ( ~ unequally_directed_opposite_lines(X,Y)
      | unequally_directed_lines(X,reverse_line(Y)) ),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_19,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ~ unequally_directed_lines(L,reverse_line(M))
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[ax9_basics]) ).

fof(normalize_0_20,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ~ unequally_directed_lines(L,reverse_line(M))
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ( ! [L,M] : ~ left_convergent_lines(L,M)
    & ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[ax11_basics]) ).

fof(normalize_0_22,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(conjunct,[],[normalize_0_21]) ).

fof(normalize_0_23,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(specialize,[],[normalize_0_22]) ).

fof(normalize_0_24,plain,
    ! [L] : equally_directed_lines(L,L),
    inference(canonicalize,[],[ax5_basics]) ).

fof(normalize_0_25,plain,
    ! [L] : equally_directed_lines(L,L),
    inference(specialize,[],[normalize_0_24]) ).

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

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

cnf(refute_0_2,plain,
    ( ~ equally_directed_opposite_lines(X,Y)
    | ~ unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_3,plain,
    ( ~ equally_directed_opposite_lines(X_54,X_55)
    | ~ unequally_directed_opposite_lines(X_54,X_55) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(X_54)),bind(Y,$fot(X_55))]]) ).

cnf(refute_0_4,plain,
    ( equally_directed_lines(X,Y)
    | unequally_directed_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( equally_directed_lines(X_32,reverse_line(X_33))
    | unequally_directed_lines(X_32,reverse_line(X_33)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_32)),bind(Y,$fot(reverse_line(X_33)))]]) ).

cnf(refute_0_6,plain,
    ( ~ unequally_directed_lines(X,reverse_line(Y))
    | unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_7,plain,
    ( ~ unequally_directed_lines(X_32,reverse_line(X_33))
    | unequally_directed_opposite_lines(X_32,X_33) ),
    inference(subst,[],[refute_0_6:[bind(X,$fot(X_32)),bind(Y,$fot(X_33))]]) ).

cnf(refute_0_8,plain,
    ( equally_directed_lines(X_32,reverse_line(X_33))
    | unequally_directed_opposite_lines(X_32,X_33) ),
    inference(resolve,[$cnf( unequally_directed_lines(X_32,reverse_line(X_33)) )],[refute_0_5,refute_0_7]) ).

cnf(refute_0_9,plain,
    ( equally_directed_lines(X_40,reverse_line(X_41))
    | unequally_directed_opposite_lines(X_40,X_41) ),
    inference(subst,[],[refute_0_8:[bind(X_32,$fot(X_40)),bind(X_33,$fot(X_41))]]) ).

cnf(refute_0_10,plain,
    ( ~ equally_directed_lines(X_38,reverse_line(X_39))
    | ~ unequally_directed_lines(X_38,reverse_line(X_39)) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(X_38)),bind(Y,$fot(reverse_line(X_39)))]]) ).

cnf(refute_0_11,plain,
    ( unequally_directed_lines(L,M)
    | unequally_directed_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_12,plain,
    ( unequally_directed_lines(X_38,X_39)
    | unequally_directed_lines(X_38,reverse_line(X_39)) ),
    inference(subst,[],[refute_0_11:[bind(L,$fot(X_38)),bind(M,$fot(X_39))]]) ).

cnf(refute_0_13,plain,
    ( ~ equally_directed_lines(X_38,reverse_line(X_39))
    | unequally_directed_lines(X_38,X_39) ),
    inference(resolve,[$cnf( unequally_directed_lines(X_38,reverse_line(X_39)) )],[refute_0_12,refute_0_10]) ).

cnf(refute_0_14,plain,
    ( ~ equally_directed_lines(X_40,reverse_line(X_41))
    | unequally_directed_lines(X_40,X_41) ),
    inference(subst,[],[refute_0_13:[bind(X_38,$fot(X_40)),bind(X_39,$fot(X_41))]]) ).

cnf(refute_0_15,plain,
    ( unequally_directed_lines(X_40,X_41)
    | unequally_directed_opposite_lines(X_40,X_41) ),
    inference(resolve,[$cnf( equally_directed_lines(X_40,reverse_line(X_41)) )],[refute_0_9,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( unequally_directed_lines(X_54,X_55)
    | unequally_directed_opposite_lines(X_54,X_55) ),
    inference(subst,[],[refute_0_15:[bind(X_40,$fot(X_54)),bind(X_41,$fot(X_55))]]) ).

cnf(refute_0_17,plain,
    ( ~ equally_directed_opposite_lines(X_54,X_55)
    | unequally_directed_lines(X_54,X_55) ),
    inference(resolve,[$cnf( unequally_directed_opposite_lines(X_54,X_55) )],[refute_0_16,refute_0_3]) ).

cnf(refute_0_18,plain,
    ( ~ equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
    | unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
    inference(subst,[],[refute_0_17:[bind(X_54,$fot(skolemFOFtoCNF_L)),bind(X_55,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_19,plain,
    ~ equally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_L)),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_20,plain,
    ( equally_directed_opposite_lines(X,Y)
    | unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_21,plain,
    ( equally_directed_opposite_lines(X_36,X_37)
    | unequally_directed_opposite_lines(X_36,X_37) ),
    inference(subst,[],[refute_0_20:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).

cnf(refute_0_22,plain,
    ( ~ unequally_directed_opposite_lines(X,Y)
    | unequally_directed_lines(X,reverse_line(Y)) ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_23,plain,
    ( ~ unequally_directed_opposite_lines(X_36,X_37)
    | unequally_directed_lines(X_36,reverse_line(X_37)) ),
    inference(subst,[],[refute_0_22:[bind(X,$fot(X_36)),bind(Y,$fot(X_37))]]) ).

cnf(refute_0_24,plain,
    ( equally_directed_opposite_lines(X_36,X_37)
    | unequally_directed_lines(X_36,reverse_line(X_37)) ),
    inference(resolve,[$cnf( unequally_directed_opposite_lines(X_36,X_37) )],[refute_0_21,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( equally_directed_opposite_lines(X_138,X_37)
    | unequally_directed_lines(X_138,reverse_line(X_37)) ),
    inference(subst,[],[refute_0_24:[bind(X_36,$fot(X_138))]]) ).

cnf(refute_0_26,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M))
    | left_convergent_lines(L,M)
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_27,plain,
    ~ left_convergent_lines(L,M),
    inference(canonicalize,[],[normalize_0_23]) ).

cnf(refute_0_28,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M))
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_26,refute_0_27]) ).

cnf(refute_0_29,plain,
    ~ left_convergent_lines(L,reverse_line(M)),
    inference(subst,[],[refute_0_27:[bind(M,$fot(reverse_line(M)))]]) ).

cnf(refute_0_30,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M)) ),
    inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( ~ unequally_directed_lines(X_91,X_92)
    | ~ unequally_directed_lines(X_91,reverse_line(X_92)) ),
    inference(subst,[],[refute_0_30:[bind(L,$fot(X_91)),bind(M,$fot(X_92))]]) ).

cnf(refute_0_32,plain,
    ( equally_directed_opposite_lines(X_91,X_92)
    | unequally_directed_lines(X_91,reverse_line(X_92)) ),
    inference(subst,[],[refute_0_24:[bind(X_36,$fot(X_91)),bind(X_37,$fot(X_92))]]) ).

cnf(refute_0_33,plain,
    ( ~ unequally_directed_lines(X_91,X_92)
    | equally_directed_opposite_lines(X_91,X_92) ),
    inference(resolve,[$cnf( unequally_directed_lines(X_91,reverse_line(X_92)) )],[refute_0_32,refute_0_31]) ).

cnf(refute_0_34,plain,
    ( ~ unequally_directed_lines(X_138,reverse_line(X_37))
    | equally_directed_opposite_lines(X_138,reverse_line(X_37)) ),
    inference(subst,[],[refute_0_33:[bind(X_91,$fot(X_138)),bind(X_92,$fot(reverse_line(X_37)))]]) ).

cnf(refute_0_35,plain,
    ( equally_directed_opposite_lines(X_138,X_37)
    | equally_directed_opposite_lines(X_138,reverse_line(X_37)) ),
    inference(resolve,[$cnf( unequally_directed_lines(X_138,reverse_line(X_37)) )],[refute_0_25,refute_0_34]) ).

cnf(refute_0_36,plain,
    ( equally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_L))
    | equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
    inference(subst,[],[refute_0_35:[bind(X_138,$fot(skolemFOFtoCNF_L)),bind(X_37,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_37,plain,
    equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
    inference(resolve,[$cnf( equally_directed_opposite_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_L)) )],[refute_0_36,refute_0_19]) ).

cnf(refute_0_38,plain,
    unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
    inference(resolve,[$cnf( equally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_37,refute_0_18]) ).

cnf(refute_0_39,plain,
    ~ equally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
    inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_38,refute_0_1]) ).

cnf(refute_0_40,plain,
    equally_directed_lines(L,L),
    inference(canonicalize,[],[normalize_0_25]) ).

cnf(refute_0_41,plain,
    equally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
    inference(subst,[],[refute_0_40:[bind(L,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_42,plain,
    $false,
    inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_41,refute_0_39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : GEO269+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Fri Jun 17 20:29:28 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 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  
%------------------------------------------------------------------------------