TSTP Solution File: GEO498+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n028.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 05:26:54 EDT 2022

% Result   : Theorem 0.18s 0.51s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   27 (  16 unt;   0 def)
%            Number of atoms       :   46 (  45 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   43 (  24   ~;  11   |;   6   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  18   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(aSatz7_7,axiom,
    ! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp ).

fof(aSatz7_8,conjecture,
    ! [Xa,Xp,Xr,Xq] :
      ( s(Xa,Xp) != Xr
      | s(Xa,Xq) != Xr
      | Xp = Xq ) ).

fof(subgoal_0,plain,
    ! [Xa,Xp,Xr,Xq] :
      ( ( ~ ( s(Xa,Xp) != Xr )
        & ~ ( s(Xa,Xq) != Xr ) )
     => Xp = Xq ),
    inference(strip,[],[aSatz7_8]) ).

fof(negate_0_0,plain,
    ~ ! [Xa,Xp,Xr,Xq] :
        ( ( ~ ( s(Xa,Xp) != Xr )
          & ~ ( s(Xa,Xq) != Xr ) )
       => Xp = Xq ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
    inference(canonicalize,[],[aSatz7_7]) ).

fof(normalize_0_1,plain,
    ! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [Xa,Xp,Xq,Xr] :
      ( Xp != Xq
      & s(Xa,Xp) = Xr
      & s(Xa,Xq) = Xr ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_3,plain,
    ( skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq
    & s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr
    & s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr ),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr,
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr,
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_6,plain,
    skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    s(Xa,s(Xa,Xp)) = Xp,
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) = skolemFOFtoCNF_Xq,
    inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xq))]]) ).

cnf(refute_0_2,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) = skolemFOFtoCNF_Xr,
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq) != skolemFOFtoCNF_Xr
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq ),
    introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) ),[0,1],$fot(skolemFOFtoCNF_Xr)]]) ).

cnf(refute_0_4,plain,
    ( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)) != skolemFOFtoCNF_Xq
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq ),
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq),skolemFOFtoCNF_Xr) )],[refute_0_2,refute_0_3]) ).

cnf(refute_0_5,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xq,
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xq)),skolemFOFtoCNF_Xq) )],[refute_0_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) = skolemFOFtoCNF_Xp,
    inference(subst,[],[refute_0_0:[bind(Xa,$fot(skolemFOFtoCNF_Xa)),bind(Xp,$fot(skolemFOFtoCNF_Xp))]]) ).

cnf(refute_0_7,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) = skolemFOFtoCNF_Xr,
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_8,plain,
    ( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp) != skolemFOFtoCNF_Xr
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp ),
    introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) ),[0,1],$fot(skolemFOFtoCNF_Xr)]]) ).

cnf(refute_0_9,plain,
    ( s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)) != skolemFOFtoCNF_Xp
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp ),
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp),skolemFOFtoCNF_Xr) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) = skolemFOFtoCNF_Xp,
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xp)),skolemFOFtoCNF_Xp) )],[refute_0_6,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xp
    | s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xq
    | skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq ),
    introduced(tautology,[equality,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xq) ),[0],$fot(skolemFOFtoCNF_Xp)]]) ).

cnf(refute_0_12,plain,
    ( s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr) != skolemFOFtoCNF_Xq
    | skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq ),
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xp) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    skolemFOFtoCNF_Xp = skolemFOFtoCNF_Xq,
    inference(resolve,[$cnf( $equal(s(skolemFOFtoCNF_Xa,skolemFOFtoCNF_Xr),skolemFOFtoCNF_Xq) )],[refute_0_5,refute_0_12]) ).

cnf(refute_0_14,plain,
    skolemFOFtoCNF_Xp != skolemFOFtoCNF_Xq,
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_15,plain,
    $false,
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Xp,skolemFOFtoCNF_Xq) )],[refute_0_13,refute_0_14]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO498+1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 13:20:14 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.51  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.51  
% 0.18/0.51  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.52  
%------------------------------------------------------------------------------