TSTP Solution File: GEO500+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n003.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  : 300s
% DateTime : Tue Apr 30 20:18:09 EDT 2024

% Result   : Theorem 151.60s 19.44s
% Output   : CNFRefutation 152.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   56 (  22 unt;   0 def)
%            Number of atoms       :  107 (  55 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  103 (  52   ~;  44   |;   7   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-4 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  138 ( 132   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f96,axiom,
    ! [Xp,Xa] : s_m(Xp,Xa,s(Xa,Xp)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f99,axiom,
    ! [Xa,Xp] : s(Xa,s(Xa,Xp)) = Xp,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f100,axiom,
    ! [Xa,Xp,Xr,Xq] :
      ( s(Xa,Xp) != Xr
      | s(Xa,Xq) != Xr
      | Xp = Xq ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f102,axiom,
    ! [Xa,Xp] :
      ( s(Xa,Xp) != Xp
      | Xp = Xa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f103,axiom,
    ! [Xa,Xp] :
      ( s(Xa,Xp) = Xp
      | Xp != Xa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f104,axiom,
    ! [Xp,Xq,Xa] : s_e(Xp,Xq,s(Xa,Xp),s(Xa,Xq)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f105,axiom,
    ! [Xp,Xq,Xr,Xa] :
      ( ~ s_t(Xp,Xq,Xr)
      | s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f107,axiom,
    ! [Xp,Xq,Xr,Xcs,Xa] :
      ( ~ s_e(Xp,Xq,Xr,Xcs)
      | s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f109,axiom,
    ! [Xp,Xa,Xq,Xb] :
      ( ~ s_m(Xp,Xa,Xq)
      | ~ s_m(Xp,Xb,Xq)
      | Xa = Xb ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f110,axiom,
    ! [Xa,Xp,Xb] :
      ( s(Xa,Xp) != s(Xb,Xp)
      | Xa = Xb ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f111,conjecture,
    ! [Xa,Xb,Xp] :
      ( s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp))
      | Xa = Xb ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f112,negated_conjecture,
    ~ ! [Xa,Xb,Xp] :
        ( s(Xa,s(Xb,Xp)) != s(Xb,s(Xa,Xp))
        | Xa = Xb ),
    inference(negated_conjecture,[status(cth)],[f111]) ).

fof(f121,axiom,
    ! [Xa,Xm,Xb] :
      ( ( ~ s_m(Xa,Xm,Xb)
        | s_t(Xa,Xm,Xb) )
      & ( ~ s_m(Xa,Xm,Xb)
        | s_e(Xm,Xa,Xm,Xb) )
      & ( ~ s_t(Xa,Xm,Xb)
        | ~ s_e(Xm,Xa,Xm,Xb)
        | s_m(Xa,Xm,Xb) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f283,plain,
    ! [X0,X1] : s_m(X0,X1,s(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f96]) ).

fof(f287,plain,
    ! [X0,X1] : s(X0,s(X0,X1)) = X1,
    inference(cnf_transformation,[status(esa)],[f99]) ).

fof(f288,plain,
    ! [Xp,Xq] :
      ( ! [Xa,Xr] :
          ( s(Xa,Xp) != Xr
          | s(Xa,Xq) != Xr )
      | Xp = Xq ),
    inference(miniscoping,[status(esa)],[f100]) ).

fof(f289,plain,
    ! [X0,X1,X2,X3] :
      ( s(X0,X1) != X2
      | s(X0,X3) != X2
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f288]) ).

fof(f292,plain,
    ! [X0,X1] :
      ( s(X0,X1) != X1
      | X1 = X0 ),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f293,plain,
    ! [X0,X1] :
      ( s(X0,X1) = X1
      | X1 != X0 ),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f294,plain,
    ! [X0,X1,X2] : s_e(X0,X1,s(X2,X0),s(X2,X1)),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f295,plain,
    ! [Xp,Xq,Xr] :
      ( ~ s_t(Xp,Xq,Xr)
      | ! [Xa] : s_t(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr)) ),
    inference(miniscoping,[status(esa)],[f105]) ).

fof(f296,plain,
    ! [X0,X1,X2,X3] :
      ( ~ s_t(X0,X1,X2)
      | s_t(s(X3,X0),s(X3,X1),s(X3,X2)) ),
    inference(cnf_transformation,[status(esa)],[f295]) ).

fof(f299,plain,
    ! [Xp,Xq,Xr,Xcs] :
      ( ~ s_e(Xp,Xq,Xr,Xcs)
      | ! [Xa] : s_e(s(Xa,Xp),s(Xa,Xq),s(Xa,Xr),s(Xa,Xcs)) ),
    inference(miniscoping,[status(esa)],[f107]) ).

fof(f300,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ s_e(X0,X1,X2,X3)
      | s_e(s(X4,X0),s(X4,X1),s(X4,X2),s(X4,X3)) ),
    inference(cnf_transformation,[status(esa)],[f299]) ).

fof(f303,plain,
    ! [Xa,Xb] :
      ( ! [Xp,Xq] :
          ( ~ s_m(Xp,Xa,Xq)
          | ~ s_m(Xp,Xb,Xq) )
      | Xa = Xb ),
    inference(miniscoping,[status(esa)],[f109]) ).

fof(f304,plain,
    ! [X0,X1,X2,X3] :
      ( ~ s_m(X0,X1,X2)
      | ~ s_m(X0,X3,X2)
      | X1 = X3 ),
    inference(cnf_transformation,[status(esa)],[f303]) ).

fof(f305,plain,
    ! [Xa,Xb] :
      ( ! [Xp] : s(Xa,Xp) != s(Xb,Xp)
      | Xa = Xb ),
    inference(miniscoping,[status(esa)],[f110]) ).

fof(f306,plain,
    ! [X0,X1,X2] :
      ( s(X0,X1) != s(X2,X1)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f305]) ).

fof(f307,plain,
    ? [Xa,Xb,Xp] :
      ( s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp))
      & Xa != Xb ),
    inference(pre_NNF_transformation,[status(esa)],[f112]) ).

fof(f308,plain,
    ? [Xa,Xb] :
      ( ? [Xp] : s(Xa,s(Xb,Xp)) = s(Xb,s(Xa,Xp))
      & Xa != Xb ),
    inference(miniscoping,[status(esa)],[f307]) ).

fof(f309,plain,
    ( s(sk0_0,s(sk0_1,sk0_2)) = s(sk0_1,s(sk0_0,sk0_2))
    & sk0_0 != sk0_1 ),
    inference(skolemization,[status(esa)],[f308]) ).

fof(f310,plain,
    s(sk0_0,s(sk0_1,sk0_2)) = s(sk0_1,s(sk0_0,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f309]) ).

fof(f311,plain,
    sk0_0 != sk0_1,
    inference(cnf_transformation,[status(esa)],[f309]) ).

fof(f355,plain,
    ( ! [Xa,Xm,Xb] :
        ( ~ s_m(Xa,Xm,Xb)
        | s_t(Xa,Xm,Xb) )
    & ! [Xa,Xm,Xb] :
        ( ~ s_m(Xa,Xm,Xb)
        | s_e(Xm,Xa,Xm,Xb) )
    & ! [Xa,Xm,Xb] :
        ( ~ s_t(Xa,Xm,Xb)
        | ~ s_e(Xm,Xa,Xm,Xb)
        | s_m(Xa,Xm,Xb) ) ),
    inference(miniscoping,[status(esa)],[f121]) ).

fof(f356,plain,
    ! [X0,X1,X2] :
      ( ~ s_m(X0,X1,X2)
      | s_t(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f355]) ).

fof(f358,plain,
    ! [X0,X1,X2] :
      ( ~ s_t(X0,X1,X2)
      | ~ s_e(X1,X0,X1,X2)
      | s_m(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f355]) ).

fof(f371,plain,
    ! [X0,X1,X2] :
      ( s(X0,X1) != s(X0,X2)
      | X2 = X1 ),
    inference(destructive_equality_resolution,[status(esa)],[f289]) ).

fof(f372,plain,
    ! [X0] : s(X0,X0) = X0,
    inference(destructive_equality_resolution,[status(esa)],[f293]) ).

fof(f383,plain,
    s(sk0_1,s(sk0_0,s(sk0_1,sk0_2))) = s(sk0_0,sk0_2),
    inference(paramodulation,[status(thm)],[f310,f287]) ).

fof(f394,plain,
    ! [X0] :
      ( s(sk0_0,sk0_2) != s(sk0_1,X0)
      | X0 = s(sk0_0,s(sk0_1,sk0_2)) ),
    inference(paramodulation,[status(thm)],[f383,f371]) ).

fof(f815,plain,
    ! [X0,X1] : s_e(X0,X1,X0,s(X0,X1)),
    inference(paramodulation,[status(thm)],[f372,f294]) ).

fof(f883,plain,
    ! [X0,X1,X2] : s_e(s(X0,X1),s(X0,X2),s(X0,X1),s(X0,s(X1,X2))),
    inference(resolution,[status(thm)],[f815,f300]) ).

fof(f918,plain,
    ! [X0,X1] : s_t(X0,X1,s(X1,X0)),
    inference(resolution,[status(thm)],[f356,f283]) ).

fof(f928,plain,
    ! [X0,X1,X2] : s_t(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))),
    inference(resolution,[status(thm)],[f918,f296]) ).

fof(f2103,plain,
    ! [X0,X1,X2] :
      ( ~ s_m(X0,X1,s(X2,X0))
      | X1 = X2 ),
    inference(resolution,[status(thm)],[f304,f283]) ).

fof(f11270,plain,
    ! [X0] :
      ( s(sk0_0,sk0_2) != s(sk0_1,s(X0,s(sk0_1,sk0_2)))
      | X0 = sk0_0 ),
    inference(resolution,[status(thm)],[f394,f306]) ).

fof(f11407,plain,
    ! [X0] :
      ( s(sk0_0,sk0_2) != s(sk0_1,s(s(X0,sk0_0),s(sk0_1,sk0_2)))
      | sk0_0 = X0 ),
    inference(resolution,[status(thm)],[f11270,f292]) ).

fof(f15930,plain,
    s(sk0_0,sk0_2) != s(sk0_1,s(s(sk0_1,sk0_0),s(sk0_1,sk0_2))),
    inference(resolution,[status(thm)],[f11407,f311]) ).

fof(f37454,plain,
    ! [X0,X1,X2] :
      ( ~ s_t(s(X0,X1),s(X0,X2),s(X0,s(X2,X1)))
      | s_m(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))) ),
    inference(resolution,[status(thm)],[f358,f883]) ).

fof(f37455,plain,
    ! [X0,X1,X2] : s_m(s(X0,X1),s(X0,X2),s(X0,s(X2,X1))),
    inference(forward_subsumption_resolution,[status(thm)],[f37454,f928]) ).

fof(f40563,plain,
    s_m(s(sk0_1,s(sk0_1,sk0_2)),s(sk0_1,sk0_0),s(sk0_0,sk0_2)),
    inference(paramodulation,[status(thm)],[f383,f37455]) ).

fof(f40564,plain,
    s_m(sk0_2,s(sk0_1,sk0_0),s(sk0_0,sk0_2)),
    inference(forward_demodulation,[status(thm)],[f287,f40563]) ).

fof(f43161,plain,
    s(sk0_1,sk0_0) = sk0_0,
    inference(resolution,[status(thm)],[f40564,f2103]) ).

fof(f43222,plain,
    s(sk0_0,sk0_2) != s(sk0_1,s(sk0_0,s(sk0_1,sk0_2))),
    inference(backward_demodulation,[status(thm)],[f43161,f15930]) ).

fof(f43223,plain,
    s(sk0_0,sk0_2) != s(sk0_0,sk0_2),
    inference(forward_demodulation,[status(thm)],[f383,f43222]) ).

fof(f43224,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f43223]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO500+1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n003.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  : 300
% 0.13/0.34  % DateTime : Tue Apr 30 01:41:03 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 151.60/19.44  % Refutation found
% 151.60/19.44  % SZS status Theorem for theBenchmark: Theorem is valid
% 151.60/19.44  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 152.66/19.60  % Elapsed time: 19.235271 seconds
% 152.66/19.60  % CPU time: 152.434524 seconds
% 152.66/19.60  % Total memory used: 712.146 MB
% 152.66/19.60  % Net memory used: 674.386 MB
%------------------------------------------------------------------------------