TSTP Solution File: GRA010+1 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% 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 : Thu Aug 31 00:03:12 EDT 2023

% Result   : Theorem 1.17s 1.24s
% Output   : CNFRefutation 1.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   36 (   5 unt;   0 def)
%            Number of atoms       :  159 (  32 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  191 (  68   ~;  64   |;  43   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  119 (  16 sgn;  67   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f16,axiom,
    ! [X3,X1,X2] :
      ( ( ! [X6,X7] :
            ( ( sequential(X6,X7)
              & on_path(X7,X3)
              & on_path(X6,X3) )
           => ? [X8] : triangle(X6,X7,X8) )
        & path(X1,X2,X3) )
     => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).

fof(f18,conjecture,
    ( complete
   => ! [X3,X1,X2] :
        ( ( ! [X6,X7] :
              ( ( sequential(X6,X7)
                & on_path(X7,X3)
                & on_path(X6,X3) )
             => ? [X8] : triangle(X6,X7,X8) )
          & path(X1,X2,X3) )
       => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).

fof(f19,negated_conjecture,
    ~ ( complete
     => ! [X3,X1,X2] :
          ( ( ! [X6,X7] :
                ( ( sequential(X6,X7)
                  & on_path(X7,X3)
                  & on_path(X6,X3) )
               => ? [X8] : triangle(X6,X7,X8) )
            & path(X1,X2,X3) )
         => number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ) ),
    inference(negated_conjecture,[],[f18]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3,X4] :
            ( ( sequential(X3,X4)
              & on_path(X4,X0)
              & on_path(X3,X0) )
           => ? [X5] : triangle(X3,X4,X5) )
        & path(X1,X2,X0) )
     => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(rectify,[],[f16]) ).

fof(f35,plain,
    ~ ( complete
     => ! [X0,X1,X2] :
          ( ( ! [X3,X4] :
                ( ( sequential(X3,X4)
                  & on_path(X4,X0)
                  & on_path(X3,X0) )
               => ? [X5] : triangle(X3,X4,X5) )
            & path(X1,X2,X0) )
         => number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
    inference(rectify,[],[f19]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f58,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
      | ~ path(X1,X2,X0) ),
    inference(flattening,[],[f57]) ).

fof(f59,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
    & complete ),
    inference(ennf_transformation,[],[f35]) ).

fof(f60,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
    & complete ),
    inference(flattening,[],[f59]) ).

fof(f84,plain,
    ! [X0] :
      ( ? [X3,X4] :
          ( ! [X5] : ~ triangle(X3,X4,X5)
          & sequential(X3,X4)
          & on_path(X4,X0)
          & on_path(X3,X0) )
     => ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
        & sequential(sK6(X0),sK7(X0))
        & on_path(sK7(X0),X0)
        & on_path(sK6(X0),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
        & sequential(sK6(X0),sK7(X0))
        & on_path(sK7(X0),X0)
        & on_path(sK6(X0),X0) )
      | ~ path(X1,X2,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f58,f84]) ).

fof(f86,plain,
    ( ? [X0,X1,X2] :
        ( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
        & ! [X3,X4] :
            ( ? [X5] : triangle(X3,X4,X5)
            | ~ sequential(X3,X4)
            | ~ on_path(X4,X0)
            | ~ on_path(X3,X0) )
        & path(X1,X2,X0) )
   => ( number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8)
      & ! [X4,X3] :
          ( ? [X5] : triangle(X3,X4,X5)
          | ~ sequential(X3,X4)
          | ~ on_path(X4,sK8)
          | ~ on_path(X3,sK8) )
      & path(sK9,sK10,sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X3,X4] :
      ( ? [X5] : triangle(X3,X4,X5)
     => triangle(X3,X4,sK11(X3,X4)) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ( number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8)
    & ! [X3,X4] :
        ( triangle(X3,X4,sK11(X3,X4))
        | ~ sequential(X3,X4)
        | ~ on_path(X4,sK8)
        | ~ on_path(X3,sK8) )
    & path(sK9,sK10,sK8)
    & complete ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f60,f87,f86]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | on_path(sK6(X0),X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f141,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | on_path(sK7(X0),X0)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f142,plain,
    ! [X2,X0,X1] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | sequential(sK6(X0),sK7(X0))
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f143,plain,
    ! [X2,X0,X1,X5] :
      ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
      | ~ triangle(sK6(X0),sK7(X0),X5)
      | ~ path(X1,X2,X0) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f146,plain,
    path(sK9,sK10,sK8),
    inference(cnf_transformation,[],[f88]) ).

fof(f147,plain,
    ! [X3,X4] :
      ( triangle(X3,X4,sK11(X3,X4))
      | ~ sequential(X3,X4)
      | ~ on_path(X4,sK8)
      | ~ on_path(X3,sK8) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f148,plain,
    number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_100,plain,
    ( ~ triangle(sK6(X0),sK7(X0),X1)
    | ~ path(X2,X3,X0)
    | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_101,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | sequential(sK6(X2),sK7(X2)) ),
    inference(cnf_transformation,[],[f142]) ).

cnf(c_102,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | on_path(sK7(X2),X2) ),
    inference(cnf_transformation,[],[f141]) ).

cnf(c_103,plain,
    ( ~ path(X0,X1,X2)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
    | on_path(sK6(X2),X2) ),
    inference(cnf_transformation,[],[f140]) ).

cnf(c_105,negated_conjecture,
    number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
    inference(cnf_transformation,[],[f148]) ).

cnf(c_106,negated_conjecture,
    ( ~ sequential(X0,X1)
    | ~ on_path(X0,sK8)
    | ~ on_path(X1,sK8)
    | triangle(X0,X1,sK11(X0,X1)) ),
    inference(cnf_transformation,[],[f147]) ).

cnf(c_107,negated_conjecture,
    path(sK9,sK10,sK8),
    inference(cnf_transformation,[],[f146]) ).

cnf(c_1239,plain,
    ( sK11(X1,X2) != X3
    | sK6(X0) != X1
    | sK7(X0) != X2
    | ~ path(X4,X5,X0)
    | ~ sequential(X1,X2)
    | ~ on_path(X1,sK8)
    | ~ on_path(X2,sK8)
    | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(resolution_lifted,[status(thm)],[c_100,c_106]) ).

cnf(c_1240,plain,
    ( ~ sequential(sK6(X0),sK7(X0))
    | ~ path(X1,X2,X0)
    | ~ on_path(sK6(X0),sK8)
    | ~ on_path(sK7(X0),sK8)
    | number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
    inference(unflattening,[status(thm)],[c_1239]) ).

cnf(c_1252,plain,
    ( ~ path(X0,X1,X2)
    | ~ on_path(sK6(X2),sK8)
    | ~ on_path(sK7(X2),sK8)
    | number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1240,c_101]) ).

cnf(c_3189,plain,
    ( ~ on_path(sK6(sK8),sK8)
    | ~ on_path(sK7(sK8),sK8)
    | number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) ),
    inference(superposition,[status(thm)],[c_107,c_1252]) ).

cnf(c_3190,plain,
    ( ~ on_path(sK6(sK8),sK8)
    | ~ on_path(sK7(sK8),sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_3189,c_105]) ).

cnf(c_3911,plain,
    ( ~ path(sK9,sK10,sK8)
    | number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
    | on_path(sK7(sK8),sK8) ),
    inference(instantiation,[status(thm)],[c_102]) ).

cnf(c_3941,plain,
    ( ~ path(sK9,sK10,sK8)
    | number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
    | on_path(sK6(sK8),sK8) ),
    inference(instantiation,[status(thm)],[c_103]) ).

cnf(c_3942,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_3941,c_3911,c_3190,c_105,c_107]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : GRA010+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.14  % Command  : run_iprover %s %d THM
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.21/0.36  % CPULimit : 300
% 0.21/0.36  % WCLimit  : 300
% 0.21/0.36  % DateTime : Sun Aug 27 03:19:54 EDT 2023
% 0.21/0.36  % CPUTime  : 
% 0.21/0.50  Running first-order theorem proving
% 0.21/0.50  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.17/1.24  % SZS status Started for theBenchmark.p
% 1.17/1.24  % SZS status Theorem for theBenchmark.p
% 1.17/1.24  
% 1.17/1.24  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.17/1.24  
% 1.17/1.24  ------  iProver source info
% 1.17/1.24  
% 1.17/1.24  git: date: 2023-05-31 18:12:56 +0000
% 1.17/1.24  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.17/1.24  git: non_committed_changes: false
% 1.17/1.24  git: last_make_outside_of_git: false
% 1.17/1.24  
% 1.17/1.24  ------ Parsing...
% 1.17/1.24  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 1.17/1.24  
% 1.17/1.24  ------ Preprocessing... sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe:1:0s pe_e  sup_sim: 0  sf_s  rm: 2 0s  sf_e  pe_s  pe_e 
% 1.17/1.24  
% 1.17/1.24  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 1.17/1.24  
% 1.17/1.24  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.17/1.24  ------ Proving...
% 1.17/1.24  ------ Problem Properties 
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  clauses                                 55
% 1.17/1.24  conjectures                             2
% 1.17/1.24  EPR                                     14
% 1.17/1.24  Horn                                    37
% 1.17/1.24  unary                                   4
% 1.17/1.24  binary                                  13
% 1.17/1.24  lits                                    178
% 1.17/1.24  lits eq                                 46
% 1.17/1.24  fd_pure                                 0
% 1.17/1.24  fd_pseudo                               0
% 1.17/1.24  fd_cond                                 0
% 1.17/1.24  fd_pseudo_cond                          5
% 1.17/1.24  AC symbols                              0
% 1.17/1.24  
% 1.17/1.24  ------ Schedule dynamic 5 is on 
% 1.17/1.24  
% 1.17/1.24  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  ------ 
% 1.17/1.24  Current options:
% 1.17/1.24  ------ 
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  ------ Proving...
% 1.17/1.24  
% 1.17/1.24  
% 1.17/1.24  % SZS status Theorem for theBenchmark.p
% 1.17/1.24  
% 1.17/1.24  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.17/1.24  
% 1.17/1.24  
%------------------------------------------------------------------------------