TSTP Solution File: GEO177+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GEO177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n012.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 : Wed Aug 30 23:09:53 EDT 2023

% Result   : Theorem 0.41s 1.11s
% Output   : CNFRefutation 0.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   58 (  16 unt;   0 def)
%            Number of atoms       :  197 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  212 (  73   ~;  99   |;  28   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   96 (   0 sgn;  61   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => ( distinct_points(X2,X1)
          & distinct_points(X2,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).

fof(f9,axiom,
    ! [X0,X1,X3,X4] :
      ( ( distinct_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X1,X4)
        | apart_point_and_line(X1,X3)
        | apart_point_and_line(X0,X4)
        | apart_point_and_line(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).

fof(f11,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).

fof(f13,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( distinct_points(X3,X4)
        & distinct_points(X0,X1) )
     => ( ( apart_point_and_line(X1,line_connecting(X3,X4))
          | apart_point_and_line(X0,line_connecting(X3,X4)) )
       => ( apart_point_and_line(X4,line_connecting(X0,X1))
          | apart_point_and_line(X3,line_connecting(X0,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( distinct_points(X3,X4)
          & distinct_points(X0,X1) )
       => ( ( apart_point_and_line(X1,line_connecting(X3,X4))
            | apart_point_and_line(X0,line_connecting(X3,X4)) )
         => ( apart_point_and_line(X4,line_connecting(X0,X1))
            | apart_point_and_line(X3,line_connecting(X0,X1)) ) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f15,plain,
    ! [X0,X1,X2,X3] :
      ( ( distinct_lines(X2,X3)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X1,X3)
        | apart_point_and_line(X1,X2)
        | apart_point_and_line(X0,X3)
        | apart_point_and_line(X0,X2) ) ),
    inference(rectify,[],[f9]) ).

fof(f16,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( distinct_points(X2,X3)
          & distinct_points(X0,X1) )
       => ( ( apart_point_and_line(X1,line_connecting(X2,X3))
            | apart_point_and_line(X0,line_connecting(X2,X3)) )
         => ( apart_point_and_line(X3,line_connecting(X0,X1))
            | apart_point_and_line(X2,line_connecting(X0,X1)) ) ) ),
    inference(rectify,[],[f14]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( distinct_points(X2,X1)
        & distinct_points(X2,X0) )
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( distinct_points(X2,X1)
        & distinct_points(X2,X0) )
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f23]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f28,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f27]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f31]) ).

fof(f34,plain,
    ? [X0,X1,X2,X3] :
      ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
      & ~ apart_point_and_line(X2,line_connecting(X0,X1))
      & ( apart_point_and_line(X1,line_connecting(X2,X3))
        | apart_point_and_line(X0,line_connecting(X2,X3)) )
      & distinct_points(X2,X3)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f35,plain,
    ? [X0,X1,X2,X3] :
      ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
      & ~ apart_point_and_line(X2,line_connecting(X0,X1))
      & ( apart_point_and_line(X1,line_connecting(X2,X3))
        | apart_point_and_line(X0,line_connecting(X2,X3)) )
      & distinct_points(X2,X3)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f34]) ).

fof(f36,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
        & ~ apart_point_and_line(X2,line_connecting(X0,X1))
        & ( apart_point_and_line(X1,line_connecting(X2,X3))
          | apart_point_and_line(X0,line_connecting(X2,X3)) )
        & distinct_points(X2,X3)
        & distinct_points(X0,X1) )
   => ( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
      & ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
      & ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
        | apart_point_and_line(sK0,line_connecting(sK2,sK3)) )
      & distinct_points(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ( ~ apart_point_and_line(sK3,line_connecting(sK0,sK1))
    & ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
    & ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
      | apart_point_and_line(sK0,line_connecting(sK2,sK3)) )
    & distinct_points(sK2,sK3)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f35,f36]) ).

fof(f38,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X0)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X1)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f48,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X1,X3)
      | apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X3)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f52,plain,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f37]) ).

fof(f53,plain,
    distinct_points(sK2,sK3),
    inference(cnf_transformation,[],[f37]) ).

fof(f54,plain,
    ( apart_point_and_line(sK1,line_connecting(sK2,sK3))
    | apart_point_and_line(sK0,line_connecting(sK2,sK3)) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f55,plain,
    ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f37]) ).

fof(f56,plain,
    ~ apart_point_and_line(sK3,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_49,plain,
    ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f38]) ).

cnf(c_55,plain,
    ( ~ apart_point_and_line(X0,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2)
    | distinct_points(X0,X2) ),
    inference(cnf_transformation,[],[f45]) ).

cnf(c_56,plain,
    ( ~ apart_point_and_line(X0,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2)
    | distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_59,plain,
    ( ~ distinct_points(X0,X1)
    | ~ distinct_lines(X2,X3)
    | apart_point_and_line(X0,X2)
    | apart_point_and_line(X0,X3)
    | apart_point_and_line(X1,X2)
    | apart_point_and_line(X1,X3) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_61,plain,
    ( ~ apart_point_and_line(X0,X1)
    | distinct_lines(X1,X2)
    | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_63,negated_conjecture,
    ~ apart_point_and_line(sK3,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_64,negated_conjecture,
    ~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f55]) ).

cnf(c_65,negated_conjecture,
    ( apart_point_and_line(sK0,line_connecting(sK2,sK3))
    | apart_point_and_line(sK1,line_connecting(sK2,sK3)) ),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_66,negated_conjecture,
    distinct_points(sK2,sK3),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_67,negated_conjecture,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_70,plain,
    ~ distinct_points(sK0,sK0),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_228,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
    | distinct_lines(line_connecting(sK2,sK3),X0)
    | apart_point_and_line(sK0,X0) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_230,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
    | ~ distinct_points(sK2,sK3)
    | distinct_points(X0,sK3) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_232,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(X0,sK1) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_233,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK2,sK3))
    | ~ distinct_points(sK2,sK3)
    | distinct_points(X0,sK2) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_235,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(X0,sK0) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_236,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(sK0,sK0) ),
    inference(instantiation,[status(thm)],[c_235]) ).

cnf(c_237,plain,
    ( ~ distinct_lines(X0,X1)
    | ~ distinct_points(sK2,sK3)
    | apart_point_and_line(sK3,X0)
    | apart_point_and_line(sK3,X1)
    | apart_point_and_line(sK2,X0)
    | apart_point_and_line(sK2,X1) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_252,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
    | distinct_lines(line_connecting(sK2,sK3),X0)
    | apart_point_and_line(sK1,X0) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_257,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(sK1,sK1) ),
    inference(instantiation,[status(thm)],[c_232]) ).

cnf(c_258,plain,
    ~ distinct_points(sK1,sK1),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_265,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK2,sK3))
    | distinct_lines(line_connecting(sK2,sK3),line_connecting(sK0,sK1))
    | apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_228]) ).

cnf(c_267,plain,
    ( ~ apart_point_and_line(sK3,line_connecting(sK2,sK3))
    | ~ distinct_points(sK2,sK3)
    | distinct_points(sK3,sK3) ),
    inference(instantiation,[status(thm)],[c_230]) ).

cnf(c_268,plain,
    ~ distinct_points(sK3,sK3),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_275,plain,
    ( ~ apart_point_and_line(sK2,line_connecting(sK2,sK3))
    | ~ distinct_points(sK2,sK3)
    | distinct_points(sK2,sK2) ),
    inference(instantiation,[status(thm)],[c_233]) ).

cnf(c_276,plain,
    ~ distinct_points(sK2,sK2),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_404,plain,
    ( ~ distinct_lines(line_connecting(sK2,sK3),X0)
    | ~ distinct_points(sK2,sK3)
    | apart_point_and_line(sK3,line_connecting(sK2,sK3))
    | apart_point_and_line(sK2,line_connecting(sK2,sK3))
    | apart_point_and_line(sK3,X0)
    | apart_point_and_line(sK2,X0) ),
    inference(instantiation,[status(thm)],[c_237]) ).

cnf(c_709,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK2,sK3))
    | distinct_lines(line_connecting(sK2,sK3),line_connecting(sK0,sK1))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_252]) ).

cnf(c_941,plain,
    ( ~ distinct_lines(line_connecting(sK2,sK3),line_connecting(sK0,sK1))
    | ~ distinct_points(sK2,sK3)
    | apart_point_and_line(sK3,line_connecting(sK0,sK1))
    | apart_point_and_line(sK3,line_connecting(sK2,sK3))
    | apart_point_and_line(sK2,line_connecting(sK0,sK1))
    | apart_point_and_line(sK2,line_connecting(sK2,sK3)) ),
    inference(instantiation,[status(thm)],[c_404]) ).

cnf(c_942,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_941,c_709,c_276,c_275,c_268,c_267,c_265,c_258,c_257,c_236,c_65,c_63,c_64,c_70,c_66,c_67]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.10  % Problem  : GEO177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.10  % Command  : run_iprover %s %d THM
% 0.10/0.30  % Computer : n012.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Tue Aug 29 23:50:08 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.16/0.41  Running first-order theorem proving
% 0.16/0.41  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.41/1.11  % SZS status Started for theBenchmark.p
% 0.41/1.11  % SZS status Theorem for theBenchmark.p
% 0.41/1.11  
% 0.41/1.11  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.41/1.11  
% 0.41/1.11  ------  iProver source info
% 0.41/1.11  
% 0.41/1.11  git: date: 2023-05-31 18:12:56 +0000
% 0.41/1.11  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.41/1.11  git: non_committed_changes: false
% 0.41/1.11  git: last_make_outside_of_git: false
% 0.41/1.11  
% 0.41/1.11  ------ Parsing...
% 0.41/1.11  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 0.41/1.11  
% 0.41/1.11  ------ Preprocessing... sf_s  rm: 5 0s  sf_e  pe_s  pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 0.41/1.11  
% 0.41/1.11  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 0.41/1.11  ------ Proving...
% 0.41/1.11  ------ Problem Properties 
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  clauses                                 14
% 0.41/1.11  conjectures                             5
% 0.41/1.11  EPR                                     9
% 0.41/1.11  Horn                                    8
% 0.41/1.11  unary                                   6
% 0.41/1.11  binary                                  1
% 0.41/1.11  lits                                    32
% 0.41/1.11  lits eq                                 0
% 0.41/1.11  fd_pure                                 0
% 0.41/1.11  fd_pseudo                               0
% 0.41/1.11  fd_cond                                 0
% 0.41/1.11  fd_pseudo_cond                          0
% 0.41/1.11  AC symbols                              0
% 0.41/1.11  
% 0.41/1.11  ------ Schedule dynamic 5 is on 
% 0.41/1.11  
% 0.41/1.11  ------ no equalities: superposition off 
% 0.41/1.11  
% 0.41/1.11  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  ------ 
% 0.41/1.11  Current options:
% 0.41/1.11  ------ 
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  ------ Proving...
% 0.41/1.11  
% 0.41/1.11  
% 0.41/1.11  % SZS status Theorem for theBenchmark.p
% 0.41/1.11  
% 0.41/1.11  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.41/1.11  
% 0.41/1.12  
%------------------------------------------------------------------------------