TSTP Solution File: GEO182+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : GEO182+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n022.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 23:09:57 EDT 2023

% Result   : Theorem 2.18s 1.25s
% Output   : CNFRefutation 2.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   58 (  12 unt;   0 def)
%            Number of atoms       :  186 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  199 (  71   ~; 102   |;  15   &)
%                                         (   0 <=>;  11  =>;   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    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :  106 (   0 sgn;  67   !;   9   ?)

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

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X1,X2)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).

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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ceq2) ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( distinct_points(X0,X1)
       => ( apart_point_and_line(X2,line_connecting(X0,X1))
         => apart_point_and_line(X2,line_connecting(X1,X0)) ) ),
    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] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(flattening,[],[f16]) ).

fof(f22,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(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(flattening,[],[f22]) ).

fof(f26,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(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(flattening,[],[f26]) ).

fof(f30,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(f31,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f30]) ).

fof(f33,plain,
    ? [X0,X1,X2] :
      ( ~ apart_point_and_line(X2,line_connecting(X1,X0))
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f34,plain,
    ? [X0,X1,X2] :
      ( ~ apart_point_and_line(X2,line_connecting(X1,X0))
      & apart_point_and_line(X2,line_connecting(X0,X1))
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f33]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( ~ apart_point_and_line(X2,line_connecting(X1,X0))
        & apart_point_and_line(X2,line_connecting(X0,X1))
        & distinct_points(X0,X1) )
   => ( ~ apart_point_and_line(sK2,line_connecting(sK1,sK0))
      & apart_point_and_line(sK2,line_connecting(sK0,sK1))
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ( ~ apart_point_and_line(sK2,line_connecting(sK1,sK0))
    & apart_point_and_line(sK2,line_connecting(sK0,sK1))
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f35]) ).

fof(f37,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f40,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X1,X2)
      | distinct_points(X0,X2)
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X0)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X1)
      | ~ apart_point_and_line(X2,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f47,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,[],[f27]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X2)
      | distinct_lines(X1,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f51,plain,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f36]) ).

fof(f52,plain,
    apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f36]) ).

fof(f53,plain,
    ~ apart_point_and_line(sK2,line_connecting(sK1,sK0)),
    inference(cnf_transformation,[],[f36]) ).

cnf(c_49,plain,
    ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f37]) ).

cnf(c_52,plain,
    ( ~ distinct_points(X0,X1)
    | distinct_points(X0,X2)
    | distinct_points(X1,X2) ),
    inference(cnf_transformation,[],[f40]) ).

cnf(c_55,plain,
    ( ~ apart_point_and_line(X0,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2)
    | distinct_points(X0,X2) ),
    inference(cnf_transformation,[],[f44]) ).

cnf(c_56,plain,
    ( ~ apart_point_and_line(X0,line_connecting(X1,X2))
    | ~ distinct_points(X1,X2)
    | distinct_points(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

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,[],[f47]) ).

cnf(c_61,plain,
    ( ~ apart_point_and_line(X0,X1)
    | distinct_lines(X1,X2)
    | apart_point_and_line(X0,X2) ),
    inference(cnf_transformation,[],[f49]) ).

cnf(c_63,negated_conjecture,
    ~ apart_point_and_line(sK2,line_connecting(sK1,sK0)),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_64,negated_conjecture,
    apart_point_and_line(sK2,line_connecting(sK0,sK1)),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_65,negated_conjecture,
    distinct_points(sK0,sK1),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_68,plain,
    ~ distinct_points(sK0,sK0),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_209,plain,
    ( ~ distinct_points(sK0,sK1)
    | distinct_points(sK1,X0)
    | distinct_points(sK0,X0) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_210,plain,
    ( ~ distinct_points(sK0,sK1)
    | distinct_points(sK1,sK0)
    | distinct_points(sK0,sK0) ),
    inference(instantiation,[status(thm)],[c_209]) ).

cnf(c_213,plain,
    ( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
    | distinct_lines(line_connecting(sK0,sK1),X0)
    | apart_point_and_line(sK2,X0) ),
    inference(instantiation,[status(thm)],[c_61]) ).

cnf(c_215,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_216,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_217,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(sK0,sK0) ),
    inference(instantiation,[status(thm)],[c_216]) ).

cnf(c_218,plain,
    ( ~ distinct_lines(X0,X1)
    | ~ distinct_points(sK0,sK1)
    | apart_point_and_line(sK1,X0)
    | apart_point_and_line(sK1,X1)
    | apart_point_and_line(sK0,X0)
    | apart_point_and_line(sK0,X1) ),
    inference(instantiation,[status(thm)],[c_59]) ).

cnf(c_222,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK1,X1))
    | ~ distinct_points(sK1,X1)
    | distinct_points(X0,sK1) ),
    inference(instantiation,[status(thm)],[c_56]) ).

cnf(c_223,plain,
    ( ~ apart_point_and_line(X0,line_connecting(sK1,X1))
    | ~ distinct_points(sK1,X1)
    | distinct_points(X0,X1) ),
    inference(instantiation,[status(thm)],[c_55]) ).

cnf(c_224,plain,
    ( ~ apart_point_and_line(sK0,line_connecting(sK1,sK0))
    | ~ distinct_points(sK1,sK0)
    | distinct_points(sK0,sK0) ),
    inference(instantiation,[status(thm)],[c_223]) ).

cnf(c_234,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | ~ distinct_points(sK0,sK1)
    | distinct_points(sK1,sK1) ),
    inference(instantiation,[status(thm)],[c_215]) ).

cnf(c_235,plain,
    ~ distinct_points(sK1,sK1),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_241,plain,
    ( ~ distinct_lines(line_connecting(sK0,sK1),X0)
    | ~ distinct_points(sK0,sK1)
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | apart_point_and_line(sK0,line_connecting(sK0,sK1))
    | apart_point_and_line(sK1,X0)
    | apart_point_and_line(sK0,X0) ),
    inference(instantiation,[status(thm)],[c_218]) ).

cnf(c_269,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK1,X0))
    | ~ distinct_points(sK1,X0)
    | distinct_points(sK1,sK1) ),
    inference(instantiation,[status(thm)],[c_222]) ).

cnf(c_270,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK1,sK0))
    | ~ distinct_points(sK1,sK0)
    | distinct_points(sK1,sK1) ),
    inference(instantiation,[status(thm)],[c_269]) ).

cnf(c_315,plain,
    ( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,X0))
    | ~ distinct_points(sK0,sK1)
    | apart_point_and_line(sK1,line_connecting(sK1,X0))
    | apart_point_and_line(sK0,line_connecting(sK1,X0))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_241]) ).

cnf(c_316,plain,
    ( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0))
    | ~ distinct_points(sK0,sK1)
    | apart_point_and_line(sK1,line_connecting(sK1,sK0))
    | apart_point_and_line(sK1,line_connecting(sK0,sK1))
    | apart_point_and_line(sK0,line_connecting(sK1,sK0))
    | apart_point_and_line(sK0,line_connecting(sK0,sK1)) ),
    inference(instantiation,[status(thm)],[c_315]) ).

cnf(c_317,plain,
    ( ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
    | distinct_lines(line_connecting(sK0,sK1),line_connecting(sK1,sK0))
    | apart_point_and_line(sK2,line_connecting(sK1,sK0)) ),
    inference(instantiation,[status(thm)],[c_213]) ).

cnf(c_318,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_317,c_316,c_270,c_235,c_234,c_224,c_217,c_210,c_63,c_64,c_68,c_65]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.15  % Problem  : GEO182+2 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.16  % Command  : run_iprover %s %d THM
% 0.17/0.38  % Computer : n022.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Tue Aug 29 20:45:23 EDT 2023
% 0.17/0.38  % CPUTime  : 
% 0.39/0.54  Running first-order theorem proving
% 0.39/0.54  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.18/1.25  % SZS status Started for theBenchmark.p
% 2.18/1.25  % SZS status Theorem for theBenchmark.p
% 2.18/1.25  
% 2.18/1.25  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.18/1.25  
% 2.18/1.25  ------  iProver source info
% 2.18/1.25  
% 2.18/1.25  git: date: 2023-05-31 18:12:56 +0000
% 2.18/1.25  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.18/1.25  git: non_committed_changes: false
% 2.18/1.25  git: last_make_outside_of_git: false
% 2.18/1.25  
% 2.18/1.25  ------ Parsing...
% 2.18/1.25  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.18/1.25  
% 2.18/1.25  ------ Preprocessing... sf_s  rm: 5 0s  sf_e  pe_s  pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 2.18/1.25  
% 2.18/1.25  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.18/1.25  ------ Proving...
% 2.18/1.25  ------ Problem Properties 
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  clauses                                 12
% 2.18/1.25  conjectures                             3
% 2.18/1.25  EPR                                     8
% 2.18/1.25  Horn                                    7
% 2.18/1.25  unary                                   5
% 2.18/1.25  binary                                  0
% 2.18/1.25  lits                                    29
% 2.18/1.25  lits eq                                 0
% 2.18/1.25  fd_pure                                 0
% 2.18/1.25  fd_pseudo                               0
% 2.18/1.25  fd_cond                                 0
% 2.18/1.25  fd_pseudo_cond                          0
% 2.18/1.25  AC symbols                              0
% 2.18/1.25  
% 2.18/1.25  ------ Schedule dynamic 5 is on 
% 2.18/1.25  
% 2.18/1.25  ------ no equalities: superposition off 
% 2.18/1.25  
% 2.18/1.25  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  ------ 
% 2.18/1.25  Current options:
% 2.18/1.25  ------ 
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  ------ Proving...
% 2.18/1.25  
% 2.18/1.25  
% 2.18/1.25  % SZS status Theorem for theBenchmark.p
% 2.18/1.25  
% 2.18/1.25  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.18/1.25  
% 2.18/1.25  
%------------------------------------------------------------------------------