TSTP Solution File: GEO172+2 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : GEO172+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n008.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 : Fri May  3 02:16:39 EDT 2024

% Result   : Theorem 2.32s 1.14s
% Output   : CNFRefutation 2.32s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

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

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( distinct_points(X0,X1)
     => ( distinct_points(X1,X2)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( distinct_lines(X0,X1)
     => ( distinct_lines(X1,X2)
        | distinct_lines(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( ( apart_point_and_line(X2,X1)
          | apart_point_and_line(X2,X0) )
       => distinct_points(X2,intersection_point(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).

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(f10,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X2,X1)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).

fof(f13,conjecture,
    ! [X0,X1,X2] :
      ( ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0)
        & convergent_lines(X0,X1) )
     => ~ distinct_points(X2,intersection_point(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( ~ apart_point_and_line(X2,X1)
          & ~ apart_point_and_line(X2,X0)
          & convergent_lines(X0,X1) )
       => ~ distinct_points(X2,intersection_point(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] :
      ( 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(f18,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(flattening,[],[f18]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0) )
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0) )
      | ~ convergent_lines(X0,X1) ),
    inference(flattening,[],[f24]) ).

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(f28,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f28]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

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

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

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

fof(f36,plain,
    ( distinct_points(sK2,intersection_point(sK0,sK1))
    & ~ apart_point_and_line(sK2,sK1)
    & ~ apart_point_and_line(sK2,sK0)
    & convergent_lines(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(f38,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

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

fof(f41,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

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(f48,plain,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f29]) ).

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

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

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

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

fof(f54,plain,
    distinct_points(sK2,intersection_point(sK0,sK1)),
    inference(cnf_transformation,[],[f36]) ).

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

cnf(c_50,plain,
    ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f38]) ).

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

cnf(c_53,plain,
    ( ~ distinct_lines(X0,X1)
    | distinct_lines(X0,X2)
    | distinct_lines(X1,X2) ),
    inference(cnf_transformation,[],[f41]) ).

cnf(c_57,plain,
    ( ~ convergent_lines(X0,X1)
    | ~ apart_point_and_line(X2,X1)
    | distinct_points(X2,intersection_point(X0,X1)) ),
    inference(cnf_transformation,[],[f46]) ).

cnf(c_58,plain,
    ( ~ convergent_lines(X0,X1)
    | ~ apart_point_and_line(X2,X0)
    | distinct_points(X2,intersection_point(X0,X1)) ),
    inference(cnf_transformation,[],[f45]) ).

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_60,plain,
    ( ~ apart_point_and_line(X0,X1)
    | distinct_points(X0,X2)
    | apart_point_and_line(X2,X1) ),
    inference(cnf_transformation,[],[f48]) ).

cnf(c_62,plain,
    ( ~ convergent_lines(X0,X1)
    | distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f50]) ).

cnf(c_63,negated_conjecture,
    distinct_points(sK2,intersection_point(sK0,sK1)),
    inference(cnf_transformation,[],[f54]) ).

cnf(c_64,negated_conjecture,
    ~ apart_point_and_line(sK2,sK1),
    inference(cnf_transformation,[],[f53]) ).

cnf(c_65,negated_conjecture,
    ~ apart_point_and_line(sK2,sK0),
    inference(cnf_transformation,[],[f52]) ).

cnf(c_66,negated_conjecture,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f51]) ).

cnf(c_154,plain,
    intersection_point(sK0,sK1) = sP0_iProver_def,
    definition ).

cnf(c_155,negated_conjecture,
    convergent_lines(sK0,sK1),
    inference(demodulation,[status(thm)],[c_66]) ).

cnf(c_156,negated_conjecture,
    ~ apart_point_and_line(sK2,sK0),
    inference(demodulation,[status(thm)],[c_65]) ).

cnf(c_157,negated_conjecture,
    ~ apart_point_and_line(sK2,sK1),
    inference(demodulation,[status(thm)],[c_64]) ).

cnf(c_158,negated_conjecture,
    distinct_points(sK2,sP0_iProver_def),
    inference(demodulation,[status(thm)],[c_63,c_154]) ).

cnf(c_422,plain,
    ( distinct_points(sK2,X0)
    | distinct_points(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_158,c_52]) ).

cnf(c_430,plain,
    distinct_lines(sK0,sK1),
    inference(superposition,[status(thm)],[c_155,c_62]) ).

cnf(c_453,plain,
    ( distinct_lines(sK0,X0)
    | distinct_lines(sK1,X0) ),
    inference(superposition,[status(thm)],[c_430,c_53]) ).

cnf(c_461,plain,
    distinct_points(sP0_iProver_def,sK2),
    inference(superposition,[status(thm)],[c_422,c_49]) ).

cnf(c_462,plain,
    ( distinct_points(X0,X1)
    | distinct_points(sK2,X1)
    | distinct_points(sP0_iProver_def,X0) ),
    inference(superposition,[status(thm)],[c_422,c_52]) ).

cnf(c_485,plain,
    ( distinct_lines(X0,X1)
    | distinct_lines(sK0,X0)
    | distinct_lines(sK1,X1) ),
    inference(superposition,[status(thm)],[c_453,c_53]) ).

cnf(c_505,plain,
    ( distinct_points(X0,X1)
    | distinct_points(X0,X2)
    | distinct_points(sK2,X1)
    | distinct_points(sP0_iProver_def,X2) ),
    inference(superposition,[status(thm)],[c_462,c_52]) ).

cnf(c_617,plain,
    ( distinct_lines(sK0,sK0)
    | distinct_lines(sK1,sK0) ),
    inference(equality_factoring,[status(thm)],[c_485]) ).

cnf(c_618,plain,
    distinct_lines(sK1,sK0),
    inference(forward_subsumption_resolution,[status(thm)],[c_617,c_50]) ).

cnf(c_670,plain,
    ( distinct_points(X0,X1)
    | distinct_points(X0,sP0_iProver_def)
    | distinct_points(sK2,X1) ),
    inference(superposition,[status(thm)],[c_505,c_49]) ).

cnf(c_732,plain,
    ( ~ distinct_points(sP0_iProver_def,X0)
    | distinct_points(X0,X1)
    | distinct_points(sP0_iProver_def,X1) ),
    inference(instantiation,[status(thm)],[c_52]) ).

cnf(c_763,plain,
    ( ~ apart_point_and_line(X0,sK1)
    | ~ convergent_lines(sK0,sK1)
    | distinct_points(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_154,c_57]) ).

cnf(c_768,plain,
    ( ~ apart_point_and_line(X0,sK1)
    | distinct_points(X0,sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_763,c_155]) ).

cnf(c_884,plain,
    ~ distinct_points(sP0_iProver_def,sP0_iProver_def),
    inference(instantiation,[status(thm)],[c_49]) ).

cnf(c_1228,plain,
    ( ~ apart_point_and_line(X0,sK0)
    | ~ convergent_lines(sK0,sK1)
    | distinct_points(X0,sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_154,c_58]) ).

cnf(c_1233,plain,
    ( ~ apart_point_and_line(X0,sK0)
    | distinct_points(X0,sP0_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1228,c_155]) ).

cnf(c_1269,plain,
    ( ~ distinct_lines(X0,X1)
    | apart_point_and_line(sK2,X0)
    | apart_point_and_line(sK2,X1)
    | apart_point_and_line(sP0_iProver_def,X0)
    | apart_point_and_line(sP0_iProver_def,X1) ),
    inference(superposition,[status(thm)],[c_461,c_59]) ).

cnf(c_1549,plain,
    ( ~ distinct_points(sP0_iProver_def,X0)
    | distinct_points(X0,sP0_iProver_def)
    | distinct_points(sP0_iProver_def,sP0_iProver_def) ),
    inference(instantiation,[status(thm)],[c_732]) ).

cnf(c_1687,plain,
    ( ~ apart_point_and_line(sP0_iProver_def,sK0)
    | distinct_points(sP0_iProver_def,X0)
    | apart_point_and_line(X0,sK0) ),
    inference(instantiation,[status(thm)],[c_60]) ).

cnf(c_1773,plain,
    ( apart_point_and_line(sK2,sK0)
    | apart_point_and_line(sK2,sK1)
    | apart_point_and_line(sP0_iProver_def,sK0)
    | apart_point_and_line(sP0_iProver_def,sK1) ),
    inference(superposition,[status(thm)],[c_618,c_1269]) ).

cnf(c_1779,plain,
    ( apart_point_and_line(sP0_iProver_def,sK0)
    | apart_point_and_line(sP0_iProver_def,sK1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_1773,c_157,c_156]) ).

cnf(c_1890,plain,
    ( distinct_points(sP0_iProver_def,sP0_iProver_def)
    | apart_point_and_line(sP0_iProver_def,sK0) ),
    inference(superposition,[status(thm)],[c_1779,c_768]) ).

cnf(c_1891,plain,
    apart_point_and_line(sP0_iProver_def,sK0),
    inference(forward_subsumption_resolution,[status(thm)],[c_1890,c_49]) ).

cnf(c_1944,plain,
    distinct_points(X0,sP0_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_670,c_884,c_1233,c_1549,c_1687,c_1891]) ).

cnf(c_1947,plain,
    $false,
    inference(superposition,[status(thm)],[c_1944,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO172+2 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12  % Command  : run_iprover %s %d THM
% 0.12/0.33  % Computer : n008.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  : 300
% 0.12/0.33  % DateTime : Fri May  3 01:22:13 EDT 2024
% 0.12/0.33  % CPUTime  : 
% 0.18/0.45  Running first-order theorem proving
% 0.18/0.45  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.32/1.14  % SZS status Started for theBenchmark.p
% 2.32/1.14  % SZS status Theorem for theBenchmark.p
% 2.32/1.14  
% 2.32/1.14  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.32/1.14  
% 2.32/1.14  ------  iProver source info
% 2.32/1.14  
% 2.32/1.14  git: date: 2024-05-02 19:28:25 +0000
% 2.32/1.14  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.32/1.14  git: non_committed_changes: false
% 2.32/1.14  
% 2.32/1.14  ------ Parsing...
% 2.32/1.14  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.32/1.14  
% 2.32/1.14  ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e 
% 2.32/1.14  
% 2.32/1.14  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.32/1.14  
% 2.32/1.14  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.32/1.14  ------ Proving...
% 2.32/1.14  ------ Problem Properties 
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  clauses                                 19
% 2.32/1.14  conjectures                             4
% 2.32/1.14  EPR                                     14
% 2.32/1.14  Horn                                    13
% 2.32/1.14  unary                                   8
% 2.32/1.14  binary                                  1
% 2.32/1.14  lits                                    43
% 2.32/1.14  lits eq                                 1
% 2.32/1.14  fd_pure                                 0
% 2.32/1.14  fd_pseudo                               0
% 2.32/1.14  fd_cond                                 0
% 2.32/1.14  fd_pseudo_cond                          0
% 2.32/1.14  AC symbols                              0
% 2.32/1.14  
% 2.32/1.14  ------ Schedule dynamic 5 is on 
% 2.32/1.14  
% 2.32/1.14  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  ------ 
% 2.32/1.14  Current options:
% 2.32/1.14  ------ 
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  ------ Proving...
% 2.32/1.14  
% 2.32/1.14  
% 2.32/1.14  % SZS status Theorem for theBenchmark.p
% 2.32/1.14  
% 2.32/1.14  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.32/1.14  
% 2.32/1.15  
%------------------------------------------------------------------------------