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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : GEO191+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM

% Computer : n008.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 01:20:13 PM UTC 2026

% Result   : Theorem 1.94s 6.28s
% Output   : CNFRefutation 1.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   92 (  28 unt;   2 def)
%            Number of atoms       :  281 (   2 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :  224 (  71   ~; 127   |;  17   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  143 (   0 sgn 135   !;   8   ?;  47   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).

fof(f3,axiom,
    ! [X0] : ~ convergent_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( distinct_lines(X0,X1)
     => ( distinct_lines(X1,X2)
        | distinct_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).

fof(f11,axiom,
    ! [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) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X2,X1)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).

fof(f14,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).

fof(f15,conjecture,
    ! [X0,X1,X2,X3] :
      ( ( ( apart_point_and_line(intersection_point(X0,X1),X3)
          | apart_point_and_line(intersection_point(X0,X1),X2) )
        & convergent_lines(X2,X3)
        & convergent_lines(X0,X1) )
     => ( apart_point_and_line(intersection_point(X2,X3),X1)
        | apart_point_and_line(intersection_point(X2,X3),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X2,X3] :
        ( ( ( apart_point_and_line(intersection_point(X0,X1),X3)
            | apart_point_and_line(intersection_point(X0,X1),X2) )
          & convergent_lines(X2,X3)
          & convergent_lines(X0,X1) )
       => ( apart_point_and_line(intersection_point(X2,X3),X1)
          | apart_point_and_line(intersection_point(X2,X3),X0) ) ),
    inference(negated_conjecture,[status(cth)],[f15]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X1,X2)
      | distinct_lines(X0,X2) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X1,X2)
      | distinct_lines(X0,X2) ),
    inference(flattening,[],[f19]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(flattening,[],[f21]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f27,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(ennf_transformation,[],[f11]) ).

fof(f28,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(flattening,[],[f27]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | distinct_points(X0,X2) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f30,plain,
    ! [X0,X1,X2] :
      ( ~ apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | distinct_points(X0,X2) ),
    inference(flattening,[],[f29]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    inference(ennf_transformation,[],[f14]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    inference(flattening,[],[f33]) ).

fof(f35,plain,
    ? [X0,X1,X2,X3] :
      ( ( apart_point_and_line(intersection_point(X0,X1),X3)
        | apart_point_and_line(intersection_point(X0,X1),X2) )
      & convergent_lines(X2,X3)
      & convergent_lines(X0,X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f36,plain,
    ? [X0,X1,X2,X3] :
      ( ( apart_point_and_line(intersection_point(X0,X1),X3)
        | apart_point_and_line(intersection_point(X0,X1),X2) )
      & convergent_lines(X2,X3)
      & convergent_lines(X0,X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X1)
      & ~ apart_point_and_line(intersection_point(X2,X3),X0) ),
    inference(flattening,[],[f35]) ).

fof(f37,plain,
    ( ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
      | apart_point_and_line(intersection_point(sK0,sK1),sK2) )
    & convergent_lines(sK2,sK3)
    & convergent_lines(sK0,sK1)
    & ~ apart_point_and_line(intersection_point(sK2,sK3),sK1)
    & ~ apart_point_and_line(intersection_point(sK2,sK3),sK0) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f36]) ).

fof(f39,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f40,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ distinct_lines(X0,X1)
      | distinct_lines(X1,X2)
      | distinct_lines(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f22]) ).

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

fof(f47,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f48,plain,
    ! [X2,X3,X0,X1] :
      ( ~ 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(cnf_transformation,[],[f28]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | apart_point_and_line(X2,X1)
      | distinct_points(X0,X2) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X0,X2)
      | distinct_lines(X1,X2) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f52,plain,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
    | apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    inference(cnf_transformation,[],[f37]) ).

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

fof(f54,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f37]) ).

fof(f55,plain,
    ~ apart_point_and_line(intersection_point(sK2,sK3),sK1),
    inference(cnf_transformation,[],[f37]) ).

fof(f56,plain,
    ~ apart_point_and_line(intersection_point(sK2,sK3),sK0),
    inference(cnf_transformation,[],[f37]) ).

tcf(c_50,plain,
    ! [X0: $i] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f39]) ).

tcf(c_51,plain,
    ! [X0: $i] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f40]) ).

tcf(c_53,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( distinct_lines(X1,X2)
      | distinct_lines(X0,X2)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

tcf(c_57,plain,
    ! [X0: $i,X1: $i] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    inference(cnf_transformation,[],[f46]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i] :
      ( ~ convergent_lines(X0,X1)
      | ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    inference(cnf_transformation,[],[f47]) ).

tcf(c_59,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( 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,[],[f48]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_62,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( convergent_lines(X0,X2)
      | distinct_lines(X1,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f51]) ).

tcf(c_63,negated_conjecture,
    ~ apart_point_and_line(intersection_point(sK2,sK3),sK0),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_64,negated_conjecture,
    ~ apart_point_and_line(intersection_point(sK2,sK3),sK1),
    inference(cnf_transformation,[],[f55]) ).

tcf(c_65,negated_conjecture,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f54]) ).

tcf(c_66,negated_conjecture,
    convergent_lines(sK2,sK3),
    inference(cnf_transformation,[],[f53]) ).

tcf(c_67,negated_conjecture,
    ( apart_point_and_line(intersection_point(sK0,sK1),sK3)
    | apart_point_and_line(intersection_point(sK0,sK1),sK2) ),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_153,definition,
    iPr_def_10 = intersection_point(sK0,sK1),
    introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).

tcf(c_154,definition,
    iPr_def_11 = intersection_point(sK2,sK3),
    introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).

tcf(c_155,negated_conjecture,
    ( apart_point_and_line(iPr_def_10,sK3)
    | apart_point_and_line(iPr_def_10,sK2) ),
    inference(demodulation,[status(thm)],[c_67,c_153]) ).

tcf(c_156,negated_conjecture,
    convergent_lines(sK2,sK3),
    inference(demodulation,[status(thm)],[c_66]) ).

tcf(c_157,negated_conjecture,
    convergent_lines(sK0,sK1),
    inference(demodulation,[status(thm)],[c_65]) ).

tcf(c_158,negated_conjecture,
    ~ apart_point_and_line(iPr_def_11,sK1),
    inference(demodulation,[status(thm)],[c_64,c_154]) ).

tcf(c_159,negated_conjecture,
    ~ apart_point_and_line(iPr_def_11,sK0),
    inference(demodulation,[status(thm)],[c_63]) ).

tcf(c_423,plain,
    ! [X0: $i] :
      ( convergent_lines(sK1,X0)
      | convergent_lines(sK0,X0) ),
    inference(superposition,[status(thm)],[c_157,c_54]) ).

tcf(c_436,plain,
    ! [X0: $i,X1: $i] :
      ( convergent_lines(sK1,X1)
      | convergent_lines(sK0,X0)
      | convergent_lines(X0,X1) ),
    inference(superposition,[status(thm)],[c_423,c_54]) ).

tcf(c_455,plain,
    ! [X0: $i] :
      ( convergent_lines(sK0,X0)
      | convergent_lines(X0,sK1) ),
    inference(superposition,[status(thm)],[c_436,c_51]) ).

tcf(c_860,plain,
    ( ~ apart_point_and_line(iPr_def_11,sK2)
    | ~ convergent_lines(sK2,sK3) ),
    inference(superposition,[status(thm)],[c_154,c_57]) ).

tcf(c_861,plain,
    ( ~ apart_point_and_line(iPr_def_10,sK0)
    | ~ convergent_lines(sK0,sK1) ),
    inference(superposition,[status(thm)],[c_153,c_57]) ).

tcf(c_862,plain,
    ~ apart_point_and_line(iPr_def_10,sK0),
    inference(forward_subsumption_resolution,[status(thm)],[c_861,c_157]) ).

tcf(c_863,plain,
    ~ apart_point_and_line(iPr_def_11,sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_860,c_156]) ).

tcf(c_868,plain,
    ( ~ apart_point_and_line(iPr_def_11,sK3)
    | ~ convergent_lines(sK2,sK3) ),
    inference(superposition,[status(thm)],[c_154,c_58]) ).

tcf(c_869,plain,
    ( ~ apart_point_and_line(iPr_def_10,sK1)
    | ~ convergent_lines(sK0,sK1) ),
    inference(superposition,[status(thm)],[c_153,c_58]) ).

tcf(c_870,plain,
    ~ apart_point_and_line(iPr_def_10,sK1),
    inference(forward_subsumption_resolution,[status(thm)],[c_869,c_157]) ).

tcf(c_871,plain,
    ~ apart_point_and_line(iPr_def_11,sK3),
    inference(forward_subsumption_resolution,[status(thm)],[c_868,c_156]) ).

tcf(c_1157,plain,
    ! [X0: $i] :
      ( apart_point_and_line(iPr_def_10,sK2)
      | apart_point_and_line(X0,sK3)
      | distinct_points(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_155,c_60]) ).

tcf(c_1209,plain,
    ! [X0: $i] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X0) ),
    inference(superposition,[status(thm)],[c_157,c_62]) ).

tcf(c_1231,plain,
    ! [X0: $i,X1: $i] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X1)
      | convergent_lines(X0,X1) ),
    inference(superposition,[status(thm)],[c_455,c_62]) ).

tcf(c_1848,plain,
    ! [X0: $i,X1: $i] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(sK1,X1)
      | distinct_lines(X0,X1) ),
    inference(superposition,[status(thm)],[c_1209,c_53]) ).

tcf(c_1869,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apart_point_and_line(iPr_def_10,sK2)
      | apart_point_and_line(iPr_def_10,X1)
      | apart_point_and_line(iPr_def_10,X0)
      | apart_point_and_line(X2,sK3)
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X2,X0)
      | ~ distinct_lines(X0,X1) ),
    inference(superposition,[status(thm)],[c_1157,c_59]) ).

tcf(c_1943,plain,
    ! [X0: $i] :
      ( convergent_lines(sK0,X0)
      | distinct_lines(X0,sK1) ),
    inference(superposition,[status(thm)],[c_1848,c_50]) ).

tcf(c_2521,plain,
    ! [X0: $i,X1: $i] :
      ( apart_point_and_line(iPr_def_10,sK1)
      | apart_point_and_line(iPr_def_10,sK2)
      | apart_point_and_line(iPr_def_10,X1)
      | apart_point_and_line(X0,sK1)
      | apart_point_and_line(X0,sK3)
      | convergent_lines(sK0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(superposition,[status(thm)],[c_1943,c_1869]) ).

tcf(c_2529,plain,
    ! [X0: $i,X1: $i] :
      ( apart_point_and_line(iPr_def_10,sK2)
      | apart_point_and_line(iPr_def_10,X1)
      | apart_point_and_line(X0,sK1)
      | apart_point_and_line(X0,sK3)
      | convergent_lines(sK0,X1)
      | apart_point_and_line(X0,X1) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_2521,c_870]) ).

tcf(c_2687,plain,
    ( apart_point_and_line(iPr_def_11,sK1)
    | apart_point_and_line(iPr_def_11,sK3)
    | apart_point_and_line(iPr_def_10,sK0)
    | apart_point_and_line(iPr_def_10,sK2)
    | convergent_lines(sK0,sK0) ),
    inference(superposition,[status(thm)],[c_2529,c_159]) ).

tcf(c_2697,plain,
    apart_point_and_line(iPr_def_10,sK2),
    inference(forward_subsumption_resolution,[status(thm)],[c_2687,c_158,c_871,c_862,c_51]) ).

tcf(c_2702,plain,
    ! [X0: $i] :
      ( apart_point_and_line(X0,sK2)
      | distinct_points(iPr_def_10,X0) ),
    inference(superposition,[status(thm)],[c_2697,c_60]) ).

tcf(c_2723,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( apart_point_and_line(iPr_def_10,X1)
      | apart_point_and_line(iPr_def_10,X0)
      | apart_point_and_line(X2,sK2)
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X2,X0)
      | ~ distinct_lines(X0,X1) ),
    inference(superposition,[status(thm)],[c_2702,c_59]) ).

tcf(c_2912,plain,
    ( convergent_lines(sK0,sK0)
    | distinct_lines(sK1,sK0) ),
    inference(equality_factoring,[status(thm)],[c_1231]) ).

tcf(c_2914,plain,
    distinct_lines(sK1,sK0),
    inference(forward_subsumption_resolution,[status(thm)],[c_2912,c_51]) ).

tcf(c_3040,plain,
    ! [X0: $i] :
      ( distinct_lines(sK1,X0)
      | distinct_lines(sK0,X0) ),
    inference(superposition,[status(thm)],[c_2914,c_53]) ).

tcf(c_3059,plain,
    distinct_lines(sK0,sK1),
    inference(superposition,[status(thm)],[c_3040,c_50]) ).

tcf(c_4706,plain,
    ! [X0: $i] :
      ( apart_point_and_line(iPr_def_10,sK1)
      | apart_point_and_line(iPr_def_10,sK0)
      | apart_point_and_line(X0,sK1)
      | apart_point_and_line(X0,sK0)
      | apart_point_and_line(X0,sK2) ),
    inference(superposition,[status(thm)],[c_3059,c_2723]) ).

tcf(c_4714,plain,
    ! [X0: $i] :
      ( apart_point_and_line(X0,sK1)
      | apart_point_and_line(X0,sK0)
      | apart_point_and_line(X0,sK2) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_4706,c_870,c_862]) ).

tcf(c_5521,plain,
    ( apart_point_and_line(iPr_def_11,sK0)
    | apart_point_and_line(iPr_def_11,sK2) ),
    inference(superposition,[status(thm)],[c_4714,c_158]) ).

tcf(c_5523,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5521,c_159,c_863]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : GEO191+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/5.37  % Computer : n008.cluster.edu
% 0.08/5.37  % Model    : x86_64 x86_64
% 0.08/5.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37  % Memory   : 8046.5625MB
% 0.08/5.37  % OS       : Linux 6.8.0-71-generic
% 0.08/5.37  % CPULimit : 300
% 0.08/5.37  % WCLimit  : 300
% 0.08/5.37  % DateTime : Wed Sep 23 11:23:45 UTC 2026
% 0.08/5.37  % CPUTime  : 
% 0.08/5.37  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/5.41  Running first-order theorem proving
% 0.14/5.41  Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/5.42  
% 0.14/5.42  % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.42  
% 0.14/5.42  % Detected problem language: tptp
% 0.14/5.43  % Proving...
% 1.94/6.28  % SZS status Started for theBenchmark.p
% 1.94/6.28  % SZS status Theorem for theBenchmark.p
% 1.94/6.28  
% 1.94/6.28  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.94/6.28  
% 1.94/6.28  % ------  iProver source info
% 1.94/6.28  
% 1.94/6.28  % git: date: 2026-07-19 20:42:38 +0200
% 1.94/6.28  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.94/6.28  % git: non_committed_changes: false
% 1.94/6.28  
% 1.94/6.28  % ------ Parsing...
% 1.94/6.28  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 1.94/6.28  
% 1.94/6.28  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 1.94/6.28  
% 1.94/6.28  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 1.94/6.28  
% 1.94/6.28  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.94/6.28  % ------ Proving...
% 1.94/6.28  % ------ Problem Properties 
% 1.94/6.28  
% 1.94/6.28  % 
% 1.94/6.28  % clauses                               21
% 1.94/6.28  % conjectures                           5
% 1.94/6.28  % EPR                                   15
% 1.94/6.28  % Horn                                  13
% 1.94/6.28  % unary                                 9
% 1.94/6.28  % binary                                5
% 1.94/6.28  % lits                                  43
% 1.94/6.28  % lits eq                               2
% 1.94/6.28  % fd_pure                               0
% 1.94/6.28  % fd_pseudo                             0
% 1.94/6.28  % fd_cond                               0
% 1.94/6.28  % fd_pseudo_cond                        0
% 1.94/6.28  % AC symbols                            0
% 1.94/6.28  
% 1.94/6.28  % ------ Schedule dynamic 5 is on 
% 1.94/6.28  
% 1.94/6.28  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.94/6.28  
% 1.94/6.28  
% 1.94/6.28  % ------ 
% 1.94/6.28  % Current options:
% 1.94/6.28  % ------ 
% 1.94/6.28  
% 1.94/6.28  
% 1.94/6.28  % 
% 1.94/6.28  
% 1.94/6.28  % ------ Proving...
% 1.94/6.28  % 
% 1.94/6.28  
% 1.94/6.28  % SZS status Theorem for theBenchmark.p
% 1.94/6.28  
% 1.94/6.28  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.94/6.28  
% 1.94/6.28  
%------------------------------------------------------------------------------