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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : GEO222+2 : 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 : n010.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 01:20:26 PM UTC 2026

% Result   : Theorem 3.86s 1.32s
% Output   : CNFRefutation 3.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   72 (  23 unt;   0 def)
%            Number of atoms       :  202 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  206 (  76   ~; 119   |;   7   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  142 (   0 sgn 140   !;   2   ?;  70   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X0] : ~ convergent_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart3) ).

fof(f6,axiom,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( unorthogonal_lines(X0,X1)
      | convergent_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).

fof(f17,axiom,
    ! [X0,X1,X2] :
      ( ( unorthogonal_lines(X0,X1)
        & convergent_lines(X0,X1) )
     => ( ( unorthogonal_lines(X1,X2)
          & convergent_lines(X1,X2) )
        | ( unorthogonal_lines(X0,X2)
          & convergent_lines(X0,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).

fof(f18,axiom,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).

fof(f19,axiom,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).

fof(f20,axiom,
    ! [X0,X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( unorthogonal_lines(X2,X3)
        | unorthogonal_lines(X1,X3)
        | apart_point_and_line(X0,X2)
        | apart_point_and_line(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).

fof(f21,conjecture,
    ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f22,negated_conjecture,
    ~ ! [X0,X1] : ~ convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
    inference(negated_conjecture,[status(cth)],[f21]) ).

fof(f23,plain,
    ? [X0,X1] : convergent_lines(X1,orthogonal_through_point(orthogonal_through_point(X1,X0),X0)),
    inference(ennf_transformation,[],[f22]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(flattening,[],[f27]) ).

fof(f37,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_lines(X1,X2)
      | unorthogonal_lines(X2,X3)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f38,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_lines(X1,X2)
      | unorthogonal_lines(X2,X3)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f37]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1)
      | ( unorthogonal_lines(X1,X2)
        & convergent_lines(X1,X2) )
      | ( unorthogonal_lines(X0,X2)
        & convergent_lines(X0,X2) ) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1)
      | ( unorthogonal_lines(X1,X2)
        & convergent_lines(X1,X2) )
      | ( unorthogonal_lines(X0,X2)
        & convergent_lines(X0,X2) ) ),
    inference(flattening,[],[f39]) ).

fof(f43,plain,
    convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f23]) ).

fof(f44,plain,
    convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f48,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f49,plain,
    ! [X0,X1] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(cnf_transformation,[],[f19]) ).

fof(f50,plain,
    ! [X0,X1] : ~ unorthogonal_lines(orthogonal_through_point(X1,X0),X1),
    inference(cnf_transformation,[],[f18]) ).

fof(f56,plain,
    ! [X2,X3,X0,X1] :
      ( ~ distinct_lines(X1,X2)
      | unorthogonal_lines(X2,X3)
      | unorthogonal_lines(X1,X3)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1) ),
    inference(cnf_transformation,[],[f38]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1)
      | unorthogonal_lines(X1,X2)
      | unorthogonal_lines(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1)
      | convergent_lines(X1,X2)
      | unorthogonal_lines(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f59,plain,
    ! [X2,X0,X1] :
      ( ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1)
      | unorthogonal_lines(X1,X2)
      | convergent_lines(X0,X2) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( unorthogonal_lines(X0,X1)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

tcf(c_49,negated_conjecture,
    convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
    inference(cnf_transformation,[],[f44]) ).

tcf(c_51,plain,
    ! [X0: $i,X1: $i] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f46]) ).

tcf(c_52,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( convergent_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

tcf(c_53,plain,
    ! [X0: $i] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f48]) ).

tcf(c_54,plain,
    ! [X0: $i,X1: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(X1,X0)),
    inference(cnf_transformation,[],[f49]) ).

tcf(c_55,plain,
    ! [X0: $i,X1: $i] : ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X0),
    inference(cnf_transformation,[],[f50]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( unorthogonal_lines(X1,X3)
      | unorthogonal_lines(X0,X3)
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X2,X0)
      | ~ distinct_lines(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

tcf(c_63,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(X1,X2)
      | convergent_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(X0,X2)
      | convergent_lines(X1,X2)
      | ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

tcf(c_65,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(X1,X2)
      | unorthogonal_lines(X0,X2)
      | ~ unorthogonal_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

tcf(c_66,plain,
    ! [X0: $i,X1: $i] :
      ( unorthogonal_lines(X0,X1)
      | convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_286,plain,
    ! [X0: $i,X1: $i] :
      ( unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
      | convergent_lines(orthogonal_through_point(X0,X1),X0) ),
    inference(instantiation,[status(thm)],[c_66]) ).

tcf(c_288,plain,
    ! [X0: $i] :
      ( convergent_lines(sK1,X0)
      | convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
      | ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
    inference(instantiation,[status(thm)],[c_52]) ).

tcf(c_290,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( convergent_lines(X0,X1)
      | unorthogonal_lines(orthogonal_through_point(X1,X2),X1)
      | ~ unorthogonal_lines(X0,orthogonal_through_point(X1,X2))
      | ~ convergent_lines(X0,orthogonal_through_point(X1,X2)) ),
    inference(instantiation,[status(thm)],[c_63]) ).

tcf(c_292,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( convergent_lines(X2,X0)
      | unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
      | ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
      | ~ convergent_lines(orthogonal_through_point(X0,X1),X2) ),
    inference(instantiation,[status(thm)],[c_64]) ).

tcf(c_293,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(X2,X0)
      | unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
      | ~ unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
      | ~ convergent_lines(orthogonal_through_point(X0,X1),X2) ),
    inference(instantiation,[status(thm)],[c_65]) ).

tcf(c_303,plain,
    ( convergent_lines(sK1,sK1)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
    | ~ convergent_lines(sK1,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)) ),
    inference(instantiation,[status(thm)],[c_288]) ).

tcf(c_304,plain,
    ~ convergent_lines(sK1,sK1),
    inference(instantiation,[status(thm)],[c_53]) ).

tcf(c_310,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1))
      | convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_286]) ).

tcf(c_314,plain,
    ! [X0: $i] :
      ( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
      | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
    inference(instantiation,[status(thm)],[c_51]) ).

tcf(c_321,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( unorthogonal_lines(X2,X4)
      | apart_point_and_line(X3,X2)
      | unorthogonal_lines(orthogonal_through_point(X0,X1),X4)
      | apart_point_and_line(X3,orthogonal_through_point(X0,X1))
      | ~ distinct_lines(orthogonal_through_point(X0,X1),X2) ),
    inference(instantiation,[status(thm)],[c_61]) ).

tcf(c_424,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
      ( unorthogonal_lines(orthogonal_through_point(X2,X3),X2)
      | unorthogonal_lines(orthogonal_through_point(X0,X1),X2)
      | apart_point_and_line(X4,orthogonal_through_point(X2,X3))
      | apart_point_and_line(X4,orthogonal_through_point(X0,X1))
      | ~ distinct_lines(orthogonal_through_point(X0,X1),orthogonal_through_point(X2,X3)) ),
    inference(instantiation,[status(thm)],[c_321]) ).

tcf(c_475,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( unorthogonal_lines(X3,orthogonal_through_point(X0,X1))
      | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1))
      | ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X3)
      | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X3) ),
    inference(instantiation,[status(thm)],[c_293]) ).

tcf(c_535,plain,
    ! [X0: $i,X1: $i] :
      ( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(X0,X1))
      | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_314]) ).

tcf(c_722,plain,
    ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)) ),
    inference(instantiation,[status(thm)],[c_310]) ).

tcf(c_806,plain,
    ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_915,plain,
    ~ apart_point_and_line(sK0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0)),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_1212,plain,
    ! [X0: $i] :
      ( convergent_lines(X0,orthogonal_through_point(sK1,sK0))
      | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
      | ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0)
      | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),X0) ),
    inference(instantiation,[status(thm)],[c_292]) ).

tcf(c_1451,plain,
    ! [X0: $i,X1: $i,X2: $i,X3: $i] :
      ( unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
      | apart_point_and_line(X3,orthogonal_through_point(X0,X1))
      | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),X0)
      | apart_point_and_line(X3,orthogonal_through_point(orthogonal_through_point(X0,X1),X2))
      | ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(X0,X1),X2),orthogonal_through_point(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_424]) ).

tcf(c_1479,plain,
    ( unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
    | ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
    | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1) ),
    inference(instantiation,[status(thm)],[c_475]) ).

tcf(c_1561,plain,
    ! [X0: $i,X1: $i] :
      ( convergent_lines(sK1,X0)
      | unorthogonal_lines(orthogonal_through_point(X0,X1),X0)
      | ~ unorthogonal_lines(sK1,orthogonal_through_point(X0,X1))
      | ~ convergent_lines(sK1,orthogonal_through_point(X0,X1)) ),
    inference(instantiation,[status(thm)],[c_290]) ).

tcf(c_1620,plain,
    ! [X0: $i] : ~ unorthogonal_lines(orthogonal_through_point(sK1,X0),sK1),
    inference(instantiation,[status(thm)],[c_55]) ).

tcf(c_1621,plain,
    ~ unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1),
    inference(instantiation,[status(thm)],[c_1620]) ).

tcf(c_2650,plain,
    ( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
    | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)) ),
    inference(instantiation,[status(thm)],[c_535]) ).

tcf(c_2673,plain,
    ( convergent_lines(sK1,orthogonal_through_point(sK1,sK0))
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0))
    | ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
    | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1) ),
    inference(instantiation,[status(thm)],[c_1212]) ).

tcf(c_4197,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( unorthogonal_lines(orthogonal_through_point(sK1,X0),sK1)
      | apart_point_and_line(X2,orthogonal_through_point(sK1,X0))
      | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,X0),X1),sK1)
      | apart_point_and_line(X2,orthogonal_through_point(orthogonal_through_point(sK1,X0),X1))
      | ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,X0),X1),orthogonal_through_point(sK1,X0)) ),
    inference(instantiation,[status(thm)],[c_1451]) ).

tcf(c_4201,plain,
    ( unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
    | apart_point_and_line(sK0,orthogonal_through_point(sK1,sK0))
    | unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),sK1)
    | apart_point_and_line(sK0,orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0))
    | ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(sK1,sK0),sK0),orthogonal_through_point(sK1,sK0)) ),
    inference(instantiation,[status(thm)],[c_4197]) ).

tcf(c_4281,plain,
    ! [X0: $i] :
      ( convergent_lines(sK1,sK1)
      | unorthogonal_lines(orthogonal_through_point(sK1,X0),sK1)
      | ~ unorthogonal_lines(sK1,orthogonal_through_point(sK1,X0))
      | ~ convergent_lines(sK1,orthogonal_through_point(sK1,X0)) ),
    inference(instantiation,[status(thm)],[c_1561]) ).

tcf(c_4282,plain,
    ( convergent_lines(sK1,sK1)
    | unorthogonal_lines(orthogonal_through_point(sK1,sK0),sK1)
    | ~ unorthogonal_lines(sK1,orthogonal_through_point(sK1,sK0))
    | ~ convergent_lines(sK1,orthogonal_through_point(sK1,sK0)) ),
    inference(instantiation,[status(thm)],[c_4281]) ).

tcf(c_4594,plain,
    ! [X0: $i] : ~ apart_point_and_line(X0,orthogonal_through_point(sK1,X0)),
    inference(instantiation,[status(thm)],[c_54]) ).

tcf(c_4595,plain,
    ~ apart_point_and_line(sK0,orthogonal_through_point(sK1,sK0)),
    inference(instantiation,[status(thm)],[c_4594]) ).

tcf(c_4596,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_4595,c_4282,c_4201,c_2673,c_2650,c_1621,c_1479,c_915,c_806,c_722,c_304,c_303,c_49]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05  % Command  : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38  % Computer : n010.cluster.edu
% 0.10/0.38  % Model    : x86_64 x86_64
% 0.10/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38  % Memory   : 8046.5625MB
% 0.10/0.38  % OS       : Linux 6.8.0-71-generic
% 0.10/0.38  % CPULimit : 300
% 0.10/0.38  % WCLimit  : 300
% 0.10/0.38  % DateTime : Wed Sep 23 11:33:43 UTC 2026
% 0.03/0.39  % CPUTime  : 
% 0.03/0.39  Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.43  Running first-order theorem proving
% 0.03/0.43  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
% 0.03/0.44  
% 0.03/0.44  % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.44  
% 0.03/0.44  % Detected problem language: tptp
% 0.03/0.45  % Proving...
% 3.86/1.32  % SZS status Started for theBenchmark.p
% 3.86/1.32  % SZS status Theorem for theBenchmark.p
% 3.86/1.32  
% 3.86/1.32  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.86/1.32  
% 3.86/1.32  % ------  iProver source info
% 3.86/1.32  
% 3.86/1.32  % git: date: 2026-07-19 20:42:38 +0200
% 3.86/1.32  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.86/1.32  % git: non_committed_changes: false
% 3.86/1.32  
% 3.86/1.32  % ------ Parsing...
% 3.86/1.32  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 3.86/1.32  
% 3.86/1.32  % ------ Preprocessing... sf_s  rm: 0 0s  sf_e  pe_s  pe_e  sf_s  rm: 0 0s  sf_e  pe_s  pe_e % 
% 3.86/1.32  
% 3.86/1.32  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 3.86/1.32  % ------ Proving...
% 3.86/1.32  % ------ Problem Properties 
% 3.86/1.32  
% 3.86/1.32  % 
% 3.86/1.32  % clauses                               19
% 3.86/1.32  % conjectures                           1
% 3.86/1.32  % EPR                                   16
% 3.86/1.32  % Horn                                  7
% 3.86/1.32  % unary                                 6
% 3.86/1.32  % binary                                2
% 3.86/1.32  % lits                                  52
% 3.86/1.32  % lits eq                               0
% 3.86/1.32  % fd_pure                               0
% 3.86/1.32  % fd_pseudo                             0
% 3.86/1.32  % fd_cond                               0
% 3.86/1.32  % fd_pseudo_cond                        0
% 3.86/1.32  % AC symbols                            0
% 3.86/1.32  
% 3.86/1.32  % ------ Schedule dynamic 5 is on 
% 3.86/1.32  
% 3.86/1.32  % ------ no equalities: superposition off 
% 3.86/1.32  
% 3.86/1.32  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.86/1.32  
% 3.86/1.32  
% 3.86/1.32  % ------ 
% 3.86/1.32  % Current options:
% 3.86/1.32  % ------ 
% 3.86/1.32  
% 3.86/1.32  
% 3.86/1.32  % 
% 3.86/1.32  
% 3.86/1.32  % ------ Proving...
% 3.86/1.32  % 
% 3.86/1.32  
% 3.86/1.32  % SZS status Theorem for theBenchmark.p
% 3.86/1.32  
% 3.86/1.32  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.86/1.32  
% 3.86/1.32  
%------------------------------------------------------------------------------