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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : GEO223+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n018.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 : Tue May  5 04:20:00 PM UTC 2026

% Result   : Theorem 3.80s 3.18s
% Output   : CNFRefutation 3.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   83 (  34 unt;   0 def)
%            Number of atoms       :  193 (   0 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  171 (  61   ~;  94   |;   6   &)
%                                         (   0 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  178 (  19 sgn  88   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(ooc1,axiom,
    ! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).

fof(apart5,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X1,X3)
        | distinct_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart5) ).

fof(occu1,axiom,
    ! [X6,X7] :
      ( convergent_lines(X6,X7)
      | unorthogonal_lines(X6,X7) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).

fof(ceq3,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( distinct_lines(X2,X3)
        | convergent_lines(X1,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq3) ).

fof(apart2,axiom,
    ! [X1] : ~ distinct_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).

fof(ax6,axiom,
    ! [X1,X2,X3] :
      ( convergent_lines(X1,X2)
     => ( convergent_lines(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ax6) ).

fof(apart3,axiom,
    ! [X1] : ~ convergent_lines(X1,X1),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).

fof(ouo1,axiom,
    ! [X9,X6,X7,X8] :
      ( distinct_lines(X6,X7)
     => ( apart_point_and_line(X9,X6)
        | apart_point_and_line(X9,X7)
        | unorthogonal_lines(X6,X8)
        | unorthogonal_lines(X7,X8) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ouo1) ).

fof(ci3,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci3) ).

fof(ooc2,axiom,
    ! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc2) ).

fof(cup1,axiom,
    ! [X1,X2,X3] :
      ( distinct_lines(X2,X3)
     => ( apart_point_and_line(X1,X2)
        | apart_point_and_line(X1,X3)
        | convergent_lines(X2,X3) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cup1) ).

fof(cp1,axiom,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).

fof(ci4,axiom,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci4) ).

fof(cp2,axiom,
    ! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp2) ).

fof(oac1,axiom,
    ! [X6,X7,X8] :
      ( ( convergent_lines(X6,X7)
        & unorthogonal_lines(X6,X7) )
     => ( ( convergent_lines(X6,X8)
          & unorthogonal_lines(X6,X8) )
        | ( convergent_lines(X7,X8)
          & unorthogonal_lines(X7,X8) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',oac1) ).

fof(c_0_16,negated_conjecture,
    ~ ! [X9,X6] : ~ distinct_lines(parallel_through_point(X6,X9),orthogonal_through_point(orthogonal_through_point(X6,X9),X9)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).

fof(c_0_17,plain,
    ! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
    inference(fof_simplification,[status(thm)],[ooc1]) ).

fof(c_0_18,plain,
    ! [X71,X72,X73] :
      ( ~ distinct_lines(X71,X72)
      | distinct_lines(X71,X73)
      | distinct_lines(X72,X73) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).

fof(c_0_19,negated_conjecture,
    distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).

fof(c_0_20,plain,
    ! [X110,X111] : ~ unorthogonal_lines(orthogonal_through_point(X111,X110),X111),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

fof(c_0_21,plain,
    ! [X105,X106] :
      ( convergent_lines(X105,X106)
      | unorthogonal_lines(X105,X106) ),
    inference(variable_rename,[status(thm)],[occu1]) ).

cnf(c_0_22,plain,
    ( distinct_lines(X1,X3)
    | distinct_lines(X2,X3)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_23,negated_conjecture,
    distinct_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_24,plain,
    ! [X95,X96,X97] :
      ( ~ convergent_lines(X95,X96)
      | distinct_lines(X96,X97)
      | convergent_lines(X95,X97) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).

cnf(c_0_25,plain,
    ~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_26,plain,
    ( convergent_lines(X1,X2)
    | unorthogonal_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    ( distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_28,plain,
    ! [X1] : ~ distinct_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart2]) ).

fof(c_0_29,plain,
    ! [X74,X75,X76] :
      ( ~ convergent_lines(X74,X75)
      | convergent_lines(X74,X76)
      | convergent_lines(X75,X76) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).

cnf(c_0_30,plain,
    ( distinct_lines(X2,X3)
    | convergent_lines(X1,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    convergent_lines(orthogonal_through_point(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,negated_conjecture,
    ( distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X2)
    | distinct_lines(X2,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_27]) ).

fof(c_0_33,plain,
    ! [X66] : ~ distinct_lines(X66,X66),
    inference(variable_rename,[status(thm)],[c_0_28]) ).

cnf(c_0_34,plain,
    ( convergent_lines(X1,X3)
    | convergent_lines(X2,X3)
    | ~ convergent_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_35,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | distinct_lines(X1,X3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    ( distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X2)
    | distinct_lines(X2,X3)
    | distinct_lines(X1,X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_32]) ).

cnf(c_0_37,plain,
    ~ distinct_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

fof(c_0_38,plain,
    ! [X1] : ~ convergent_lines(X1,X1),
    inference(fof_simplification,[status(thm)],[apart3]) ).

cnf(c_0_39,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(X4,X3)
    | distinct_lines(X1,X4) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

fof(c_0_40,plain,
    ! [X114,X115,X116,X117] :
      ( ~ distinct_lines(X115,X116)
      | apart_point_and_line(X114,X115)
      | apart_point_and_line(X114,X116)
      | unorthogonal_lines(X115,X117)
      | unorthogonal_lines(X116,X117) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).

cnf(c_0_41,negated_conjecture,
    ( distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | distinct_lines(X1,parallel_through_point(esk2_0,esk1_0)) ),
    inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_36]),c_0_37]) ).

fof(c_0_42,plain,
    ! [X67] : ~ convergent_lines(X67,X67),
    inference(variable_rename,[status(thm)],[c_0_38]) ).

cnf(c_0_43,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(X4,X5)
    | convergent_lines(X3,X5)
    | distinct_lines(X1,X4) ),
    inference(spm,[status(thm)],[c_0_34,c_0_39]) ).

fof(c_0_44,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(fof_simplification,[status(thm)],[ci3]) ).

cnf(c_0_45,plain,
    ( apart_point_and_line(X3,X1)
    | apart_point_and_line(X3,X2)
    | unorthogonal_lines(X1,X4)
    | unorthogonal_lines(X2,X4)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_46,negated_conjecture,
    distinct_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0)),
    inference(spm,[status(thm)],[c_0_37,c_0_41]) ).

fof(c_0_47,plain,
    ! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
    inference(fof_simplification,[status(thm)],[ooc2]) ).

fof(c_0_48,plain,
    ! [X102,X103,X104] :
      ( ~ distinct_lines(X103,X104)
      | apart_point_and_line(X102,X103)
      | apart_point_and_line(X102,X104)
      | convergent_lines(X103,X104) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).

fof(c_0_49,plain,
    ! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
    inference(fof_simplification,[status(thm)],[cp1]) ).

cnf(c_0_50,plain,
    ~ convergent_lines(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_51,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(X3,X4)
    | convergent_lines(X1,X4) ),
    inference(spm,[status(thm)],[c_0_37,c_0_43]) ).

fof(c_0_52,plain,
    ! [X81,X82] :
      ( ~ convergent_lines(X81,X82)
      | ~ apart_point_and_line(intersection_point(X81,X82),X81) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])]) ).

cnf(c_0_53,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),X1)
    | apart_point_and_line(X2,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
    | apart_point_and_line(X2,parallel_through_point(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_46]) ).

fof(c_0_54,plain,
    ! [X112,X113] : ~ apart_point_and_line(X112,orthogonal_through_point(X113,X112)),
    inference(variable_rename,[status(thm)],[c_0_47]) ).

cnf(c_0_55,plain,
    ( apart_point_and_line(X3,X1)
    | apart_point_and_line(X3,X2)
    | convergent_lines(X1,X2)
    | ~ distinct_lines(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

fof(c_0_56,plain,
    ! [X98,X99] : ~ convergent_lines(parallel_through_point(X99,X98),X99),
    inference(variable_rename,[status(thm)],[c_0_49]) ).

cnf(c_0_57,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(X3,X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

fof(c_0_58,plain,
    ! [X1,X2] :
      ( convergent_lines(X1,X2)
     => ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(fof_simplification,[status(thm)],[ci4]) ).

cnf(c_0_59,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_60,negated_conjecture,
    ( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
    | apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
    | apart_point_and_line(X1,parallel_through_point(esk2_0,esk1_0)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_53]) ).

cnf(c_0_61,plain,
    ~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_62,negated_conjecture,
    ( apart_point_and_line(X1,orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0))
    | apart_point_and_line(X1,X2)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X2)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_27]) ).

fof(c_0_63,plain,
    ! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    inference(fof_simplification,[status(thm)],[cp2]) ).

cnf(c_0_64,plain,
    ~ convergent_lines(parallel_through_point(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_56]) ).

cnf(c_0_65,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(X4,X1)
    | distinct_lines(X4,X3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_57]) ).

fof(c_0_66,plain,
    ! [X83,X84] :
      ( ~ convergent_lines(X83,X84)
      | ~ apart_point_and_line(intersection_point(X83,X84),X84) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])]) ).

cnf(c_0_67,negated_conjecture,
    ( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
    | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1),parallel_through_point(esk2_0,esk1_0))
    | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_68,negated_conjecture,
    ( apart_point_and_line(esk1_0,X1)
    | convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_69,plain,
    ! [X100,X101] : ~ apart_point_and_line(X100,parallel_through_point(X101,X100)),
    inference(variable_rename,[status(thm)],[c_0_63]) ).

cnf(c_0_70,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | distinct_lines(parallel_through_point(X1,X4),X3) ),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_71,plain,
    ( ~ convergent_lines(X1,X2)
    | ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_72,negated_conjecture,
    ( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
    | apart_point_and_line(intersection_point(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),X1),parallel_through_point(esk2_0,esk1_0))
    | apart_point_and_line(esk1_0,X1)
    | distinct_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_73,plain,
    ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_74,plain,
    convergent_lines(orthogonal_through_point(X1,X2),parallel_through_point(X1,X3)),
    inference(spm,[status(thm)],[c_0_37,c_0_70]) ).

fof(c_0_75,plain,
    ! [X107,X108,X109] :
      ( ( convergent_lines(X108,X109)
        | convergent_lines(X107,X109)
        | ~ convergent_lines(X107,X108)
        | ~ unorthogonal_lines(X107,X108) )
      & ( unorthogonal_lines(X108,X109)
        | convergent_lines(X107,X109)
        | ~ convergent_lines(X107,X108)
        | ~ unorthogonal_lines(X107,X108) )
      & ( convergent_lines(X108,X109)
        | unorthogonal_lines(X107,X109)
        | ~ convergent_lines(X107,X108)
        | ~ unorthogonal_lines(X107,X108) )
      & ( unorthogonal_lines(X108,X109)
        | unorthogonal_lines(X107,X109)
        | ~ convergent_lines(X107,X108)
        | ~ unorthogonal_lines(X107,X108) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).

cnf(c_0_76,negated_conjecture,
    ( unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0))
    | ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(esk2_0,esk1_0),esk1_0),parallel_through_point(esk2_0,esk1_0)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_37]) ).

cnf(c_0_77,plain,
    ( convergent_lines(orthogonal_through_point(X1,X2),X3)
    | convergent_lines(parallel_through_point(X1,X4),X3) ),
    inference(spm,[status(thm)],[c_0_34,c_0_74]) ).

cnf(c_0_78,plain,
    ( unorthogonal_lines(X1,X2)
    | convergent_lines(X3,X2)
    | ~ convergent_lines(X3,X1)
    | ~ unorthogonal_lines(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_79,negated_conjecture,
    unorthogonal_lines(parallel_through_point(esk2_0,esk1_0),orthogonal_through_point(esk2_0,esk1_0)),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_68]),c_0_73]),c_0_37]) ).

cnf(c_0_80,plain,
    convergent_lines(parallel_through_point(X1,X2),orthogonal_through_point(X1,X3)),
    inference(spm,[status(thm)],[c_0_50,c_0_77]) ).

cnf(c_0_81,negated_conjecture,
    ( unorthogonal_lines(orthogonal_through_point(esk2_0,esk1_0),X1)
    | convergent_lines(parallel_through_point(esk2_0,esk1_0),X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).

cnf(c_0_82,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_81]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GEO223+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32  % Computer : n018.cluster.edu
% 0.14/0.32  % Model    : x86_64 x86_64
% 0.14/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32  % Memory   : 8042.1875MB
% 0.14/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32  % CPULimit   : 300
% 0.14/0.32  % WCLimit    : 300
% 0.14/0.32  % DateTime   : Mon May  4 17:48:32 EDT 2026
% 0.14/0.32  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 3.80/3.18  % Version  : CSE_E---1.7
% 3.80/3.18  % Problem  : theBenchmark.p
% 3.80/3.18  % SZS status Theorem for theBenchmark.p
% 3.80/3.18  % SZS output start CNFRefutation
% See solution above
% 3.80/3.19  % Total time : 2.371s
%------------------------------------------------------------------------------