%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO221+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 : 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 : Tue May 5 04:19:59 PM UTC 2026
% Result : Theorem 0.45s 1.62s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 23
% Syntax : Number of formulae : 107 ( 45 unt; 0 def)
% Number of atoms : 251 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 256 ( 112 ~; 116 |; 8 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 232 ( 12 sgn 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ci1,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+2.ax',cp1) ).
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(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(con,conjecture,
! [X9,X10,X6] :
( ~ apart_point_and_line(X10,orthogonal_through_point(X6,X9))
=> ~ distinct_lines(orthogonal_through_point(X6,X9),orthogonal_through_point(X6,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(cu1,axiom,
! [X1,X2,X4,X5] :
( ( distinct_points(X1,X2)
& distinct_lines(X4,X5) )
=> ( apart_point_and_line(X1,X4)
| apart_point_and_line(X1,X5)
| apart_point_and_line(X2,X4)
| apart_point_and_line(X2,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',cu1) ).
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(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(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(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(ceq2,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq2) ).
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(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(ceq1,axiom,
! [X1,X2,X3] :
( apart_point_and_line(X1,X2)
=> ( distinct_points(X1,X3)
| apart_point_and_line(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',ceq1) ).
fof(apart4,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( distinct_points(X1,X3)
| distinct_points(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(i_0_23,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(fof_simplification,[status(thm)],[ci3]) ).
fof(i_0_24,plain,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(fof_simplification,[status(thm)],[ci4]) ).
fof(i_0_25,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci1]) ).
fof(i_0_26,plain,
! [X1,X2] :
( distinct_points(X1,X2)
=> ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(fof_simplification,[status(thm)],[ci2]) ).
fof(i_0_27,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(i_0_28,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_29,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(i_0_30,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_31,negated_conjecture,
~ ! [X9,X10,X6] :
( ~ apart_point_and_line(X10,orthogonal_through_point(X6,X9))
=> ~ distinct_lines(orthogonal_through_point(X6,X9),orthogonal_through_point(X6,X10)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_32,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_33,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_34,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_35,plain,
! [X87,X88,X89,X90] :
( ~ distinct_points(X87,X88)
| ~ distinct_lines(X89,X90)
| apart_point_and_line(X87,X89)
| apart_point_and_line(X87,X90)
| apart_point_and_line(X88,X89)
| apart_point_and_line(X88,X90) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_36,plain,
! [X83,X84] :
( ~ convergent_lines(X83,X84)
| ~ apart_point_and_line(intersection_point(X83,X84),X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_23])]) ).
fof(i_0_37,plain,
! [X85,X86] :
( ~ convergent_lines(X85,X86)
| ~ apart_point_and_line(intersection_point(X85,X86),X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])]) ).
fof(i_0_38,plain,
! [X79,X80] :
( ~ distinct_points(X79,X80)
| ~ apart_point_and_line(X79,line_connecting(X79,X80)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_25])]) ).
fof(i_0_39,plain,
! [X81,X82] :
( ~ distinct_points(X81,X82)
| ~ apart_point_and_line(X82,line_connecting(X81,X82)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])]) ).
fof(i_0_40,plain,
! [X116,X117,X118,X119] :
( ~ distinct_lines(X117,X118)
| apart_point_and_line(X116,X117)
| apart_point_and_line(X116,X118)
| unorthogonal_lines(X117,X119)
| unorthogonal_lines(X118,X119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(i_0_41,plain,
! [X109,X110,X111] :
( ( convergent_lines(X110,X111)
| convergent_lines(X109,X111)
| ~ convergent_lines(X109,X110)
| ~ unorthogonal_lines(X109,X110) )
& ( unorthogonal_lines(X110,X111)
| convergent_lines(X109,X111)
| ~ convergent_lines(X109,X110)
| ~ unorthogonal_lines(X109,X110) )
& ( convergent_lines(X110,X111)
| unorthogonal_lines(X109,X111)
| ~ convergent_lines(X109,X110)
| ~ unorthogonal_lines(X109,X110) )
& ( unorthogonal_lines(X110,X111)
| unorthogonal_lines(X109,X111)
| ~ convergent_lines(X109,X110)
| ~ unorthogonal_lines(X109,X110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
fof(i_0_42,plain,
! [X104,X105,X106] :
( ~ distinct_lines(X105,X106)
| apart_point_and_line(X104,X105)
| apart_point_and_line(X104,X106)
| convergent_lines(X105,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_43,plain,
! [X112,X113] : ~ unorthogonal_lines(orthogonal_through_point(X113,X112),X113),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_44,plain,
! [X100,X101] : ~ convergent_lines(parallel_through_point(X101,X100),X101),
inference(variable_rename,[status(thm)],[i_0_28]) ).
fof(i_0_45,plain,
! [X114,X115] : ~ apart_point_and_line(X114,orthogonal_through_point(X115,X114)),
inference(variable_rename,[status(thm)],[i_0_29]) ).
fof(i_0_46,plain,
! [X102,X103] : ~ apart_point_and_line(X102,parallel_through_point(X103,X102)),
inference(variable_rename,[status(thm)],[i_0_30]) ).
fof(i_0_47,negated_conjecture,
( ~ apart_point_and_line(esk2_0,orthogonal_through_point(esk3_0,esk1_0))
& distinct_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_31])])]) ).
fof(i_0_48,plain,
! [X76,X77,X78] :
( ~ convergent_lines(X76,X77)
| convergent_lines(X76,X78)
| convergent_lines(X77,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_49,plain,
! [X94,X95,X96] :
( ~ apart_point_and_line(X94,X95)
| distinct_lines(X95,X96)
| apart_point_and_line(X94,X96) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_50,plain,
! [X97,X98,X99] :
( ~ convergent_lines(X97,X98)
| distinct_lines(X98,X99)
| convergent_lines(X97,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_51,plain,
! [X73,X74,X75] :
( ~ distinct_lines(X73,X74)
| distinct_lines(X73,X75)
| distinct_lines(X74,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_52,plain,
! [X91,X92,X93] :
( ~ apart_point_and_line(X91,X92)
| distinct_points(X91,X93)
| apart_point_and_line(X93,X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_53,plain,
! [X70,X71,X72] :
( ~ distinct_points(X70,X71)
| distinct_points(X70,X72)
| distinct_points(X71,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_54,plain,
! [X107,X108] :
( convergent_lines(X107,X108)
| unorthogonal_lines(X107,X108) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(i_0_55,plain,
! [X69] : ~ convergent_lines(X69,X69),
inference(variable_rename,[status(thm)],[i_0_32]) ).
fof(i_0_56,plain,
! [X68] : ~ distinct_lines(X68,X68),
inference(variable_rename,[status(thm)],[i_0_33]) ).
fof(i_0_57,plain,
! [X67] : ~ distinct_points(X67,X67),
inference(variable_rename,[status(thm)],[i_0_34]) ).
cnf(i_0_58,plain,
( apart_point_and_line(X1,X3)
| apart_point_and_line(X1,X4)
| apart_point_and_line(X2,X3)
| apart_point_and_line(X2,X4)
| ~ distinct_points(X1,X2)
| ~ distinct_lines(X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_59,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_60,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_61,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_62,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_63,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)],[i_0_40]),
[final] ).
cnf(i_0_64,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_65,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_66,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_67,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_68,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)],[i_0_42]),
[final] ).
cnf(i_0_69,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_70,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_71,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_72,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_73,negated_conjecture,
distinct_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_74,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_75,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_76,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_77,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_78,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_79,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_80,negated_conjecture,
~ apart_point_and_line(esk2_0,orthogonal_through_point(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_81,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_82,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_83,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_84,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_85,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(scs_inference,[],[i_0_69,i_0_81]) ).
cnf(i_0_86,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_87,plain,
distinct_lines(orthogonal_through_point(esk3_0,esk2_0),orthogonal_through_point(esk3_0,esk1_0)),
inference(scs_inference,[],[i_0_73,i_0_83,i_0_69,i_0_81,i_0_77]) ).
cnf(i_0_88,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_83]) ).
cnf(i_0_89,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_90,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_73,i_0_82,i_0_83,i_0_69,i_0_81,i_0_77,i_0_74]) ).
cnf(i_0_91,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_92,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_93,plain,
~ distinct_lines(parallel_through_point(orthogonal_through_point(esk3_0,esk1_0),esk2_0),orthogonal_through_point(esk3_0,esk1_0)),
inference(scs_inference,[],[i_0_73,i_0_80,i_0_82,i_0_83,i_0_69,i_0_70,i_0_72,i_0_81,i_0_77,i_0_74,i_0_68]) ).
cnf(i_0_94,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_70]) ).
cnf(i_0_95,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(rename_variables,[],[i_0_72]) ).
cnf(i_0_96,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2)
| apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) ),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_97,plain,
~ unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_73,i_0_80,i_0_82,i_0_91,i_0_83,i_0_69,i_0_70,i_0_72,i_0_81,i_0_77,i_0_74,i_0_68,i_0_66]) ).
cnf(i_0_98,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_99,plain,
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_100,plain,
unorthogonal_lines(orthogonal_through_point(esk3_0,esk1_0),esk3_0),
inference(scs_inference,[],[i_0_73,i_0_80,i_0_82,i_0_91,i_0_83,i_0_69,i_0_98,i_0_70,i_0_71,i_0_72,i_0_81,i_0_77,i_0_74,i_0_68,i_0_66,i_0_63]) ).
cnf(i_0_101,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_69]) ).
cnf(i_0_102,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_103,plain,
( unorthogonal_lines(X1,X2)
| ~ distinct_lines(X3,X1)
| apart_point_and_line(X4,X3)
| apart_point_and_line(X4,X1)
| unorthogonal_lines(X3,X2) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_104,plain,
unorthogonal_lines(orthogonal_through_point(esk3_0,esk1_0),orthogonal_through_point(esk3_0,esk1_0)),
inference(scs_inference,[],[i_0_73,i_0_80,i_0_82,i_0_91,i_0_83,i_0_69,i_0_98,i_0_70,i_0_71,i_0_72,i_0_81,i_0_77,i_0_74,i_0_68,i_0_66,i_0_63,i_0_64]) ).
cnf(i_0_105,plain,
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| unorthogonal_lines(X1,X3) ),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_106,plain,
$false,
inference(scs_inference,[],[i_0_73,i_0_80,i_0_82,i_0_91,i_0_83,i_0_69,i_0_98,i_0_101,i_0_70,i_0_71,i_0_72,i_0_81,i_0_77,i_0_74,i_0_68,i_0_66,i_0_63,i_0_64,i_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO221+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
% 0.16/0.33 % Computer : n022.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 17:48:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 0.45/1.62 % Version : CSE_E---1.7
% 0.45/1.62 % Problem : theBenchmark.p
% 0.45/1.62 % SZS status Theorem for theBenchmark.p
% 0.45/1.62 % SZS output start CNFRefutation
% See solution above
% 0.45/1.69 % Total time : 1.272s
%------------------------------------------------------------------------------