%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO221+2 : 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 : n027.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 0.48s 1.62s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 21
% Syntax : Number of formulae : 107 ( 50 unt; 0 def)
% Number of atoms : 261 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 267 ( 113 ~; 127 |; 11 &)
% ( 0 <=>; 16 =>; 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 : 237 ( 14 sgn 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/GEO008+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+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/GEO008+0.ax',cu1) ).
fof(con1,axiom,
! [X1,X2,X3] :
( distinct_points(X1,X2)
=> ( apart_point_and_line(X3,line_connecting(X1,X2))
=> ( distinct_points(X3,X1)
& distinct_points(X3,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con1) ).
fof(con2,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( ( apart_point_and_line(X3,X1)
| apart_point_and_line(X3,X2) )
=> distinct_points(X3,intersection_point(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',con2) ).
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(apart6,axiom,
! [X1,X2,X3] :
( convergent_lines(X1,X2)
=> ( convergent_lines(X1,X3)
| convergent_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',apart6) ).
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/GEO008+0.ax',ceq2) ).
fof(apart5,axiom,
! [X1,X2,X3] :
( distinct_lines(X1,X2)
=> ( distinct_lines(X1,X3)
| distinct_lines(X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+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/GEO008+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/GEO008+0.ax',apart4) ).
fof(ceq3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> distinct_lines(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/GEO008+0.ax',ceq3) ).
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_21,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(i_0_22,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_23,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(i_0_24,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_25,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_26,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_27,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_28,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_29,plain,
! [X82,X83,X84,X85] :
( ~ distinct_points(X82,X83)
| ~ distinct_lines(X84,X85)
| apart_point_and_line(X82,X84)
| apart_point_and_line(X82,X85)
| apart_point_and_line(X83,X84)
| apart_point_and_line(X83,X85) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_30,plain,
! [X76,X77,X78] :
( ( distinct_points(X78,X76)
| ~ apart_point_and_line(X78,line_connecting(X76,X77))
| ~ distinct_points(X76,X77) )
& ( distinct_points(X78,X77)
| ~ apart_point_and_line(X78,line_connecting(X76,X77))
| ~ distinct_points(X76,X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])])]) ).
fof(i_0_31,plain,
! [X79,X80,X81] :
( ( ~ apart_point_and_line(X81,X79)
| distinct_points(X81,intersection_point(X79,X80))
| ~ convergent_lines(X79,X80) )
& ( ~ apart_point_and_line(X81,X80)
| distinct_points(X81,intersection_point(X79,X80))
| ~ convergent_lines(X79,X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con2])])]) ).
fof(i_0_32,plain,
! [X110,X111,X112,X113] :
( ~ distinct_lines(X111,X112)
| apart_point_and_line(X110,X111)
| apart_point_and_line(X110,X112)
| unorthogonal_lines(X111,X113)
| unorthogonal_lines(X112,X113) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(i_0_33,plain,
! [X103,X104,X105] :
( ( convergent_lines(X104,X105)
| convergent_lines(X103,X105)
| ~ convergent_lines(X103,X104)
| ~ unorthogonal_lines(X103,X104) )
& ( unorthogonal_lines(X104,X105)
| convergent_lines(X103,X105)
| ~ convergent_lines(X103,X104)
| ~ unorthogonal_lines(X103,X104) )
& ( convergent_lines(X104,X105)
| unorthogonal_lines(X103,X105)
| ~ convergent_lines(X103,X104)
| ~ unorthogonal_lines(X103,X104) )
& ( unorthogonal_lines(X104,X105)
| unorthogonal_lines(X103,X105)
| ~ convergent_lines(X103,X104)
| ~ unorthogonal_lines(X103,X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
fof(i_0_34,plain,
! [X98,X99,X100] :
( ~ distinct_lines(X99,X100)
| apart_point_and_line(X98,X99)
| apart_point_and_line(X98,X100)
| convergent_lines(X99,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_35,plain,
! [X106,X107] : ~ unorthogonal_lines(orthogonal_through_point(X107,X106),X107),
inference(variable_rename,[status(thm)],[i_0_21]) ).
fof(i_0_36,plain,
! [X94,X95] : ~ convergent_lines(parallel_through_point(X95,X94),X95),
inference(variable_rename,[status(thm)],[i_0_22]) ).
fof(i_0_37,plain,
! [X108,X109] : ~ apart_point_and_line(X108,orthogonal_through_point(X109,X108)),
inference(variable_rename,[status(thm)],[i_0_23]) ).
fof(i_0_38,plain,
! [X96,X97] : ~ apart_point_and_line(X96,parallel_through_point(X97,X96)),
inference(variable_rename,[status(thm)],[i_0_24]) ).
fof(i_0_39,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_25])])]) ).
fof(i_0_40,plain,
! [X73,X74,X75] :
( ~ convergent_lines(X73,X74)
| convergent_lines(X73,X75)
| convergent_lines(X74,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart6])]) ).
fof(i_0_41,plain,
! [X89,X90,X91] :
( ~ apart_point_and_line(X89,X90)
| distinct_lines(X90,X91)
| apart_point_and_line(X89,X91) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_42,plain,
! [X70,X71,X72] :
( ~ distinct_lines(X70,X71)
| distinct_lines(X70,X72)
| distinct_lines(X71,X72) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_43,plain,
! [X86,X87,X88] :
( ~ apart_point_and_line(X86,X87)
| distinct_points(X86,X88)
| apart_point_and_line(X88,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_44,plain,
! [X67,X68,X69] :
( ~ distinct_points(X67,X68)
| distinct_points(X67,X69)
| distinct_points(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_45,plain,
! [X92,X93] :
( ~ convergent_lines(X92,X93)
| distinct_lines(X92,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_46,plain,
! [X101,X102] :
( convergent_lines(X101,X102)
| unorthogonal_lines(X101,X102) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(i_0_47,plain,
! [X66] : ~ convergent_lines(X66,X66),
inference(variable_rename,[status(thm)],[i_0_26]) ).
fof(i_0_48,plain,
! [X65] : ~ distinct_lines(X65,X65),
inference(variable_rename,[status(thm)],[i_0_27]) ).
fof(i_0_49,plain,
! [X64] : ~ distinct_points(X64,X64),
inference(variable_rename,[status(thm)],[i_0_28]) ).
cnf(i_0_50,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_29]),
[final] ).
cnf(i_0_51,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X2,X3))
| ~ distinct_points(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_52,plain,
( distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X3,X2))
| ~ distinct_points(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_53,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_54,plain,
( distinct_points(X1,intersection_point(X3,X2))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_55,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_32]),
[final] ).
cnf(i_0_56,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_57,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_58,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_60,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_34]),
[final] ).
cnf(i_0_61,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_62,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_63,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_64,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_65,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_39]),
[final] ).
cnf(i_0_66,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_67,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_68,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_69,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_70,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_71,negated_conjecture,
~ apart_point_and_line(esk2_0,orthogonal_through_point(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_72,plain,
( distinct_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_73,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_74,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_75,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_76,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_77,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(scs_inference,[],[i_0_61,i_0_73]) ).
cnf(i_0_78,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_73]) ).
cnf(i_0_79,plain,
distinct_lines(orthogonal_through_point(esk3_0,esk2_0),orthogonal_through_point(esk3_0,esk1_0)),
inference(scs_inference,[],[i_0_65,i_0_75,i_0_61,i_0_73,i_0_68]) ).
cnf(i_0_80,plain,
~ distinct_lines(X1,X1),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_81,plain,
( ~ distinct_lines(X1,X2)
| distinct_lines(X1,X3)
| distinct_lines(X2,X3) ),
inference(rename_variables,[],[i_0_68]) ).
cnf(i_0_82,plain,
~ apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_65,i_0_75,i_0_76,i_0_61,i_0_73,i_0_68,i_0_53]) ).
cnf(i_0_83,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_84,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X2)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_85,plain,
~ apart_point_and_line(intersection_point(orthogonal_through_point(X1,X2),X1),X1),
inference(scs_inference,[],[i_0_65,i_0_75,i_0_76,i_0_83,i_0_61,i_0_73,i_0_68,i_0_53,i_0_54]) ).
cnf(i_0_86,plain,
~ distinct_points(X1,X1),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_87,plain,
( distinct_points(X1,intersection_point(X2,X3))
| ~ apart_point_and_line(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_88,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_65,i_0_74,i_0_75,i_0_76,i_0_83,i_0_61,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66]) ).
cnf(i_0_89,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_90,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_66]) ).
cnf(i_0_91,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_65,i_0_71,i_0_74,i_0_75,i_0_76,i_0_83,i_0_61,i_0_62,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60]) ).
cnf(i_0_92,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_93,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(rename_variables,[],[i_0_64]) ).
cnf(i_0_94,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_60]) ).
cnf(i_0_95,plain,
~ unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_65,i_0_71,i_0_74,i_0_89,i_0_75,i_0_76,i_0_83,i_0_61,i_0_62,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60,i_0_58]) ).
cnf(i_0_96,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_97,plain,
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| unorthogonal_lines(X2,X3)
| convergent_lines(X1,X3) ),
inference(rename_variables,[],[i_0_58]) ).
cnf(i_0_98,plain,
unorthogonal_lines(orthogonal_through_point(esk3_0,esk1_0),esk3_0),
inference(scs_inference,[],[i_0_65,i_0_71,i_0_74,i_0_89,i_0_75,i_0_76,i_0_83,i_0_61,i_0_96,i_0_62,i_0_63,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60,i_0_58,i_0_55]) ).
cnf(i_0_99,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_61]) ).
cnf(i_0_100,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_101,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_55]) ).
cnf(i_0_102,plain,
distinct_lines(orthogonal_through_point(X1,X2),X1),
inference(scs_inference,[],[i_0_65,i_0_71,i_0_74,i_0_89,i_0_75,i_0_76,i_0_83,i_0_61,i_0_96,i_0_62,i_0_63,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60,i_0_58,i_0_55,i_0_72]) ).
cnf(i_0_103,plain,
( ~ convergent_lines(X1,X2)
| distinct_lines(X1,X2) ),
inference(rename_variables,[],[i_0_72]) ).
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_65,i_0_71,i_0_74,i_0_89,i_0_75,i_0_76,i_0_83,i_0_61,i_0_96,i_0_62,i_0_63,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60,i_0_58,i_0_55,i_0_72,i_0_56]) ).
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_56]) ).
cnf(i_0_106,plain,
$false,
inference(scs_inference,[],[i_0_65,i_0_71,i_0_74,i_0_89,i_0_75,i_0_76,i_0_83,i_0_61,i_0_96,i_0_99,i_0_62,i_0_63,i_0_64,i_0_73,i_0_68,i_0_53,i_0_54,i_0_66,i_0_60,i_0_58,i_0_55,i_0_72,i_0_56,i_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO221+2 : 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
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 17:49:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.48/1.62 % Version : CSE_E---1.7
% 0.48/1.62 % Problem : theBenchmark.p
% 0.48/1.62 % SZS status Theorem for theBenchmark.p
% 0.48/1.62 % SZS output start CNFRefutation
% See solution above
% 0.59/1.72 % Total time : 1.271s
%------------------------------------------------------------------------------