%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO216+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.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 04:19:58 PM UTC 2026
% Result : Theorem 0.28s 1.61s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 36
% Syntax : Number of formulae : 159 ( 44 unt; 0 def)
% Number of atoms : 412 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 455 ( 202 ~; 189 |; 27 &)
% ( 10 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 349 ( 10 sgn 201 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci3,axiom,
! [X1,X2] :
( convergent_lines(X1,X2)
=> ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',ci2) ).
fof(cotno1,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/sandbox2/benchmark/Axioms/GEO006+4.ax',cotno1) ).
fof(ooc1,axiom,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc1) ).
fof(cp1,axiom,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp1) ).
fof(ooc2,axiom,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',ooc2) ).
fof(cp2,axiom,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+2.ax',cp2) ).
fof(couo1,axiom,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
fof(a5,axiom,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a5) ).
fof(a4,axiom,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a4) ).
fof(a3,axiom,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',a3) ).
fof(ax2,axiom,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax2) ).
fof(ax1,axiom,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+6.ax',ax1) ).
fof(coipo1,axiom,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',coipo1) ).
fof(apart3,axiom,
! [X1] : ~ convergent_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart3) ).
fof(apart2,axiom,
! [X1] : ~ distinct_lines(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart2) ).
fof(apart1,axiom,
! [X1] : ~ distinct_points(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+0.ax',apart1) ).
fof(con,conjecture,
! [X6] : ~ orthogonal_lines(X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+3.ax',oac1) ).
fof(con1,axiom,
! [X9,X10] :
( ( point(X9)
& point(X10)
& distinct_points(X9,X10) )
=> line(line_connecting(X9,X10)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',con1) ).
fof(int1,axiom,
! [X6,X7] :
( ( line(X6)
& line(X7)
& convergent_lines(X6,X7) )
=> point(intersection_point(X6,X7)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',int1) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/GEO006+0.ax',apart4) ).
fof(orth1,axiom,
! [X6,X9] :
( ( line(X6)
& point(X9) )
=> line(orthogonal_through_point(X6,X9)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',orth1) ).
fof(par1,axiom,
! [X6,X9] :
( ( line(X6)
& point(X9) )
=> line(parallel_through_point(X6,X9)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+5.ax',par1) ).
fof(p1,axiom,
! [X1,X2] :
( distinct_lines(X1,X2)
=> convergent_lines(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+1.ax',p1) ).
fof(occu1,axiom,
! [X6,X7] :
( convergent_lines(X6,X7)
| unorthogonal_lines(X6,X7) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+3.ax',occu1) ).
fof(i_0_36,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_37,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_38,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_39,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_40,plain,
! [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) ) ),
inference(fof_simplification,[status(thm)],[cotno1]) ).
fof(i_0_41,plain,
! [X9,X6] : ~ unorthogonal_lines(orthogonal_through_point(X6,X9),X6),
inference(fof_simplification,[status(thm)],[ooc1]) ).
fof(i_0_42,plain,
! [X1,X2] : ~ convergent_lines(parallel_through_point(X2,X1),X2),
inference(fof_simplification,[status(thm)],[cp1]) ).
fof(i_0_43,plain,
! [X9,X6] : ~ apart_point_and_line(X9,orthogonal_through_point(X6,X9)),
inference(fof_simplification,[status(thm)],[ooc2]) ).
fof(i_0_44,plain,
! [X1,X2] : ~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(fof_simplification,[status(thm)],[cp2]) ).
fof(i_0_45,plain,
! [X6,X7,X8] :
( ( ~ unorthogonal_lines(X6,X7)
& ~ unorthogonal_lines(X6,X8) )
=> ~ convergent_lines(X7,X8) ),
inference(fof_simplification,[status(thm)],[couo1]) ).
fof(i_0_46,plain,
! [X1,X2] :
( orthogonal_lines(X1,X2)
<=> ~ unorthogonal_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a5]) ).
fof(i_0_47,plain,
! [X1,X2] :
( incident_point_and_line(X1,X2)
<=> ~ apart_point_and_line(X1,X2) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(i_0_48,plain,
! [X1,X2] :
( parallel_lines(X1,X2)
<=> ~ convergent_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(i_0_49,plain,
! [X1,X2] :
( equal_lines(X1,X2)
<=> ~ distinct_lines(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax2]) ).
fof(i_0_50,plain,
! [X1,X2] :
( equal_points(X1,X2)
<=> ~ distinct_points(X1,X2) ),
inference(fof_simplification,[status(thm)],[ax1]) ).
fof(i_0_51,plain,
! [X6,X7] :
~ ( ~ convergent_lines(X6,X7)
& ~ unorthogonal_lines(X6,X7) ),
inference(fof_simplification,[status(thm)],[coipo1]) ).
fof(i_0_52,plain,
! [X1] : ~ convergent_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart3]) ).
fof(i_0_53,plain,
! [X1] : ~ distinct_lines(X1,X1),
inference(fof_simplification,[status(thm)],[apart2]) ).
fof(i_0_54,plain,
! [X1] : ~ distinct_points(X1,X1),
inference(fof_simplification,[status(thm)],[apart1]) ).
fof(i_0_55,negated_conjecture,
~ ! [X6] : ~ orthogonal_lines(X6,X6),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[con])]) ).
fof(i_0_56,plain,
! [X113,X114,X115,X116] :
( ~ distinct_points(X113,X114)
| ~ distinct_lines(X115,X116)
| apart_point_and_line(X113,X115)
| apart_point_and_line(X113,X116)
| apart_point_and_line(X114,X115)
| apart_point_and_line(X114,X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cu1])]) ).
fof(i_0_57,plain,
! [X109,X110] :
( ~ convergent_lines(X109,X110)
| ~ apart_point_and_line(intersection_point(X109,X110),X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])]) ).
fof(i_0_58,plain,
! [X111,X112] :
( ~ convergent_lines(X111,X112)
| ~ apart_point_and_line(intersection_point(X111,X112),X112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_37])]) ).
fof(i_0_59,plain,
! [X105,X106] :
( ~ distinct_points(X105,X106)
| ~ apart_point_and_line(X105,line_connecting(X105,X106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])]) ).
fof(i_0_60,plain,
! [X107,X108] :
( ~ distinct_points(X107,X108)
| ~ apart_point_and_line(X108,line_connecting(X107,X108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_39])]) ).
fof(i_0_61,plain,
! [X144,X145,X146,X147] :
( ~ distinct_lines(X145,X146)
| apart_point_and_line(X144,X145)
| apart_point_and_line(X144,X146)
| unorthogonal_lines(X145,X147)
| unorthogonal_lines(X146,X147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ouo1])]) ).
fof(i_0_62,plain,
! [X150,X151,X152] :
( ( convergent_lines(X150,X152)
| convergent_lines(X150,X151)
| ~ convergent_lines(X151,X152)
| ~ unorthogonal_lines(X151,X152) )
& ( unorthogonal_lines(X150,X152)
| convergent_lines(X150,X151)
| ~ convergent_lines(X151,X152)
| ~ unorthogonal_lines(X151,X152) )
& ( convergent_lines(X150,X152)
| unorthogonal_lines(X150,X151)
| ~ convergent_lines(X151,X152)
| ~ unorthogonal_lines(X151,X152) )
& ( unorthogonal_lines(X150,X152)
| unorthogonal_lines(X150,X151)
| ~ convergent_lines(X151,X152)
| ~ unorthogonal_lines(X151,X152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_40])])]) ).
fof(i_0_63,plain,
! [X137,X138,X139] :
( ( convergent_lines(X138,X139)
| convergent_lines(X137,X139)
| ~ convergent_lines(X137,X138)
| ~ unorthogonal_lines(X137,X138) )
& ( unorthogonal_lines(X138,X139)
| convergent_lines(X137,X139)
| ~ convergent_lines(X137,X138)
| ~ unorthogonal_lines(X137,X138) )
& ( convergent_lines(X138,X139)
| unorthogonal_lines(X137,X139)
| ~ convergent_lines(X137,X138)
| ~ unorthogonal_lines(X137,X138) )
& ( unorthogonal_lines(X138,X139)
| unorthogonal_lines(X137,X139)
| ~ convergent_lines(X137,X138)
| ~ unorthogonal_lines(X137,X138) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[oac1])])]) ).
fof(i_0_64,plain,
! [X156,X157] :
( ~ point(X156)
| ~ point(X157)
| ~ distinct_points(X156,X157)
| line(line_connecting(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[con1])]) ).
fof(i_0_65,plain,
! [X158,X159] :
( ~ line(X158)
| ~ line(X159)
| ~ convergent_lines(X158,X159)
| point(intersection_point(X158,X159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int1])]) ).
fof(i_0_66,plain,
! [X132,X133,X134] :
( ~ distinct_lines(X133,X134)
| apart_point_and_line(X132,X133)
| apart_point_and_line(X132,X134)
| convergent_lines(X133,X134) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cup1])]) ).
fof(i_0_67,plain,
! [X140,X141] : ~ unorthogonal_lines(orthogonal_through_point(X141,X140),X141),
inference(variable_rename,[status(thm)],[i_0_41]) ).
fof(i_0_68,plain,
! [X128,X129] : ~ convergent_lines(parallel_through_point(X129,X128),X129),
inference(variable_rename,[status(thm)],[i_0_42]) ).
fof(i_0_69,plain,
! [X142,X143] : ~ apart_point_and_line(X142,orthogonal_through_point(X143,X142)),
inference(variable_rename,[status(thm)],[i_0_43]) ).
fof(i_0_70,plain,
! [X130,X131] : ~ apart_point_and_line(X130,parallel_through_point(X131,X130)),
inference(variable_rename,[status(thm)],[i_0_44]) ).
fof(i_0_71,plain,
! [X153,X154,X155] :
( unorthogonal_lines(X153,X154)
| unorthogonal_lines(X153,X155)
| ~ convergent_lines(X154,X155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])]) ).
fof(i_0_72,plain,
! [X102,X103,X104] :
( ~ convergent_lines(X102,X103)
| convergent_lines(X102,X104)
| convergent_lines(X103,X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax6])]) ).
fof(i_0_73,plain,
! [X120,X121,X122] :
( ~ apart_point_and_line(X120,X121)
| distinct_lines(X121,X122)
| apart_point_and_line(X120,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq2])]) ).
fof(i_0_74,plain,
! [X123,X124,X125] :
( ~ convergent_lines(X123,X124)
| distinct_lines(X124,X125)
| convergent_lines(X123,X125) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq3])]) ).
fof(i_0_75,plain,
! [X99,X100,X101] :
( ~ distinct_lines(X99,X100)
| distinct_lines(X99,X101)
| distinct_lines(X100,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart5])]) ).
fof(i_0_76,plain,
! [X117,X118,X119] :
( ~ apart_point_and_line(X117,X118)
| distinct_points(X117,X119)
| apart_point_and_line(X119,X118) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ceq1])]) ).
fof(i_0_77,plain,
! [X96,X97,X98] :
( ~ distinct_points(X96,X97)
| distinct_points(X96,X98)
| distinct_points(X97,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[apart4])]) ).
fof(i_0_78,plain,
! [X172,X173] :
( ( ~ orthogonal_lines(X172,X173)
| ~ unorthogonal_lines(X172,X173) )
& ( unorthogonal_lines(X172,X173)
| orthogonal_lines(X172,X173) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])]) ).
fof(i_0_79,plain,
! [X170,X171] :
( ( ~ incident_point_and_line(X170,X171)
| ~ apart_point_and_line(X170,X171) )
& ( apart_point_and_line(X170,X171)
| incident_point_and_line(X170,X171) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_47])]) ).
fof(i_0_80,plain,
! [X168,X169] :
( ( ~ parallel_lines(X168,X169)
| ~ convergent_lines(X168,X169) )
& ( convergent_lines(X168,X169)
| parallel_lines(X168,X169) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_48])]) ).
fof(i_0_81,plain,
! [X166,X167] :
( ( ~ equal_lines(X166,X167)
| ~ distinct_lines(X166,X167) )
& ( distinct_lines(X166,X167)
| equal_lines(X166,X167) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_49])]) ).
fof(i_0_82,plain,
! [X164,X165] :
( ( ~ equal_points(X164,X165)
| ~ distinct_points(X164,X165) )
& ( distinct_points(X164,X165)
| equal_points(X164,X165) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_50])]) ).
fof(i_0_83,plain,
! [X162,X163] :
( ~ line(X162)
| ~ point(X163)
| line(orthogonal_through_point(X162,X163)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[orth1])]) ).
fof(i_0_84,plain,
! [X160,X161] :
( ~ line(X160)
| ~ point(X161)
| line(parallel_through_point(X160,X161)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[par1])]) ).
fof(i_0_85,plain,
! [X126,X127] :
( ~ distinct_lines(X126,X127)
| convergent_lines(X126,X127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])]) ).
fof(i_0_86,plain,
! [X148,X149] :
( convergent_lines(X148,X149)
| unorthogonal_lines(X148,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_51])]) ).
fof(i_0_87,plain,
! [X135,X136] :
( convergent_lines(X135,X136)
| unorthogonal_lines(X135,X136) ),
inference(variable_rename,[status(thm)],[occu1]) ).
fof(i_0_88,plain,
! [X95] : ~ convergent_lines(X95,X95),
inference(variable_rename,[status(thm)],[i_0_52]) ).
fof(i_0_89,plain,
! [X94] : ~ distinct_lines(X94,X94),
inference(variable_rename,[status(thm)],[i_0_53]) ).
fof(i_0_90,plain,
! [X93] : ~ distinct_points(X93,X93),
inference(variable_rename,[status(thm)],[i_0_54]) ).
fof(i_0_91,negated_conjecture,
orthogonal_lines(esk1_0,esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_55])])]) ).
cnf(i_0_92,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_56]),
[final] ).
cnf(i_0_93,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_94,plain,
( ~ convergent_lines(X1,X2)
| ~ apart_point_and_line(intersection_point(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_95,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X1,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_96,plain,
( ~ distinct_points(X1,X2)
| ~ apart_point_and_line(X2,line_connecting(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_97,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_61]),
[final] ).
cnf(i_0_98,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_99,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_100,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_101,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_102,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_103,plain,
( convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| ~ convergent_lines(X3,X2)
| ~ unorthogonal_lines(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_104,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_105,plain,
( convergent_lines(X1,X2)
| convergent_lines(X3,X2)
| ~ convergent_lines(X3,X1)
| ~ unorthogonal_lines(X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_106,plain,
( line(line_connecting(X1,X2))
| ~ point(X1)
| ~ point(X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_107,plain,
( point(intersection_point(X1,X2))
| ~ line(X1)
| ~ line(X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_108,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_66]),
[final] ).
cnf(i_0_109,plain,
~ unorthogonal_lines(orthogonal_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_110,plain,
~ convergent_lines(parallel_through_point(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_111,plain,
~ apart_point_and_line(X1,orthogonal_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_112,plain,
~ apart_point_and_line(X1,parallel_through_point(X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_113,plain,
( unorthogonal_lines(X1,X2)
| unorthogonal_lines(X1,X3)
| ~ convergent_lines(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_114,plain,
( convergent_lines(X1,X3)
| convergent_lines(X2,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_115,plain,
( distinct_lines(X2,X3)
| apart_point_and_line(X1,X3)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_116,plain,
( distinct_lines(X2,X3)
| convergent_lines(X1,X3)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_117,plain,
( distinct_lines(X1,X3)
| distinct_lines(X2,X3)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_118,plain,
( distinct_points(X1,X3)
| apart_point_and_line(X3,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_119,plain,
( distinct_points(X1,X3)
| distinct_points(X2,X3)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_120,plain,
( ~ orthogonal_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_121,plain,
( ~ incident_point_and_line(X1,X2)
| ~ apart_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_122,plain,
( ~ parallel_lines(X1,X2)
| ~ convergent_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_123,plain,
( ~ equal_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_124,plain,
( ~ equal_points(X1,X2)
| ~ distinct_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_125,plain,
( line(orthogonal_through_point(X1,X2))
| ~ line(X1)
| ~ point(X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_126,plain,
( line(parallel_through_point(X1,X2))
| ~ line(X1)
| ~ point(X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_127,plain,
( convergent_lines(X1,X2)
| ~ distinct_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_128,plain,
( unorthogonal_lines(X1,X2)
| orthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_129,plain,
( apart_point_and_line(X1,X2)
| incident_point_and_line(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_130,plain,
( convergent_lines(X1,X2)
| parallel_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_131,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_132,plain,
( convergent_lines(X1,X2)
| unorthogonal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_133,plain,
( distinct_lines(X1,X2)
| equal_lines(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_134,plain,
( distinct_points(X1,X2)
| equal_points(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_135,plain,
~ convergent_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_136,plain,
~ distinct_lines(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_137,plain,
~ distinct_points(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_138,negated_conjecture,
orthogonal_lines(esk1_0,esk1_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_139,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(scs_inference,[],[i_0_109,i_0_132]) ).
cnf(i_0_140,plain,
( unorthogonal_lines(X1,X2)
| convergent_lines(X1,X2) ),
inference(rename_variables,[],[i_0_132]) ).
cnf(i_0_141,plain,
~ parallel_lines(orthogonal_through_point(X1,X2),X1),
inference(scs_inference,[],[i_0_109,i_0_132,i_0_122]) ).
cnf(i_0_142,plain,
( ~ convergent_lines(X1,X2)
| ~ parallel_lines(X1,X2) ),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_143,plain,
unorthogonal_lines(orthogonal_through_point(X1,X2),orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_109,i_0_132,i_0_122,i_0_113]) ).
cnf(i_0_144,plain,
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X3,X1)
| unorthogonal_lines(X3,X2) ),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_145,plain,
convergent_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_135,i_0_109,i_0_132,i_0_122,i_0_113,i_0_114]) ).
cnf(i_0_146,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_135]) ).
cnf(i_0_147,plain,
( ~ convergent_lines(X1,X2)
| convergent_lines(X1,X3)
| convergent_lines(X2,X3) ),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_148,plain,
~ unorthogonal_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_135,i_0_146,i_0_109,i_0_132,i_0_122,i_0_113,i_0_114,i_0_100]) ).
cnf(i_0_149,plain,
~ convergent_lines(X1,X1),
inference(rename_variables,[],[i_0_135]) ).
cnf(i_0_150,plain,
( ~ convergent_lines(X1,X2)
| ~ unorthogonal_lines(X1,X2)
| convergent_lines(X3,X2)
| unorthogonal_lines(X3,X1) ),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_151,plain,
~ orthogonal_lines(orthogonal_through_point(X1,X2),orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_135,i_0_146,i_0_109,i_0_132,i_0_122,i_0_113,i_0_114,i_0_100,i_0_120]) ).
cnf(i_0_152,plain,
( ~ unorthogonal_lines(X1,X2)
| ~ orthogonal_lines(X1,X2) ),
inference(rename_variables,[],[i_0_120]) ).
cnf(i_0_153,plain,
~ parallel_lines(X1,orthogonal_through_point(X1,X2)),
inference(scs_inference,[],[i_0_145,i_0_122]) ).
cnf(i_0_154,plain,
( ~ convergent_lines(X1,X2)
| ~ parallel_lines(X1,X2) ),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_155,plain,
unorthogonal_lines(X1,X1),
inference(scs_inference,[],[i_0_139,i_0_148,i_0_145,i_0_122,i_0_113]) ).
cnf(i_0_156,plain,
convergent_lines(orthogonal_through_point(X1,X2),X1),
inference(rename_variables,[],[i_0_139]) ).
cnf(i_0_157,plain,
( ~ convergent_lines(X1,X2)
| unorthogonal_lines(X3,X1)
| unorthogonal_lines(X3,X2) ),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_158,plain,
$false,
inference(scs_inference,[],[i_0_138,i_0_139,i_0_148,i_0_145,i_0_122,i_0_113,i_0_120]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO216+3 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n005.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 17:49:00 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.28/1.61 % Version : CSE_E---1.7
% 0.28/1.61 % Problem : theBenchmark.p
% 0.28/1.61 % SZS status Theorem for theBenchmark.p
% 0.28/1.61 % SZS output start CNFRefutation
% See solution above
% 0.28/1.66 % Total time : 1.272s
%------------------------------------------------------------------------------