%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:12:45 AM UTC 2026
% Result : Theorem 84.51s 23.64s
% Output : Refutation 86.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 38
% Syntax : Number of formulae : 1119 ( 272 unt; 0 typ; 3 def)
% Number of atoms : 4005 ( 742 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 13059 (1892 ~;1716 |; 61 &;9314 @)
% ( 4 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 5 con; 0-2 aty)
% Number of variables : 4008 ( 0 ^;3994 !; 11 ?;4008 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(equal_points_decl,type,
equal_points: $i > $i > $o ).
thf(equal_lines_decl,type,
equal_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
thf(orthogonal_lines_decl,type,
orthogonal_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(line_decl,type,
line: $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( B @ equal_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ equal_lines ) )
& ( C @ ( A @ distinct_points ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ equal_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ( ( B @ ( sk1 @ line_connecting ) @ ( A @ ( sk1 @ line_connecting ) @ equal_lines ) )
& ( B @ ( sk1 @ distinct_points ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ ( sk2 @ equal_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ( A @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) )
& ( A @ ( sk1 @ distinct_points ) ) ) ) ) ) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
<=> ~ ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ equal_lines ) ) )
& ( ( B @ ( A @ equal_lines ) )
=> ~ ( B @ ( A @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(140,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ equal_lines ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
=> ~ ( B @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[139]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_lines ) )
| ( D @ ( C @ distinct_lines ) ) )
& ( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(cnfConj,[status(thm)],[141]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(3712,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ distinct_lines ) )
!= ( C @ ( A @ distinct_lines ) ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[100]) ).
thf(3713,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[3712:[bind(A,$thf( B ))]]) ).
thf(3715,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3713]) ).
thf(3765,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[144,3715]) ).
thf(3766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[3765]) ).
thf(3767,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[3766:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(3798,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[3767]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[109]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[144,110]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(235,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(48,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,50]) ).
thf(261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[261:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(12,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(77,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(78,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[77]) ).
thf(79,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[78]) ).
thf(531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[269,79]) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[531]) ).
thf(533,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[532:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(544,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(simp,[status(thm)],[533]) ).
thf(185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,79]) ).
thf(186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[186:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[187]) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ( A @ ( B @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[544,205]) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(simp,[status(thm)],[844]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[845:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(19,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(95,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(96,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[96]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[144,97]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(229,plain,
! [A: $i] : ( A @ ( A @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(236,plain,
! [A: $i] : ( A @ ( A @ equal_lines ) ),
inference(simp,[status(thm)],[229]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ equal_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ equal_lines ) )
& ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ equal_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ equal_lines ) )
& ( C @ ( A @ distinct_points ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(37,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ equal_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ equal_lines ) )
& ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,plain,
( ( ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) )
& ( sk3 @ ( sk2 @ equal_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[38]) ).
thf(41,plain,
( ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(150,plain,
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( sk2 @ ( sk1 @ distinct_points ) ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,41]) ).
thf(151,plain,
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( sk2 @ ( sk1 @ distinct_points ) ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(152,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
( ( sk3 != sk2 )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(242,plain,
! [A: $i] :
( ( ( A @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[236,153]) ).
thf(243,plain,
! [A: $i] :
( ( ( A @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[242]) ).
thf(245,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( A
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[243]) ).
thf(247,plain,
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[245]) ).
thf(248,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
sk3 != sk2,
inference(simp,[status(thm)],[248]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
thf(45,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(miniscope,[status(thm)],[45]) ).
thf(47,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(cnf,[status(esa)],[46]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[59,47]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( F @ ( B @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(161,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[160]) ).
thf(176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,50]) ).
thf(177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(178,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[177:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ orthogonal_through_point ) )),bind(D,$thf( F ))]]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,79]) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(360,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( H @ ( G @ orthogonal_through_point ) )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) ))]]) ).
thf(367,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(simp,[status(thm)],[360]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(60,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(986,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( A @ unorthogonal_lines ) )
!= ( B @ ( A @ unorthogonal_lines ) ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[986:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(994,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[987]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
<=> ~ ( B @ ( A @ unorthogonal_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ unorthogonal_lines ) )
=> ( B @ ( A @ orthogonal_lines ) ) )
& ( ( B @ ( A @ orthogonal_lines ) )
=> ~ ( B @ ( A @ unorthogonal_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(72,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
=> ( B @ ( A @ orthogonal_lines ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
=> ~ ( B @ ( A @ unorthogonal_lines ) ) ) ),
inference(miniscope,[status(thm)],[71]) ).
thf(73,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ orthogonal_lines ) )
| ( D @ ( C @ unorthogonal_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ) ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) )
| ~ ( B @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[994,74]) ).
thf(1539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ~ ( B @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1538]) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ~ ( B @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1539:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,1540]) ).
thf(1817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1816]) ).
thf(1841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= D )
| ( A != D )
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1817]) ).
thf(1850,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ orthogonal_through_point ) )
!= C )
| ~ ( C @ ( B @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1841]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
thf(104,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[104]) ).
thf(466,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,105]) ).
thf(467,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[466]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[467:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ convergent_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ convergent_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ point )
| ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[87]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
thf(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,81]) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(354,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ orthogonal_through_point ) )),bind(E,$thf( A ))]]) ).
thf(365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[354]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
thf(136,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[136]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[137]) ).
thf(664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,205]) ).
thf(665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[664]) ).
thf(666,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[665:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( A )),bind(E,$thf( G @ ( F @ orthogonal_through_point ) ))]]) ).
thf(673,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[666]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
thf(42,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(43,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(44,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(cnf,[status(esa)],[43]) ).
thf(191,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,44]) ).
thf(192,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[192:[bind(A,$thf( G @ ( C @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[193]) ).
thf(7053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[199,44]) ).
thf(7054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[7053]) ).
thf(7055,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[7054:[bind(A,$thf( G @ ( B @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).
thf(7161,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[7055]) ).
thf(8065,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[199,7161]) ).
thf(8066,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8065]) ).
thf(8067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[8066:[bind(A,$thf( H @ ( I @ parallel_through_point ) )),bind(B,$thf( J @ ( I @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[8067]) ).
thf(11291,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[673,8107]) ).
thf(11292,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[11291]) ).
thf(11293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[11292:[bind(A,$thf( M @ ( L @ parallel_through_point ) )),bind(B,$thf( I @ ( K @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( K ))]]) ).
thf(11352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[11293]) ).
thf(8026,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( C @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,7161]) ).
thf(8027,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( C @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8026]) ).
thf(8100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( E @ ( C @ parallel_through_point ) ) )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[8027]) ).
thf(8129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( B @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8100]) ).
thf(4220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[673,44]) ).
thf(4221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4220]) ).
thf(4222,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[4221:[bind(A,$thf( A )),bind(B,$thf( G @ ( A @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( A ))]]) ).
thf(4339,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(simp,[status(thm)],[4222]) ).
thf(3760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3715,110]) ).
thf(3761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3760]) ).
thf(3762,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[3761:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6983,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,199]) ).
thf(6984,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[6983]) ).
thf(6985,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[6984:[bind(A,$thf( N @ ( M @ parallel_through_point ) )),bind(B,$thf( J )),bind(C,$thf( L )),bind(D,$thf( J @ ( L @ ( N @ ( M @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )),bind(E,$thf( M )),bind(F,$thf( N ))]]) ).
thf(7176,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[6985]) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,81]) ).
thf(648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(649,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[648:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(10405,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ~ ( E @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,649]) ).
thf(10406,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ~ ( E @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[10405]) ).
thf(10407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[10406:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) ))]]) ).
thf(10478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[10407]) ).
thf(513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[269,44]) ).
thf(514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[514:[bind(A,$thf( G @ ( C @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(539,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[515]) ).
thf(644,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,44]) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(646,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ parallel_through_point ) @ ( A @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( F @ ( B @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(667,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ parallel_through_point ) @ ( A @ convergent_lines ) ),
inference(simp,[status(thm)],[646]) ).
thf(3039,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[539,667]) ).
thf(3040,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[3039]) ).
thf(3041,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[3040:[bind(A,$thf( F )),bind(B,$thf( G @ ( F @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(3056,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[3041]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ),
inference(cnfConj,[status(thm)],[141]) ).
thf(3279,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3056,142]) ).
thf(3280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3279]) ).
thf(3281,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[3280:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ parallel_through_point ) @ parallel_through_point ) )),bind(E,$thf( H ))]]) ).
thf(3285,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[3281]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ! [C: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(273,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,55]) ).
thf(274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ unorthogonal_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
| ~ ( B @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ orthogonal_through_point ) )),bind(D,$thf( F ))]]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ unorthogonal_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
| ~ ( B @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(179,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,50]) ).
thf(180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[180:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(4556,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,81]) ).
thf(4557,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4556]) ).
thf(4558,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4557:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( H )),bind(E,$thf( G @ ( I @ ( H @ parallel_through_point ) @ orthogonal_through_point ) ))]]) ).
thf(4603,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4558]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(394,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,50]) ).
thf(395,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[396]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',par1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[119]) ).
thf(40,plain,
sk3 @ ( sk2 @ equal_points ),
inference(cnfConj,[status(thm)],[38]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
<=> ~ ( B @ ( A @ distinct_points ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ distinct_points ) )
=> ( B @ ( A @ equal_points ) ) )
& ( ( B @ ( A @ equal_points ) )
=> ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(122,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ distinct_points ) )
=> ( B @ ( A @ equal_points ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
=> ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[121]) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_points ) )
| ( D @ ( C @ distinct_points ) ) )
& ( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(cnfConj,[status(thm)],[123]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ equal_points ) )
!= ( B @ ( A @ equal_points ) ) )
| ~ ( B @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,124]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ equal_points ) )
!= ( B @ ( A @ equal_points ) ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
~ ( sk3 @ ( sk2 @ distinct_points ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(6661,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[138,211]) ).
thf(6662,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[6661]) ).
thf(6663,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6662:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk3 ))]]) ).
thf(8167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6663,124]) ).
thf(8168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8167]) ).
thf(8169,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_points ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8168:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( D @ ( C @ unorthogonal_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[544,994]) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1572,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unorthogonal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(1591,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unorthogonal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[1572]) ).
thf(6658,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[138,211]) ).
thf(6659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[6658]) ).
thf(6660,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6659:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(6759,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6660]) ).
thf(516,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[269,44]) ).
thf(517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[516]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[517:[bind(A,$thf( A )),bind(B,$thf( G @ ( C @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(540,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(11231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,8107]) ).
thf(11232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[11231]) ).
thf(11233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[11232:[bind(A,$thf( H @ ( J @ ( K @ parallel_through_point ) @ parallel_through_point ) )),bind(B,$thf( L @ ( K @ parallel_through_point ) )),bind(C,$thf( H )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( J ))]]) ).
thf(11386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[11233]) ).
thf(15223,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[540,11386]) ).
thf(15224,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[15223]) ).
thf(15225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ ( B @ ( D @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[15224:[bind(A,$thf( I @ ( L @ parallel_through_point ) )),bind(B,$thf( K @ ( M @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( I ))]]) ).
thf(15384,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ ( B @ ( D @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[15225]) ).
thf(6721,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,138]) ).
thf(6722,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[6721]) ).
thf(6723,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6722:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6758,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6723]) ).
thf(6858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6758,138]) ).
thf(6859,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6858]) ).
thf(6860,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6859:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(6917,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6860]) ).
thf(13180,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[6917]) ).
thf(13189,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[13180:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(35,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(145,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(146,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[145]) ).
thf(147,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[146]) ).
thf(14263,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[13189,147]) ).
thf(14264,plain,
sk1 @ ( sk2 @ distinct_points ),
inference(simp,[status(thm)],[14263]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[148]) ).
thf(14290,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14264,149]) ).
thf(14291,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[14290]) ).
thf(14292,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[14291:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(3670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[100,97]) ).
thf(3671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3670]) ).
thf(3672,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[3671:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(3725,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3672]) ).
thf(4341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ( A @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3798,3725]) ).
thf(4342,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[4341]) ).
thf(4343,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[4342:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(802,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,667]) ).
thf(803,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[802]) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[803:[bind(A,$thf( I @ ( K @ ( J @ orthogonal_through_point ) @ parallel_through_point ) )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( K @ ( J @ orthogonal_through_point ) )),bind(E,$thf( I ))]]) ).
thf(810,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) ),
inference(simp,[status(thm)],[804]) ).
thf(1014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,205]) ).
thf(1015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1014]) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[1015:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ orthogonal_through_point ) @ parallel_through_point ) )),bind(E,$thf( H ))]]) ).
thf(1046,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[1016]) ).
thf(1559,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( D @ ( C @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[367,994]) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1589,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= D )
| ( A != D )
| ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[1560]) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ orthogonal_through_point ) )
!= C )
| ( C @ ( B @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[1589]) ).
thf(376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,81]) ).
thf(377,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[376]) ).
thf(378,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ orthogonal_through_point ) ))]]) ).
thf(389,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[378]) ).
thf(9430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6759,124]) ).
thf(9431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(simp,[status(thm)],[9430]) ).
thf(9432,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_points ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9431:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(4347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3725,142]) ).
thf(4348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4347]) ).
thf(4349,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4348:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(154,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,147]) ).
thf(155,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(156,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
sk2 != sk1,
inference(simp,[status(thm)],[156]) ).
thf(10384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,205]) ).
thf(10385,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10384]) ).
thf(10386,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[10385:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) ))]]) ).
thf(10469,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) ),
inference(simp,[status(thm)],[10386]) ).
thf(6871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6758,124]) ).
thf(6872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6871]) ).
thf(6873,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6872:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(8018,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,7161]) ).
thf(8019,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8018]) ).
thf(8098,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( F @ ( D @ parallel_through_point ) ) )
| ( B
!= ( E @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[8019]) ).
thf(8126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( E @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8098]) ).
thf(15269,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[673,11386]) ).
thf(15270,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15269]) ).
thf(15271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[15270:[bind(A,$thf( K @ ( M @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(B,$thf( I @ ( L @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( I ))]]) ).
thf(15338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[15271]) ).
thf(194,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,44]) ).
thf(195,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[194]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( A )),bind(B,$thf( G @ ( C @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(201,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(10368,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( G @ ( F @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,201]) ).
thf(10369,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( G @ ( F @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10368]) ).
thf(10370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[10369:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( O @ ( N @ parallel_through_point ) )),bind(D,$thf( M )),bind(E,$thf( I @ ( K @ ( M @ ( O @ ( N @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )),bind(F,$thf( N )),bind(G,$thf( O ))]]) ).
thf(10455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[10370]) ).
thf(20542,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10455,205]) ).
thf(20543,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20542]) ).
thf(20544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[20543:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( N )),bind(G,$thf( I @ ( K @ ( M @ ( O @ ( N @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) ))]]) ).
thf(20675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ convergent_lines ) ),
inference(simp,[status(thm)],[20544]) ).
thf(423,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,55]) ).
thf(424,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[424:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[425]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[53]) ).
thf(1799,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) )
| ~ ( E @ ( D @ orthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,1540]) ).
thf(1800,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) )
| ~ ( E @ ( D @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1799]) ).
thf(1838,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= E )
| ( B != E )
| ~ ( E @ ( D @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1800]) ).
thf(1847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ orthogonal_through_point ) @ parallel_through_point ) )
!= D )
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[1838]) ).
thf(9449,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( sk2 @ distinct_points ) ) )
| ( sk3 @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6758,6759]) ).
thf(9450,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( sk2 @ distinct_points ) ) )
| ( sk3 @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[9449]) ).
thf(9451,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9450:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(9766,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[9451,124]) ).
thf(9767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[9766]) ).
thf(9768,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ equal_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9767:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(9710,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( sk2 @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ equal_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6758,9432]) ).
thf(9711,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( sk2 @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[9710]) ).
thf(9712,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9711:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(8068,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[673,7161]) ).
thf(8069,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8068]) ).
thf(8070,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[8069:[bind(A,$thf( J @ ( I @ parallel_through_point ) )),bind(B,$thf( H @ ( I @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8109,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[8070]) ).
thf(6863,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6758,211]) ).
thf(6864,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( sk3 @ ( sk2 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6863]) ).
thf(6865,plain,
sk3 @ ( sk1 @ distinct_points ),
inference(pattern_uni,[status(thm)],[6864:[bind(A,$thf( sk3 ))]]) ).
thf(6946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6865,138]) ).
thf(6947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[6946]) ).
thf(6948,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[6947:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(6970,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[6948]) ).
thf(7310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6970,138]) ).
thf(7311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[7310]) ).
thf(7312,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[7311:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(7337,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[7312]) ).
thf(20247,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[7337]) ).
thf(20261,plain,
( ( sk1 @ ( sk3 @ distinct_points ) )
| ( sk1 @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[20247:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(20843,plain,
( ( sk1 @ ( sk3 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[20261,147]) ).
thf(20844,plain,
sk1 @ ( sk3 @ distinct_points ),
inference(simp,[status(thm)],[20843]) ).
thf(20875,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20844,149]) ).
thf(20876,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[20875]) ).
thf(20877,plain,
~ ( sk1 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[20876:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(7017,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,199]) ).
thf(7018,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[7017]) ).
thf(7019,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[7018:[bind(A,$thf( J )),bind(B,$thf( N @ ( M @ parallel_through_point ) )),bind(C,$thf( L )),bind(D,$thf( J @ ( L @ ( N @ ( M @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )),bind(E,$thf( M )),bind(F,$thf( N ))]]) ).
thf(7195,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[7019]) ).
thf(10545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ~ ( E @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,649]) ).
thf(10546,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ~ ( E @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[10545]) ).
thf(10547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[10546:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) ))]]) ).
thf(10623,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[10547]) ).
thf(12039,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8109,205]) ).
thf(12040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[12039]) ).
thf(12041,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[12040:[bind(A,$thf( J )),bind(B,$thf( L )),bind(C,$thf( K )),bind(D,$thf( H )),bind(E,$thf( J @ ( L @ ( K @ parallel_through_point ) @ orthogonal_through_point ) )),bind(F,$thf( H @ ( K @ parallel_through_point ) ))]]) ).
thf(12123,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[12041]) ).
thf(15911,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12123,44]) ).
thf(15912,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15911]) ).
thf(15981,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) )
!= F )
| ( ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[15912]) ).
thf(16018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( A @ ( C @ parallel_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[15981]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ convergent_lines ) )
!= ( C @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[50]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( B ))]]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[203,205]) ).
thf(630,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[629]) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[630:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[631,81]) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[129]) ).
thf(6962,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6865,130]) ).
thf(6963,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[6962]) ).
thf(6964,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[6963:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
thf(82,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(83,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[83]) ).
thf(1139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ( C @ ( D @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,631]) ).
thf(1140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ( C @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1139]) ).
thf(1172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= C )
| ( A != C )
| ( C @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1140]) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ orthogonal_through_point ) )
!= B )
| ( B @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1049,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,130]) ).
thf(1050,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1049]) ).
thf(1051,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(1856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_lines ) )
!= ( E @ ( D @ orthogonal_lines ) ) )
| ( ( C @ ( E @ orthogonal_through_point ) )
!= E )
| ~ $true
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[76,1850]) ).
thf(1857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_lines ) )
!= ( E @ ( D @ orthogonal_lines ) ) )
| ( ( C @ ( E @ orthogonal_through_point ) )
!= E )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ orthogonal_through_point ) )
!= B )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[1857:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(23,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
thf(106,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(14282,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[14264,124]) ).
thf(14283,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[14282]) ).
thf(14284,plain,
~ ( sk1 @ ( sk2 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[14283:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(1437,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,667]) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( E @ ( D @ parallel_through_point ) ) )
| ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= D ) ),
inference(simp,[status(thm)],[1438]) ).
thf(1447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ parallel_through_point ) )
!= B ),
inference(simp,[status(thm)],[1442]) ).
thf(400,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,56]) ).
thf(401,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[401:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[402]) ).
thf(15280,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[539,11386]) ).
thf(15281,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[15280]) ).
thf(15282,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ parallel_through_point ) @ ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[15281:[bind(A,$thf( I @ ( L @ parallel_through_point ) )),bind(B,$thf( K @ ( M @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( I ))]]) ).
thf(15343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( D @ parallel_through_point ) @ ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[15282]) ).
thf(409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,74]) ).
thf(410,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ orthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ incident_point_and_line ) )
<=> ~ ( B @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ apart_point_and_line ) )
=> ( B @ ( A @ incident_point_and_line ) ) )
& ( ( B @ ( A @ incident_point_and_line ) )
=> ~ ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(114,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ apart_point_and_line ) )
=> ( B @ ( A @ incident_point_and_line ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ incident_point_and_line ) )
=> ~ ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(miniscope,[status(thm)],[113]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ incident_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) ) )
& ( ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ incident_point_and_line ) ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ incident_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(10392,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,44]) ).
thf(10393,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10392]) ).
thf(10442,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != F )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[10393]) ).
thf(10459,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( E @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[10442]) ).
thf(1827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ~ $true
| ( A @ ( B @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[544,1540]) ).
thf(1828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( A @ ( B @ equal_lines ) ) ),
inference(simp,[status(thm)],[1827]) ).
thf(1829,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ orthogonal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[1828:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ orthogonal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[1829]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
thf(89,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ! [C: $i] :
( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[131]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(282,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,55]) ).
thf(283,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(7987,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,7161]) ).
thf(7988,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[7987]) ).
thf(8096,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( F @ ( D @ parallel_through_point ) ) )
| ( A
!= ( E @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[7988]) ).
thf(8123,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8096]) ).
thf(302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,55]) ).
thf(303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[302]) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[303:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(429,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,56]) ).
thf(430,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[430:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(452,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,44]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( F @ ( B @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(270,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[265]) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,205]) ).
thf(660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[659]) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(9438,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6759,149]) ).
thf(9439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(simp,[status(thm)],[9438]) ).
thf(9440,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9439:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(1019,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,81]) ).
thf(1020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1019]) ).
thf(1021,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1020:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( H )),bind(E,$thf( G @ ( I @ ( H @ orthogonal_through_point ) @ parallel_through_point ) ))]]) ).
thf(1047,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1021]) ).
thf(3448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[1858,74]) ).
thf(3449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(simp,[status(thm)],[3448]) ).
thf(3450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[3449:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(20884,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20844,130]) ).
thf(20885,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[20884]) ).
thf(20886,plain,
~ ( sk1 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[20885:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
thf(85,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14293,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14264,130]) ).
thf(14294,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[14293]) ).
thf(14295,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[14294:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(24653,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11352,205]) ).
thf(24654,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[24653]) ).
thf(24655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ parallel_through_point ) @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[24654:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( O )),bind(D,$thf( N )),bind(E,$thf( I )),bind(F,$thf( K @ ( M @ ( O @ ( N @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )),bind(G,$thf( I @ ( N @ parallel_through_point ) ))]]) ).
thf(24797,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ parallel_through_point ) @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[24655]) ).
thf(36803,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ parallel_through_point ) @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24797,79]) ).
thf(36804,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ parallel_through_point ) @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[36803]) ).
thf(36821,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ parallel_through_point ) )
!= F )
| ( ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= F ) ),
inference(simp,[status(thm)],[36804]) ).
thf(36874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ parallel_through_point ) )
!= ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[36821]) ).
thf(355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,55]) ).
thf(356,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ convergent_lines ) )
| ~ ( A @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[356:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) )),bind(E,$thf( A ))]]) ).
thf(366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ convergent_lines ) )
| ~ ( A @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(8076,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[539,7161]) ).
thf(8077,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[8076]) ).
thf(8078,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[8077:[bind(A,$thf( H @ ( I @ parallel_through_point ) )),bind(B,$thf( J @ ( I @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8113,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[8078]) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,79]) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1030]) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= D )
| ( B != D ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ orthogonal_through_point ) @ parallel_through_point ) )
!= C ),
inference(simp,[status(thm)],[1035]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(92,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(8162,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6663,147]) ).
thf(8163,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8162]) ).
thf(8164,plain,
~ ( sk2 @ ( sk3 @ distinct_points ) ),
inference(pattern_uni,[status(thm)],[8163:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(8727,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( sk2 @ ( sk3 @ distinct_points ) ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[138,8164]) ).
thf(8728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( sk2 @ ( sk3 @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8727]) ).
thf(8729,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8728:[bind(A,$thf( sk3 )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(8750,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[8729]) ).
thf(17736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,130]) ).
thf(17737,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17736]) ).
thf(17738,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17737:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(12994,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10469,667]) ).
thf(12995,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[12994]) ).
thf(13013,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( F @ ( E @ parallel_through_point ) ) )
| ( C != E ) ),
inference(simp,[status(thm)],[12995]) ).
thf(13034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[13013]) ).
thf(638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,105]) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[638]) ).
thf(640,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[639:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4573,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,640]) ).
thf(4574,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4573]) ).
thf(4575,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4574:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ parallel_through_point ) @ orthogonal_through_point ) )),bind(E,$thf( H ))]]) ).
thf(4608,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4575]) ).
thf(10524,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,205]) ).
thf(10525,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( F @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10524]) ).
thf(10526,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[10525:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( K )),bind(F,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) ))]]) ).
thf(10614,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) ),
inference(simp,[status(thm)],[10526]) ).
thf(14193,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10614,667]) ).
thf(14194,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[14193]) ).
thf(14202,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( F @ ( E @ parallel_through_point ) ) )
| ( C != E ) ),
inference(simp,[status(thm)],[14194]) ).
thf(14248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[14202]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ line_connecting ) @ line )
| ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(cnf,[status(esa)],[134]) ).
thf(6443,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( A @ line_connecting ) @ line )
| ~ $true
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(paramod_ordered,[status(thm)],[39,135]) ).
thf(6444,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( A @ line_connecting ) @ line )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(simp,[status(thm)],[6443]) ).
thf(6445,plain,
( ( sk2 @ ( sk1 @ line_connecting ) @ line )
| ~ ( sk2 @ point )
| ~ ( sk1 @ point ) ),
inference(pattern_uni,[status(thm)],[6444:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3294,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[144,3285]) ).
thf(3295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[3294]) ).
thf(3296,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( A @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[3295:[bind(A,$thf( G @ ( I @ ( B @ parallel_through_point ) @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( B )),bind(E,$thf( I ))]]) ).
thf(3297,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( A @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[3296]) ).
thf(8179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6663,130]) ).
thf(8180,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8179]) ).
thf(8181,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8180:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(15237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( D @ ( E @ parallel_through_point ) @ parallel_through_point ) @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,11386]) ).
thf(15238,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( D @ ( E @ parallel_through_point ) @ parallel_through_point ) @ ( F @ ( E @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15237]) ).
thf(15319,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= ( C @ ( D @ ( E @ parallel_through_point ) @ parallel_through_point ) ) )
| ( A
!= ( F @ ( E @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[15238]) ).
thf(15368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[15319]) ).
thf(435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,56]) ).
thf(436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[435]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[436:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(456,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[437]) ).
thf(14139,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10614,44]) ).
thf(14140,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[14139]) ).
thf(14211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= F )
| ( C
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[14140]) ).
thf(14217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= E ),
inference(simp,[status(thm)],[14211]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(4666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ $true
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3725,4349]) ).
thf(4667,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4666]) ).
thf(4668,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4667:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(6953,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[6865,124]) ).
thf(6954,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[6953]) ).
thf(6955,plain,
~ ( sk3 @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[6954:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(13097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk2 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ~ $true
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6917,147]) ).
thf(13098,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk2 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[13097]) ).
thf(13099,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[13098:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 ))]]) ).
thf(10508,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( G @ ( F @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,201]) ).
thf(10509,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( G @ ( F @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10508]) ).
thf(10510,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[10509:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( O @ ( N @ parallel_through_point ) )),bind(D,$thf( M )),bind(E,$thf( I @ ( K @ ( M @ ( O @ ( N @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )),bind(F,$thf( N )),bind(G,$thf( O ))]]) ).
thf(10600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[10510]) ).
thf(23088,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10600,205]) ).
thf(23089,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( G @ convergent_lines ) ) )
| ( G @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23088]) ).
thf(23090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( D @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[23089:[bind(A,$thf( I )),bind(B,$thf( K )),bind(C,$thf( M )),bind(D,$thf( N )),bind(E,$thf( O )),bind(F,$thf( N )),bind(G,$thf( I @ ( K @ ( M @ ( O @ ( N @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) ))]]) ).
thf(23218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ ( D @ convergent_lines ) ),
inference(simp,[status(thm)],[23090]) ).
thf(15973,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12123,79]) ).
thf(15974,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15973]) ).
thf(15992,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) )
!= E )
| ( ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[15974]) ).
thf(16031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ parallel_through_point ) )
!= ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[15992]) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,44]) ).
thf(165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(169,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(3003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[539,44]) ).
thf(3004,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[3003]) ).
thf(3005,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[3004:[bind(A,$thf( G @ ( B @ parallel_through_point ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( B ))]]) ).
thf(3062,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[3005]) ).
thf(3290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[3062,41]) ).
thf(3291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3290]) ).
thf(3292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( ( B @ ( A @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3291]) ).
thf(6940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( ( B @ ( A @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3292,6865]) ).
thf(6941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( ( B @ ( A @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ) ),
inference(simp,[status(thm)],[6940]) ).
thf(6965,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( A @ line_connecting ) @ line )
| ~ $true
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(paramod_ordered,[status(thm)],[6865,135]) ).
thf(6966,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( A @ line_connecting ) @ line )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(simp,[status(thm)],[6965]) ).
thf(6967,plain,
( ( sk3 @ ( sk1 @ line_connecting ) @ line )
| ~ ( sk3 @ point )
| ~ ( sk1 @ point ) ),
inference(pattern_uni,[status(thm)],[6966:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(2321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,649]) ).
thf(2322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2321]) ).
thf(2323,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2322:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,81]) ).
thf(338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(3624,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[540,667]) ).
thf(3625,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[3624]) ).
thf(3626,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[3625:[bind(A,$thf( F )),bind(B,$thf( G @ ( F @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(3643,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) ),
inference(simp,[status(thm)],[3626]) ).
thf(469,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,105]) ).
thf(470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[470:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(4544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,205]) ).
thf(4545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4544]) ).
thf(4546,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[4545:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ parallel_through_point ) @ orthogonal_through_point ) )),bind(E,$thf( H ))]]) ).
thf(4601,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[4546]) ).
thf(8037,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4601,7161]) ).
thf(8038,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8037]) ).
thf(8103,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( F @ ( D @ parallel_through_point ) ) )
| ( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[8038]) ).
thf(8132,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8103]) ).
thf(475,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,105]) ).
thf(476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[475]) ).
thf(477,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[476:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ orthogonal_through_point ) ))]]) ).
thf(489,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[477]) ).
thf(6934,plain,
( ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) )
| ~ $true ),
inference(rewrite,[status(thm)],[41,6865]) ).
thf(6935,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ),
inference(simp,[status(thm)],[6934]) ).
thf(1017,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,44]) ).
thf(1018,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1017]) ).
thf(1033,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= E )
| ( B
!= ( D @ ( E @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[1018]) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= D ),
inference(simp,[status(thm)],[1033]) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,79]) ).
thf(1440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= D ) ),
inference(simp,[status(thm)],[1440]) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= B ),
inference(simp,[status(thm)],[1445]) ).
thf(1426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,81]) ).
thf(1427,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1426]) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1427:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ orthogonal_through_point ) @ parallel_through_point ) )),bind(E,$thf( H ))]]) ).
thf(1456,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1428]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
thf(127,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[127]) ).
thf(5299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,128]) ).
thf(5300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[5299]) ).
thf(5301,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk2 @ apart_point_and_line ) )
| ( B @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[5300:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(5467,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk2 @ apart_point_and_line ) )
| ( B @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[5301]) ).
thf(5651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( sk2 @ apart_point_and_line ) )
| ( C @ ( sk2 @ apart_point_and_line ) )
| ( D @ ( sk1 @ apart_point_and_line ) )
| ( C @ ( sk1 @ apart_point_and_line ) )
| ~ $true
| ( A @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3798,5467]) ).
thf(5652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( sk2 @ apart_point_and_line ) )
| ( C @ ( sk2 @ apart_point_and_line ) )
| ( D @ ( sk1 @ apart_point_and_line ) )
| ( C @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[5651]) ).
thf(5653,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk2 @ apart_point_and_line ) )
| ( B @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[5652:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(5803,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( sk2 @ apart_point_and_line ) )
!= ( A @ ( sk2 @ apart_point_and_line ) ) )
| ( A @ ( sk2 @ apart_point_and_line ) )
| ( B @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[5653]) ).
thf(5849,plain,
! [A: $i] :
( ( A @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[5803:[bind(A,$thf( B ))]]) ).
thf(5900,plain,
! [A: $i] :
( ( A @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk1 @ apart_point_and_line ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[5849]) ).
thf(406,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,56]) ).
thf(407,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[408]) ).
thf(8730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( sk2 @ ( sk3 @ distinct_points ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[138,8164]) ).
thf(8731,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( sk2 @ ( sk3 @ distinct_points ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8730]) ).
thf(8732,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8731:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 ))]]) ).
thf(4586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,667]) ).
thf(4587,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4586]) ).
thf(4600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) )
| ( A != D ) ),
inference(simp,[status(thm)],[4587]) ).
thf(4625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[4600]) ).
thf(296,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(297,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[203,105]) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(558,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[557:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3282,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[3056,41]) ).
thf(3283,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3282]) ).
thf(3284,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3283]) ).
thf(3286,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3284]) ).
thf(6930,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3286,6865]) ).
thf(6931,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[6930]) ).
thf(23170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10600,79]) ).
thf(23171,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23170]) ).
thf(23183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D != F )
| ( ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= F ) ),
inference(simp,[status(thm)],[23171]) ).
thf(23203,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= D ),
inference(simp,[status(thm)],[23183]) ).
thf(10381,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ~ ( F @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,105]) ).
thf(10382,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ~ ( F @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[10381]) ).
thf(10383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[10382:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )),bind(F,$thf( K ))]]) ).
thf(10465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[10383]) ).
thf(17729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,149]) ).
thf(17730,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17729]) ).
thf(17731,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17730:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(10532,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,44]) ).
thf(10533,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10532]) ).
thf(10584,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != F )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[10533]) ).
thf(10607,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( E @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[10584]) ).
thf(17714,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,124]) ).
thf(17715,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17714]) ).
thf(17716,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ equal_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17715:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(8012,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( ( A @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[1183,7161]) ).
thf(8013,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( ( A @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(simp,[status(thm)],[8012]) ).
thf(8014,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( B @ parallel_through_point ) ) ),
inference(pattern_uni,[status(thm)],[8013:[bind(A,$thf( A )),bind(B,$thf( J @ ( I @ parallel_through_point ) )),bind(C,$thf( H @ ( I @ parallel_through_point ) )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8112,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( B @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8014]) ).
thf(2374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_lines ) )
!= ( C @ ( D @ orthogonal_lines ) ) )
| ~ $true
| ( C @ ( C @ equal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[76,1843]) ).
thf(2375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_lines ) )
!= ( C @ ( D @ orthogonal_lines ) ) )
| ( C @ ( C @ equal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[2374]) ).
thf(2376,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ equal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[2375:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(4660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3715,4349]) ).
thf(4661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4660]) ).
thf(4662,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4661:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[631,105]) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1123]) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1124:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(4463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3762,640]) ).
thf(4464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4463]) ).
thf(4465,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4464:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(182,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,50]) ).
thf(183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(8173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6663,149]) ).
thf(8174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8173]) ).
thf(8175,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8174:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(17742,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,8175]) ).
thf(17743,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17742]) ).
thf(17744,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17743:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(20862,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[20844,124]) ).
thf(20863,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[20862]) ).
thf(20864,plain,
~ ( sk1 @ ( sk3 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[20863:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,149]) ).
thf(1463,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1462]) ).
thf(1464,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1463:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(17684,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ equal_points ) )
| ~ $true
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,8169]) ).
thf(17685,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ equal_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17684]) ).
thf(17686,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_points ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17685:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(299,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,55]) ).
thf(300,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[301]) ).
thf(3734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[3643,41]) ).
thf(3735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3734]) ).
thf(3736,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( B
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3735]) ).
thf(3738,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[3736]) ).
thf(6936,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3738,6865]) ).
thf(6937,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[6936]) ).
thf(170,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[59,74]) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[171:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(417,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,81]) ).
thf(418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[418:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(2244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[205,640]) ).
thf(2245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2244]) ).
thf(2246,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2245:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(12098,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8109,667]) ).
thf(12099,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[12098]) ).
thf(12117,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( F @ ( E @ parallel_through_point ) ) )
| ( ( D @ ( C @ parallel_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[12099]) ).
thf(12136,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( E @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[12117]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( A @ ( B @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[200]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( A @ ( B @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(397,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,56]) ).
thf(398,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[399]) ).
thf(4961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4601,79]) ).
thf(4962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4961]) ).
thf(4964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != D )
| ( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= D ) ),
inference(simp,[status(thm)],[4962]) ).
thf(4985,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= B ),
inference(simp,[status(thm)],[4964]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(107,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[106]) ).
thf(108,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[107]) ).
thf(4959,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4601,667]) ).
thf(4960,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4959]) ).
thf(4968,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( E @ ( D @ parallel_through_point ) ) )
| ( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= D ) ),
inference(simp,[status(thm)],[4960]) ).
thf(4990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= B ),
inference(simp,[status(thm)],[4968]) ).
thf(780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,667]) ).
thf(781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[780]) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ ( C @ parallel_through_point ) ) )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[781]) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ orthogonal_through_point ) @ parallel_through_point ) )
!= A ),
inference(simp,[status(thm)],[805]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,79]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[383]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ orthogonal_through_point ) )
!= B ),
inference(simp,[status(thm)],[385]) ).
thf(5918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[133,1051]) ).
thf(5919,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[5918]) ).
thf(5920,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[5919:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( sk2 ))]]) ).
thf(4443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3762,81]) ).
thf(4444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4443]) ).
thf(4445,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4444:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,81]) ).
thf(344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(15971,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12123,667]) ).
thf(15972,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ parallel_through_point ) @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15971]) ).
thf(15985,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ parallel_through_point ) )
!= ( F @ ( E @ parallel_through_point ) ) )
| ( ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[15972]) ).
thf(16020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ parallel_through_point ) )
!= ( E @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[15985]) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[101]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[102]) ).
thf(90,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ! [D: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(miniscope,[status(thm)],[89]) ).
thf(91,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[90]) ).
thf(8042,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( C @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,7161]) ).
thf(8043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( C @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8042]) ).
thf(8102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= ( E @ ( C @ parallel_through_point ) ) )
| ( A
!= ( D @ ( C @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[8043]) ).
thf(8131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( D @ ( B @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8102]) ).
thf(3757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3715,142]) ).
thf(3758,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3757]) ).
thf(3759,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[3758:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(17706,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8750,8181]) ).
thf(17707,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk2 @ ( B @ distinct_points ) ) )
| ~ ( sk3 @ ( B @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[17706]) ).
thf(17708,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ~ ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[17707:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(403,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ $true
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,56]) ).
thf(404,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[403]) ).
thf(405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[404:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[405]) ).
thf(20624,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10455,79]) ).
thf(20625,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20624]) ).
thf(20638,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D != F )
| ( ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= F ) ),
inference(simp,[status(thm)],[20625]) ).
thf(20660,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= D ),
inference(simp,[status(thm)],[20638]) ).
thf(10577,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,79]) ).
thf(10578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10577]) ).
thf(10592,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != E )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[10578]) ).
thf(10617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= C ),
inference(simp,[status(thm)],[10592]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( A != A )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ orthogonal_through_point ) )
!= B )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(2663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ~ $true
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[368,205]) ).
thf(2664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( E @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(simp,[status(thm)],[2663]) ).
thf(2665,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(pattern_uni,[status(thm)],[2664:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(8082,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(paramod_ordered,[status(thm)],[368,7161]) ).
thf(8083,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= B ) ),
inference(simp,[status(thm)],[8082]) ).
thf(8084,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(pattern_uni,[status(thm)],[8083:[bind(A,$thf( J @ ( I @ parallel_through_point ) )),bind(B,$thf( H @ ( I @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8116,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8084]) ).
thf(463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,105]) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[463]) ).
thf(465,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[464:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(487,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[465]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orth1) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[111]) ).
thf(340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,81]) ).
thf(341,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ ( E @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,47]) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ unorthogonal_lines ) )
!= ( E @ ( D @ ( E @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[440]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( G @ ( C @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[442]) ).
thf(6951,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6865,147]) ).
thf(6952,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[6951]) ).
thf(6969,plain,
! [A: $i] :
( ( sk3 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[6952]) ).
thf(6973,plain,
sk3 != sk1,
inference(simp,[status(thm)],[6969]) ).
thf(3287,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3062,142]) ).
thf(3288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ parallel_through_point ) @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3287]) ).
thf(3289,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ parallel_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[3288:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( I )),bind(D,$thf( G @ ( H @ parallel_through_point ) )),bind(E,$thf( I @ ( H @ parallel_through_point ) ))]]) ).
thf(3293,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ parallel_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[3289]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ convergent_lines ) )
!= ( C @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[269]) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( B ))]]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[538]) ).
thf(4925,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4601,44]) ).
thf(4926,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4925]) ).
thf(4965,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != E )
| ( ( A @ ( C @ ( B @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[4926]) ).
thf(4986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[4965]) ).
thf(3731,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3643,142]) ).
thf(3732,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ equal_lines ) )
!= ( E @ ( D @ equal_lines ) ) )
| ~ ( E @ ( D @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3731]) ).
thf(3733,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[3732:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( H )),bind(E,$thf( G @ ( I @ ( H @ parallel_through_point ) @ parallel_through_point ) ))]]) ).
thf(3737,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ parallel_through_point ) @ parallel_through_point ) @ ( B @ distinct_lines ) ),
inference(simp,[status(thm)],[3733]) ).
thf(237,plain,
! [A: $i] :
( ( ( A @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[236,41]) ).
thf(238,plain,
! [A: $i] :
( ( ( A @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(244,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( A
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(246,plain,
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(6944,plain,
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[246,6865]) ).
thf(6945,plain,
( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[6944]) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ( A @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[548,205]) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(8034,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[540,7161]) ).
thf(8035,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ( C @ ( B @ parallel_through_point ) @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[8034]) ).
thf(8036,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( B @ ( C @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[8035:[bind(A,$thf( H @ ( I @ parallel_through_point ) )),bind(B,$thf( J @ ( I @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( H )),bind(F,$thf( J ))]]) ).
thf(8128,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( B @ ( C @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[8036]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,55]) ).
thf(280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ~ ( C @ ( A @ unorthogonal_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(12946,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10469,44]) ).
thf(12947,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[12946]) ).
thf(13011,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= F )
| ( C
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[12947]) ).
thf(13032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= E ),
inference(simp,[status(thm)],[13011]) ).
thf(11259,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,8107]) ).
thf(11260,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[11259]) ).
thf(11337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) )
| ( A
!= ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[11260]) ).
thf(11374,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[11337]) ).
thf(9732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[9451,138]) ).
thf(9733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[9732]) ).
thf(9734,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9733:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(9815,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[9734]) ).
thf(29348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk1 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ~ $true
| ( B @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[9815,147]) ).
thf(29349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk1 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[29348]) ).
thf(29350,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[29349:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk1 ))]]) ).
thf(32234,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( sk3 @ ( B @ distinct_points ) ) )
| ( sk2 @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[29350,8732]) ).
thf(32235,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( sk3 @ ( B @ distinct_points ) ) )
| ( sk2 @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[32234]) ).
thf(32236,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[32235:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[235,667]) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[799]) ).
thf(801,plain,
! [B: $i,A: $i] : ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[800:[bind(A,$thf( E )),bind(B,$thf( F @ ( E @ parallel_through_point ) )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(808,plain,
! [B: $i,A: $i] : ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) ),
inference(simp,[status(thm)],[801]) ).
thf(10575,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,667]) ).
thf(10576,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10575]) ).
thf(10589,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( F @ ( E @ parallel_through_point ) ) )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[10576]) ).
thf(10613,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ parallel_through_point ) )
!= C ),
inference(simp,[status(thm)],[10589]) ).
thf(1028,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,667]) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ parallel_through_point ) @ ( D @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1028]) ).
thf(1032,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) )
| ( B != D ) ),
inference(simp,[status(thm)],[1029]) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(347,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,50]) ).
thf(348,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ convergent_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[348:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) )),bind(E,$thf( A ))]]) ).
thf(370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ convergent_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(9443,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6759,130]) ).
thf(9444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(simp,[status(thm)],[9443]) ).
thf(9445,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9444:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(11299,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[539,8107]) ).
thf(11300,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( C @ ( B @ parallel_through_point ) @ equal_lines ) ) ),
inference(simp,[status(thm)],[11299]) ).
thf(11301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ ( A @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(pattern_uni,[status(thm)],[11300:[bind(A,$thf( I @ ( K @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(B,$thf( M @ ( L @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( K ))]]) ).
thf(11354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ ( A @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) ),
inference(simp,[status(thm)],[11301]) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[50,81]) ).
thf(335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( D @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(336,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,44]) ).
thf(375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= D )
| ( A
!= ( C @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(386,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= C ),
inference(simp,[status(thm)],[384]) ).
thf(11288,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[199,8107]) ).
thf(11289,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( E @ ( F @ parallel_through_point ) @ ( D @ ( G @ ( F @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[11288]) ).
thf(11290,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ ( A @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[11289:[bind(A,$thf( I @ ( K @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(B,$thf( M @ ( L @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( I )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( K ))]]) ).
thf(11351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ ( A @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[11290]) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[808,41]) ).
thf(817,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[816]) ).
thf(821,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( A
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[817]) ).
thf(823,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[821]) ).
thf(6942,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[823,6865]) ).
thf(6943,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[6942]) ).
thf(285,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ ( E @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,47]) ).
thf(286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ ( E @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( G @ ( C @ orthogonal_through_point ) )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( C ))]]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,56]) ).
thf(421,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
| ( A @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( B @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[421:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ orthogonal_through_point ) ))]]) ).
thf(446,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
| ( A @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( B @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(426,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[56,55]) ).
thf(427,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[426]) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[427:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(10436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,79]) ).
thf(10437,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10436]) ).
thf(10446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != E )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[10437]) ).
thf(10464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= C ),
inference(simp,[status(thm)],[10446]) ).
thf(579,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[203,81]) ).
thf(580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[579]) ).
thf(581,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[580:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(12050,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8109,44]) ).
thf(12051,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ ( D @ ( C @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ ( F @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[12050]) ).
thf(12111,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= F )
| ( ( D @ ( C @ parallel_through_point ) )
!= ( E @ ( F @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[12051]) ).
thf(12130,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ parallel_through_point ) )
!= ( E @ ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[12111]) ).
thf(1415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,105]) ).
thf(1416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1416:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( G @ ( I @ ( H @ orthogonal_through_point ) @ parallel_through_point ) )),bind(E,$thf( H ))]]) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1417]) ).
thf(795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,667]) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ parallel_through_point ) @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[795]) ).
thf(806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[796]) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ orthogonal_through_point ) )
!= ( C @ ( B @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[806]) ).
thf(379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,55]) ).
thf(380,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ unorthogonal_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[379]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( B @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ orthogonal_through_point ) ))]]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( B @ convergent_lines ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( B @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(4449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3762,649]) ).
thf(4450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( C @ ( D @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4449]) ).
thf(4451,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4450:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(10521,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ~ ( F @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7195,105]) ).
thf(10522,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ~ ( F @ ( F @ ( E @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[10521]) ).
thf(10523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[10522:[bind(A,$thf( H )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( L )),bind(E,$thf( H @ ( J @ ( L @ ( K @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )),bind(F,$thf( K ))]]) ).
thf(10610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( C @ ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[10523]) ).
thf(12158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( F @ ( E @ equal_lines ) ) )
| ~ $true
| ~ ( E @ ( F @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[8113,4349]) ).
thf(12159,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( F @ ( E @ equal_lines ) ) )
| ~ ( E @ ( F @ distinct_lines ) ) ),
inference(simp,[status(thm)],[12158]) ).
thf(12160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[12159:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( H @ ( J @ ( K @ parallel_through_point ) @ parallel_through_point ) )),bind(F,$thf( L @ ( K @ parallel_through_point ) ))]]) ).
thf(12176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[12160]) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,81]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(333,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(346,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[333]) ).
thf(11240,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,8107]) ).
thf(11241,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( E @ parallel_through_point ) @ ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[11240]) ).
thf(11342,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( D @ ( E @ parallel_through_point ) ) )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= ( C @ ( F @ ( E @ parallel_through_point ) @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[11241]) ).
thf(11381,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( D @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( B @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[11342]) ).
thf(4552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4339,44]) ).
thf(4553,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4552]) ).
thf(4595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( A @ parallel_through_point ) @ orthogonal_through_point ) )
!= E )
| ( A
!= ( D @ ( E @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[4553]) ).
thf(4619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= D ),
inference(simp,[status(thm)],[4595]) ).
thf(212,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[39,124]) ).
thf(213,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
~ ( sk2 @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,74]) ).
thf(289,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ~ ( E @ ( D @ orthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ orthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(1011,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[810,105]) ).
thf(1012,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ~ ( E @ ( E @ ( D @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1011]) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1012:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( H )),bind(E,$thf( G @ ( I @ ( H @ orthogonal_through_point ) @ parallel_through_point ) ))]]) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ ( B @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1013]) ).
thf(391,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,56]) ).
thf(392,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ unorthogonal_lines ) )
| ~ ( D @ ( C @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( B @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ orthogonal_through_point ) )),bind(D,$thf( F ))]]) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( B @ ( C @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(15266,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[199,11386]) ).
thf(15267,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( E @ ( F @ parallel_through_point ) @ parallel_through_point ) @ ( G @ ( F @ parallel_through_point ) @ convergent_lines ) ) )
| ~ ( A @ ( C @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[15266]) ).
thf(15268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( D @ parallel_through_point ) @ ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[15267:[bind(A,$thf( I @ ( L @ parallel_through_point ) )),bind(B,$thf( K @ ( M @ ( L @ parallel_through_point ) @ parallel_through_point ) )),bind(C,$thf( C )),bind(D,$thf( K )),bind(E,$thf( M )),bind(F,$thf( L )),bind(G,$thf( I ))]]) ).
thf(15337,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
~ ( B @ ( D @ parallel_through_point ) @ ( A @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[15268]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[161,79]) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(166,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[163]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) )
!= A ),
inference(simp,[status(thm)],[166]) ).
thf(4355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[144,3725]) ).
thf(4356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[4355]) ).
thf(4357,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ( B @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[4356:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(12161,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( F @ equal_lines ) ) )
| ~ $true
| ~ ( E @ ( F @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[8113,4668]) ).
thf(12162,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ parallel_through_point ) @ ( A @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ equal_lines ) )
!= ( E @ ( F @ equal_lines ) ) )
| ~ ( E @ ( F @ distinct_lines ) ) ),
inference(simp,[status(thm)],[12161]) ).
thf(12163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ parallel_through_point ) @ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[12162:[bind(A,$thf( H )),bind(B,$thf( L )),bind(C,$thf( K )),bind(D,$thf( J )),bind(E,$thf( L @ ( K @ parallel_through_point ) )),bind(F,$thf( H @ ( J @ ( K @ parallel_through_point ) @ parallel_through_point ) ))]]) ).
thf(12177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
~ ( D @ ( C @ parallel_through_point ) @ ( A @ ( B @ ( C @ parallel_through_point ) @ parallel_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[12163]) ).
thf(4425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3762,105]) ).
thf(4426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4425]) ).
thf(4427,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4426:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(10434,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7176,667]) ).
thf(10435,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ convergent_lines ) )
!= ( F @ ( E @ parallel_through_point ) @ ( E @ convergent_lines ) ) ),
inference(simp,[status(thm)],[10434]) ).
thf(10452,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C
!= ( F @ ( E @ parallel_through_point ) ) )
| ( ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) )
!= E ) ),
inference(simp,[status(thm)],[10435]) ).
thf(10472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ ( B @ ( D @ ( C @ parallel_through_point ) @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= C ),
inference(simp,[status(thm)],[10452]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ $true
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[270,41]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ equal_lines ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(320,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ( ( B @ ( A @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[319]) ).
thf(321,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(6928,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[321,6865]) ).
thf(6929,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[6928]) ).
thf(93,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ! [C: $i] :
( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(cnf,[status(esa)],[93]) ).
thf(125,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[123]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(443,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,56]) ).
thf(444,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ unorthogonal_lines ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[443]) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( A @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[444:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) )),bind(E,$thf( A ))]]) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ~ ( A @ ( D @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( A @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(32093,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15338,79]) ).
thf(32094,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) @ ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( F @ convergent_lines ) ) ),
inference(simp,[status(thm)],[32093]) ).
thf(32110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) )
!= F )
| ( ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) )
!= F ) ),
inference(simp,[status(thm)],[32094]) ).
thf(32164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( E @ ( D @ parallel_through_point ) @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[32110]) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) )
!= ( D @ ( C @ equal_lines ) ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[808,142]) ).
thf(819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( A @ equal_lines ) )
!= ( D @ ( C @ equal_lines ) ) )
| ~ ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[818]) ).
thf(820,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ parallel_through_point ) @ ( A @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[819:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ parallel_through_point ) ))]]) ).
thf(822,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ parallel_through_point ) @ ( A @ distinct_lines ) ),
inference(simp,[status(thm)],[820]) ).
thf(2537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( B @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2376,74]) ).
thf(2538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( B @ equal_lines ) ) ),
inference(simp,[status(thm)],[2537]) ).
thf(2539,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( B @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[2538:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(68,plain,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3798,142]) ).
thf(3811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(simp,[status(thm)],[3810]) ).
thf(3812,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ( A @ ( A @ equal_lines ) ) ),
inference(pattern_uni,[status(thm)],[3811:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[200,44]) ).
thf(351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(364,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A != E )
| ( ( C @ ( B @ orthogonal_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[351]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) )
| ( D @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,203]) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[582]) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= C )
| ( A != C )
| ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[583]) ).
thf(607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ orthogonal_through_point ) )
!= B )
| ( C @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( D @ ( C @ equal_lines ) ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[270,142]) ).
thf(316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ parallel_through_point ) @ equal_lines ) )
!= ( D @ ( C @ equal_lines ) ) )
| ~ ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(317,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ parallel_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[316:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ parallel_through_point ) )),bind(D,$thf( E ))]]) ).
thf(322,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ parallel_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[317]) ).
thf(5984,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[133,1464]) ).
thf(5985,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[5984]) ).
thf(5986,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[5985:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( sk1 ))]]) ).
thf(1424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,44]) ).
thf(1425,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( E @ ( D @ ( E @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1424]) ).
thf(1443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B != E )
| ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( D @ ( E @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[1425]) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[1443]) ).
thf(432,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ $true
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,56]) ).
thf(433,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
!= ( E @ ( D @ unorthogonal_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ unorthogonal_lines ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[433:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(454,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[434]) ).
thf(6959,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6865,149]) ).
thf(6960,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[6959]) ).
thf(6961,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[6960:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(8010,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1046,7161]) ).
thf(8011,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) @ convergent_lines ) )
!= ( F @ ( D @ parallel_through_point ) @ ( E @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8010]) ).
thf(8097,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B
!= ( F @ ( D @ parallel_through_point ) ) )
| ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( E @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[8011]) ).
thf(8125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( E @ ( C @ parallel_through_point ) @ orthogonal_through_point ) @ parallel_through_point ) )
!= ( D @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[8097]) ).
thf(276,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ~ $true
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[55,50]) ).
thf(277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( F @ ( E @ convergent_lines ) )
| ( F @ ( D @ convergent_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(7318,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[6970,124]) ).
thf(7319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[7318]) ).
thf(7320,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[7319:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(38722,plain,
$false,
inference(e,[status(thm)],[101,3798,846,249,1850,468,88,365,138,11352,8129,4339,3762,10478,3285,994,308,269,202,4603,449,120,8169,1591,142,6759,15384,56,14264,14292,4343,42,1046,1601,37,389,9432,110,4349,157,10469,6873,8126,15338,20675,448,57,1847,9768,9712,8109,20877,10623,16018,211,1136,6964,121,84,1183,1051,1858,106,14284,61,1447,453,15343,411,116,7337,10459,147,1843,89,133,312,74,8123,307,452,270,661,9440,1047,60,3450,201,20886,85,810,14295,6865,36874,366,8113,1042,7161,92,17738,13034,4608,14248,6445,3297,97,8181,15368,456,14217,65,4668,6955,1540,13099,23218,16031,169,6941,6967,124,2323,339,77,3643,109,471,8132,489,6935,1039,1451,1456,5900,457,10455,8732,129,128,105,4625,10614,311,558,12123,6931,23203,134,10465,205,17731,20844,8164,10607,17716,148,45,64,9451,161,8112,149,2376,4662,44,1125,4465,204,59,118,71,17744,144,236,20864,1464,540,17686,8107,313,6937,172,113,419,81,2246,4601,12136,98,362,451,76,39,649,631,4985,66,108,4990,811,387,5920,4445,345,367,16020,103,8750,91,130,8131,3759,17708,455,20660,80,135,8175,10617,2665,8116,487,112,342,458,6973,3293,548,4986,145,48,3737,640,6945,887,95,8128,310,50,5467,13032,11374,9815,127,32236,808,10613,199,673,1038,370,3715,9445,544,11354,336,11386,386,11351,6917,6943,314,29350,446,24797,450,6758,5653,10464,539,87,203,6970,581,12130,3725,104,1453,368,3056,813,40,390,139,4451,55,10610,235,12176,667,10600,346,11381,4619,214,290,119,58,82,1045,447,15337,168,51,4357,3062,12177,79,4427,10472,6929,94,126,136,459,32164,822,200,62,131,47,2539,68,7176,3812,369,607,111,7195,322,5986,6663,1449,454,100,6961,8125,309,7320]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.18/5.45 % Computer : n008.cluster.edu
% 0.18/5.45 % Model : x86_64 x86_64
% 0.18/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45 % Memory : 8046.5625MB
% 0.18/5.45 % OS : Linux 6.8.0-71-generic
% 0.18/5.45 % CPULimit : 300
% 0.18/5.45 % WCLimit : 300
% 0.18/5.45 % DateTime : Fri Sep 25 13:06:29 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.00/6.04 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.61/6.30 % [INFO] Parsing done (251ms).
% 1.61/6.31 % [INFO] Running in sequential loop mode.
% 2.25/6.71 % [INFO] eprover registered as external prover.
% 2.25/6.72 % [INFO] Scanning for conjecture ...
% 2.42/6.82 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.42/6.90 % [INFO] Axiom selection finished. Selected 34 axioms (removed 1 axioms).
% 2.60/6.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/6.97 % [INFO] Type checking passed.
% 2.60/6.98 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 84.51/23.63 % External prover 'e' found a proof!
% 84.51/23.63 % [INFO] Killing All external provers ...
% 84.51/23.63 % Time passed: 18033ms (effective reasoning time: 17310ms)
% 84.51/23.63 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 84.51/23.64 % Axioms used in derivation (34): par1, ouo1, ooc2, apart4, a5, ceq2, a4, ax1, oac1, orth1, ax2, occu1, con1, cp2, apart3, ooc1, ceq3, ax6, cup1, ci4, couo1, int1, apart5, coipo1, ci3, apart1, ci2, cp1, ceq1, cu1, ci1, apart2, p1, cotno1
% 84.51/23.64 % No. of inferences in proof: 1116
% 84.51/23.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18033 ms resp. 17310 ms w/o parsing
% 86.01/24.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 86.41/24.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------