%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO202+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n016.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 07:12:44 AM UTC 2026
% Result : Theorem 76.99s 19.29s
% Output : Refutation 78.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 16
% Syntax : Number of formulae : 579 ( 35 unt; 0 typ; 3 def)
% Number of atoms : 2672 ( 359 equ; 0 cnn)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 8676 (1110 ~;1427 |; 22 &;6080 @)
% ( 0 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 1694 ( 0 ^;1688 !; 3 ?;1694 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_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 @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk1 @ line_connecting ) @ ( A @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( B @ ( sk1 @ distinct_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ~ ( sk1 @ ( B @ ( sk1 @ line_connecting ) @ ( A @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( A @ ( sk1 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ~ ( sk1 @ ( A @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(11,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(49,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)],[11]) ).
thf(50,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)],[49]) ).
thf(777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ apart_point_and_line ) ) )
| ( D @ ( 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(eqfactor_ordered,[status(thm)],[50]) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[777:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[781]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).
thf(44,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) )
& ( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(410,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[48,42]) ).
thf(411,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( H @ ( G @ intersection_point ) ))]]) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(2186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( F @ ( C @ apart_point_and_line ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( F @ ( E @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ~ ( F @ ( E @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[793,439]) ).
thf(2187,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( F @ ( C @ apart_point_and_line ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( F @ ( E @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( F @ ( E @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[2186]) ).
thf(2188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( D @ intersection_point ) @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( D @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[2187:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( B ))]]) ).
thf(2306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( D @ intersection_point ) @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( D @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[2188]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
& ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( sk3 @ ( sk1 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(19,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ),
inference(cnfConj,[status(thm)],[16]) ).
thf(8,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',apart6) ).
thf(36,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)],[8]) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(270,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,38]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(293,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(222,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[47,42]) ).
thf(223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( H @ ( G @ intersection_point ) ))]]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( C @ ( A @ apart_point_and_line ) ) )
| ( A @ ( B @ distinct_points ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[236]) ).
thf(245,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) )
!= C )
| ( B != A )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ intersection_point ) @ ( A @ line_connecting ) )
!= B )
| ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( ( D @ ( C @ intersection_point ) @ ( B @ line_connecting ) )
!= C )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ~ $true
| ( B @ ( B @ distinct_points ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,246]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( ( D @ ( C @ intersection_point ) @ ( B @ line_connecting ) )
!= C )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ( B @ ( B @ distinct_points ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(333,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ line_connecting ) )
!= ( sk3 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( B @ ( B @ distinct_points ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(D,$thf( A ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,58]) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(305,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(7,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(33,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)],[7]) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(24,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[25]) ).
thf(189,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)],[35,26]) ).
thf(190,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)],[189]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[191]) ).
thf(2557,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[305,202]) ).
thf(2558,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2557]) ).
thf(2559,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(27,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(29,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[28]) ).
thf(279,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)],[38,29]) ).
thf(280,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)],[279]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(4205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,298]) ).
thf(4206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4205]) ).
thf(4207,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4206:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4207,298]) ).
thf(4373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4372]) ).
thf(4374,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4373:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4727,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[4374]) ).
thf(4728,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4727]) ).
thf(4712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4374,58]) ).
thf(4713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4712]) ).
thf(4714,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4713:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4207,58]) ).
thf(4390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4389]) ).
thf(4391,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4390:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(428,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[48,43]) ).
thf(429,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( H @ ( G @ intersection_point ) ))]]) ).
thf(440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(3359,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ( C @ ( E @ distinct_points ) )
| ~ ( D @ ( F @ intersection_point ) @ ( C @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( D @ ( F @ convergent_lines ) )
| ~ $true
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[58,2306]) ).
thf(3360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ( C @ ( E @ distinct_points ) )
| ~ ( D @ ( F @ intersection_point ) @ ( C @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( D @ ( F @ convergent_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3359]) ).
thf(3361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ distinct_points ) )
| ~ ( A @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( A @ ( D @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3360:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B ))]]) ).
thf(3402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ distinct_points ) )
| ~ ( A @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( A @ ( D @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3361]) ).
thf(267,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,58]) ).
thf(268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(17,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[16]) ).
thf(6,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(30,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)],[6]) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[30]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(136,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)],[17,32]) ).
thf(137,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)],[136]) ).
thf(138,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(154,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(21,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[22]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,23]) ).
thf(140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(156,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[154,156]) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[904]) ).
thf(906,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[905:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(1211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[906,156]) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1211]) ).
thf(1213,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1212:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(1484,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1213,156]) ).
thf(1485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1484]) ).
thf(1486,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1485:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(18,plain,
sk3 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[16]) ).
thf(118,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)],[18,32]) ).
thf(119,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)],[118]) ).
thf(120,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(153,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(857,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[153,156]) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(1043,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)],[859,32]) ).
thf(1044,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)],[1043]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1044:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(1078,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1045]) ).
thf(13,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(54,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)],[13]) ).
thf(55,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)],[54]) ).
thf(56,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)],[55]) ).
thf(887,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( B @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,156]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( B @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[887]) ).
thf(889,plain,
sk1 @ ( sk2 @ distinct_points ),
inference(pattern_uni,[status(thm)],[888:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(920,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[889,42]) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[920]) ).
thf(922,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk2 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(945,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk2 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[922]) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[859,156]) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1031]) ).
thf(1033,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1032:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(1353,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1033]) ).
thf(1354,plain,
! [A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1353]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[153,43]) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(1242,plain,
! [A: $i] :
( ~ $true
| ( ( sk2 @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[906]) ).
thf(1243,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1242]) ).
thf(20,plain,
sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ),
inference(cnfConj,[status(thm)],[16]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,32]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(147,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[147,42]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(372,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,43]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(110,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,58]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(79,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(2560,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( A @ ( B @ distinct_lines ) ) )
| ( B @ ( A @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,202]) ).
thf(2561,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( A @ ( B @ distinct_lines ) ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2560]) ).
thf(2562,plain,
sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ),
inference(pattern_uni,[status(thm)],[2561:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(124,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,43]) ).
thf(125,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(157,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(1799,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk2 @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1486]) ).
thf(1800,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1799]) ).
thf(133,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(315,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[293]) ).
thf(316,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(215,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk2 @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[154]) ).
thf(216,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(875,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[147,156]) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[875]) ).
thf(877,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[877,156]) ).
thf(1931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1932,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1931:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(9712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1932,156]) ).
thf(9713,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[9712]) ).
thf(9714,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[9713:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(10724,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[9714]) ).
thf(10729,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[10724]) ).
thf(228,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ~ $true
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[47,32]) ).
thf(229,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ intersection_point ) @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( H @ ( G @ intersection_point ) ))]]) ).
thf(238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ intersection_point ) @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(511,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ apart_point_and_line ) ) )
| ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[439]) ).
thf(513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) )
!= D )
| ( B != A )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ intersection_point ) @ ( A @ line_connecting ) )
!= C )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[513]) ).
thf(231,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[47,43]) ).
thf(232,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[232:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( C )),bind(E,$thf( H @ ( G @ intersection_point ) ))]]) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[233]) ).
thf(346,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( G @ ( F @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,239]) ).
thf(347,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( G @ ( F @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(348,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( C @ ( A @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( A @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( C @ ( A @ apart_point_and_line ) ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[239]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( C @ ( A @ apart_point_and_line ) ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(291,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)],[38]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( B ))]]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(4228,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)],[296,298]) ).
thf(4229,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)],[4228]) ).
thf(4230,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4229:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[154,42]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( sk2 @ ( B @ distinct_points ) )
| ~ ( A @ ( sk2 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[204:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( sk2 @ ( B @ distinct_points ) )
| ~ ( A @ ( sk2 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(4240,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( B @ convergent_lines ) ) )
| ( B @ ( A @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,298]) ).
thf(4241,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( B @ convergent_lines ) ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4240]) ).
thf(4242,plain,
sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ),
inference(pattern_uni,[status(thm)],[4241:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4287,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4242,48]) ).
thf(4288,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4287]) ).
thf(4289,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[4288:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(4307,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4289]) ).
thf(71,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(72,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= A )
| ( ( sk2 @ ( sk1 @ line_connecting ) )
!= A ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(1336,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1033,156]) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1336]) ).
thf(1338,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1337:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(1720,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1338]) ).
thf(1721,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1720]) ).
thf(7929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( sk1 @ ( D @ distinct_points ) ) )
| ~ ( D @ ( sk3 @ distinct_points ) )
| ( sk1 @ ( D @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[47,1721]) ).
thf(7937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) )
!= sk1 )
| ( C != D )
| ~ ( D @ ( sk3 @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) )
| ( sk1 @ ( D @ distinct_points ) ) ),
inference(simp,[status(thm)],[7929]) ).
thf(7941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) )
!= sk1 )
| ~ ( C @ ( sk3 @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) )
| ( sk1 @ ( C @ distinct_points ) ) ),
inference(simp,[status(thm)],[7937]) ).
thf(8235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( E @ apart_point_and_line ) ) )
| ( ( D @ ( C @ intersection_point ) )
!= sk1 )
| ~ ( E @ ( sk3 @ distinct_points ) )
| ~ $true
| ~ ( D @ ( C @ convergent_lines ) )
| ( sk1 @ ( E @ distinct_points ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[793,7941]) ).
thf(8236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( E @ apart_point_and_line ) ) )
| ( ( D @ ( C @ intersection_point ) )
!= sk1 )
| ~ ( E @ ( sk3 @ distinct_points ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( sk1 @ ( E @ distinct_points ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8235]) ).
thf(8237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( sk1 @ ( A @ distinct_points ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8236:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(8404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( sk1 @ ( A @ distinct_points ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8237]) ).
thf(8921,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8404,43]) ).
thf(8922,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8921]) ).
thf(8923,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[8922:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( sk1 ))]]) ).
thf(9136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[8923]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( A @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,35]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( A @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(201,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(10164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( sk1 @ ( D @ distinct_points ) ) )
| ~ ( D @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( D @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[8404,1800]) ).
thf(10165,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[10164:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(2535,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[201,202]) ).
thf(2536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2535]) ).
thf(2537,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[2536:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(2592,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2537,202]) ).
thf(2593,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2592]) ).
thf(2594,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[2593:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(2903,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2594,202]) ).
thf(2904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2903]) ).
thf(2905,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[2904:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ apart_point_and_line ) ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(1695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1338,32]) ).
thf(1696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1695]) ).
thf(1697,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1696:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 ))]]) ).
thf(1723,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1697]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( B @ distinct_points ) )
!= ( C @ ( A @ distinct_points ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( B ))]]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ~ $true
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[149,156]) ).
thf(893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[893:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(300,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( E @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,236]) ).
thf(301,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( E @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(E,$thf( A ))]]) ).
thf(258,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( D @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,236]) ).
thf(259,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( D @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ distinct_points ) )
| ~ ( C @ ( A @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( A @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A )),bind(G,$thf( C ))]]) ).
thf(1501,plain,
! [A: $i] :
( ~ $true
| ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1213]) ).
thf(1502,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1501]) ).
thf(276,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( F @ distinct_points ) )
| ~ ( D @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,47]) ).
thf(277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( F @ distinct_points ) )
| ~ ( D @ ( F @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(67,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,23]) ).
thf(68,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(69,plain,
! [A: $i] :
( ( sk1 != A )
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= A ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= sk1 ),
inference(simp,[status(thm)],[69]) ).
thf(177,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ( F @ ( E @ distinct_lines ) )
| ( F @ ( D @ distinct_lines ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[35,35]) ).
thf(178,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ( F @ ( E @ distinct_lines ) )
| ( F @ ( D @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_lines ) )
| ( D @ ( A @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_lines ) )
| ( D @ ( A @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,23]) ).
thf(62,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(64,plain,
! [A: $i] :
( ( sk3 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[62]) ).
thf(65,plain,
sk3 != sk1,
inference(simp,[status(thm)],[64]) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( C @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,48]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( C @ ( D @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[416]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( A @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(435,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( A @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[418]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,42]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(97,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(365,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[147,23]) ).
thf(366,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[365]) ).
thf(367,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ),
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,42]) ).
thf(376,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(377,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[376:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( C ))]]) ).
thf(388,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(12,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(51,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)],[12]) ).
thf(52,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)],[51]) ).
thf(53,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)],[52]) ).
thf(1339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1033,32]) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1339]) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1340:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1341]) ).
thf(337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ( ( F @ ( E @ intersection_point ) @ ( D @ line_connecting ) )
!= E )
| ~ ( E @ ( D @ apart_point_and_line ) )
| ~ $true
| ( D @ ( D @ distinct_points ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,246]) ).
thf(338,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ( ( F @ ( E @ intersection_point ) @ ( D @ line_connecting ) )
!= E )
| ~ ( E @ ( D @ apart_point_and_line ) )
| ( D @ ( D @ distinct_points ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[337]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ intersection_point ) @ ( D @ line_connecting ) )
!= B )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( D @ ( D @ distinct_points ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(2113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( E @ ( C @ apart_point_and_line ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( F @ ( E @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ~ ( F @ ( E @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[793,236]) ).
thf(2114,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( E @ ( C @ apart_point_and_line ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( F @ ( E @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( F @ ( E @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[2113]) ).
thf(2115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( D @ ( B @ intersection_point ) @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(2317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( D @ ( B @ intersection_point ) @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[2115]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,43]) ).
thf(101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(109,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[201,35]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(9759,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1932]) ).
thf(9761,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( sk1 @ ( A @ distinct_points ) ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[9759]) ).
thf(158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[153,42]) ).
thf(159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(4703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4374,298]) ).
thf(4704,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( B @ ( C @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4703]) ).
thf(4705,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4704:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(4901,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[4705]) ).
thf(4902,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4901]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,47]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(227,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(237,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[227]) ).
thf(244,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( C @ ( A @ apart_point_and_line ) ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,58]) ).
thf(265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ distinct_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(2554,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[58,202]) ).
thf(2555,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2554]) ).
thf(2556,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(112,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,42]) ).
thf(113,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ distinct_points ) )
| ~ ( C @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ distinct_points ) )
| ~ ( C @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(4299,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4242,47]) ).
thf(4300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4299]) ).
thf(4301,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[4300:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(4309,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4301]) ).
thf(4234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[298,58]) ).
thf(4235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4234]) ).
thf(4236,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4235:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[154,43]) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk2 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk2 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(75,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
sk3 != sk2,
inference(simp,[status(thm)],[75]) ).
thf(306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,47]) ).
thf(307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[308]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,42]) ).
thf(89,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(98,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(4419,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[4207]) ).
thf(4420,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4419]) ).
thf(59,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,23]) ).
thf(60,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(63,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[60]) ).
thf(66,plain,
sk2 != sk1,
inference(simp,[status(thm)],[63]) ).
thf(195,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)],[35]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( B ))]]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(2540,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[198,202]) ).
thf(2541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2540]) ).
thf(2542,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[2541:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(121,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,43]) ).
thf(122,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( B @ intersection_point ) @ ( A @ line_connecting ) )
!= B )
| ~ ( B @ ( A @ apart_point_and_line ) )
| ~ $true
| ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[19,246]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( B @ intersection_point ) @ ( A @ line_connecting ) )
!= B )
| ~ ( B @ ( A @ apart_point_and_line ) )
| ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[328]) ).
thf(330,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( E @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,239]) ).
thf(344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( E @ ( D @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( D @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[344:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(E,$thf( A ))]]) ).
thf(1217,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
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[906,32]) ).
thf(1218,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 ) )
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1217]) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1218:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk1 @ distinct_points ) )
| ( sk2 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1219]) ).
thf(2619,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[2537]) ).
thf(2620,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2619]) ).
thf(285,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)],[38,38]) ).
thf(286,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)],[285]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( A @ convergent_lines ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(299,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)],[287]) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[889,43]) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(936,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk2 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(944,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk2 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[936]) ).
thf(362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[147,43]) ).
thf(363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( C @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(374,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,239]) ).
thf(341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(D,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4705,58]) ).
thf(4872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4871]) ).
thf(4873,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4872:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(5650,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4873,202]) ).
thf(5651,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[5650]) ).
thf(5652,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[5651:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(273,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( F @ distinct_points ) )
| ~ ( D @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,47]) ).
thf(274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( E @ ( D @ convergent_lines ) ) )
| ( E @ ( D @ intersection_point ) @ ( F @ distinct_points ) )
| ~ ( D @ ( F @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( A @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ intersection_point ) @ ( D @ distinct_points ) )
| ~ ( A @ ( D @ apart_point_and_line ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(8535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( C @ ( D @ distinct_lines ) )
| ~ $true
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[298,2556]) ).
thf(8536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( C @ ( D @ distinct_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[8535]) ).
thf(8537,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[8536:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(130,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(131,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( F @ ( E @ distinct_points ) )
| ( F @ ( D @ distinct_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( A @ distinct_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[131:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( A @ distinct_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(901,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( B @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,156]) ).
thf(902,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( B @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[901]) ).
thf(903,plain,
sk1 @ ( sk3 @ distinct_points ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(962,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[903,43]) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[962]) ).
thf(964,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[963:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(971,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[964]) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[305,35]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(3892,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( F @ convergent_lines ) ) )
| ( C @ ( E @ distinct_points ) )
| ~ ( D @ ( F @ intersection_point ) @ ( C @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ $true
| ~ ( D @ ( D @ distinct_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[296,2306]) ).
thf(3893,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( F @ convergent_lines ) ) )
| ( C @ ( E @ distinct_points ) )
| ~ ( D @ ( F @ intersection_point ) @ ( C @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( D @ ( D @ distinct_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3892]) ).
thf(3894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( B @ ( A @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3893:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(3949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ distinct_points ) )
| ~ ( B @ ( A @ intersection_point ) @ ( C @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3894]) ).
thf(261,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( D @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,236]) ).
thf(262,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( D @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ distinct_points ) )
| ~ ( C @ ( B @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( C ))]]) ).
thf(180,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ( F @ ( E @ distinct_lines ) )
| ( F @ ( D @ distinct_lines ) )
| ~ $true
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[35,35]) ).
thf(181,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ( F @ ( E @ distinct_lines ) )
| ( F @ ( D @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(413,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,48]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[413]) ).
thf(415,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[414:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(441,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[415]) ).
thf(13110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( sk2 @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[10165,43]) ).
thf(13111,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( E @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[13110]) ).
thf(13112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[13111:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( sk1 ))]]) ).
thf(13311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( A @ ( sk2 @ distinct_points ) )
| ( ( C @ ( B @ intersection_point ) )
!= sk1 )
| ~ ( A @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[13112]) ).
thf(13835,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ( sk1 @ ( F @ distinct_points ) )
| ~ ( sk1 @ ( C @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( C @ ( sk2 @ distinct_points ) )
| ( ( E @ ( D @ intersection_point ) )
!= sk1 )
| ~ ( C @ ( sk3 @ distinct_points ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ~ $true
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[8537,13311]) ).
thf(13836,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ distinct_lines ) )
!= ( D @ ( D @ distinct_lines ) ) )
| ( sk1 @ ( F @ distinct_points ) )
| ~ ( sk1 @ ( C @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ ( C @ ( sk2 @ distinct_points ) )
| ( ( E @ ( D @ intersection_point ) )
!= sk1 )
| ~ ( C @ ( sk3 @ distinct_points ) )
| ~ ( E @ ( D @ convergent_lines ) )
| ~ ( C @ ( C @ distinct_points ) )
| ~ ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[13835]) ).
thf(13837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( sk2 @ distinct_points ) )
| ( ( C @ ( A @ intersection_point ) )
!= sk1 )
| ~ ( B @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[13836:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(14086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( D @ distinct_points ) )
| ~ ( sk1 @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( sk2 @ distinct_points ) )
| ( ( C @ ( A @ intersection_point ) )
!= sk1 )
| ~ ( B @ ( sk3 @ distinct_points ) )
| ~ ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[13837]) ).
thf(334,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ( ( F @ ( E @ intersection_point ) @ ( D @ line_connecting ) )
!= E )
| ~ ( E @ ( D @ apart_point_and_line ) )
| ~ $true
| ( D @ ( D @ distinct_points ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,246]) ).
thf(335,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ convergent_lines ) )
!= ( F @ ( E @ convergent_lines ) ) )
| ( ( F @ ( E @ intersection_point ) @ ( D @ line_connecting ) )
!= E )
| ~ ( E @ ( D @ apart_point_and_line ) )
| ( D @ ( D @ distinct_points ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(336,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ intersection_point ) @ ( D @ line_connecting ) )
!= A )
| ~ ( A @ ( D @ apart_point_and_line ) )
| ( D @ ( D @ distinct_points ) )
| ( C @ ( B @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(1487,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1213,32]) ).
thf(1488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1487]) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1488:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(1504,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[1489]) ).
thf(164,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)],[153,32]) ).
thf(165,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)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,42]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[92:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(99,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(206,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)],[154,32]) ).
thf(207,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)],[206]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(218,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(2918,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[2594]) ).
thf(2919,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2918]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[293,38]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[314]) ).
thf(349,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( G @ ( F @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[38,239]) ).
thf(350,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ convergent_lines ) )
!= ( G @ ( F @ convergent_lines ) ) )
| ( G @ ( F @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( G @ ( F @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( F @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(351,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ intersection_point ) @ ( E @ distinct_points ) )
| ~ ( C @ ( B @ intersection_point ) @ ( D @ line_connecting ) @ ( E @ apart_point_and_line ) )
| ~ ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( B )),bind(G,$thf( C ))]]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[367,43]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[381]) ).
thf(383,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[382:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( C ))]]) ).
thf(390,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(170,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[153]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[170]) ).
thf(4743,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4391,202]) ).
thf(4744,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4743]) ).
thf(4745,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) )
| ( sk3 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4744:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) ))]]) ).
thf(115,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[32,42]) ).
thf(116,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( D @ ( F @ distinct_points ) )
| ~ ( E @ ( D @ line_connecting ) @ ( F @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ distinct_points ) )
| ~ ( C @ ( B @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(2081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[58,198]) ).
thf(2082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2081]) ).
thf(2083,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2082:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2091,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2083]) ).
thf(6995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2091,202]) ).
thf(6996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[6995]) ).
thf(6997,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[6996:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[147,32]) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(361,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(373,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(288,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)],[38,38]) ).
thf(289,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)],[288]) ).
thf(290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(294,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)],[290]) ).
thf(240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,236]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( A @ ( B @ distinct_points ) )
| ~ ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( C @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[240]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(D,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(4874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4705,58]) ).
thf(4875,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4874]) ).
thf(4876,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4875:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(183,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ( E @ ( C @ distinct_lines ) )
| ~ $true
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[58,35]) ).
thf(184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( E @ ( D @ distinct_lines ) )
| ( E @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(368,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[147]) ).
thf(369,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,43]) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(108,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(111,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(253,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[201]) ).
thf(254,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(1961,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[877]) ).
thf(1962,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1961]) ).
thf(3211,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[2905]) ).
thf(3212,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ distinct_lines ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3211]) ).
thf(1068,plain,
! [A: $i] :
( ~ $true
| ( ( sk3 @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[859]) ).
thf(1069,plain,
! [A: $i] :
( ( ( sk3 @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1068]) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ apart_point_and_line ) ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[440]) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ intersection_point ) @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ apart_point_and_line ) ) )
| ~ ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ convergent_lines ) )
| ( D @ ( C @ intersection_point ) @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[1013]) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[903,42]) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[948]) ).
thf(950,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[949:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(972,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( sk3 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[950]) ).
thf(45856,plain,
$false,
inference(e,[status(thm)],[2306,333,2559,4728,4714,4391,440,3402,269,202,1486,1078,56,945,1354,153,174,1243,42,24,372,110,2562,157,1800,20,152,57,316,29,216,10729,238,514,348,353,147,4230,877,221,293,4307,74,793,9136,201,1338,10165,2905,512,439,1723,894,302,260,38,1502,21,33,297,70,197,65,435,97,889,156,2537,388,53,1361,339,9714,2317,109,256,9761,1932,173,4902,237,244,266,7941,906,298,2556,32,148,296,17,149,44,27,8404,4309,54,4236,49,236,219,76,318,39,98,4374,4420,66,2542,155,198,330,345,367,1213,1245,2620,299,35,4207,944,374,342,5652,48,295,18,8537,150,971,327,3949,263,50,199,441,14086,336,154,1504,175,43,859,99,4873,903,218,2919,319,26,351,390,171,4705,23,2594,1721,4745,58,246,151,6997,36,30,51,19,373,305,294,79,1033,2091,239,242,4242,4876,47,15,200,369,111,254,1962,3212,13311,1069,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.13/0.39 % Computer : n016.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Fri Sep 25 13:09:46 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.17 % [INFO] Parsing done (199ms).
% 1.29/1.19 % [INFO] Running in sequential loop mode.
% 2.15/1.60 % [INFO] eprover registered as external prover.
% 2.15/1.61 % [INFO] Scanning for conjecture ...
% 2.36/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.36/1.75 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.36/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.36/1.79 % [INFO] Type checking passed.
% 2.36/1.79 % [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 ...
% 76.99/19.28 % External prover 'e' found a proof!
% 76.99/19.28 % [INFO] Killing All external provers ...
% 76.99/19.28 % Time passed: 18744ms (effective reasoning time: 18087ms)
% 76.99/19.28 % 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)>
% 76.99/19.29 % Axioms used in derivation (12): apart3, con2, ceq3, apart6, apart4, ceq2, apart5, apart1, con1, apart2, ceq1, cu1
% 76.99/19.29 % No. of inferences in proof: 576
% 76.99/19.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18744 ms resp. 18087 ms w/o parsing
% 78.30/19.56 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 78.30/19.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------