%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 83.03s 22.92s
% Output : Refutation 84.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 39
% Syntax : Number of formulae : 374 ( 91 unt; 0 typ; 3 def)
% Number of atoms : 1225 ( 165 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 3777 ( 548 ~; 448 |; 57 &;2645 @)
% ( 5 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 5 con; 0-2 aty)
% Number of variables : 906 ( 0 ^; 890 !; 13 ?; 906 :)
% ( 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(equal_points_decl,type,
equal_points: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(equal_lines_decl,type,
equal_lines: $i > $i > $o ).
thf(line_decl,type,
line: $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(orthogonal_lines_decl,type,
orthogonal_lines: $i > $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(parallel_lines_decl,type,
parallel_lines: $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 ) @ equal_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 ) @ equal_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 ) @ equal_points ) ) ) ) ) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(95,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)],[17]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ouo1) ).
thf(67,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(68,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ! [D: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(miniscope,[status(thm)],[67]) ).
thf(69,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[68]) ).
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 ) @ equal_points ) ) ),
file('/export/starexec/sandbox/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 ) @ equal_points ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,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 ) @ equal_points ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
( ~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ equal_points ) )
& ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( sk3 @ ( sk1 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(42,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ),
inference(cnfConj,[status(thm)],[39]) ).
thf(96,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[96]) ).
thf(1335,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)],[42,97]) ).
thf(1336,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)],[1335]) ).
thf(1337,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1336:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(1380,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1337]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ parallel_lines ) )
<=> ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(113,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ parallel_lines ) ) )
& ( ( B @ ( A @ parallel_lines ) )
=> ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(114,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ parallel_lines ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ parallel_lines ) )
=> ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[113]) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ parallel_lines ) )
| ( D @ ( C @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ parallel_lines ) ) ) ),
inference(cnf,[status(esa)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[1380,116]) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1409]) ).
thf(1411,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1410:[bind(A,$thf( A )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( A ))]]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cup1) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(41,plain,
sk3 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[39]) ).
thf(37,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(155,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(156,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[155]) ).
thf(157,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[156]) ).
thf(164,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,157]) ).
thf(165,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(168,plain,
! [A: $i] :
( ( sk3 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[165]) ).
thf(170,plain,
sk3 != sk1,
inference(simp,[status(thm)],[168]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coipo1) ).
thf(105,plain,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(106,plain,
~ ? [A: $i,B: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(miniscope,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[106]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(44,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(cnf,[status(esa)],[45]) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[107,46]) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(257,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[256:[bind(A,$thf( F @ ( B @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(261,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[257]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[261,116]) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( C @ parallel_lines ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(276,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ parallel_lines ) ),
inference(simp,[status(thm)],[275]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci2) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(26,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(121,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(122,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(miniscope,[status(thm)],[121]) ).
thf(123,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(cnf,[status(esa)],[122]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,123]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= ( C @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(269,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
<=> ~ ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ equal_lines ) ) )
& ( ( B @ ( A @ equal_lines ) )
=> ~ ( B @ ( A @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(54,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ equal_lines ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
=> ~ ( B @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[53]) ).
thf(55,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_lines ) )
| ( D @ ( C @ distinct_lines ) ) )
& ( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ) ),
inference(cnf,[status(esa)],[54]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).
thf(50,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)],[5]) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(248,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)],[52]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( B ))]]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(10,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(70,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(71,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[70]) ).
thf(72,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[71]) ).
thf(242,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)],[52,72]) ).
thf(243,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)],[242]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[243:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ),
inference(cnfConj,[status(thm)],[55]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[251,56]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[252,302]) ).
thf(363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equal_lines ) )
!= ( C @ ( D @ equal_lines ) ) )
| ~ $true
| ~ ( C @ ( C @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[58,364]) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ equal_lines ) )
!= ( C @ ( D @ equal_lines ) ) )
| ~ ( C @ ( C @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[559,56]) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[876]) ).
thf(878,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[877:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,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/sandbox/benchmark/theBenchmark.p',ceq2) ).
thf(47,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)],[4]) ).
thf(48,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)],[47]) ).
thf(49,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)],[48]) ).
thf(420,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[69,49]) ).
thf(421,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( B @ distinct_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[421:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(440,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( B @ distinct_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[422]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
<=> ~ ( B @ ( A @ distinct_points ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ distinct_points ) )
=> ( B @ ( A @ equal_points ) ) )
& ( ( B @ ( A @ equal_points ) )
=> ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ distinct_points ) )
=> ( B @ ( A @ equal_points ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
=> ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[87]) ).
thf(89,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_points ) )
| ( D @ ( C @ distinct_points ) ) )
& ( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(43,plain,
~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ equal_points ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equal_points ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ equal_points ) ) )
| ~ $true
| ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[92,43]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equal_points ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ equal_points ) ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).
thf(98,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)],[18]) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[99]) ).
thf(1586,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)],[216,100]) ).
thf(1587,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)],[1586]) ).
thf(1588,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1587:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(1620,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(simp,[status(thm)],[1588]) ).
thf(2000,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)],[1620,157]) ).
thf(2001,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2002,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ),
inference(pattern_uni,[status(thm)],[2001:[bind(A,$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(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(2033,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[2002,90]) ).
thf(2034,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[2033]) ).
thf(2035,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[2034:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(147,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[147]) ).
thf(338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[252,148]) ).
thf(339,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[338]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1439,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,120]) ).
thf(1440,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1439]) ).
thf(1441,plain,
~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1440:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(23,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(110,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1589,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)],[41,100]) ).
thf(1590,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)],[1589]) ).
thf(1591,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1590:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(1621,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1591]) ).
thf(1767,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)],[1621,100]) ).
thf(1768,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)],[1767]) ).
thf(1769,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1768:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(1774,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1769]) ).
thf(2414,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( B @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[1774]) ).
thf(2417,plain,
( ( sk1 @ ( sk3 @ distinct_points ) )
| ( sk1 @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[2414:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(2429,plain,
( ( sk1 @ ( sk3 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[2417,157]) ).
thf(2430,plain,
sk1 @ ( sk3 @ distinct_points ),
inference(simp,[status(thm)],[2429]) ).
thf(2442,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[2430,90]) ).
thf(2443,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[2442]) ).
thf(2444,plain,
~ ( sk1 @ ( sk3 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[2443:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(1347,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,97]) ).
thf(1348,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( E @ ( D @ convergent_lines ) )
| ( E @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ orthogonal_through_point ) )),bind(D,$thf( F ))]]) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1349]) ).
thf(111,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[110]) ).
thf(112,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[111]) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ~ $true
| ( A @ ( B @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[1374,112]) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( D @ convergent_lines ) ) )
| ( A @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1504,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[1503:[bind(A,$thf( H @ ( G @ orthogonal_through_point ) )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) ))]]) ).
thf(1511,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) ),
inference(simp,[status(thm)],[1504]) ).
thf(16,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/sandbox/benchmark/theBenchmark.p',cu1) ).
thf(93,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)],[16]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci1) ).
thf(108,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[108]) ).
thf(2022,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2002,109]) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[2022]) ).
thf(2024,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[2023:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(76,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(77,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[77]) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,142]) ).
thf(1663,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1662]) ).
thf(1664,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1663:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(2025,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2002,120]) ).
thf(2026,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[2025]) ).
thf(2027,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[2026:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ incident_point_and_line ) )
<=> ~ ( B @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ apart_point_and_line ) )
=> ( B @ ( A @ incident_point_and_line ) ) )
& ( ( B @ ( A @ incident_point_and_line ) )
=> ~ ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(82,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ apart_point_and_line ) )
=> ( B @ ( A @ incident_point_and_line ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ incident_point_and_line ) )
=> ~ ( B @ ( A @ apart_point_and_line ) ) ) ),
inference(miniscope,[status(thm)],[81]) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ incident_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) ) )
& ( ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ incident_point_and_line ) ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ incident_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
<=> ~ ( B @ ( A @ unorthogonal_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ unorthogonal_lines ) )
=> ( B @ ( A @ orthogonal_lines ) ) )
& ( ( B @ ( A @ orthogonal_lines ) )
=> ~ ( B @ ( A @ unorthogonal_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[39]) ).
thf(1592,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)],[40,100]) ).
thf(1593,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)],[1592]) ).
thf(1594,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1593:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1622,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1594]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',par1) ).
thf(59,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[59]) ).
thf(1630,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1511,112]) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1630]) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[1631]) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ orthogonal_through_point ) )
!= B ),
inference(simp,[status(thm)],[1634]) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ $true
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[559,302]) ).
thf(893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[892]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_lines ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[893:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(62,plain,
( ! [A: $i,B: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
=> ( B @ ( A @ orthogonal_lines ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
=> ~ ( B @ ( A @ unorthogonal_lines ) ) ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ orthogonal_lines ) )
| ( D @ ( C @ unorthogonal_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[107,64]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(2431,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2430,109]) ).
thf(2432,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[2431]) ).
thf(2433,plain,
~ ( sk1 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[2432:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',ceq1) ).
thf(124,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)],[27]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).
thf(143,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[143]) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,144]) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1910]) ).
thf(1912,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1911:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(1964,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1912]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[251,148]) ).
thf(313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[312]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[313:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[252,314]) ).
thf(456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[455]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(73,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1024,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[216,109]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1026,plain,
~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[457,116]) ).
thf(585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( C @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[584]) ).
thf(586,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[585:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1904,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,144]) ).
thf(1905,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1904]) ).
thf(1906,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1905:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(158,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,112]) ).
thf(159,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= A )
| ( ( sk2 @ ( sk1 @ line_connecting ) )
!= A ) ),
inference(simp,[status(thm)],[159]) ).
thf(161,plain,
( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cotno1) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[41,90]) ).
thf(203,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(204,plain,
~ ( sk3 @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[203:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[115]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[340,116]) ).
thf(465,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( C @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[464]) ).
thf(466,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ parallel_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[465:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[1511,116]) ).
thf(1625,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( C @ parallel_lines ) ) ),
inference(simp,[status(thm)],[1624]) ).
thf(1626,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[1625:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ orthogonal_through_point ) ))]]) ).
thf(1638,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ parallel_lines ) ),
inference(simp,[status(thm)],[1626]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ convergent_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int1) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ convergent_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(1027,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,109]) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1027]) ).
thf(1029,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1028:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(220,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)],[216,157]) ).
thf(221,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[220]) ).
thf(225,plain,
! [A: $i] :
( ( sk1 != A )
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= A ) ),
inference(simp,[status(thm)],[221]) ).
thf(226,plain,
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= sk1 ),
inference(simp,[status(thm)],[225]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',orth1) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[79]) ).
thf(1032,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,109]) ).
thf(1033,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1032]) ).
thf(1034,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1033:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(633,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ distinct_lines ) )
!= ( H @ ( G @ distinct_lines ) ) )
| ( J @ ( F @ apart_point_and_line ) )
| ( J @ ( G @ distinct_lines ) )
| ( I @ ( H @ unorthogonal_lines ) )
| ( I @ ( G @ unorthogonal_lines ) )
| ( H @ ( F @ apart_point_and_line ) )
| ~ $true
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[440,440]) ).
thf(634,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( B @ distinct_lines ) )
!= ( H @ ( G @ distinct_lines ) ) )
| ( J @ ( F @ apart_point_and_line ) )
| ( J @ ( G @ distinct_lines ) )
| ( I @ ( H @ unorthogonal_lines ) )
| ( I @ ( G @ unorthogonal_lines ) )
| ( H @ ( F @ apart_point_and_line ) )
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(635,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ apart_point_and_line ) )
| ( H @ ( B @ distinct_lines ) )
| ( G @ ( E @ unorthogonal_lines ) )
| ( G @ ( B @ unorthogonal_lines ) )
| ( E @ ( F @ apart_point_and_line ) )
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( B )),bind(H,$thf( E ))]]) ).
thf(749,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ apart_point_and_line ) )
| ( H @ ( B @ distinct_lines ) )
| ( G @ ( E @ unorthogonal_lines ) )
| ( G @ ( B @ unorthogonal_lines ) )
| ( E @ ( F @ apart_point_and_line ) )
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[635]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',couo1) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1622,90]) ).
thf(1789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1788]) ).
thf(1790,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1789:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(1632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1511,123]) ).
thf(1633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ ( D @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1632]) ).
thf(1635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= D )
| ( A
!= ( C @ ( D @ parallel_through_point ) ) ) ),
inference(simp,[status(thm)],[1633]) ).
thf(1637,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ parallel_through_point ) @ orthogonal_through_point ) )
!= C ),
inference(simp,[status(thm)],[1635]) ).
thf(368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ $true
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[251,302]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ $true
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[251,314]) ).
thf(462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(463,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ convergent_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[457,142]) ).
thf(1678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[1677]) ).
thf(1679,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[1678:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1511,142]) ).
thf(1666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1667,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1666:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ orthogonal_through_point ) ))]]) ).
thf(1711,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1667]) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[1621,90]) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[1764]) ).
thf(1766,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ equal_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,123]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= B )
| ( ( A @ ( B @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ parallel_through_point ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(1457,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,120]) ).
thf(1458,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1459,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1458:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ point )
| ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[103]) ).
thf(166,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,157]) ).
thf(167,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(169,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[167]) ).
thf(171,plain,
sk2 != sk1,
inference(simp,[status(thm)],[169]) ).
thf(74,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[73]) ).
thf(75,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[74]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[40,90]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
~ ( sk2 @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(270,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[42,116]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[340,142]) ).
thf(1660,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[1659]) ).
thf(1661,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[1660:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(344,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)],[252,251]) ).
thf(345,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)],[344]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,120]) ).
thf(1443,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1442]) ).
thf(1444,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1443:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,112]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[262]) ).
thf(266,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[263]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) )
!= A ),
inference(simp,[status(thm)],[266]) ).
thf(94,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)],[93]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[252,56]) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( D @ ( C @ distinct_lines ) ) )
| ~ ( D @ ( C @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(326,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(125,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)],[124]) ).
thf(126,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)],[125]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(162,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
sk3 != sk2,
inference(simp,[status(thm)],[162]) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[261,142]) ).
thf(1669,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( D @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1668]) ).
thf(1670,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1669:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(1713,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1670]) ).
thf(1907,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1511,144]) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( A @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ ( C @ ( D @ ( C @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1907]) ).
thf(1909,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[1908:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ orthogonal_through_point ) ))]]) ).
thf(1962,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ ( A @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[1909]) ).
thf(2434,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2430,120]) ).
thf(2435,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[2434]) ).
thf(2436,plain,
~ ( sk1 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[2435:[bind(A,$thf( sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(5978,plain,
$false,
inference(e,[status(thm)],[95,69,1411,138,101,170,276,120,269,878,440,56,2035,142,340,42,1441,52,110,2444,1511,157,559,46,93,2024,78,261,216,1664,2027,121,84,147,61,1622,2002,116,60,1636,894,302,260,38,70,92,252,2433,97,53,141,109,124,1964,457,129,41,73,105,1026,586,1906,148,161,64,1374,149,44,1620,204,59,118,144,49,466,1638,86,113,81,76,98,103,66,251,1029,155,108,226,80,1034,112,749,123,145,67,1790,1637,370,463,127,1679,1711,50,1766,72,175,314,143,43,1459,87,104,40,171,75,207,272,1661,346,1444,119,58,1774,1380,268,79,94,326,107,126,136,2430,47,163,1713,1621,90,1962,2436,364,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO202+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.24/0.51 % Computer : n004.cluster.edu
% 0.24/0.51 % Model : x86_64 x86_64
% 0.24/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.51 % Memory : 8046.5625MB
% 0.24/0.51 % OS : Linux 6.8.0-71-generic
% 0.24/0.51 % CPULimit : 300
% 0.24/0.51 % WCLimit : 300
% 0.24/0.51 % DateTime : Fri Sep 25 13:04:53 UTC 2026
% 0.24/0.52 % CPUTime :
% 0.24/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.56/1.41 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.14/1.79 % [INFO] Parsing done (374ms).
% 2.55/1.81 % [INFO] Running in sequential loop mode.
% 3.45/2.44 % [INFO] eprover registered as external prover.
% 3.45/2.46 % [INFO] Scanning for conjecture ...
% 3.81/2.62 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 4.00/2.74 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 4.25/2.84 % [INFO] Problem is first-order (TPTP FOF).
% 4.25/2.85 % [INFO] Type checking passed.
% 4.25/2.86 % [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 ...
% 83.03/22.92 % External prover 'e' found a proof!
% 83.03/22.92 % [INFO] Killing All external provers ...
% 83.03/22.92 % Time passed: 22188ms (effective reasoning time: 21103ms)
% 83.03/22.92 % 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)>
% 83.03/22.92 % Axioms used in derivation (35): par1, ouo1, ooc2, apart4, a5, ceq2, a4, ax1, oac1, orth1, ax2, a3, occu1, con1, cp2, apart3, ooc1, ceq3, ax6, cup1, ci4, couo1, int1, apart5, coipo1, ci3, apart1, ci2, cp1, ceq1, cu1, ci1, apart2, p1, cotno1
% 83.03/22.92 % No. of inferences in proof: 371
% 83.03/22.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 22188 ms resp. 21103 ms w/o parsing
% 84.03/23.06 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 84.03/23.07 % [INFO] Killing All external provers ...
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