%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO196+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 : n003.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 07:12:41 AM UTC 2026
% Result : Theorem 66.33s 18.70s
% Output : Refutation 83.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 40
% Syntax : Number of formulae : 1384 ( 132 unt; 0 typ; 4 def)
% Number of atoms : 5540 (1304 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 15955 (2489 ~;2563 |; 83 &;10738 @)
% ( 5 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 6 con; 0-2 aty)
% Number of variables : 2948 ( 0 ^;2931 !; 13 ?;2948 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(equal_points_decl,type,
equal_points: $i > $i > $o ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
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(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
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(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
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(sk4_decl,type,
sk4: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( C @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( D @ ( C @ convergent_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( B @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( A @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( B @ ( A @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( C @ ( B @ convergent_lines ) )
& ( A @ ( sk1 @ convergent_lines ) ) )
=> ( ( A @ ( C @ ( B @ intersection_point ) @ incident_point_and_line ) )
& ( sk1 @ ( C @ ( B @ intersection_point ) @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( B @ ( A @ convergent_lines ) )
& ( sk2 @ ( sk1 @ convergent_lines ) ) )
=> ( ( sk2 @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( sk1 @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( sk3 @ convergent_lines ) )
& ( sk2 @ ( sk1 @ convergent_lines ) ) )
=> ( ( sk2 @ ( A @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
& ( sk1 @ ( A @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ) ) ) ).
thf(36,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(150,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)],[36]) ).
thf(151,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)],[150]) ).
thf(152,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)],[151]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ incident_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(9,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(65,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)],[9]) ).
thf(66,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)],[65]) ).
thf(67,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)],[66]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( C @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( D @ ( C @ convergent_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( B @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( C @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( D @ ( C @ convergent_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( B @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(38,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( C @ ( B @ ( A @ intersection_point ) @ incident_point_and_line ) )
& ( D @ ( C @ convergent_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( B @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) )
& ( A @ ( D @ ( C @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,plain,
( ( ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
& ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
& ( sk4 @ ( sk3 @ convergent_lines ) )
& ( sk2 @ ( sk1 @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(44,plain,
sk4 @ ( sk3 @ convergent_lines ),
inference(cnfConj,[status(thm)],[39]) ).
thf(31,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(136,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)],[31]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[136]) ).
thf(3138,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,137]) ).
thf(3139,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3138]) ).
thf(3140,plain,
~ ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3139:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(3197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,3140]) ).
thf(3198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3197]) ).
thf(3199,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3198:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(3216,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3199]) ).
thf(9271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3216]) ).
thf(9272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9271]) ).
thf(9273,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[9272:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(9319,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9273]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
thf(142,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[142]) ).
thf(12782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9319,143]) ).
thf(12783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[12782]) ).
thf(12784,plain,
! [A: $i] :
( ( sk4 @ ( A @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[12783:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(40,plain,
( ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[39]) ).
thf(16214,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,40]) ).
thf(16215,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16214]) ).
thf(16216,plain,
( ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16215:[bind(A,$thf( sk2 ))]]) ).
thf(32,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(138,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)],[32]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[138]) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,139]) ).
thf(3463,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3462]) ).
thf(3464,plain,
~ ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3463:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(3521,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,3464]) ).
thf(3522,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3521]) ).
thf(3523,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3522:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(3536,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3523]) ).
thf(12182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3536]) ).
thf(12183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[12182]) ).
thf(12184,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[12183:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(12246,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[12184]) ).
thf(15380,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[12246,143]) ).
thf(15381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[15380]) ).
thf(15382,plain,
! [A: $i] :
( ( sk3 @ ( A @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[15381:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(3194,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3140]) ).
thf(3195,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3194]) ).
thf(3196,plain,
sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ),
inference(pattern_uni,[status(thm)],[3195:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(3264,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[3196,40]) ).
thf(3265,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3264]) ).
thf(3277,plain,
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3265]) ).
thf(3298,plain,
( ( sk4 != sk2 )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3277]) ).
thf(23880,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,3298]) ).
thf(23881,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23880]) ).
thf(23882,plain,
( ( sk4 != sk2 )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23881:[bind(A,$thf( sk1 ))]]) ).
thf(15,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(87,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)],[15]) ).
thf(88,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)],[87]) ).
thf(89,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)],[88]) ).
thf(42,plain,
sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ),
inference(cnfConj,[status(thm)],[39]) ).
thf(153,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ incident_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[152]) ).
thf(541,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( B @ ( A @ incident_point_and_line ) ) )
| ~ ( B @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,153]) ).
thf(542,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( B @ ( A @ incident_point_and_line ) ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[541]) ).
thf(543,plain,
~ ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[542:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,543]) ).
thf(1074,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1073]) ).
thf(1075,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk4 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1074:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(1166,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,1075]) ).
thf(1167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1168,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1167:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',orth1) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3518,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3464]) ).
thf(3519,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3518]) ).
thf(3520,plain,
sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ),
inference(pattern_uni,[status(thm)],[3519:[bind(A,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(3588,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[3520,40]) ).
thf(3589,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3588]) ).
thf(3616,plain,
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3589]) ).
thf(3618,plain,
( ( sk3 != sk2 )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3616]) ).
thf(16189,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,3618]) ).
thf(16190,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16189]) ).
thf(16191,plain,
( ( sk3 != sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16190:[bind(A,$thf( sk1 ))]]) ).
thf(16241,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16191,137]) ).
thf(16242,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16241]) ).
thf(16243,plain,
( ~ ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16242:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ parallel_lines ) )
<=> ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
thf(112,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)],[25]) ).
thf(113,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)],[112]) ).
thf(114,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)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(25529,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23882,115]) ).
thf(25530,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25529]) ).
thf(25531,plain,
( ~ ( sk3 @ ( sk1 @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[25530:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(4,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(51,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)],[4]) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[51]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(54,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(55,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[55]) ).
thf(226,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)],[53,56]) ).
thf(227,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)],[226]) ).
thf(228,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(249,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[228]) ).
thf(3262,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,40]) ).
thf(3263,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3262]) ).
thf(3291,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3263]) ).
thf(3311,plain,
( ( sk4 != sk1 )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3291]) ).
thf(23872,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,3311]) ).
thf(23873,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23872]) ).
thf(23874,plain,
( ( sk4 != sk1 )
| ( sk3 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23873:[bind(A,$thf( sk2 ))]]) ).
thf(24026,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23874,115]) ).
thf(24027,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24026]) ).
thf(24028,plain,
( ~ ( sk3 @ ( sk2 @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24027:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(43,plain,
sk2 @ ( sk1 @ convergent_lines ),
inference(cnfConj,[status(thm)],[39]) ).
thf(3483,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,139]) ).
thf(3484,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3483]) ).
thf(3485,plain,
~ ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3484:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,3485]) ).
thf(3552,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3551]) ).
thf(3553,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3552:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(3566,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3553]) ).
thf(41,plain,
sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ),
inference(cnfConj,[status(thm)],[39]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( B @ ( A @ incident_point_and_line ) ) )
| ~ ( B @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,153]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( B @ ( A @ incident_point_and_line ) ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(552,plain,
~ ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[551:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,552]) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[1040]) ).
thf(1042,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1041:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,1042]) ).
thf(1135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
<=> ~ ( B @ ( A @ distinct_points ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(45,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)],[3]) ).
thf(46,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)],[45]) ).
thf(47,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)],[46]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1136,48]) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1198]) ).
thf(1200,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1199:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(10,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(68,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)],[10]) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[68]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[69]) ).
thf(17,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(92,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(93,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[92]) ).
thf(94,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[93]) ).
thf(486,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)],[70,94]) ).
thf(487,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)],[486]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[487:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[488]) ).
thf(30,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(133,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)],[30]) ).
thf(134,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[133]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(3001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,135]) ).
thf(3002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3001]) ).
thf(3003,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( A @ ( sk2 @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[3002:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3030,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( A @ ( sk2 @ distinct_lines ) ) ),
inference(simp,[status(thm)],[3003]) ).
thf(3060,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3030,523]) ).
thf(3061,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3060]) ).
thf(3062,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3061:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(3392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3062,143]) ).
thf(3393,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3392]) ).
thf(3394,plain,
! [A: $i] :
( ( sk2 @ ( A @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3393:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(4513,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,139]) ).
thf(4514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4513]) ).
thf(4515,plain,
! [A: $i] :
( ~ ( sk1 @ ( A @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4514:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1136,53]) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1192]) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1193:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(D,$thf( D ))]]) ).
thf(1205,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( B @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1194]) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ~ $true
| ( B @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1205,56]) ).
thf(1765,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( B @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1764]) ).
thf(1766,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1765:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1808,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1766]) ).
thf(2974,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,135]) ).
thf(2975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2974]) ).
thf(2976,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( A @ ( sk4 @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[2975:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(3015,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( A @ ( sk4 @ distinct_lines ) ) ),
inference(simp,[status(thm)],[2976]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
<=> ~ ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(71,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)],[11]) ).
thf(72,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)],[71]) ).
thf(73,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)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(3038,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3015,74]) ).
thf(3039,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3038]) ).
thf(3040,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3039:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(23,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(107,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)],[23]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ point )
| ~ ( B @ ( A @ convergent_lines ) )
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[107]) ).
thf(2012,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ point )
| ~ $true
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(paramod_ordered,[status(thm)],[43,108]) ).
thf(2013,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ point )
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(simp,[status(thm)],[2012]) ).
thf(2014,plain,
( ( sk2 @ ( sk1 @ intersection_point ) @ point )
| ~ ( sk2 @ line )
| ~ ( sk1 @ line ) ),
inference(pattern_uni,[status(thm)],[2013:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(26,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(118,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(119,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(120,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(cnf,[status(esa)],[119]) ).
thf(12750,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9319,523]) ).
thf(12751,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[12750]) ).
thf(12752,plain,
! [A: $i] :
( ( A @ ( sk4 @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[12751:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(15448,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[12752,143]) ).
thf(15449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[15448]) ).
thf(15450,plain,
! [A: $i] :
( ( A @ ( sk4 @ convergent_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[15449:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(27174,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,3311]) ).
thf(27175,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27174]) ).
thf(27176,plain,
( ( sk4 != sk1 )
| ( sk2 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27175:[bind(A,$thf( sk2 ))]]) ).
thf(27279,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27176,137]) ).
thf(27280,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27279]) ).
thf(27281,plain,
( ~ ( sk2 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[27280:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(32721,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,27281]) ).
thf(32722,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[32721]) ).
thf(32723,plain,
( ( sk4 != sk1 )
| ( sk2 @ ( sk2 @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[32722:[bind(A,$thf( sk2 @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(95,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(96,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[95]) ).
thf(97,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[96]) ).
thf(621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( D @ orthogonal_through_point ) @ ( C @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,97]) ).
thf(622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( D @ orthogonal_through_point ) @ ( C @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[621]) ).
thf(623,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( F )),bind(B,$thf( F @ ( E @ orthogonal_through_point ) )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(638,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) ),
inference(simp,[status(thm)],[623]) ).
thf(717,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[638,40]) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(726,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ( B
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[718]) ).
thf(740,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[726]) ).
thf(16226,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ orthogonal_through_point ) )
!= sk1 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,740]) ).
thf(16227,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ orthogonal_through_point ) )
!= sk1 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16226]) ).
thf(16228,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16227:[bind(A,$thf( sk2 ))]]) ).
thf(16229,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16228]) ).
thf(25565,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23882,139]) ).
thf(25566,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25565]) ).
thf(25567,plain,
( ~ ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[25566:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(29704,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,25567]) ).
thf(29705,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[29704]) ).
thf(29706,plain,
( ( sk4 != sk2 )
| ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[29705:[bind(A,$thf( sk3 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(37328,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[29706,3298]) ).
thf(37329,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[37328]) ).
thf(37356,plain,
( ( sk1 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk1 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[37329]) ).
thf(37369,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk1 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[37356]) ).
thf(3159,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,137]) ).
thf(3160,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3159]) ).
thf(3161,plain,
~ ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3160:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(3227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,3161]) ).
thf(3228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3227]) ).
thf(3229,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3228:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(3246,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3229]) ).
thf(10258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk2 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3246]) ).
thf(10259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk2 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10258]) ).
thf(10260,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[10259:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(10299,plain,
! [A: $i] :
( ( sk2 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10260]) ).
thf(27,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(121,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)],[27]) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[121]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[122]) ).
thf(2192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,123]) ).
thf(2193,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2192]) ).
thf(2194,plain,
! [A: $i] :
( ( A @ ( sk2 @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2193:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(2210,plain,
! [A: $i] :
( ( A @ ( sk2 @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2194]) ).
thf(23863,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk2 @ convergent_lines ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,16216]) ).
thf(23864,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk2 @ convergent_lines ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23863]) ).
thf(23865,plain,
( ( sk4 @ ( sk2 @ convergent_lines ) )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23864:[bind(A,$thf( sk1 ))]]) ).
thf(3032,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3015,523]) ).
thf(3033,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3032]) ).
thf(3034,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3033:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(3100,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3034,143]) ).
thf(3101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3100]) ).
thf(3102,plain,
! [A: $i] :
( ( sk4 @ ( A @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3101:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(4015,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,120]) ).
thf(4016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4015]) ).
thf(4017,plain,
! [A: $i] : ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[4016:[bind(A,$thf( E @ ( sk4 @ parallel_through_point ) )),bind(B,$thf( E )),bind(C,$thf( sk4 ))]]) ).
thf(4093,plain,
! [A: $i] : ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) ),
inference(simp,[status(thm)],[4017]) ).
thf(4101,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4093,137]) ).
thf(4102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4101]) ).
thf(4103,plain,
! [A: $i] :
~ ( A @ ( sk4 @ parallel_through_point ) @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4102:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( E @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(4136,plain,
! [A: $i] :
~ ( A @ ( sk4 @ parallel_through_point ) @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4103]) ).
thf(5145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ parallel_through_point ) @ ( C @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4136]) ).
thf(5146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk4 @ parallel_through_point ) @ ( C @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[5145]) ).
thf(5147,plain,
! [A: $i] : ( A @ ( sk4 @ parallel_through_point ) @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[5146:[bind(A,$thf( I @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) )),bind(B,$thf( I @ ( sk4 @ parallel_through_point ) )),bind(C,$thf( I ))]]) ).
thf(5168,plain,
! [A: $i] : ( A @ ( sk4 @ parallel_through_point ) @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[5147]) ).
thf(7,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(59,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)],[7]) ).
thf(60,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)],[59]) ).
thf(61,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)],[60]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
<=> ~ ( B @ ( A @ unorthogonal_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5) ).
thf(79,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)],[13]) ).
thf(80,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)],[79]) ).
thf(81,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)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(383,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ unorthogonal_lines ) )
!= ( F @ ( E @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( F @ ( E @ orthogonal_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[61,82]) ).
thf(384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ unorthogonal_lines ) )
!= ( F @ ( E @ unorthogonal_lines ) ) )
| ~ ( F @ ( E @ orthogonal_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[383]) ).
thf(385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ orthogonal_lines ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( D ))]]) ).
thf(3586,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,40]) ).
thf(3587,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3586]) ).
thf(3609,plain,
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3587]) ).
thf(3630,plain,
( ( sk3 != sk1 )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3609]) ).
thf(23897,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ~ $true
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,3630]) ).
thf(23898,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23897]) ).
thf(23899,plain,
( ( sk3 != sk1 )
| ( sk3 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23898:[bind(A,$thf( sk2 ))]]) ).
thf(25590,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23899,137]) ).
thf(25591,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25590]) ).
thf(25592,plain,
( ~ ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[25591:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(29944,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,25592]) ).
thf(29945,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[29944]) ).
thf(29946,plain,
( ( sk3 != sk1 )
| ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[29945:[bind(A,$thf( sk3 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(27182,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,3298]) ).
thf(27183,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27182]) ).
thf(27184,plain,
( ( sk4 != sk2 )
| ( sk1 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27183:[bind(A,$thf( sk1 ))]]) ).
thf(28016,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27184,137]) ).
thf(28017,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28016]) ).
thf(28018,plain,
( ~ ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[28017:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(25532,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk1 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23882,120]) ).
thf(25533,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk1 @ convergent_lines ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25532]) ).
thf(25574,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25533]) ).
thf(25576,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ parallel_through_point ) )
!= sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25574]) ).
thf(16217,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,3630]) ).
thf(16218,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16217]) ).
thf(16219,plain,
( ( sk3 != sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16218:[bind(A,$thf( sk2 ))]]) ).
thf(16496,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16219,115]) ).
thf(16497,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16496]) ).
thf(16498,plain,
( ~ ( sk4 @ ( sk2 @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16497:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(3191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,3140]) ).
thf(3192,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3191]) ).
thf(3193,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk4 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3192:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk4 @ ( sk3 @ intersection_point ) ))]]) ).
thf(8349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3193]) ).
thf(8350,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[8349]) ).
thf(8351,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[8350:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(1909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[249,48]) ).
thf(1910,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ ( D @ ( C @ equal_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(simp,[status(thm)],[1909]) ).
thf(1911,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_points ) )
| ~ ( A @ ( B @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[1910:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(9182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ $true
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[8351,1911]) ).
thf(9183,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9182]) ).
thf(9184,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[9183:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,552]) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(598,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[597:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk3 ))]]) ).
thf(612,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[598]) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,612]) ).
thf(813,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(814,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[813:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(835,plain,
! [A: $i] :
( ( sk3 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[814]) ).
thf(886,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[835,70]) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[886]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[887:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( B @ ( sk3 @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(1548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ~ $true
| ( B @ ( sk3 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[896,94]) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( B @ ( sk3 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1548]) ).
thf(1550,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1549:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1588,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1550]) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1588,143]) ).
thf(1606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1605]) ).
thf(1607,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1606:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(1669,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[1607,153]) ).
thf(1670,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1669]) ).
thf(1671,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(1997,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ point )
| ~ $true
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(paramod_ordered,[status(thm)],[44,108]) ).
thf(1998,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( B @ ( A @ intersection_point ) @ point )
| ~ ( B @ line )
| ~ ( A @ line ) ),
inference(simp,[status(thm)],[1997]) ).
thf(1999,plain,
( ( sk4 @ ( sk3 @ intersection_point ) @ point )
| ~ ( sk4 @ line )
| ~ ( sk3 @ line ) ),
inference(pattern_uni,[status(thm)],[1998:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(3444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2210,139]) ).
thf(3445,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3444]) ).
thf(3446,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3445:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(3548,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3485]) ).
thf(3549,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3548]) ).
thf(3550,plain,
sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ),
inference(pattern_uni,[status(thm)],[3549:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(3224,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3161]) ).
thf(3225,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3224]) ).
thf(3226,plain,
sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ),
inference(pattern_uni,[status(thm)],[3225:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(167,plain,
( ~ $true
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(eqfactor_ordered,[status(thm)],[40]) ).
thf(171,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(3337,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[3226,171]) ).
thf(3338,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3337]) ).
thf(3360,plain,
( ( sk2 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3338]) ).
thf(3365,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3360]) ).
thf(7668,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3550,3365]) ).
thf(7669,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) ) ),
inference(simp,[status(thm)],[7668]) ).
thf(7695,plain,
( ( sk1 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) ) ),
inference(simp,[status(thm)],[7669]) ).
thf(7748,plain,
( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) ),
inference(simp,[status(thm)],[7695]) ).
thf(33,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(140,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)],[33]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnf,[status(esa)],[140]) ).
thf(3745,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[43,141]) ).
thf(3746,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[3745]) ).
thf(3747,plain,
! [A: $i] :
( ( sk2 @ ( A @ unorthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[3746:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(5190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ orthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3747,82]) ).
thf(5191,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ ( C @ ( B @ orthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[5190]) ).
thf(5192,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ orthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[5191:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(4119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( B @ convergent_lines ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4093,135]) ).
thf(4120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( B @ convergent_lines ) )
| ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4119]) ).
thf(4121,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( A @ ( B @ ( sk4 @ parallel_through_point ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4120:[bind(A,$thf( F )),bind(B,$thf( sk3 )),bind(C,$thf( F @ ( sk4 @ parallel_through_point ) )),bind(D,$thf( D ))]]) ).
thf(4142,plain,
! [B: $i,A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( A @ ( B @ ( sk4 @ parallel_through_point ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4121]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_points ) )
| ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[49]) ).
thf(1912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[50,249]) ).
thf(1913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[1912]) ).
thf(1914,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[1913:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(415,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ~ $true
| ~ ( E @ ( D @ equal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,74]) ).
thf(416,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( E @ ( D @ distinct_lines ) ) )
| ~ ( E @ ( D @ equal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[415]) ).
thf(417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ equal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[416:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(883,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[835,74]) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[883]) ).
thf(885,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[884:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(98,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(99,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[99]) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( D @ parallel_through_point ) @ ( C @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,100]) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( D @ parallel_through_point ) @ ( C @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[633]) ).
thf(635,plain,
! [B: $i,A: $i] : ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[634:[bind(A,$thf( F )),bind(B,$thf( F @ ( E @ parallel_through_point ) )),bind(C,$thf( F )),bind(D,$thf( E ))]]) ).
thf(637,plain,
! [B: $i,A: $i] : ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) ),
inference(simp,[status(thm)],[635]) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[637,40]) ).
thf(681,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[680]) ).
thf(690,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) )
!= sk2 )
| ( B
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(703,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[690]) ).
thf(3258,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,703]) ).
thf(3259,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3258]) ).
thf(3287,plain,
! [A: $i] :
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3259]) ).
thf(3308,plain,
! [A: $i] :
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3287]) ).
thf(5692,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4142,523]) ).
thf(5693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ distinct_lines ) )
!= ( C @ ( D @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[5692]) ).
thf(5694,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ distinct_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[5693:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(5723,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ distinct_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[5694]) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1588,74]) ).
thf(1600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1599]) ).
thf(1601,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1600:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(1965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[1914,48]) ).
thf(1966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ ( D @ ( C @ equal_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[1965]) ).
thf(1967,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equal_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[1966:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(4457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,120]) ).
thf(4458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4457]) ).
thf(4459,plain,
! [A: $i] : ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[4458:[bind(A,$thf( E @ ( sk2 @ parallel_through_point ) )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).
thf(4537,plain,
! [A: $i] : ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) ),
inference(simp,[status(thm)],[4459]) ).
thf(4702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,137]) ).
thf(4703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4702]) ).
thf(4704,plain,
! [A: $i] :
~ ( A @ ( sk2 @ parallel_through_point ) @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4703:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( E @ ( sk2 @ parallel_through_point ) ))]]) ).
thf(4736,plain,
! [A: $i] :
~ ( A @ ( sk2 @ parallel_through_point ) @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4704]) ).
thf(5249,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ parallel_through_point ) @ ( C @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4736]) ).
thf(5250,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ parallel_through_point ) @ ( C @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[5249]) ).
thf(5251,plain,
! [A: $i] : ( A @ ( sk2 @ parallel_through_point ) @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[5250:[bind(A,$thf( I @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )),bind(B,$thf( I @ ( sk2 @ parallel_through_point ) )),bind(C,$thf( I ))]]) ).
thf(5269,plain,
! [A: $i] : ( A @ ( sk2 @ parallel_through_point ) @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[5251]) ).
thf(4104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4093,141]) ).
thf(4105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4104]) ).
thf(4106,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[4105:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk3 )),bind(D,$thf( F @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(4137,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4106]) ).
thf(3425,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,3298]) ).
thf(3426,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3425]) ).
thf(3435,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3426]) ).
thf(3442,plain,
( ( sk4 != sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3435]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coipo1) ).
thf(109,plain,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(110,plain,
~ ? [A: $i,B: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(miniscope,[status(thm)],[109]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[110]) ).
thf(8,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(62,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(miniscope,[status(thm)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(cnf,[status(esa)],[63]) ).
thf(389,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)],[111,64]) ).
thf(390,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)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( F @ ( B @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(395,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[391]) ).
thf(3174,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)],[395,137]) ).
thf(3175,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)],[3174]) ).
thf(3176,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3175:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(3180,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[3176]) ).
thf(3778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( C @ ( D @ ( C @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3180]) ).
thf(3779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( C @ ( D @ ( C @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3778]) ).
thf(3780,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3779:[bind(A,$thf( B @ ( H @ ( B @ orthogonal_through_point ) @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( H ))]]) ).
thf(3799,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[3780]) ).
thf(4402,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3799,3618]) ).
thf(4403,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4402]) ).
thf(4424,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4403]) ).
thf(4439,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4424]) ).
thf(27165,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk2 @ convergent_lines ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,16216]) ).
thf(27166,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk2 @ convergent_lines ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27165]) ).
thf(27167,plain,
( ( sk4 @ ( sk2 @ convergent_lines ) )
| ( sk1 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27166:[bind(A,$thf( sk1 ))]]) ).
thf(28126,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[27167,115]) ).
thf(28127,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[28126]) ).
thf(28128,plain,
( ~ ( sk1 @ ( sk4 @ parallel_lines ) )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[28127:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(3724,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[44,141]) ).
thf(3725,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[3724]) ).
thf(3726,plain,
! [A: $i] :
( ( sk4 @ ( A @ unorthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[3725:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 ))]]) ).
thf(4911,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3726,64]) ).
thf(4912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4911]) ).
thf(4913,plain,
! [A: $i] : ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[4912:[bind(A,$thf( E @ ( sk4 @ orthogonal_through_point ) )),bind(B,$thf( E )),bind(C,$thf( sk4 ))]]) ).
thf(4926,plain,
! [A: $i] : ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(simp,[status(thm)],[4913]) ).
thf(4940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4926,64]) ).
thf(4941,plain,
! [C: $i,B: $i,A: $i] :
( ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4940]) ).
thf(4951,plain,
! [C: $i,B: $i,A: $i] :
( ( sk3 != C )
| ( ( A @ ( sk4 @ orthogonal_through_point ) )
!= ( B @ ( C @ orthogonal_through_point ) ) ) ),
inference(simp,[status(thm)],[4941]) ).
thf(4956,plain,
! [B: $i,A: $i] :
( ( A @ ( sk4 @ orthogonal_through_point ) )
!= ( B @ ( sk3 @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[4951]) ).
thf(16192,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,3311]) ).
thf(16193,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16192]) ).
thf(16194,plain,
( ( sk4 != sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16193:[bind(A,$thf( sk2 ))]]) ).
thf(16285,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16194,115]) ).
thf(16286,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16285]) ).
thf(16287,plain,
( ~ ( sk4 @ ( sk2 @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16286:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(16211,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,40]) ).
thf(16212,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16211]) ).
thf(16213,plain,
( ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16212:[bind(A,$thf( sk1 ))]]) ).
thf(19909,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,16213]) ).
thf(19910,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[19909]) ).
thf(19911,plain,
( ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[19910:[bind(A,$thf( sk2 ))]]) ).
thf(20015,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[19911,139]) ).
thf(20016,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20015]) ).
thf(20017,plain,
( ~ ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[20016:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,123]) ).
thf(2178,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2177]) ).
thf(2179,plain,
! [A: $i] :
( ( A @ ( sk4 @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2178:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(2207,plain,
! [A: $i] :
( ( A @ ( sk4 @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2179]) ).
thf(2215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2207,115]) ).
thf(2216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2215]) ).
thf(2217,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2216:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(4021,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,137]) ).
thf(4022,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4021]) ).
thf(4023,plain,
! [A: $i] :
( ~ ( sk4 @ ( sk4 @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4022:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(37,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(156,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(157,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[156]) ).
thf(158,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[157]) ).
thf(190,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,158]) ).
thf(191,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(194,plain,
! [A: $i] :
( ( sk4 != A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[191]) ).
thf(196,plain,
sk4 != sk3,
inference(simp,[status(thm)],[194]) ).
thf(9170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[8351,249]) ).
thf(9171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9170]) ).
thf(9172,plain,
! [A: $i] :
( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[9171:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(4723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,123]) ).
thf(4724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4723]) ).
thf(4725,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk2 @ parallel_through_point ) @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4724:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( F @ ( sk2 @ parallel_through_point ) )),bind(D,$thf( D ))]]) ).
thf(4743,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk2 @ parallel_through_point ) @ convergent_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4725]) ).
thf(3221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,3161]) ).
thf(3222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3221]) ).
thf(3223,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk2 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3222:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(9351,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3223]) ).
thf(9352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9351]) ).
thf(9353,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[9352:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(14000,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ $true
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9353,1911]) ).
thf(14001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14000]) ).
thf(14002,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ equal_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14001:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ~ $true
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[50,56]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] : ( A @ ( A @ equal_points ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(189,plain,
! [A: $i] : ( A @ ( A @ equal_points ) ),
inference(simp,[status(thm)],[188]) ).
thf(5184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3747,64]) ).
thf(5185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[5184]) ).
thf(5186,plain,
! [A: $i] : ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[5185:[bind(A,$thf( E @ ( sk2 @ orthogonal_through_point ) )),bind(B,$thf( E )),bind(C,$thf( sk2 ))]]) ).
thf(5199,plain,
! [A: $i] : ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(simp,[status(thm)],[5186]) ).
thf(27274,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk2 @ ( sk4 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27176,120]) ).
thf(27275,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk2 @ ( sk4 @ convergent_lines ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27274]) ).
thf(27315,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk4 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27275]) ).
thf(27320,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) )
!= sk4 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27315]) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,543]) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[572]) ).
thf(574,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[573:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(591,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[574]) ).
thf(643,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,591]) ).
thf(644,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[643]) ).
thf(645,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[644:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(663,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[663,70]) ).
thf(761,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ( D @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[760]) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[761:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( B @ ( sk4 @ distinct_lines ) )
| ( B @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[762]) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ~ $true
| ( B @ ( sk4 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[770,94]) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_lines ) )
!= ( C @ ( C @ distinct_lines ) ) )
| ( B @ ( sk4 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1347,plain,
! [A: $i] :
( ( A @ ( sk4 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1346:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(1383,plain,
! [A: $i] :
( ( A @ ( sk4 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1383,74]) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1396]) ).
thf(1398,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1397:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(25618,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23899,139]) ).
thf(25619,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25618]) ).
thf(25620,plain,
( ~ ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[25619:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(30184,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,25620]) ).
thf(30185,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[30184]) ).
thf(30186,plain,
( ( sk3 != sk1 )
| ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[30185:[bind(A,$thf( sk3 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(6,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(57,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)],[6]) ).
thf(58,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)],[57]) ).
thf(300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( B @ apart_point_and_line ) )
!= ( C @ ( A @ 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(eqfactor_ordered,[status(thm)],[58]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[300:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(316,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',par1) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[77]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,120]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk2 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(259,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[257]) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( sk2 @ parallel_through_point ) )
!= sk1 ),
inference(simp,[status(thm)],[259]) ).
thf(24062,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23874,139]) ).
thf(24063,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24062]) ).
thf(24064,plain,
( ~ ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24063:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(3515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,3464]) ).
thf(3516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3515]) ).
thf(3517,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk3 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3516:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 @ ( sk3 @ intersection_point ) ))]]) ).
thf(16270,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16191,139]) ).
thf(16271,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16270]) ).
thf(16272,plain,
( ~ ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16271:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(285,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,97]) ).
thf(286,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( G @ orthogonal_through_point ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(406,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( F @ ( E @ distinct_lines ) ) )
| ( G @ ( F @ unorthogonal_lines ) )
| ( G @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( E @ ( D @ apart_point_and_line ) )
| ~ $true
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,61]) ).
thf(407,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( F @ ( E @ distinct_lines ) ) )
| ( G @ ( F @ unorthogonal_lines ) )
| ( G @ ( E @ unorthogonal_lines ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( E @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[406]) ).
thf(408,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ unorthogonal_lines ) )
| ( E @ ( B @ unorthogonal_lines ) )
| ( C @ ( D @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[407:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ unorthogonal_lines ) )
| ( E @ ( B @ unorthogonal_lines ) )
| ( C @ ( D @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[408]) ).
thf(5500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4137,64]) ).
thf(5501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk4 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[5500]) ).
thf(5502,plain,
! [B: $i,A: $i] : ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[5501:[bind(A,$thf( F @ ( H @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( H @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(5526,plain,
! [B: $i,A: $i] : ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(simp,[status(thm)],[5502]) ).
thf(421,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( D @ apart_point_and_line ) ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( F @ ( E @ distinct_lines ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,67]) ).
thf(422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( D @ apart_point_and_line ) ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( F @ ( E @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[421]) ).
thf(423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ distinct_lines ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[423]) ).
thf(358,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ unorthogonal_lines ) )
!= ( F @ ( E @ ( F @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[61,64]) ).
thf(359,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ unorthogonal_lines ) )
!= ( F @ ( E @ ( F @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[359:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( H @ ( D @ orthogonal_through_point ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( D ))]]) ).
thf(376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(23869,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,3618]) ).
thf(23870,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23869]) ).
thf(23871,plain,
( ( sk3 != sk2 )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23870:[bind(A,$thf( sk1 ))]]) ).
thf(23981,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23871,137]) ).
thf(23982,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[23981]) ).
thf(23983,plain,
( ~ ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[23982:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(26151,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,23983]) ).
thf(26152,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[26151]) ).
thf(26153,plain,
( ( sk3 != sk2 )
| ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[26152:[bind(A,$thf( sk3 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(1826,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1808,48]) ).
thf(1827,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1826]) ).
thf(1828,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1827:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(247,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)],[53]) ).
thf(248,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( B ))]]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(2032,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)],[251,249]) ).
thf(2033,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)],[2032]) ).
thf(2034,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[2033:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(4452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,115]) ).
thf(4453,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4452]) ).
thf(4454,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4453:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(3471,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2207,139]) ).
thf(3472,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3471]) ).
thf(3473,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3472:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(235,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)],[53,53]) ).
thf(236,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)],[235]) ).
thf(237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(253,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)],[237]) ).
thf(4099,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4093,120]) ).
thf(4100,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4099]) ).
thf(4130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk3 ) ),
inference(simp,[status(thm)],[4100]) ).
thf(4134,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk4 @ parallel_through_point ) @ parallel_through_point ) )
!= sk3 ),
inference(simp,[status(thm)],[4130]) ).
thf(25582,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23899,115]) ).
thf(25583,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25582]) ).
thf(25584,plain,
( ~ ( sk3 @ ( sk2 @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[25583:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(719,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[638,40]) ).
thf(720,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[719]) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ( B
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[720]) ).
thf(737,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ~ ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[736]) ).
thf(3256,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,737]) ).
thf(3257,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3256]) ).
thf(3279,plain,
! [A: $i] :
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3257]) ).
thf(3300,plain,
! [A: $i] :
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3279]) ).
thf(27171,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,3618]) ).
thf(27172,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27171]) ).
thf(27173,plain,
( ( sk3 != sk2 )
| ( sk1 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27172:[bind(A,$thf( sk1 ))]]) ).
thf(27254,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27173,139]) ).
thf(27255,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27254]) ).
thf(27256,plain,
( ~ ( sk4 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[27255:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(3066,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3030,74]) ).
thf(3067,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3066]) ).
thf(3068,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3067:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(16200,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,3298]) ).
thf(16201,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16200]) ).
thf(16202,plain,
( ( sk4 != sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16201:[bind(A,$thf( sk1 ))]]) ).
thf(16452,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16202,137]) ).
thf(16453,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16452]) ).
thf(16454,plain,
( ~ ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16453:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(18735,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16454]) ).
thf(18736,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[18735]) ).
thf(18737,plain,
( ( sk4 != sk2 )
| ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[18736:[bind(A,$thf( sk4 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(27199,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ~ $true
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,3630]) ).
thf(27200,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27199]) ).
thf(27201,plain,
( ( sk3 != sk1 )
| ( sk2 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27200:[bind(A,$thf( sk2 ))]]) ).
thf(4852,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3799,3630]) ).
thf(4853,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[4852]) ).
thf(4876,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[4853]) ).
thf(4892,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ ( sk2 @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[4876]) ).
thf(4705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ~ $true
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4537,141]) ).
thf(4706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4705]) ).
thf(4707,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[4706:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( F @ ( sk2 @ parallel_through_point ) ))]]) ).
thf(4737,plain,
! [B: $i,A: $i] :
( ( B @ ( sk2 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4707]) ).
thf(6191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk2 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4737,64]) ).
thf(6192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk2 @ parallel_through_point ) @ ( A @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( sk1 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[6191]) ).
thf(6193,plain,
! [B: $i,A: $i] : ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[6192:[bind(A,$thf( F @ ( H @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) )),bind(B,$thf( H )),bind(C,$thf( F )),bind(D,$thf( H @ ( sk2 @ parallel_through_point ) ))]]) ).
thf(6210,plain,
! [B: $i,A: $i] : ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(simp,[status(thm)],[6193]) ).
thf(35,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(144,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)],[35]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) )
& ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[144]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[145]) ).
thf(10354,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( C @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3446]) ).
thf(10355,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( C @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10354]) ).
thf(10356,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( A @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[10355:[bind(A,$thf( E @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 )),bind(C,$thf( E ))]]) ).
thf(10404,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( A @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10356]) ).
thf(241,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ $true
| ~ ( E @ ( D @ equal_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[53,48]) ).
thf(242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ equal_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ equal_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(15348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[12246,523]) ).
thf(15349,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[15348]) ).
thf(15350,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[15349:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(28044,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27184,139]) ).
thf(28045,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28044]) ).
thf(28046,plain,
( ~ ( sk4 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[28045:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(264,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[53,58]) ).
thf(265,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ ( G @ ( F @ distinct_lines ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ apart_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) )
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(312,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ apart_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) )
| ( E @ ( A @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(16322,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16194,139]) ).
thf(16323,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16322]) ).
thf(16324,plain,
( ~ ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16323:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(6508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6210,64]) ).
thf(6509,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[6508]) ).
thf(6522,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk1 != D )
| ( ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( D @ orthogonal_through_point ) ) ) ),
inference(simp,[status(thm)],[6509]) ).
thf(6529,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( sk1 @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[6522]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[114]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ parallel_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(3582,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,703]) ).
thf(3583,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3582]) ).
thf(3615,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3583]) ).
thf(3635,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3615]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) @ line )
| ~ ( B @ point )
| ~ ( A @ line ) ),
inference(cnf,[status(esa)],[101]) ).
thf(3814,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3799,3298]) ).
thf(3815,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3814]) ).
thf(3840,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3815]) ).
thf(3852,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk1 @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[3840]) ).
thf(14,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(85,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)],[14]) ).
thf(14277,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk2 @ ( C @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4515]) ).
thf(14278,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk2 @ ( C @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14277]) ).
thf(14279,plain,
! [A: $i] :
( ( sk2 @ ( A @ convergent_lines ) )
| ( sk1 @ ( A @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14278:[bind(A,$thf( E @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( E ))]]) ).
thf(14342,plain,
! [A: $i] :
( ( sk2 @ ( A @ convergent_lines ) )
| ( sk1 @ ( A @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14279]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk3 @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,120]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk3 ) ),
inference(simp,[status(thm)],[255]) ).
thf(260,plain,
! [A: $i] :
( ( A @ ( sk4 @ parallel_through_point ) )
!= sk3 ),
inference(simp,[status(thm)],[258]) ).
thf(4463,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,137]) ).
thf(4464,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4463]) ).
thf(4465,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk2 @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4464:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(14130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( C @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4465]) ).
thf(14131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk2 @ ( C @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14130]) ).
thf(14132,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( sk2 @ ( A @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14131:[bind(A,$thf( sk2 @ ( D @ intersection_point ) )),bind(B,$thf( sk2 )),bind(C,$thf( D ))]]) ).
thf(14222,plain,
! [A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( sk2 @ ( A @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14132]) ).
thf(4013,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,120]) ).
thf(4014,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4013]) ).
thf(4078,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk3 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4014]) ).
thf(4091,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ parallel_through_point ) )
!= sk3 )
| ( sk4 @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4078]) ).
thf(11001,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3517]) ).
thf(11002,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[11001]) ).
thf(11003,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[11002:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(12762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9319,74]) ).
thf(12763,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[12762]) ).
thf(12764,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[12763:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(192,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,158]) ).
thf(193,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(195,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[193]) ).
thf(197,plain,
sk2 != sk1,
inference(simp,[status(thm)],[195]) ).
thf(27226,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27173,137]) ).
thf(27227,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27226]) ).
thf(27228,plain,
( ~ ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[27227:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(28061,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27201,115]) ).
thf(28062,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[28061]) ).
thf(28063,plain,
( ~ ( sk2 @ ( sk4 @ parallel_lines ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[28062:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(232,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)],[53,53]) ).
thf(233,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)],[232]) ).
thf(234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ distinct_points ) )
| ( D @ ( A @ distinct_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[233:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(252,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)],[234]) ).
thf(19978,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[19911,115]) ).
thf(19979,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[19978]) ).
thf(19980,plain,
( ~ ( sk4 @ ( sk2 @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[19979:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(282,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,100]) ).
thf(283,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ 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(simp,[status(thm)],[282]) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ parallel_through_point ) @ ( B @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ parallel_through_point ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ parallel_through_point ) @ ( B @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(17485,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16272]) ).
thf(17486,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[17485]) ).
thf(17487,plain,
( ( sk3 != sk2 )
| ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[17486:[bind(A,$thf( sk4 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(19422,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[17487,3618]) ).
thf(19423,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[19422]) ).
thf(19448,plain,
( ( sk1 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk1 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[19423]) ).
thf(19467,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk1 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[19448]) ).
thf(302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( B @ apart_point_and_line ) )
!= ( C @ ( 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(eqfactor_ordered,[status(thm)],[58]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[637,40]) ).
thf(679,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) @ ( B @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[678]) ).
thf(686,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ parallel_through_point ) )
!= sk1 )
| ( B
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[679]) ).
thf(699,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[686]) ).
thf(16208,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ parallel_through_point ) )
!= sk1 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,699]) ).
thf(16209,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16208]) ).
thf(16210,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16209:[bind(A,$thf( sk2 ))]]) ).
thf(16232,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 )
| ( sk4 @ ( sk2 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16210]) ).
thf(27307,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27176,139]) ).
thf(27308,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27307]) ).
thf(27309,plain,
( ~ ( sk4 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[27308:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(4728,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,139]) ).
thf(4729,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4728]) ).
thf(4730,plain,
! [A: $i] :
~ ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4729:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( E @ ( sk2 @ parallel_through_point ) ))]]) ).
thf(4745,plain,
! [A: $i] :
~ ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4730]) ).
thf(4763,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4745]) ).
thf(4764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[4763]) ).
thf(4765,plain,
! [A: $i] : ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4764:[bind(A,$thf( G @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( G ))]]) ).
thf(4789,plain,
! [A: $i] : ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[4765]) ).
thf(398,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)],[395,158]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[398]) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[399]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) )
!= A ),
inference(simp,[status(thm)],[401]) ).
thf(3584,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,699]) ).
thf(3585,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3584]) ).
thf(3611,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3585]) ).
thf(3632,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3611]) ).
thf(5216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5199,64]) ).
thf(5217,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[5216]) ).
thf(5227,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 != C )
| ( ( A @ ( sk2 @ orthogonal_through_point ) )
!= ( B @ ( C @ orthogonal_through_point ) ) ) ),
inference(simp,[status(thm)],[5217]) ).
thf(5233,plain,
! [B: $i,A: $i] :
( ( A @ ( sk2 @ orthogonal_through_point ) )
!= ( B @ ( sk1 @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[5227]) ).
thf(386,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ unorthogonal_lines ) )
!= ( F @ ( E @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( F @ ( E @ orthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[61,82]) ).
thf(387,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ unorthogonal_lines ) )
!= ( F @ ( E @ unorthogonal_lines ) ) )
| ~ ( F @ ( E @ orthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ orthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( C )),bind(F,$thf( D ))]]) ).
thf(17817,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16324]) ).
thf(17818,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[17817]) ).
thf(17819,plain,
( ( sk4 != sk1 )
| ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[17818:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(4010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,115]) ).
thf(4011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4010]) ).
thf(4012,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ parallel_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4011:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(28,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(124,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)],[28]) ).
thf(30664,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,27256]) ).
thf(30665,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[30664]) ).
thf(30666,plain,
( ( sk3 != sk2 )
| ( sk4 @ ( sk1 @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[30665:[bind(A,$thf( sk1 @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(4694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4537,115]) ).
thf(4695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) ) ),
inference(simp,[status(thm)],[4694]) ).
thf(4696,plain,
! [A: $i] :
~ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[4695:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( E @ ( sk2 @ parallel_through_point ) ))]]) ).
thf(4744,plain,
! [A: $i] :
~ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ parallel_lines ) ),
inference(simp,[status(thm)],[4696]) ).
thf(27271,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27176,115]) ).
thf(27272,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[27271]) ).
thf(27273,plain,
( ~ ( sk2 @ ( sk4 @ parallel_lines ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[27272:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(24009,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23871,139]) ).
thf(24010,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[24009]) ).
thf(24011,plain,
( ~ ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[24010:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(26371,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,24011]) ).
thf(26372,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[26371]) ).
thf(26373,plain,
( ( sk3 != sk2 )
| ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[26372:[bind(A,$thf( sk3 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(32436,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[26373,3618]) ).
thf(32437,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[32436]) ).
thf(32465,plain,
( ( sk1 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk1 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[32437]) ).
thf(32483,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk1 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[32465]) ).
thf(19531,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[17819,3311]) ).
thf(19532,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[19531]) ).
thf(19567,plain,
( ( sk2 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[19532]) ).
thf(19579,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[19567]) ).
thf(455,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[43,115]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(simp,[status(thm)],[455]) ).
thf(457,plain,
~ ( sk2 @ ( sk1 @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[456:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(27208,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15450,16213]) ).
thf(27209,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[27208]) ).
thf(27210,plain,
( ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[27209:[bind(A,$thf( sk2 ))]]) ).
thf(28182,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[27210,115]) ).
thf(28183,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[28182]) ).
thf(28184,plain,
( ~ ( sk2 @ ( sk4 @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[28183:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(125,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ! [C: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(miniscope,[status(thm)],[124]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[125]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(4945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ orthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4926,82]) ).
thf(4946,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ ( C @ ( B @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[4945]) ).
thf(4947,plain,
! [A: $i] :
~ ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[4946:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk4 @ orthogonal_through_point ) )),bind(C,$thf( sk3 ))]]) ).
thf(4953,plain,
! [A: $i] :
~ ( sk3 @ ( A @ ( sk4 @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(simp,[status(thm)],[4947]) ).
thf(23906,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[15382,16213]) ).
thf(23907,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23906]) ).
thf(23908,plain,
( ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk3 @ ( sk2 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23907:[bind(A,$thf( sk2 ))]]) ).
thf(25644,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[23908,115]) ).
thf(25645,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[25644]) ).
thf(25646,plain,
( ~ ( sk3 @ ( sk2 @ parallel_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[25645:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(13606,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk1 @ ( C @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3566]) ).
thf(13607,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( C @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk1 @ ( C @ distinct_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13606]) ).
thf(13608,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[13607:[bind(A,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(13693,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13608]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(22,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(105,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)],[22]) ).
thf(294,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,97]) ).
thf(295,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ 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(simp,[status(thm)],[294]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[295:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(3963,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3799,3311]) ).
thf(3964,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3963]) ).
thf(3988,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3964]) ).
thf(3999,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ ( sk2 @ orthogonal_through_point ) @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3988]) ).
thf(16533,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16219,139]) ).
thf(16534,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16533]) ).
thf(16535,plain,
( ~ ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16534:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(19263,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16535]) ).
thf(19264,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[19263]) ).
thf(19265,plain,
( ( sk3 != sk1 )
| ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[19264:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(19843,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[19265,3630]) ).
thf(19844,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[19843]) ).
thf(19857,plain,
( ( sk2 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[19844]) ).
thf(19871,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[19857]) ).
thf(20654,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,20017]) ).
thf(20655,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[20654]) ).
thf(20656,plain,
( ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[20655:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1383,143]) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1402]) ).
thf(1404,plain,
! [A: $i] :
( ( A @ ( sk4 @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1403:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[1404,153]) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[1432]) ).
thf(1434,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( A @ ( sk4 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[1433:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(763,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[663,143]) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[763]) ).
thf(765,plain,
! [A: $i] :
( ( sk4 @ ( A @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[764:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(3266,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,171]) ).
thf(3267,plain,
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3266]) ).
thf(3285,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3267]) ).
thf(3306,plain,
( ( sk4 != sk1 )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3285]) ).
thf(2218,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2207,120]) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2218]) ).
thf(2232,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk4 )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2219]) ).
thf(2235,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ parallel_through_point ) )
!= sk4 )
| ( B @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2232]) ).
thf(4917,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ orthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3726,82]) ).
thf(4918,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ ( C @ ( B @ orthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[4917]) ).
thf(4919,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ orthogonal_lines ) )
| ( sk3 @ ( A @ unorthogonal_lines ) ) ),
inference(pattern_uni,[status(thm)],[4918:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(427,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,67]) ).
thf(428,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[427]) ).
thf(429,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( C @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[428:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( C ))]]) ).
thf(444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( C @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[429]) ).
thf(20021,plain,
( ~ $true
| ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[19911]) ).
thf(20024,plain,
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20021]) ).
thf(355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ unorthogonal_lines ) )
!= ( F @ ( E @ ( F @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( D @ ( C @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(paramod_ordered,[status(thm)],[61,64]) ).
thf(356,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ unorthogonal_lines ) )
!= ( F @ ( E @ ( F @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[356:[bind(A,$thf( A )),bind(B,$thf( H @ ( D @ orthogonal_through_point ) )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( D ))]]) ).
thf(375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(2079,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[50,251]) ).
thf(2080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[2079]) ).
thf(2081,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( A @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[2080:[bind(A,$thf( B )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(2088,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( A @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[2081]) ).
thf(2258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ~ $true
| ( A @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[2088,249]) ).
thf(2259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( C @ ( D @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( A @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[2258]) ).
thf(2260,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ distinct_points ) )
| ( A @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[2259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(24029,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk2 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23874,120]) ).
thf(24030,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk2 @ convergent_lines ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24029]) ).
thf(24070,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24030]) ).
thf(24072,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ parallel_through_point ) )
!= sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24070]) ).
thf(16481,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16202,139]) ).
thf(16482,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16481]) ).
thf(16483,plain,
( ~ ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16482:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(17319,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16243]) ).
thf(17320,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[17319]) ).
thf(17321,plain,
( ( sk3 != sk2 )
| ( sk4 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[17320:[bind(A,$thf( sk4 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[145]) ).
thf(5221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ orthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[5199,82]) ).
thf(5222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( C @ ( B @ unorthogonal_lines ) ) )
| ~ ( C @ ( B @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[5221]) ).
thf(5223,plain,
! [A: $i] :
~ ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[5222:[bind(A,$thf( E )),bind(B,$thf( E @ ( sk2 @ orthogonal_through_point ) )),bind(C,$thf( sk1 ))]]) ).
thf(5230,plain,
! [A: $i] :
~ ( sk1 @ ( A @ ( sk2 @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(simp,[status(thm)],[5223]) ).
thf(3545,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[89,3485]) ).
thf(3546,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[3545]) ).
thf(3547,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ~ ( sk1 @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[3546:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(396,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)],[395,120]) ).
thf(397,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)],[396]) ).
thf(400,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)],[397]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[400]) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[765,153]) ).
thf(842,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[841]) ).
thf(843,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[842:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(3498,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)],[395,139]) ).
thf(3499,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)],[3498]) ).
thf(3500,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3499:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(3506,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)],[3500]) ).
thf(3878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( D @ ( C @ orthogonal_through_point ) @ ( C @ ( D @ ( C @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3506]) ).
thf(3879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( D @ ( C @ orthogonal_through_point ) @ ( C @ ( D @ ( C @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[3878]) ).
thf(3880,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[3879:[bind(A,$thf( I @ ( J @ ( I @ orthogonal_through_point ) @ intersection_point ) )),bind(B,$thf( J @ ( I @ orthogonal_through_point ) )),bind(C,$thf( I )),bind(D,$thf( J ))]]) ).
thf(3900,plain,
! [B: $i,A: $i] : ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[3880]) ).
thf(267,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[53,58]) ).
thf(268,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ ( G @ ( F @ distinct_lines ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ apart_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) )
| ( E @ ( B @ apart_point_and_line ) )
| ( D @ ( B @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( C ))]]) ).
thf(313,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ apart_point_and_line ) )
| ( D @ ( C @ apart_point_and_line ) )
| ( E @ ( B @ apart_point_and_line ) )
| ( D @ ( B @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_lines ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(4071,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,139]) ).
thf(4072,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4071]) ).
thf(4073,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ ( sk3 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4072:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(13893,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( C @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4073]) ).
thf(13894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( C @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13893]) ).
thf(13895,plain,
! [A: $i] :
( ( sk4 @ ( A @ convergent_lines ) )
| ( sk3 @ ( A @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[13894:[bind(A,$thf( E @ ( sk3 @ intersection_point ) )),bind(B,$thf( sk3 )),bind(C,$thf( E ))]]) ).
thf(13958,plain,
! [A: $i] :
( ( sk4 @ ( A @ convergent_lines ) )
| ( sk3 @ ( A @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13895]) ).
thf(3272,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,740]) ).
thf(3273,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3272]) ).
thf(3283,plain,
! [A: $i] :
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3273]) ).
thf(3304,plain,
! [A: $i] :
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3283]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(430,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,67]) ).
thf(431,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[430]) ).
thf(432,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( D @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[431:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( D ))]]) ).
thf(445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( A @ apart_point_and_line ) )
| ( E @ ( D @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[835,143]) ).
thf(890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(891,plain,
! [A: $i] :
( ( sk3 @ ( A @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[890:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(934,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ~ $true
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[891,153]) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( C @ ( B @ incident_point_and_line ) ) )
| ~ ( C @ ( B @ apart_point_and_line ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[934]) ).
thf(936,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[935:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(4799,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4789,3298]) ).
thf(4800,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4799]) ).
thf(4824,plain,
! [A: $i] :
( ( sk1 != sk1 )
| ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4800]) ).
thf(4837,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[4824]) ).
thf(25585,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk2 @ convergent_lines ) ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23899,120]) ).
thf(25586,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk2 @ convergent_lines ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25585]) ).
thf(25627,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25586]) ).
thf(25633,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ parallel_through_point ) )
!= sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[25627]) ).
thf(3578,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,737]) ).
thf(3579,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3578]) ).
thf(3610,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3579]) ).
thf(3631,plain,
! [A: $i] :
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 ) ),
inference(simp,[status(thm)],[3610]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(cnfConj,[status(thm)],[73]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(16203,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ parallel_through_point ) )
!= sk2 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,703]) ).
thf(16204,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16203]) ).
thf(16205,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16204:[bind(A,$thf( sk1 ))]]) ).
thf(16231,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16205]) ).
thf(4793,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4789,3618]) ).
thf(4794,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4793]) ).
thf(4832,plain,
! [A: $i] :
( ( sk1 != sk1 )
| ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4794]) ).
thf(4833,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4832]) ).
thf(21,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(103,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)],[21]) ).
thf(279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,100]) ).
thf(280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ 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(simp,[status(thm)],[279]) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ parallel_through_point ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(16,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(90,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)],[16]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ line_connecting ) @ line )
| ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ point )
| ~ ( A @ point ) ),
inference(cnf,[status(esa)],[90]) ).
thf(25537,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23882,137]) ).
thf(25538,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[25537]) ).
thf(25539,plain,
( ~ ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[25538:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(27031,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,25539]) ).
thf(27032,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[27031]) ).
thf(27033,plain,
( ( sk4 != sk2 )
| ( sk3 @ ( sk3 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[27032:[bind(A,$thf( sk3 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(4007,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3102,115]) ).
thf(4008,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4007]) ).
thf(4009,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ parallel_lines ) )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4008:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ $true
| ~ ( E @ ( D @ equal_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[53,48]) ).
thf(239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ equal_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[238]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equal_points ) )
| ( C @ ( B @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[239:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[126]) ).
thf(392,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)],[111,82]) ).
thf(393,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)],[392]) ).
thf(394,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(14612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[11003,48]) ).
thf(14613,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14612]) ).
thf(14614,plain,
! [A: $i] :
( ~ ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14613:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 @ ( sk3 @ intersection_point ) ))]]) ).
thf(23973,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23871,115]) ).
thf(23974,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[23973]) ).
thf(23975,plain,
( ~ ( sk3 @ ( sk1 @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[23974:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(32977,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,27309]) ).
thf(32978,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[32977]) ).
thf(32979,plain,
( ( sk4 != sk1 )
| ( sk4 @ ( sk2 @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[32978:[bind(A,$thf( sk2 @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(424,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( G @ ( F @ distinct_lines ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ $true
| ~ ( E @ ( D @ distinct_points ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,58]) ).
thf(425,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ distinct_lines ) )
!= ( G @ ( F @ distinct_lines ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( F @ ( E @ apart_point_and_line ) )
| ( G @ ( D @ apart_point_and_line ) )
| ( F @ ( D @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_points ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[424]) ).
thf(426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ apart_point_and_line ) )
| ( B @ ( E @ apart_point_and_line ) )
| ( C @ ( D @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( E @ ( D @ distinct_points ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$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(28097,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27201,139]) ).
thf(28098,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[28097]) ).
thf(28099,plain,
( ~ ( sk4 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[28098:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(18911,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16483]) ).
thf(18912,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[18911]) ).
thf(18913,plain,
( ( sk4 != sk2 )
| ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[18912:[bind(A,$thf( sk4 @ ( sk1 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(2239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2210,120]) ).
thf(2240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2239]) ).
thf(2253,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk2 )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2240]) ).
thf(2256,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( B @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2253]) ).
thf(4416,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,3618]) ).
thf(4417,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4416]) ).
thf(4429,plain,
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4417]) ).
thf(4441,plain,
( ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[4429]) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1168,249]) ).
thf(1872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1871]) ).
thf(1873,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1872:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(14404,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[10299,143]) ).
thf(14405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14404]) ).
thf(14406,plain,
! [A: $i] :
( ( sk2 @ ( A @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14405:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(16504,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16219,137]) ).
thf(16505,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16504]) ).
thf(16506,plain,
( ~ ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16505:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(14372,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[10299,523]) ).
thf(14373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14372]) ).
thf(14374,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14373:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(19087,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16506]) ).
thf(19088,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[19087]) ).
thf(19089,plain,
( ( sk3 != sk1 )
| ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[19088:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1168,48]) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1265]) ).
thf(1267,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1266:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(13988,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9353,249]) ).
thf(13989,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13988]) ).
thf(13990,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[13989:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(13476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3547]) ).
thf(13477,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( C @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ intersection_point ) @ ( C @ distinct_points ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13476]) ).
thf(13478,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
| ( sk1 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[13477:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(16343,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[13478,249]) ).
thf(16344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk1 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[16343]) ).
thf(16345,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
| ( sk1 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[16344:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(163,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,40]) ).
thf(164,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[163]) ).
thf(168,plain,
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ~ ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(202,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,168]) ).
thf(203,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk4 @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(208,plain,
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[203]) ).
thf(212,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk2 @ ( sk1 @ intersection_point ) ) )
| ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[208]) ).
thf(262,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[212]) ).
thf(263,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[262]) ).
thf(16499,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16219,120]) ).
thf(16500,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16499]) ).
thf(16540,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16500]) ).
thf(16547,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[16540]) ).
thf(291,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,97]) ).
thf(292,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ 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(simp,[status(thm)],[291]) ).
thf(293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ orthogonal_through_point ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ orthogonal_through_point ) @ distinct_lines ) )
| ~ ( D @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(16288,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16194,120]) ).
thf(16289,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16288]) ).
thf(16328,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16289]) ).
thf(16330,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16328]) ).
thf(9212,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[8351,48]) ).
thf(9213,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[9212]) ).
thf(9214,plain,
! [A: $i] :
( ~ ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[9213:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 @ ( sk3 @ intersection_point ) ))]]) ).
thf(16293,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[16194,137]) ).
thf(16294,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[16293]) ).
thf(16295,plain,
( ~ ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[16294:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(26811,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,24064]) ).
thf(26812,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[26811]) ).
thf(26813,plain,
( ( sk4 != sk1 )
| ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[26812:[bind(A,$thf( sk3 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk2 ))]]) ).
thf(32552,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[26813,3311]) ).
thf(32553,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[32552]) ).
thf(32595,plain,
( ( sk2 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk2 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[32553]) ).
thf(32606,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk3 @ ( sk2 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[32595]) ).
thf(27218,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27173,115]) ).
thf(27219,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27218]) ).
thf(27220,plain,
( ~ ( sk1 @ ( sk4 @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[27219:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[44,115]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) ) ),
inference(simp,[status(thm)],[461]) ).
thf(463,plain,
~ ( sk4 @ ( sk3 @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[462:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(19986,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[19911,137]) ).
thf(19987,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[19986]) ).
thf(19988,plain,
( ~ ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[19987:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(4127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4093,139]) ).
thf(4128,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( B @ ( C @ ( B @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[4127]) ).
thf(4129,plain,
! [A: $i] :
~ ( sk3 @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4128:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( E @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(4132,plain,
! [A: $i] :
~ ( sk3 @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[4129]) ).
thf(28069,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[27201,137]) ).
thf(28070,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[28069]) ).
thf(28071,plain,
( ~ ( sk2 @ ( sk2 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[28070:[bind(A,$thf( sk4 )),bind(B,$thf( sk2 ))]]) ).
thf(3596,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,740]) ).
thf(3597,plain,
! [A: $i] :
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3596]) ).
thf(3602,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3597]) ).
thf(3623,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3602]) ).
thf(5663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5526,64]) ).
thf(5664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[5663]) ).
thf(5677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( sk3 != D )
| ( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( D @ orthogonal_through_point ) ) ) ),
inference(simp,[status(thm)],[5664]) ).
thf(5684,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) )
!= ( C @ ( sk3 @ orthogonal_through_point ) ) ),
inference(simp,[status(thm)],[5677]) ).
thf(16444,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16202,115]) ).
thf(16445,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16444]) ).
thf(16446,plain,
( ~ ( sk4 @ ( sk1 @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16445:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(4096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) ) ),
inference(paramod_ordered,[status(thm)],[4093,115]) ).
thf(4097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) ) ),
inference(simp,[status(thm)],[4096]) ).
thf(4098,plain,
! [A: $i] :
~ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[4097:[bind(A,$thf( E )),bind(B,$thf( sk3 )),bind(C,$thf( E @ ( sk4 @ parallel_through_point ) ))]]) ).
thf(4133,plain,
! [A: $i] :
~ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ parallel_lines ) ),
inference(simp,[status(thm)],[4098]) ).
thf(28011,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk1 @ ( sk4 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27184,120]) ).
thf(28012,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk1 @ ( sk4 @ convergent_lines ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28011]) ).
thf(28053,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk4 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28012]) ).
thf(28058,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ parallel_through_point ) )
!= sk4 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28053]) ).
thf(6516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[6210,82]) ).
thf(6517,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[6516]) ).
thf(6518,plain,
! [B: $i,A: $i] :
~ ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[6517:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) )),bind(D,$thf( sk1 ))]]) ).
thf(6526,plain,
! [B: $i,A: $i] :
~ ( sk1 @ ( A @ ( B @ ( sk2 @ parallel_through_point ) @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(simp,[status(thm)],[6518]) ).
thf(3386,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3062,74]) ).
thf(3387,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3386]) ).
thf(3388,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ equal_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3387:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(4316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4132]) ).
thf(4317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( C @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ apart_point_and_line ) ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[4316]) ).
thf(4318,plain,
! [A: $i] : ( sk3 @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ),
inference(pattern_uni,[status(thm)],[4317:[bind(A,$thf( G @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) )),bind(B,$thf( sk3 )),bind(C,$thf( G ))]]) ).
thf(4342,plain,
! [A: $i] : ( sk3 @ ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ),
inference(simp,[status(thm)],[4318]) ).
thf(301,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( D @ ( B @ apart_point_and_line ) )
!= ( D @ ( A @ 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(eqfactor_ordered,[status(thm)],[58]) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[301:[bind(A,$thf( B ))]]) ).
thf(314,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(433,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,67]) ).
thf(434,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ( 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(simp,[status(thm)],[433]) ).
thf(435,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ apart_point_and_line ) )
| ( E @ ( C @ distinct_lines ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[434:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( C ))]]) ).
thf(446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ apart_point_and_line ) )
| ( E @ ( C @ distinct_lines ) )
| ( 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(simp,[status(thm)],[435]) ).
thf(24034,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[23874,137]) ).
thf(24035,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[24034]) ).
thf(24036,plain,
( ~ ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) )
| ( sk4 != sk1 ) ),
inference(pattern_uni,[status(thm)],[24035:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(26591,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,24036]) ).
thf(26592,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[26591]) ).
thf(26593,plain,
( ( sk4 != sk1 )
| ( sk3 @ ( sk3 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[26592:[bind(A,$thf( sk3 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk3 ))]]) ).
thf(16197,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ orthogonal_through_point ) )
!= sk2 )
| ~ $true
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[12784,737]) ).
thf(16198,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( B @ orthogonal_through_point ) )
!= sk2 )
| ( sk4 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16197]) ).
thf(16199,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[16198:[bind(A,$thf( sk1 ))]]) ).
thf(16230,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ orthogonal_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[16199]) ).
thf(4697,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,120]) ).
thf(4698,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4697]) ).
thf(4734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) )
!= C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[4698]) ).
thf(4748,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( sk2 @ parallel_through_point ) @ parallel_through_point ) )
!= sk1 ),
inference(simp,[status(thm)],[4734]) ).
thf(4122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4093,123]) ).
thf(4123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) @ ( sk3 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( C @ convergent_lines ) )
| ( D @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4122]) ).
thf(4124,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4123:[bind(A,$thf( F )),bind(B,$thf( sk3 )),bind(C,$thf( F @ ( sk4 @ parallel_through_point ) )),bind(D,$thf( D ))]]) ).
thf(4143,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( sk4 @ parallel_through_point ) @ convergent_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4124]) ).
thf(19981,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[19911,120]) ).
thf(19982,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk2 @ convergent_lines ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[19981]) ).
thf(20023,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[19982]) ).
thf(20030,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= sk2 )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20023]) ).
thf(4455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ~ $true
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,120]) ).
thf(4456,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ ( C @ parallel_through_point ) @ convergent_lines ) ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4455]) ).
thf(4526,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( C @ parallel_through_point ) )
!= sk1 )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4456]) ).
thf(4538,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk2 @ ( B @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4526]) ).
thf(244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ( E @ ( D @ distinct_points ) )
| ( E @ ( C @ distinct_points ) )
| ~ $true
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[50,53]) ).
thf(245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ( E @ ( D @ distinct_points ) )
| ( E @ ( C @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[244]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(20476,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,19988]) ).
thf(20477,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[20476]) ).
thf(20478,plain,
( ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[20477:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(2076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ $true
| ~ ( D @ ( C @ equal_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[251,48]) ).
thf(2077,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ~ ( D @ ( C @ equal_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[2076]) ).
thf(2078,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ equal_points ) )
| ~ ( A @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[2077:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(519,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)],[70]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( B ))]]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[663,74]) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[757]) ).
thf(759,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(3590,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,171]) ).
thf(3591,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3590]) ).
thf(3604,plain,
( ( sk3 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3591]) ).
thf(3625,plain,
( ( sk3 != sk1 )
| ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ) ),
inference(simp,[status(thm)],[3604]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[103]) ).
thf(27221,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk1 @ ( sk4 @ convergent_lines ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27173,120]) ).
thf(27222,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk1 @ ( sk4 @ convergent_lines ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27221]) ).
thf(27263,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk4 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27222]) ).
thf(27270,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ parallel_through_point ) )
!= sk4 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[27263]) ).
thf(1938,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[1873,48]) ).
thf(1939,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[1938]) ).
thf(1940,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ equal_points ) )
| ( sk4 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[1939:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(273,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,100]) ).
thf(274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( G @ parallel_through_point ) )),bind(D,$thf( D )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ apart_point_and_line ) )
| ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( B @ ( D @ ( C @ parallel_through_point ) @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(23916,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[23865,115]) ).
thf(23917,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk2 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[23916]) ).
thf(23918,plain,
( ~ ( sk4 @ ( sk2 @ parallel_lines ) )
| ( sk3 @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[23917:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 ))]]) ).
thf(4449,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3394,115]) ).
thf(4450,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[4449]) ).
thf(4451,plain,
! [A: $i] :
( ~ ( A @ ( sk1 @ parallel_lines ) )
| ( sk2 @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[4450:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(14039,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[9353,48]) ).
thf(14040,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14039]) ).
thf(14041,plain,
! [A: $i] :
( ~ ( sk2 @ ( sk1 @ intersection_point ) @ ( A @ equal_points ) )
| ( sk2 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14040:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 @ ( sk1 @ intersection_point ) ))]]) ).
thf(19647,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[18913,3298]) ).
thf(19648,plain,
( ( ( sk1 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk1 @ ( sk4 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[19647]) ).
thf(19672,plain,
( ( sk1 != sk1 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk1 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[19648]) ).
thf(19686,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk1 @ intersection_point ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[19672]) ).
thf(15360,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[12246,74]) ).
thf(15361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[15360]) ).
thf(15362,plain,
! [A: $i] :
( ~ ( sk3 @ ( A @ equal_lines ) )
| ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[15361:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk3 ))]]) ).
thf(34777,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,28018]) ).
thf(34778,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[34777]) ).
thf(34779,plain,
( ( sk4 != sk2 )
| ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[34778:[bind(A,$thf( sk1 @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(30424,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,27228]) ).
thf(30425,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk3 != sk2 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[30424]) ).
thf(30426,plain,
( ( sk3 != sk2 )
| ( sk1 @ ( sk1 @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[30425:[bind(A,$thf( sk1 @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(14573,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ~ $true
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[11003,1911]) ).
thf(14574,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ~ ( C @ ( B @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14573]) ).
thf(14575,plain,
! [A: $i] :
( ~ ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ equal_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14574:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(23976,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk1 @ convergent_lines ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[23871,120]) ).
thf(23977,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk3 @ ( sk1 @ convergent_lines ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[23976]) ).
thf(24018,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[23977]) ).
thf(24023,plain,
! [A: $i] :
( ( ( A @ ( sk3 @ parallel_through_point ) )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[24018]) ).
thf(17651,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,16295]) ).
thf(17652,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk4 != sk1 )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[17651]) ).
thf(17653,plain,
( ( sk4 != sk1 )
| ( sk4 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[17652:[bind(A,$thf( sk4 @ ( sk2 @ intersection_point ) )),bind(B,$thf( sk4 ))]]) ).
thf(436,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ~ $true
| ( 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(paramod_ordered,[status(thm)],[58,67]) ).
thf(437,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( B @ apart_point_and_line ) )
!= ( F @ ( E @ apart_point_and_line ) ) )
| ( G @ ( E @ apart_point_and_line ) )
| ( G @ ( F @ distinct_lines ) )
| ( 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(simp,[status(thm)],[436]) ).
thf(438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ apart_point_and_line ) )
| ( E @ ( D @ distinct_lines ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( D ))]]) ).
thf(447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ apart_point_and_line ) )
| ( E @ ( D @ distinct_lines ) )
| ( 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(simp,[status(thm)],[438]) ).
thf(270,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( E @ ( D @ apart_point_and_line ) )
| ( F @ ( C @ apart_point_and_line ) )
| ( E @ ( C @ apart_point_and_line ) )
| ~ ( F @ ( E @ distinct_lines ) )
| ~ $true
| ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[50,58]) ).
thf(271,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ distinct_points ) )
!= ( D @ ( C @ distinct_points ) ) )
| ( F @ ( D @ apart_point_and_line ) )
| ( E @ ( D @ apart_point_and_line ) )
| ( F @ ( C @ apart_point_and_line ) )
| ( E @ ( C @ apart_point_and_line ) )
| ~ ( F @ ( E @ distinct_lines ) )
| ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ( B @ ( A @ equal_points ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(315,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 @ equal_points ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(3975,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3520,3311]) ).
thf(3976,plain,
( ( ( sk3 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3975]) ).
thf(3984,plain,
( ( sk3 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3976]) ).
thf(3997,plain,
( ( sk3 != sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[3984]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[145]) ).
thf(19694,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ $true
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[13693,523]) ).
thf(19695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ distinct_lines ) )
!= ( B @ ( C @ distinct_lines ) ) )
| ( C @ ( B @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[19694]) ).
thf(19696,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[19695:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(14384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[10299,74]) ).
thf(14385,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14384]) ).
thf(14386,plain,
! [A: $i] :
( ~ ( sk2 @ ( A @ equal_lines ) )
| ( A @ ( sk2 @ ( sk1 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14385:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(16233,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16191,115]) ).
thf(16234,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk1 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16233]) ).
thf(16235,plain,
( ~ ( sk4 @ ( sk1 @ parallel_lines ) )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[16234:[bind(A,$thf( sk1 )),bind(B,$thf( sk4 ))]]) ).
thf(369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( C @ ( A @ apart_point_and_line ) )
!= ( B @ ( A @ apart_point_and_line ) ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ distinct_lines ) ) ),
inference(eqfactor_ordered,[status(thm)],[61]) ).
thf(371,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( C @ ( B @ unorthogonal_lines ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[369:[bind(A,$thf( A )),bind(B,$thf( C ))]]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unorthogonal_lines ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( B @ distinct_lines ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(10895,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( sk3 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,3473]) ).
thf(10896,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( C @ ( sk4 @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( sk3 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10895]) ).
thf(10897,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( sk4 @ ( A @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[10896:[bind(A,$thf( E @ ( sk4 @ intersection_point ) )),bind(B,$thf( sk4 )),bind(C,$thf( E ))]]) ).
thf(10941,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( sk4 @ ( A @ ( sk4 @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[10897]) ).
thf(13749,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( C @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( sk3 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[155,4023]) ).
thf(13750,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ apart_point_and_line ) )
!= ( sk4 @ ( sk4 @ ( C @ intersection_point ) @ apart_point_and_line ) ) )
| ( C @ ( sk3 @ convergent_lines ) )
| ( B @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13749]) ).
thf(13751,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( sk4 @ ( sk4 @ ( A @ intersection_point ) @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[13750:[bind(A,$thf( sk4 @ ( D @ intersection_point ) )),bind(B,$thf( sk4 )),bind(C,$thf( D ))]]) ).
thf(13842,plain,
! [A: $i] :
( ( A @ ( sk3 @ convergent_lines ) )
| ( sk4 @ ( sk4 @ ( A @ intersection_point ) @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[13751]) ).
thf(14561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ~ $true
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[11003,249]) ).
thf(14562,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ distinct_points ) )
!= ( B @ ( C @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[14561]) ).
thf(14563,plain,
! [A: $i] :
( ( A @ ( sk4 @ ( sk3 @ intersection_point ) @ distinct_points ) )
| ( sk3 @ ( A @ incident_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[14562:[bind(A,$thf( A )),bind(B,$thf( sk4 @ ( sk3 @ intersection_point ) )),bind(C,$thf( A ))]]) ).
thf(458,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)],[395,115]) ).
thf(459,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)],[458]) ).
thf(460,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ parallel_lines ) ),
inference(pattern_uni,[status(thm)],[459:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(464,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ orthogonal_through_point ) @ parallel_lines ) ),
inference(simp,[status(thm)],[460]) ).
thf(5671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ $true
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(paramod_ordered,[status(thm)],[5526,82]) ).
thf(5672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ unorthogonal_lines ) ) )
| ~ ( D @ ( C @ orthogonal_lines ) ) ),
inference(simp,[status(thm)],[5671]) ).
thf(5673,plain,
! [B: $i,A: $i] :
~ ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(pattern_uni,[status(thm)],[5672:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( F @ ( H @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) )),bind(D,$thf( sk3 ))]]) ).
thf(5681,plain,
! [B: $i,A: $i] :
~ ( sk3 @ ( A @ ( B @ ( sk4 @ parallel_through_point ) @ orthogonal_through_point ) @ orthogonal_lines ) ),
inference(simp,[status(thm)],[5673]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(418,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( D @ ( E @ orthogonal_through_point ) @ ( D @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[67,97]) ).
thf(419,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ apart_point_and_line ) )
!= ( D @ ( E @ orthogonal_through_point ) @ ( D @ apart_point_and_line ) ) )
| ( C @ ( B @ distinct_lines ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[418]) ).
thf(420,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ orthogonal_through_point ) @ ( A @ distinct_lines ) )
| ~ ( A @ ( C @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( G )),bind(B,$thf( B )),bind(C,$thf( G @ ( F @ orthogonal_through_point ) )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ orthogonal_through_point ) @ ( A @ distinct_lines ) )
| ~ ( A @ ( C @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(16447,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16202,120]) ).
thf(16448,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16447]) ).
thf(16488,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16448]) ).
thf(16490,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= sk1 )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[16488]) ).
thf(16236,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[16191,120]) ).
thf(16237,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) )
!= ( sk4 @ ( sk1 @ convergent_lines ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16236]) ).
thf(16277,plain,
! [B: $i,A: $i] :
( ( B != sk4 )
| ( ( A @ ( B @ parallel_through_point ) )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16237]) ).
thf(16282,plain,
! [A: $i] :
( ( ( A @ ( sk4 @ parallel_through_point ) )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[16277]) ).
thf(28008,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ $true
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[27184,115]) ).
thf(28009,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk4 @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( B @ ( A @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[28008]) ).
thf(28010,plain,
( ~ ( sk1 @ ( sk4 @ parallel_lines ) )
| ( sk4 != sk2 ) ),
inference(pattern_uni,[status(thm)],[28009:[bind(A,$thf( sk4 )),bind(B,$thf( sk1 ))]]) ).
thf(276,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,100]) ).
thf(277,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ parallel_through_point ) @ ( E @ apart_point_and_line ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( D @ ( C @ parallel_through_point ) @ ( B @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ parallel_through_point ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ parallel_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( D @ ( C @ parallel_through_point ) @ ( B @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(3260,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3196,699]) ).
thf(3261,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3260]) ).
thf(3278,plain,
! [A: $i] :
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk3 @ intersection_point ) ) )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3261]) ).
thf(3299,plain,
! [A: $i] :
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) @ ( A @ parallel_through_point ) )
!= sk1 ) ),
inference(simp,[status(thm)],[3278]) ).
thf(3094,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[3034,74]) ).
thf(3095,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( A @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ~ ( C @ ( B @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[3094]) ).
thf(3096,plain,
! [A: $i] :
( ~ ( sk4 @ ( A @ equal_lines ) )
| ( A @ ( sk3 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[3095:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk4 ))]]) ).
thf(288,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ~ $true
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[58,97]) ).
thf(289,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ apart_point_and_line ) )
!= ( E @ ( F @ orthogonal_through_point ) @ ( E @ apart_point_and_line ) ) )
| ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) )
| ~ ( D @ ( C @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ orthogonal_through_point ) )),bind(E,$thf( H )),bind(F,$thf( G ))]]) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ( B @ ( D @ apart_point_and_line ) )
| ~ ( D @ ( C @ orthogonal_through_point ) @ ( B @ distinct_lines ) )
| ~ ( A @ ( D @ distinct_points ) ) ),
inference(simp,[status(thm)],[290]) ).
thf(20846,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk1 @ convergent_lines ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[20656,16213]) ).
thf(20847,plain,
( ( ( sk2 @ ( sk4 @ ( sk3 @ intersection_point ) @ incident_point_and_line ) )
!= ( sk2 @ ( sk4 @ ( sk2 @ intersection_point ) @ incident_point_and_line ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20846]) ).
thf(20863,plain,
( ( sk2 != sk2 )
| ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20847]) ).
thf(20878,plain,
( ( ( sk4 @ ( sk3 @ intersection_point ) )
!= ( sk4 @ ( sk2 @ intersection_point ) ) )
| ( sk4 @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[20863]) ).
thf(2236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ $true
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[2210,115]) ).
thf(2237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ~ ( C @ ( B @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(simp,[status(thm)],[2236]) ).
thf(2238,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ parallel_lines ) )
| ( A @ ( sk1 @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[2237:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(4720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( B @ convergent_lines ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,135]) ).
thf(4721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ parallel_through_point ) @ ( sk1 @ convergent_lines ) )
!= ( C @ ( B @ convergent_lines ) ) )
| ( D @ ( B @ convergent_lines ) )
| ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4720]) ).
thf(4722,plain,
! [B: $i,A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( A @ ( B @ ( sk2 @ parallel_through_point ) @ distinct_lines ) ) ),
inference(pattern_uni,[status(thm)],[4721:[bind(A,$thf( F )),bind(B,$thf( sk1 )),bind(C,$thf( F @ ( sk2 @ parallel_through_point ) )),bind(D,$thf( D ))]]) ).
thf(4742,plain,
! [B: $i,A: $i] :
( ( A @ ( sk1 @ convergent_lines ) )
| ( A @ ( B @ ( sk2 @ parallel_through_point ) @ distinct_lines ) ) ),
inference(simp,[status(thm)],[4722]) ).
thf(40582,plain,
$false,
inference(e,[status(thm)],[16216,23882,138,1168,101,16243,25531,249,24028,3566,1200,523,115,4515,1808,3040,2014,1205,120,32723,16229,37369,15450,10299,2210,23865,5168,385,56,142,29946,28018,153,25576,16498,9184,1671,1999,3446,7748,5192,4142,1914,42,417,885,3308,5723,1601,1967,5269,3140,4137,3442,4439,28128,4956,16287,20017,2217,3485,4023,196,9172,4743,14002,189,5199,27320,1398,30186,316,3180,78,16191,261,24064,3517,638,3216,770,16272,325,448,57,5526,591,443,376,26153,1136,1828,121,2034,9319,1911,4454,3473,253,1383,4134,25584,23983,84,3300,27256,3068,25567,61,18737,27201,4892,16219,6210,147,10404,89,133,243,15350,3226,28046,312,74,16324,6529,117,3635,102,3550,3852,85,23871,14342,1042,260,38,14222,70,4091,11003,137,92,12764,197,65,27228,97,28063,252,3618,19980,324,3799,19467,317,156,16232,27309,4789,403,3102,3632,5233,388,17819,53,141,4012,109,3311,124,77,30666,637,4744,27273,1075,32483,23874,4736,1588,8351,19911,19579,457,28184,129,4953,25646,41,13693,128,105,311,3999,19871,20656,1434,765,3306,2235,4919,45,64,444,20024,375,2260,24072,16483,17321,148,5230,3536,3547,402,44,843,4926,29706,27210,4465,3900,59,118,54,313,144,13958,3304,15382,86,3223,16194,4537,71,445,936,3726,4837,26373,25633,3631,16454,76,737,4073,98,16231,12246,3747,4833,103,323,140,23899,91,3298,24011,27033,155,27281,16535,4009,552,3034,240,251,108,27176,130,394,135,14614,2207,12784,23975,32979,426,663,3161,17487,28099,18913,123,2256,16202,4441,4136,1873,3193,112,14406,16506,48,14374,25592,19089,150,95,1267,13990,16345,263,16547,310,16330,67,9214,16295,32606,27220,25620,463,19988,4132,28071,3623,50,5684,19265,3246,12752,16446,4737,27184,1404,27167,703,4133,28058,6526,3388,4093,4342,314,446,612,3520,26593,9353,16230,4748,4143,20030,4538,143,43,250,2088,20478,87,2078,524,759,891,3625,104,27270,1940,699,319,896,40,3630,171,139,23918,4451,158,14041,19686,16213,58,15362,1607,34779,30426,14575,82,24023,4745,17653,26813,447,315,3997,835,146,51,3464,19696,14386,16235,373,3062,3015,136,10941,79,13842,3030,14563,3506,94,25539,107,3196,27173,395,740,464,23908,5681,131,62,3394,442,16490,16282,28010,68,322,3299,3096,309,543,100,90,111,20878,2238,4742,24036,13478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO196+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.14/0.40 % Computer : n003.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 13:06:08 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.89/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.28 % [INFO] Parsing done (250ms).
% 1.38/1.30 % [INFO] Running in sequential loop mode.
% 2.23/1.69 % [INFO] eprover registered as external prover.
% 2.43/1.70 % [INFO] Scanning for conjecture ...
% 2.62/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.62/1.88 % [INFO] Axiom selection finished. Selected 35 axioms (removed 0 axioms).
% 2.84/1.94 % [INFO] Problem is first-order (TPTP FOF).
% 2.84/1.95 % [INFO] Type checking passed.
% 2.84/1.96 % [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 ...
% 80.90/18.69 % External prover 'e' found a proof!
% 80.90/18.69 % [INFO] Killing All external provers ...
% 80.90/18.70 % Time passed: 18149ms (effective reasoning time: 17394ms)
% 80.90/18.70 % 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)>
% 66.33/18.70 % 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
% 66.33/18.70 % No. of inferences in proof: 1380
% 66.33/18.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 18149 ms resp. 17394 ms w/o parsing
% 83.28/19.08 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 83.28/19.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------