%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 07:12:53 AM UTC 2026
% Result : Theorem 13.58s 3.93s
% Output : Refutation 14.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 150 ( 50 unt; 0 typ; 2 def)
% Number of atoms : 462 ( 57 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1685 ( 177 ~; 183 |; 13 &;1278 @)
% ( 0 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 401 ( 0 ^; 385 !; 14 ?; 401 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
? [B: $i] : ( A @ ( A @ ( B @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( sk1 @ ( sk1 @ ( A @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( A @ parallel_through_point ) @ distinct_lines ) ) ) ) ).
thf(10,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)],[10]) ).
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(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',occu1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc1) ).
thf(65,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(66,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(miniscope,[status(thm)],[65]) ).
thf(67,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(cnf,[status(esa)],[66]) ).
thf(94,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)],[45,67]) ).
thf(95,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)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( F @ ( B @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(97,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[96]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( B @ ( A @ distinct_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[88]) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ distinct_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[97,89]) ).
thf(236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( D @ ( C @ convergent_lines ) ) )
| ( D @ ( C @ distinct_lines ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ distinct_lines ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(238,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ distinct_lines ) ),
inference(simp,[status(thm)],[237]) ).
thf(4,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(31,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)],[4]) ).
thf(32,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)],[31]) ).
thf(33,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)],[32]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
~ ~ ? [A: $i,B: $i] : ( A @ ( A @ ( B @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( B @ parallel_through_point ) @ distinct_lines ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ distinct_lines ),
inference(cnf,[status(esa)],[24]) ).
thf(13,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(62,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)],[13]) ).
thf(63,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)],[62]) ).
thf(64,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)],[63]) ).
thf(124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ distinct_lines ) )
!= ( C @ ( B @ distinct_lines ) ) )
| ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,64]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ distinct_lines ) )
!= ( 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(simp,[status(thm)],[124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( B @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( sk2 @ parallel_through_point ) )),bind(C,$thf( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )),bind(D,$thf( D ))]]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( B @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
| ( B @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( B @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[162,67]) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( D @ ( C @ ( D @ orthogonal_through_point ) @ unorthogonal_lines ) ) )
| ( B @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(169,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( A )),bind(B,$thf( sk1 @ ( sk2 @ orthogonal_through_point ) )),bind(C,$thf( sk1 )),bind(D,$thf( sk1 @ ( sk2 @ orthogonal_through_point ) ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1) ).
thf(71,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(72,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(miniscope,[status(thm)],[71]) ).
thf(73,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(cnf,[status(esa)],[72]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ooc2) ).
thf(80,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).
thf(26,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
| ( A @ ( C @ apart_point_and_line ) ) )
=> ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) )
& ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[30,56]) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ ( B @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ intersection_point ) )),bind(D,$thf( F @ ( E @ intersection_point ) ))]]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(247,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)],[97,233]) ).
thf(248,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)],[247]) ).
thf(249,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(264,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(simp,[status(thm)],[249]) ).
thf(267,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( B @ ( B @ ( C @ ( B @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ~ $true
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[169,264]) ).
thf(268,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( B @ ( B @ ( C @ ( B @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( G @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ orthogonal_through_point ) @ intersection_point ) )),bind(B,$thf( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )),bind(C,$thf( G ))]]) ).
thf(282,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(81,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[81]) ).
thf(441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( D @ ( E @ orthogonal_through_point ) @ ( D @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[33,82]) ).
thf(442,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( D @ ( E @ orthogonal_through_point ) @ ( D @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[441]) ).
thf(443,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ distinct_points ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[442:[bind(A,$thf( A )),bind(B,$thf( G @ ( F @ orthogonal_through_point ) )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ distinct_points ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[443]) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( D @ ( C @ orthogonal_through_point ) @ ( B @ apart_point_and_line ) ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[169,488]) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( D @ ( C @ orthogonal_through_point ) @ ( B @ apart_point_and_line ) ) )
| ( D @ ( B @ distinct_points ) )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[535]) ).
thf(537,plain,
! [A: $i] :
( ( sk1 @ ( A @ distinct_points ) )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[536:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 @ ( sk2 @ orthogonal_through_point ) )),bind(D,$thf( sk1 ))]]) ).
thf(681,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) ) )
| ~ $true
| ( sk1 @ ( A @ distinct_points ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[537,67]) ).
thf(682,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ orthogonal_through_point ) @ unorthogonal_lines ) )
!= ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) ) )
| ( sk1 @ ( A @ distinct_points ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sk1 @ ( sk2 @ orthogonal_through_point ) ) )
| ( ( B @ ( C @ orthogonal_through_point ) )
!= ( sk1 @ ( sk2 @ parallel_through_point ) ) )
| ( sk1 @ ( A @ distinct_points ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[682]) ).
thf(688,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )
!= ( sk1 @ ( sk2 @ parallel_through_point ) ) )
| ( sk1 @ ( A @ distinct_points ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[686]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp2) ).
thf(83,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(84,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[84]) ).
thf(203,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( B @ ( C @ parallel_through_point ) @ ( B @ apart_point_and_line ) ) )
| ~ $true
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[169,85]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) )
!= ( B @ ( C @ parallel_through_point ) @ ( B @ apart_point_and_line ) ) )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[203]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) )
| ( A != B )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(210,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )
!= ( A @ ( B @ parallel_through_point ) ) )
| ( sk1 @ ( sk2 @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ unorthogonal_lines ) )
| ( sk1 @ ( sk2 @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ $true
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(paramod_ordered,[status(thm)],[29,56]) ).
thf(99,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection_point ) @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ ( A @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ intersection_point ) )),bind(D,$thf( F @ ( E @ intersection_point ) ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( D @ ( E @ parallel_through_point ) @ ( D @ apart_point_and_line ) ) )
| ~ $true
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[33,85]) ).
thf(458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ apart_point_and_line ) )
!= ( D @ ( E @ parallel_through_point ) @ ( D @ apart_point_and_line ) ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[457]) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ distinct_points ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[458:[bind(A,$thf( A )),bind(B,$thf( G @ ( F @ parallel_through_point ) )),bind(C,$thf( G )),bind(D,$thf( G )),bind(E,$thf( F ))]]) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ distinct_points ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[459]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oac1) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(17,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(74,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(75,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[74]) ).
thf(76,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[75]) ).
thf(90,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ distinct_lines ) )
!= ( A @ ( A @ distinct_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,76]) ).
thf(91,plain,
! [A: $i] :
( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) @ ( sk1 @ ( sk2 @ parallel_through_point ) @ distinct_lines ) )
!= ( A @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(92,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )
!= A )
| ( ( sk1 @ ( sk2 @ parallel_through_point ) )
!= A ) ),
inference(simp,[status(thm)],[91]) ).
thf(93,plain,
( ( sk1 @ ( sk1 @ ( sk2 @ orthogonal_through_point ) @ orthogonal_through_point ) )
!= ( sk1 @ ( sk2 @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(11,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(57,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,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(60,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)],[12]) ).
thf(114,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)],[97,101]) ).
thf(115,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)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ orthogonal_through_point ) @ ( A @ ( B @ ( A @ orthogonal_through_point ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ orthogonal_through_point ) )),bind(D,$thf( E ))]]) ).
thf(117,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)],[116]) ).
thf(47,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
=> ( ( B @ ( C @ distinct_points ) )
& ( A @ ( C @ distinct_points ) ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) )
& ( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ distinct_points ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[49,56]) ).
thf(284,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ distinct_points ) )
!= ( D @ ( D @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(18,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(77,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)],[18]) ).
thf(545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[488,285]) ).
thf(546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(5,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(34,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)],[5]) ).
thf(58,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[58]) ).
thf(21,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(86,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)],[21]) ).
thf(104,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)],[97,59]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[105]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) )
!= A ),
inference(simp,[status(thm)],[110]) ).
thf(507,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ $true
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[479,285]) ).
thf(508,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ distinct_points ) )
!= ( E @ ( D @ distinct_points ) ) )
| ~ ( E @ ( D @ line_connecting ) @ ( D @ apart_point_and_line ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[507]) ).
thf(509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( C @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ) ),
inference(pattern_uni,[status(thm)],[508:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( C ))]]) ).
thf(102,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)],[97,73]) ).
thf(103,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)],[102]) ).
thf(109,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)],[103]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(9,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',apart6) ).
thf(51,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)],[9]) ).
thf(15,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(68,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)],[15]) ).
thf(1098,plain,
$false,
inference(e,[status(thm)],[56,238,33,169,73,80,282,688,82,210,83,101,479,88,37,25,46,93,57,29,89,74,233,85,60,117,65,97,285,488,77,537,547,34,264,45,64,44,59,71,54,49,86,113,76,509,162,112,67,31,26,23,30,51,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.15/0.40 % Computer : n011.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Fri Sep 25 13:07:58 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 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
% 0.89/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/1.07 % [INFO] Parsing done (137ms).
% 1.18/1.08 % [INFO] Running in sequential loop mode.
% 1.88/1.49 % [INFO] eprover registered as external prover.
% 2.10/1.50 % [INFO] Scanning for conjecture ...
% 2.27/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 2.27/1.64 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.27/1.67 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/1.67 % [INFO] Type checking passed.
% 2.27/1.67 % [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 ...
% 13.58/3.92 % External prover 'e' found a proof!
% 13.58/3.92 % [INFO] Killing All external provers ...
% 13.58/3.93 % Time passed: 3384ms (effective reasoning time: 2839ms)
% 13.58/3.93 % 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)>
% 13.58/3.93 % Axioms used in derivation (20): con2, ouo1, apart4, ceq2, oac1, apart5, apart1, occu1, con1, apart2, cp2, apart3, ooc1, ceq3, cup1, apart6, ooc2, cp1, ceq1, cu1
% 13.58/3.93 % No. of inferences in proof: 148
% 13.58/3.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3384 ms resp. 2839 ms w/o parsing
% 14.43/4.05 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.43/4.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------