%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 07:12:37 AM UTC 2026
% Result : Theorem 7.21s 3.37s
% Output : Refutation 7.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 39
% Syntax : Number of formulae : 151 ( 48 unt; 0 typ; 4 def)
% Number of atoms : 436 ( 67 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1370 ( 183 ~; 105 |; 68 &; 946 @)
% ( 4 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 298 ( 0 ^; 283 !; 11 ?; 298 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(unorthogonal_lines_decl,type,
unorthogonal_lines: $i > $i > $o ).
thf(orthogonal_through_point_decl,type,
orthogonal_through_point: $i > $i > $i ).
thf(orthogonal_lines_decl,type,
orthogonal_lines: $i > $i > $o ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(equal_lines_decl,type,
equal_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(line_decl,type,
line: $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(equal_points_decl,type,
equal_points: $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 @ ( C @ line_connecting ) @ ( B @ incident_point_and_line ) )
& ( D @ ( C @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( B @ ( A @ line_connecting ) @ ( D @ incident_point_and_line ) )
& ( B @ ( A @ line_connecting ) @ ( C @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( B @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( C @ ( B @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ( ( A @ ( sk1 @ line_connecting ) @ ( C @ incident_point_and_line ) )
& ( A @ ( sk1 @ line_connecting ) @ ( B @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( A @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
& ( B @ ( A @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
& ( B @ ( A @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ( sk2 @ ( sk1 @ line_connecting ) @ ( B @ incident_point_and_line ) )
& ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ incident_point_and_line ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( A @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
& ( A @ ( sk3 @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
& ( A @ ( sk3 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) ) ) ) ) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
thf(50,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[50]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(10,axiom,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(70,plain,
! [A: $i,B: $i] :
~ ( ~ ( B @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ orthogonal_lines ) )
<=> ~ ( B @ ( A @ unorthogonal_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ unorthogonal_lines ) )
=> ( B @ ( A @ orthogonal_lines ) ) )
& ( ( B @ ( A @ orthogonal_lines ) )
=> ~ ( B @ ( A @ unorthogonal_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ line_connecting ) @ ( B @ incident_point_and_line ) )
& ( D @ ( C @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( B @ ( A @ line_connecting ) @ ( D @ incident_point_and_line ) )
& ( B @ ( A @ line_connecting ) @ ( C @ incident_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ line_connecting ) @ ( B @ incident_point_and_line ) )
& ( D @ ( C @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( B @ ( A @ line_connecting ) @ ( D @ incident_point_and_line ) )
& ( B @ ( A @ line_connecting ) @ ( C @ incident_point_and_line ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(37,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ line_connecting ) @ ( B @ incident_point_and_line ) )
& ( D @ ( C @ line_connecting ) @ ( A @ incident_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( B @ ( A @ line_connecting ) @ ( D @ incident_point_and_line ) )
& ( B @ ( A @ line_connecting ) @ ( C @ incident_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,plain,
( ( ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) )
& ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
& ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
& ( sk4 @ ( sk3 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(43,plain,
sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ incident_point_and_line ),
inference(cnfConj,[status(thm)],[38]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_lines ) )
<=> ~ ( B @ ( A @ distinct_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(85,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)],[14]) ).
thf(86,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)],[85]) ).
thf(87,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)],[86]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ equal_lines ) ) ),
inference(cnfConj,[status(thm)],[87]) ).
thf(42,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1) ).
thf(44,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(45,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ convergent_lines ) ),
inference(cnf,[status(esa)],[45]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2) ).
thf(93,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(74,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)],[73]) ).
thf(75,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)],[74]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_lines ) )
| ( B @ ( A @ unorthogonal_lines ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(41,plain,
sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ),
inference(cnfConj,[status(thm)],[38]) ).
thf(39,plain,
( ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[38]) ).
thf(152,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,39]) ).
thf(153,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(161,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[153]) ).
thf(184,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41,161]) ).
thf(185,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[184]) ).
thf(189,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[185]) ).
thf(195,plain,
( ( sk4 != sk2 )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[189]) ).
thf(210,plain,
( ( sk4 != sk2 )
| ( sk4 != sk2 )
| ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[195]) ).
thf(211,plain,
( ( sk4 != sk2 )
| ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[210]) ).
thf(21,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart2) ).
thf(106,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',par1) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(147,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_points ) )
<=> ~ ( B @ ( A @ distinct_points ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ distinct_points ) )
=> ( B @ ( A @ equal_points ) ) )
& ( ( B @ ( A @ equal_points ) )
=> ~ ( B @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(124,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)],[123]) ).
thf(125,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)],[124]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(cnfConj,[status(thm)],[125]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_points ) ) ),
inference(paramod_ordered,[status(thm)],[42,126]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ equal_points ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
~ ( sk2 @ ( sk1 @ equal_points ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',occu1) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unorthogonal_lines ) )
| ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( C @ apart_point_and_line ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc2) ).
thf(114,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(115,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[114]) ).
thf(116,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ orthogonal_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[115]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( B @ ( A @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ooc1) ).
thf(47,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,plain,
~ ? [A: $i,B: $i] : ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ orthogonal_through_point ) @ unorthogonal_lines ) ),
inference(cnf,[status(esa)],[48]) ).
thf(198,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)],[61,49]) ).
thf(199,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)],[198]) ).
thf(200,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( F @ ( B @ orthogonal_through_point ) )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( B ))]]) ).
thf(201,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) ),
inference(simp,[status(thm)],[200]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ unorthogonal_lines ) )
& ( B @ ( A @ convergent_lines ) ) )
=> ( ( ( C @ ( B @ unorthogonal_lines ) )
& ( C @ ( B @ convergent_lines ) ) )
| ( ( C @ ( A @ unorthogonal_lines ) )
& ( C @ ( A @ convergent_lines ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oac1) ).
thf(53,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(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ incident_point_and_line ) )
<=> ~ ( B @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
thf(141,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)],[34]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( A @ convergent_lines ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq3) ).
thf(109,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)],[22]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cup1) ).
thf(96,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)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
thf(129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ ( B @ apart_point_and_line ) )
| ( C @ ( B @ apart_point_and_line ) )
| ( D @ ( A @ apart_point_and_line ) )
| ( C @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( A @ unorthogonal_lines ) )
| ~ ( C @ ( A @ convergent_lines ) ) )
& ( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ) )
=> ( ~ ( C @ ( B @ unorthogonal_lines ) )
| ~ ( C @ ( B @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(148,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[147]) ).
thf(149,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[148]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[117]) ).
thf(40,plain,
sk4 @ ( sk3 @ distinct_points ),
inference(cnfConj,[status(thm)],[38]) ).
thf(175,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,149]) ).
thf(176,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(179,plain,
! [A: $i] :
( ( sk4 != A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[176]) ).
thf(181,plain,
sk4 != sk3,
inference(simp,[status(thm)],[179]) ).
thf(12,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart3) ).
thf(79,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(80,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[79]) ).
thf(81,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[80]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ unorthogonal_lines ) )
| ~ ( B @ ( A @ orthogonal_lines ) ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ convergent_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int1) ).
thf(98,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)],[18]) ).
thf(202,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)],[201,46]) ).
thf(203,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)],[202]) ).
thf(206,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)],[203]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ orthogonal_through_point ) )
!= ( B @ ( C @ parallel_through_point ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ apart_point_and_line ) )
=> ( ( C @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(103,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)],[20]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci3) ).
thf(91,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)],[15]) ).
thf(107,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[106]) ).
thf(108,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[107]) ).
thf(204,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)],[201,81]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ orthogonal_through_point ) @ convergent_lines ) )
!= ( C @ ( C @ convergent_lines ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( ( B @ ( A @ orthogonal_through_point ) )
!= C ) ),
inference(simp,[status(thm)],[205]) ).
thf(209,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ orthogonal_through_point ) )
!= A ),
inference(simp,[status(thm)],[207]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci4) ).
thf(112,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)],[23]) ).
thf(186,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,161]) ).
thf(187,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) ) )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[186]) ).
thf(192,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[187]) ).
thf(194,plain,
( ( sk4 != sk1 )
| ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[192]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(94,plain,
~ ? [A: $i,B: $i] : ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(miniscope,[status(thm)],[93]) ).
thf(95,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(cnf,[status(esa)],[94]) ).
thf(177,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,149]) ).
thf(178,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(180,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[178]) ).
thf(182,plain,
sk2 != sk1,
inference(simp,[status(thm)],[180]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orth1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( B @ point )
& ( A @ line ) )
=> ( B @ ( A @ orthogonal_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart5) ).
thf(82,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)],[13]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con1) ).
thf(136,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(160,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) ),
inference(eqfactor_ordered,[status(thm)],[39]) ).
thf(163,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ incident_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) )
| ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ incident_point_and_line ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ ( A @ unorthogonal_lines ) )
& ~ ( B @ ( A @ unorthogonal_lines ) ) )
=> ~ ( C @ ( B @ convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(cnfConj,[status(thm)],[87]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equal_lines ) )
| ( B @ ( A @ distinct_lines ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( B @ distinct_lines ) )
=> ( ( D @ ( C @ unorthogonal_lines ) )
| ( D @ ( B @ unorthogonal_lines ) )
| ( C @ ( A @ apart_point_and_line ) )
| ( B @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ouo1) ).
thf(100,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)],[19]) ).
thf(356,plain,
$false,
inference(e,[status(thm)],[52,70,73,43,138,88,42,37,46,93,78,211,106,121,147,280,61,133,116,60,117,85,201,53,141,109,96,129,41,161,64,149,44,118,49,181,81,76,39,98,208,103,91,108,209,112,123,194,150,95,50,182,40,114,119,82,79,195,126,136,163,62,131,47,90,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO187+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n018.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 13:05:35 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.84/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.24 % [INFO] Parsing done (241ms).
% 1.34/1.26 % [INFO] Running in sequential loop mode.
% 2.01/1.66 % [INFO] eprover registered as external prover.
% 2.01/1.67 % [INFO] Scanning for conjecture ...
% 2.22/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 35 axioms. Running axiom selection ...
% 2.38/1.85 % [INFO] Axiom selection finished. Selected 34 axioms (removed 1 axioms).
% 2.59/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.59/1.92 % [INFO] Type checking passed.
% 2.59/1.92 % [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 ...
% 7.21/3.37 % External prover 'e' found a proof!
% 7.21/3.37 % [INFO] Killing All external provers ...
% 7.21/3.37 % Time passed: 2814ms (effective reasoning time: 2103ms)
% 7.21/3.37 % 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)>
% 7.21/3.37 % Axioms used in derivation (34): par1, ouo1, ooc2, apart4, a5, ceq2, a4, ax1, oac1, orth1, ax2, occu1, con1, cp2, apart3, ooc1, ceq3, ax6, cup1, ci4, couo1, int1, apart5, coipo1, ci3, apart1, ci2, cp1, ceq1, cu1, ci1, apart2, p1, cotno1
% 7.21/3.37 % No. of inferences in proof: 147
% 7.21/3.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2814 ms resp. 2103 ms w/o parsing
% 7.24/3.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.24/3.48 % [INFO] Killing All external provers ...
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