%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO187+1 : 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 : 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 07:12:37 AM UTC 2026
% Result : Theorem 43.13s 9.42s
% Output : Refutation 36.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 133 ( 35 unt; 0 typ; 4 def)
% Number of atoms : 425 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1247 ( 183 ~; 138 |; 34 &; 860 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 205 ( 0 ^; 198 !; 3 ?; 205 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
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 @ apart_point_and_line ) )
& ~ ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ~ ( C @ ( B @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ~ ( C @ ( B @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
& ( C @ ( B @ distinct_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ( ~ ( A @ ( sk1 @ line_connecting ) @ ( C @ apart_point_and_line ) )
& ~ ( A @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ~ ( B @ ( A @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
& ( B @ ( A @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ~ ( A @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
& ~ ( A @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
& ( A @ ( sk3 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) )
& ( D @ ( C @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( D @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( C @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) )
& ~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
& ~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
& ( sk4 @ ( sk3 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(20,plain,
( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(23,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[18]) ).
thf(9,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(42,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)],[9]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,43]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(94,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(100,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[20,94]) ).
thf(101,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk4 != sk1 )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( sk4 != sk1 )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(22,plain,
sk4 @ ( sk3 @ distinct_points ),
inference(cnfConj,[status(thm)],[18]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,43]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(136,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[103,89]) ).
thf(137,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[136]) ).
thf(148,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk3 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[137]) ).
thf(153,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[148]) ).
thf(14,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(52,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)],[14]) ).
thf(6,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(33,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,35]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
! [A: $i] :
( ( A @ ( sk4 @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(133,plain,
! [A: $i] :
( ( A @ ( sk4 @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[133,35]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk4 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk4 @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( A ))]]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk4 @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(24,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(25,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(26,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[25]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk4 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ~ $true
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[186,26]) ).
thf(223,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( sk4 @ distinct_points ) )
!= ( C @ ( C @ distinct_points ) ) )
| ( B @ ( A @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [A: $i] :
( ( sk4 @ ( A @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( sk4 )),bind(C,$thf( sk4 ))]]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,35]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(127,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[127]) ).
thf(188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[135,35]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ( D @ ( C @ distinct_points ) )
| ( D @ ( B @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(190,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ distinct_points ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[190]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[201]) ).
thf(337,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[332:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(344,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[337,26]) ).
thf(345,plain,
sk1 @ ( sk2 @ distinct_points ),
inference(simp,[status(thm)],[344]) ).
thf(10,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(44,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)],[10]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,45]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(388,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[387:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(16,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(58,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)],[16]) ).
thf(63,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,26]) ).
thf(64,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(66,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[64]) ).
thf(68,plain,
sk2 != sk1,
inference(simp,[status(thm)],[66]) ).
thf(11,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(46,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)],[11]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(27,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[27]) ).
thf(29,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[28]) ).
thf(409,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,45]) ).
thf(410,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[409]) ).
thf(411,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[410:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(229,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk3 @ distinct_points ) ) )
| ( B @ ( sk4 @ distinct_points ) )
| ( A @ ( sk3 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[186]) ).
thf(233,plain,
( ( sk3 @ ( sk4 @ distinct_points ) )
| ( sk3 @ ( sk3 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(241,plain,
( ( sk3 @ ( sk4 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[233,26]) ).
thf(242,plain,
sk3 @ ( sk4 @ distinct_points ),
inference(simp,[status(thm)],[241]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,43]) ).
thf(247,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(248,plain,
~ ( sk3 @ ( sk4 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(434,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[103,411]) ).
thf(435,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[434]) ).
thf(437,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[435]) ).
thf(439,plain,
( ( sk3 != sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[437]) ).
thf(7,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(36,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(21,plain,
~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(8,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(39,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,45]) ).
thf(370,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(371,plain,
~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[370:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(30,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[30]) ).
thf(32,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[31]) ).
thf(73,plain,
( ~ $true
| ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(eqfactor_ordered,[status(thm)],[20]) ).
thf(76,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) )
| ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(12,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(48,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)],[12]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,45]) ).
thf(413,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk4 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(414,plain,
~ ( sk3 @ ( sk4 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[413:[bind(A,$thf( sk4 )),bind(B,$thf( sk3 ))]]) ).
thf(13,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(50,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)],[13]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,26]) ).
thf(62,plain,
! [A: $i] :
( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(65,plain,
! [A: $i] :
( ( sk4 != A )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[62]) ).
thf(67,plain,
sk4 != sk3,
inference(simp,[status(thm)],[65]) ).
thf(145,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[103,94]) ).
thf(146,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[145]) ).
thf(151,plain,
( ( ( sk2 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk1 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[146]) ).
thf(154,plain,
( ( sk3 != sk1 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[151]) ).
thf(349,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[345,43]) ).
thf(350,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(351,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[350:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
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(55,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(19,plain,
~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(8857,plain,
$false,
inference(e,[status(thm)],[153,52,224,388,58,68,42,24,20,46,29,411,89,133,248,439,201,38,21,33,41,371,32,45,17,22,44,27,76,39,345,103,135,35,48,414,50,67,154,43,26,351,186,55,23,36,30,19,242,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO187+1 : 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 : n003.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 13:05:08 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.86/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (201ms).
% 1.48/1.20 % [INFO] Running in sequential loop mode.
% 1.97/1.59 % [INFO] eprover registered as external prover.
% 2.19/1.60 % [INFO] Scanning for conjecture ...
% 2.38/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.38/1.74 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.38/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.38/1.78 % [INFO] Type checking passed.
% 2.38/1.78 % [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 ...
% 43.13/9.41 % External prover 'e' found a proof!
% 43.13/9.42 % [INFO] Killing All external provers ...
% 43.13/9.42 % Time passed: 8868ms (effective reasoning time: 8213ms)
% 43.13/9.42 % 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)>
% 43.13/9.42 % Axioms used in derivation (14): apart3, apart4, ci4, ceq2, apart5, ceq3, ax6, ci3, apart1, ci2, ceq1, cu1, ci1, apart2
% 43.13/9.42 % No. of inferences in proof: 129
% 43.13/9.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8868 ms resp. 8213 ms w/o parsing
% 36.62/9.55 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.62/9.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------