%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO202+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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:12:44 AM UTC 2026
% Result : Theorem 14.43s 11.32s
% Output : Refutation 13.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 128 ( 39 unt; 0 typ; 3 def)
% Number of atoms : 378 ( 60 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1279 ( 154 ~; 115 |; 17 &; 962 @)
% ( 0 <=>; 31 =>; 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 : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 216 ( 0 ^; 210 !; 3 ?; 216 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( B @ ( sk1 @ line_connecting ) @ ( A @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( B @ ( sk1 @ distinct_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ~ ( sk1 @ ( B @ ( sk1 @ line_connecting ) @ ( A @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( A @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( A @ ( sk1 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ~ ( sk1 @ ( A @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ convergent_lines ) )
& ( C @ ( A @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ~ ( A @ ( C @ ( A @ line_connecting ) @ ( B @ ( A @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
& ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
& ( sk3 @ ( sk1 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(22,plain,
sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ),
inference(cnfConj,[status(thm)],[18]) ).
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(32,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(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
inference(miniscope,[status(thm)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,34]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(116,plain,
! [A: $i] :
( ( A @ ( sk1 @ distinct_points ) )
| ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(3,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).
thf(23,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_points ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(cnf,[status(esa)],[24]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[116,25]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( B @ distinct_points ) ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(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(43,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(44,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[198,44]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
thf(21,plain,
sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ),
inference(cnfConj,[status(thm)],[18]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(29,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
~ ? [A: $i] : ( A @ ( A @ convergent_lines ) ),
inference(miniscope,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
~ ( A @ ( A @ convergent_lines ) ),
inference(cnf,[status(esa)],[30]) ).
thf(72,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,31]) ).
thf(73,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( A @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) )
!= A )
| ( ( sk2 @ ( sk1 @ line_connecting ) )
!= A ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
( ( sk3 @ ( sk1 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
( ( sk3 != sk2 )
| ( sk1 != sk1 ) ),
inference(simp,[status(thm)],[75]) ).
thf(77,plain,
sk3 != sk2,
inference(simp,[status(thm)],[76]) ).
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(41,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(19,plain,
sk2 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[18]) ).
thf(99,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)],[19,34]) ).
thf(100,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)],[99]) ).
thf(101,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(118,plain,
! [A: $i] :
( ( A @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ ( B @ ( A @ distinct_points ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[118,42]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
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(45,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(46,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,46]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(245,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[244:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) ))]]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[198,42]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(209,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) ))]]) ).
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(38,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(39,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ) ),
inference(miniscope,[status(thm)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ ( B @ ( A @ convergent_lines ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,40]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
!= ( B @ ( A @ convergent_lines ) ) )
| ( C @ ( B @ convergent_lines ) )
| ( C @ ( A @ convergent_lines ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( sk2 @ ( sk1 @ line_connecting ) )),bind(B,$thf( sk3 @ ( sk1 @ line_connecting ) )),bind(C,$thf( C ))]]) ).
thf(242,plain,
! [A: $i] :
( ( A @ ( sk3 @ ( sk1 @ line_connecting ) @ convergent_lines ) )
| ( A @ ( sk2 @ ( sk1 @ line_connecting ) @ convergent_lines ) ) ),
inference(simp,[status(thm)],[223]) ).
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(47,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(81,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,42]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[82:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
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(35,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(36,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ! [C: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
inference(miniscope,[status(thm)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) )
| ~ ( B @ ( A @ distinct_lines ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(20,plain,
sk3 @ ( sk1 @ distinct_points ),
inference(cnfConj,[status(thm)],[18]) ).
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(57,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(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,34]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(89,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(119,plain,
! [A: $i] :
( ( A @ ( sk3 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[119,42]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk3 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(160,plain,
! [A: $i] :
( ~ ( A @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[159:[bind(A,$thf( A )),bind(B,$thf( sk3 )),bind(C,$thf( A ))]]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).
thf(26,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
~ ? [A: $i] : ( A @ ( A @ distinct_lines ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(cnf,[status(esa)],[27]) ).
thf(178,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)],[19,44]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(180,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(68,plain,
! [A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,25]) ).
thf(69,plain,
! [A: $i] :
( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( sk1 != A )
| ( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= A ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
( ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )
!= sk1 ),
inference(simp,[status(thm)],[70]) ).
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(54,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(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(49,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(84,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)],[19,42]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(86,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(60,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,25]) ).
thf(61,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(64,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[61]) ).
thf(66,plain,
sk2 != sk1,
inference(simp,[status(thm)],[64]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,42]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[79:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
thf(62,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,25]) ).
thf(63,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( A @ ( A @ distinct_points ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(65,plain,
! [A: $i] :
( ( sk3 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[63]) ).
thf(67,plain,
sk3 != sk1,
inference(simp,[status(thm)],[65]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ~ $true
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(paramod_ordered,[status(thm)],[118,44]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk2 @ distinct_points ) )
!= ( C @ ( B @ distinct_points ) ) )
| ~ ( C @ ( B @ line_connecting ) @ ( C @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
! [A: $i] :
( ~ ( A @ ( sk2 @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,44]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(171,plain,
~ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 ))]]) ).
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(51,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(181,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,44]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(183,plain,
~ ( sk1 @ ( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( sk3 @ ( sk1 @ line_connecting ) @ ( sk2 @ ( sk1 @ line_connecting ) @ intersection_point ) )),bind(B,$thf( sk1 ))]]) ).
thf(1566,plain,
$false,
inference(e,[status(thm)],[217,116,77,41,128,245,209,43,242,47,83,42,37,25,20,46,57,29,160,21,28,38,45,180,17,32,34,22,44,118,71,54,49,86,66,198,80,35,67,31,40,26,186,171,23,75,119,51,183,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO202+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
% 0.15/5.54 % Computer : n006.cluster.edu
% 0.15/5.54 % Model : x86_64 x86_64
% 0.15/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.54 % Memory : 8046.5625MB
% 0.15/5.54 % OS : Linux 6.8.0-71-generic
% 0.15/5.55 % CPULimit : 300
% 0.15/5.55 % WCLimit : 300
% 0.15/5.55 % DateTime : Fri Sep 25 13:04:51 UTC 2026
% 0.15/5.55 % CPUTime :
% 0.15/5.55 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.03/6.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/6.35 % [INFO] Parsing done (208ms).
% 1.33/6.36 % [INFO] Running in sequential loop mode.
% 2.22/6.81 % [INFO] eprover registered as external prover.
% 2.22/6.83 % [INFO] Scanning for conjecture ...
% 2.35/6.96 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.35/7.02 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.56/7.07 % [INFO] Problem is first-order (TPTP FOF).
% 2.56/7.07 % [INFO] Type checking passed.
% 2.56/7.08 % [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 ...
% 14.43/11.32 % External prover 'e' found a proof!
% 14.43/11.32 % [INFO] Killing All external provers ...
% 14.43/11.32 % Time passed: 5628ms (effective reasoning time: 4950ms)
% 14.43/11.32 % 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)>
% 14.43/11.32 % Axioms used in derivation (14): apart3, apart4, ci4, ceq2, apart5, ceq3, ax6, ci3, apart1, ci2, ceq1, cu1, ci1, apart2
% 14.43/11.32 % No. of inferences in proof: 125
% 14.43/11.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5628 ms resp. 4950 ms w/o parsing
% 13.03/11.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.03/11.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------