%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO177+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 07:12:33 AM UTC 2026
% Result : Theorem 21.56s 10.36s
% Output : Refutation 18.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 130 ( 34 unt; 0 typ; 4 def)
% Number of atoms : 415 ( 74 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1190 ( 149 ~; 149 |; 13 &; 840 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 201 ( 0 ^; 194 !; 3 ?; 201 :)
% ( 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 @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( A @ ( sk1 @ distinct_points ) ) )
=> ( ( ( C @ ( B @ line_connecting ) @ ( A @ apart_point_and_line ) )
| ( C @ ( B @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ( ( B @ ( A @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
| ( B @ ( A @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( sk2 @ ( sk1 @ distinct_points ) ) )
=> ( ( ( A @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
| ( A @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) ) )
=> ( ( 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 @ distinct_points ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( ( D @ ( C @ line_connecting ) @ ( B @ apart_point_and_line ) )
| ( D @ ( C @ line_connecting ) @ ( A @ apart_point_and_line ) ) )
=> ( ( 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(23,plain,
sk2 @ ( sk1 @ 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(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(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(333,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( B @ ( A @ distinct_points ) )
!= ( A @ ( sk1 @ distinct_points ) ) )
| ( B @ ( sk2 @ distinct_points ) )
| ( A @ ( sk1 @ distinct_points ) ) ),
inference(eqfactor_ordered,[status(thm)],[201]) ).
thf(335,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| ( sk1 @ ( sk1 @ distinct_points ) ) ),
inference(pattern_uni,[status(thm)],[333:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 ))]]) ).
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(345,plain,
( ( sk1 @ ( sk2 @ distinct_points ) )
| $false ),
inference(rewrite,[status(thm)],[335,26]) ).
thf(346,plain,
sk1 @ ( sk2 @ distinct_points ),
inference(simp,[status(thm)],[345]) ).
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(350,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)],[346,43]) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[350]) ).
thf(352,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[351:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(19,plain,
( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
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(97,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ) )
| ~ $true
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(paramod_ordered,[status(thm)],[19,89]) ).
thf(98,plain,
( ( ( sk4 @ ( sk3 @ 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 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk4 @ ( sk3 @ line_connecting ) ) )
| ( sk3 != sk2 )
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
( ( sk3 != sk2 )
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(136,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[100,89]) ).
thf(137,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[136]) ).
thf(148,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk4 @ ( sk3 @ line_connecting ) ) )
| ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[137]) ).
thf(153,plain,
( ( sk3 != sk1 )
| ( sk3 != sk2 ) ),
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(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(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(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(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(20,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) ),
inference(cnfConj,[status(thm)],[18]) ).
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(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(364,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(365,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk3 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[364]) ).
thf(366,plain,
~ ( sk4 @ ( sk3 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[365:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).
thf(423,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[100,366]) ).
thf(424,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk4 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[423]) ).
thf(426,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk4 @ ( sk3 @ line_connecting ) ) )
| ( sk4 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[424]) ).
thf(428,plain,
( ( sk4 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[426]) ).
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(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,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk3 @ apart_point_and_line ) ),
inference(cnfConj,[status(thm)],[18]) ).
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(404,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(405,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[404]) ).
thf(406,plain,
~ ( sk2 @ ( sk1 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(73,plain,
( ~ $true
| ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(76,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk2 @ apart_point_and_line ) )
!= ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[73]) ).
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(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(143,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[100,94]) ).
thf(144,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) )
!= ( sk2 @ ( sk1 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[143]) ).
thf(149,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk1 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[144]) ).
thf(154,plain,
( ( ( sk4 @ ( sk3 @ line_connecting ) )
!= ( sk2 @ ( sk1 @ line_connecting ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[149]) ).
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(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(367,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)],[346,45]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ distinct_points ) )
!= ( B @ ( A @ distinct_points ) ) )
| ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(369,plain,
~ ( sk1 @ ( sk2 @ line_connecting ) @ ( sk1 @ apart_point_and_line ) ),
inference(pattern_uni,[status(thm)],[368:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(4923,plain,
$false,
inference(e,[status(thm)],[352,153,52,224,41,48,100,42,24,20,46,29,428,89,133,248,201,366,38,21,33,32,45,17,22,44,27,406,76,39,135,35,50,67,154,43,26,186,55,23,58,346,36,30,19,242,94,68,369]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO177+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % 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
% 0.13/5.40 % Computer : n006.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.17/5.40 % CPULimit : 300
% 0.17/5.40 % WCLimit : 300
% 0.17/5.40 % DateTime : Fri Sep 25 13:01:33 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.17/5.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/6.19 % [INFO] Parsing done (200ms).
% 1.48/6.20 % [INFO] Running in sequential loop mode.
% 2.19/6.61 % [INFO] eprover registered as external prover.
% 2.19/6.62 % [INFO] Scanning for conjecture ...
% 2.38/6.72 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.38/6.76 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.38/6.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.60/6.80 % [INFO] Type checking passed.
% 2.60/6.80 % [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 ...
% 21.56/10.35 % External prover 'e' found a proof!
% 21.56/10.35 % [INFO] Killing All external provers ...
% 21.56/10.36 % Time passed: 4813ms (effective reasoning time: 4147ms)
% 21.56/10.36 % 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)>
% 21.56/10.36 % Axioms used in derivation (14): apart3, apart4, ci4, ceq2, apart5, ceq3, ax6, ci3, apart1, ci2, ceq1, cu1, ci1, apart2
% 21.56/10.36 % No. of inferences in proof: 126
% 21.56/10.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4813 ms resp. 4147 ms w/o parsing
% 18.98/10.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.98/10.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------