%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO232+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 07:12:55 AM UTC 2026
% Result : Theorem 5.45s 3.27s
% Output : Refutation 5.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 32
% Syntax : Number of formulae : 66 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 234 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 777 ( 37 ~; 53 |; 63 &; 572 @)
% ( 5 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 16 usr; 1 con; 0-4 aty)
% Number of variables : 145 ( 0 ^; 145 !; 0 ?; 145 :)
% Comments :
%------------------------------------------------------------------------------
thf(line_decl,type,
line: $i > $o ).
thf(unequally_directed_lines_decl,type,
unequally_directed_lines: $i > $i > $o ).
thf(reverse_line_decl,type,
reverse_line: $i > $i ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(between_on_line_decl,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(before_on_line_decl,type,
before_on_line: $i > $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(left_apart_point_decl,type,
left_apart_point: $i > $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
thf(left_convergent_lines_decl,type,
left_convergent_lines: $i > $i > $o ).
thf(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(divides_points_decl,type,
divides_points: $i > $i > $i > $o ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_lines ) )
=> ( ( C @ ( B @ distinct_lines ) )
| ( C @ ( A @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag4) ).
thf(69,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)],[11]) ).
thf(6,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag1) ).
thf(56,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco5) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ~ ( B @ ( A @ line_connecting ) @ ( B @ apart_point_and_line ) )
& ~ ( B @ ( A @ line_connecting ) @ ( A @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ left_convergent_lines ) )
=> ( ( C @ ( A @ left_convergent_lines ) )
| ( C @ ( B @ unequally_directed_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagsub3) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ left_convergent_lines ) )
=> ( ( C @ ( A @ left_convergent_lines ) )
| ( C @ ( B @ unequally_directed_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( ( C @ ( B @ distinct_points ) )
| ( C @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag2) ).
thf(38,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)],[3]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ apart_point_and_line ) )
<=> ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apt_def) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) )
=> ( B @ ( A @ apart_point_and_line ) ) )
& ( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag3) ).
thf(59,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ unequally_directed_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco9) ).
thf(81,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ unequally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ reverse_line @ ( B @ left_apart_point ) )
| ( D @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ reverse_line @ ( B @ left_apart_point ) )
| ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( D @ ( B @ left_apart_point ) )
| ( D @ ( A @ left_apart_point ) )
| ( C @ ( B @ left_apart_point ) )
| ( C @ ( A @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oaguc1) ).
thf(150,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ distinct_lines ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( D @ reverse_line @ ( B @ left_apart_point ) )
| ( D @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ reverse_line @ ( B @ left_apart_point ) )
| ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( D @ ( B @ left_apart_point ) )
| ( D @ ( A @ left_apart_point ) )
| ( C @ ( B @ left_apart_point ) )
| ( C @ ( A @ left_apart_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ left_apart_point ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( B @ ( A @ line_connecting ) @ left_convergent_lines ) )
| ( C @ ( B @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oaguc2) ).
thf(67,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ left_apart_point ) )
& ( B @ ( A @ distinct_points ) ) )
=> ( ( C @ ( B @ ( A @ line_connecting ) @ left_convergent_lines ) )
| ( C @ ( B @ left_apart_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco4) ).
thf(146,plain,
! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ left_apart_point ) )
=> ( ( C @ ( B @ left_apart_point ) )
| ( B @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagsub1) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ left_apart_point ) )
=> ( ( C @ ( B @ left_apart_point ) )
| ( B @ ( A @ distinct_points ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ unequally_directed_lines ) )
& ( B @ ( A @ left_apart_point ) ) )
=> ( ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagsub2) ).
thf(152,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ unequally_directed_lines ) )
& ( B @ ( A @ left_apart_point ) ) )
=> ( ( C @ reverse_line @ ( A @ left_apart_point ) )
| ( C @ ( B @ distinct_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ unequally_directed_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco10) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ parallel_through_point ) @ unequally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ line )
& ( A @ line ) )
=> ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
| ( B @ ( A @ unequally_directed_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag8) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ( B @ line )
& ( A @ line ) )
=> ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
| ( B @ ( A @ unequally_directed_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ( ( C @ reverse_line @ ( B @ unequally_directed_lines ) )
& ( C @ ( B @ unequally_directed_lines ) ) )
| ( ( C @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( C @ ( A @ unequally_directed_lines ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag7) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ( ( C @ reverse_line @ ( B @ unequally_directed_lines ) )
& ( C @ ( B @ unequally_directed_lines ) ) )
| ( ( C @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( C @ ( A @ unequally_directed_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ( A @ line )
& ( B @ point ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco3) ).
thf(132,plain,
! [A: $i,B: $i] :
( ( ( A @ line )
& ( B @ point ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
& ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco6) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ~ ( B @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) )
& ~ ( A @ ( B @ ( A @ intersection_point ) @ apart_point_and_line ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,axiom,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco8) ).
thf(129,plain,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
<=> ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bet_def) ).
thf(41,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ between_on_line ) ) ) )
=> ( ( ( B @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( D @ ( A @ before_on_line ) ) ) )
| ( ( D @ ( C @ ( A @ before_on_line ) ) )
& ( C @ ( B @ ( A @ before_on_line ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,axiom,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
| ( B @ ( A @ left_convergent_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
thf(134,plain,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
| ( B @ ( A @ left_convergent_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ unequally_directed_lines ) )
=> ( ( C @ ( B @ unequally_directed_lines ) )
| ( C @ ( A @ unequally_directed_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag6) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ unequally_directed_lines ) )
=> ( ( C @ ( B @ unequally_directed_lines ) )
| ( C @ ( A @ unequally_directed_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ ( A @ unequally_directed_lines ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ ( A @ unequally_directed_lines ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(34,plain,
~ ! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ ( A @ unequally_directed_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco2) ).
thf(148,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) )
& ( B @ line )
& ( A @ line ) )
=> ( B @ ( A @ intersection_point ) @ point ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco7) ).
thf(64,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(26,axiom,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag10) ).
thf(140,plain,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ before_on_line ) ) )
<=> ( ~ ( C @ ( B @ line_connecting ) @ ( A @ unequally_directed_lines ) )
& ~ ( ( A @ reverse_line @ ( C @ left_apart_point ) )
| ( A @ ( C @ left_apart_point ) ) )
& ~ ( ( A @ reverse_line @ ( B @ left_apart_point ) )
| ( A @ ( B @ left_apart_point ) ) )
& ( C @ ( B @ distinct_points ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bf_def) ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( C @ ( B @ line_connecting ) @ ( A @ unequally_directed_lines ) )
& ~ ( ( A @ reverse_line @ ( C @ left_apart_point ) )
| ( A @ ( C @ left_apart_point ) ) )
& ~ ( ( A @ reverse_line @ ( B @ left_apart_point ) )
| ( A @ ( B @ left_apart_point ) ) )
& ( C @ ( B @ distinct_points ) ) )
=> ( C @ ( B @ ( A @ before_on_line ) ) ) )
& ( ( C @ ( B @ ( A @ before_on_line ) ) )
=> ( ~ ( C @ ( B @ line_connecting ) @ ( A @ unequally_directed_lines ) )
& ~ ( ( A @ reverse_line @ ( C @ left_apart_point ) )
| ( A @ ( C @ left_apart_point ) ) )
& ~ ( ( A @ reverse_line @ ( B @ left_apart_point ) )
| ( A @ ( B @ left_apart_point ) ) )
& ( C @ ( B @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] :
~ ( A @ ( A @ unequally_directed_lines ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag5) ).
thf(108,plain,
! [A: $i] :
~ ( A @ ( A @ unequally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco1) ).
thf(154,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
| ( B @ ( A @ left_convergent_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag9) ).
thf(72,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
| ( B @ ( A @ left_convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ divides_points ) ) )
<=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ reverse_line @ ( A @ left_apart_point ) ) )
| ( ( C @ reverse_line @ ( B @ left_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',div_def) ).
thf(111,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ reverse_line @ ( A @ left_apart_point ) ) )
| ( ( C @ reverse_line @ ( B @ left_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) )
=> ( B @ ( A @ ( C @ divides_points ) ) ) )
& ( ( B @ ( A @ ( C @ divides_points ) ) )
=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ reverse_line @ ( A @ left_apart_point ) ) )
| ( ( C @ reverse_line @ ( B @ left_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
<=> ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con_def) ).
thf(122,plain,
! [A: $i,B: $i] :
( ( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( B @ ( A @ convergent_lines ) ) )
& ( ( B @ ( A @ convergent_lines ) )
=> ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(166,plain,
$false,
inference(e,[status(thm)],[69,56,52,102,38,156,59,81,150,67,146,62,152,78,164,84,132,74,129,41,134,105,34,148,64,140,91,108,154,72,111,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO232+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n015.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Fri Sep 25 13:12:12 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.34/1.21 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.88/1.54 % [INFO] Parsing done (330ms).
% 1.88/1.56 % [INFO] Running in sequential loop mode.
% 2.81/2.11 % [INFO] eprover registered as external prover.
% 2.81/2.12 % [INFO] Scanning for conjecture ...
% 3.10/2.21 % [INFO] Found a conjecture (or negated_conjecture) and 31 axioms. Running axiom selection ...
% 3.10/2.28 % [INFO] Axiom selection finished. Selected 31 axioms (removed 0 axioms).
% 3.27/2.35 % [INFO] Problem is first-order (TPTP FOF).
% 3.27/2.36 % [INFO] Type checking passed.
% 3.27/2.37 % [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 ...
% 5.45/3.27 % External prover 'e' found a proof!
% 5.45/3.27 % [INFO] Killing All external provers ...
% 5.45/3.27 % Time passed: 2722ms (effective reasoning time: 1693ms)
% 5.45/3.27 % 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)>
% 5.45/3.27 % Axioms used in derivation (31): oag11, oag9, oagsub1, oag7, oagco1, div_def, oag5, bet_def, oag10, oag3, oagco10, oagco2, oagco8, oag8, oagco5, oagco7, oaguc2, oag4, oagco4, oag1, oaguc1, oagsub2, oag6, oagco6, apt_def, oagco9, con_def, oag2, oagco3, bf_def, oagsub3
% 5.45/3.27 % No. of inferences in proof: 66
% 5.45/3.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2722 ms resp. 1693 ms w/o parsing
% 5.74/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.74/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------