%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n016.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 4.97s 2.88s
% Output : Refutation 5.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 37
% Syntax : Number of formulae : 76 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 828 ( 28 ~; 47 |; 69 &; 617 @)
% ( 10 <=>; 57 =>; 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 : 23 ( 22 usr; 1 con; 0-4 aty)
% Number of variables : 171 ( 0 ^; 171 !; 0 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(equally_directed_opposite_lines_decl,type,
equally_directed_opposite_lines: $i > $i > $o ).
thf(equally_directed_lines_decl,type,
equally_directed_lines: $i > $i > $o ).
thf(apart_point_and_line_decl,type,
apart_point_and_line: $i > $i > $o ).
thf(left_apart_point_decl,type,
left_apart_point: $i > $i > $o ).
thf(right_apart_point_decl,type,
right_apart_point: $i > $i > $o ).
thf(distinct_lines_decl,type,
distinct_lines: $i > $i > $o ).
thf(divides_points_decl,type,
divides_points: $i > $i > $i > $o ).
thf(reverse_line_decl,type,
reverse_line: $i > $i ).
thf(unequally_directed_lines_decl,type,
unequally_directed_lines: $i > $i > $o ).
thf(distinct_points_decl,type,
distinct_points: $i > $i > $o ).
thf(left_convergent_lines_decl,type,
left_convergent_lines: $i > $i > $o ).
thf(line_connecting_decl,type,
line_connecting: $i > $i > $i ).
thf(unequally_directed_opposite_lines_decl,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(point_decl,type,
point: $i > $o ).
thf(line_decl,type,
line: $i > $o ).
thf(parallel_through_point_decl,type,
parallel_through_point: $i > $i > $i ).
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(intersection_point_decl,type,
intersection_point: $i > $i > $i ).
thf(right_convergent_lines_decl,type,
right_convergent_lines: $i > $i > $o ).
thf(convergent_lines_decl,type,
convergent_lines: $i > $i > $o ).
thf(incident_point_and_line_decl,type,
incident_point_and_line: $i > $i > $o ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equally_directed_opposite_lines ) )
<=> ~ ( B @ ( A @ unequally_directed_opposite_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_defns) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ unequally_directed_opposite_lines ) )
=> ( B @ ( A @ equally_directed_opposite_lines ) ) )
& ( ( B @ ( A @ equally_directed_opposite_lines ) )
=> ~ ( B @ ( A @ unequally_directed_opposite_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_cons_objs) ).
thf(92,plain,
! [A: $i] :
( ( A @ line )
=> ( A @ reverse_line @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,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/sandbox/benchmark/theBenchmark.p',ax6_basics) ).
thf(96,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)],[14]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equally_directed_lines ) )
<=> ~ ( B @ ( A @ unequally_directed_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4_defns) ).
thf(180,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ unequally_directed_lines ) )
=> ( B @ ( A @ equally_directed_lines ) ) )
& ( ( B @ ( A @ equally_directed_lines ) )
=> ~ ( B @ ( A @ unequally_directed_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(30,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',ax2_basics) ).
thf(159,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)],[30]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ equally_directed_lines ) )
& ( B @ ( A @ equally_directed_opposite_lines ) ) )
=> ( C @ ( B @ equally_directed_opposite_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ equally_directed_lines ) )
& ( B @ ( A @ equally_directed_opposite_lines ) ) )
=> ( C @ ( B @ equally_directed_opposite_lines ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(39,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ equally_directed_lines ) )
& ( B @ ( A @ equally_directed_opposite_lines ) ) )
=> ( C @ ( B @ equally_directed_opposite_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,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/sandbox/benchmark/theBenchmark.p',ax3_subs) ).
thf(135,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)],[24]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',ax1_uniq_cons) ).
thf(162,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)],[31]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ convergent_lines ) )
<=> ( ( B @ ( A @ unequally_directed_opposite_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7_defns) ).
thf(150,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ unequally_directed_opposite_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) )
=> ( B @ ( A @ convergent_lines ) ) )
& ( ( B @ ( A @ convergent_lines ) )
=> ( ( B @ ( A @ unequally_directed_opposite_lines ) )
& ( B @ ( A @ unequally_directed_lines ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(22,axiom,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
| ( B @ ( A @ left_convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax11_basics) ).
thf(127,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)],[22]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',ax5_cons_objs) ).
thf(99,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)],[15]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',ax6_cons_objs) ).
thf(146,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)],[27]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ equally_directed_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_cons_objs) ).
thf(178,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ parallel_through_point ) @ equally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( ( B @ reverse_line @ ( A @ left_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax10_basics) ).
thf(69,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)],[7]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
| ( B @ ( A @ unequally_directed_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_basics) ).
thf(138,plain,
! [A: $i,B: $i] :
( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
| ( B @ ( A @ unequally_directed_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(4,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_basics) ).
thf(52,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,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/sandbox/benchmark/theBenchmark.p',ax2_subs) ).
thf(157,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)],[29]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ right_apart_point ) )
<=> ( B @ reverse_line @ ( A @ left_apart_point ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_defns) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ left_apart_point ) )
=> ( B @ ( A @ right_apart_point ) ) )
& ( ( B @ ( A @ right_apart_point ) )
=> ( B @ reverse_line @ ( A @ left_apart_point ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,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/sandbox/benchmark/theBenchmark.p',ax9_basics) ).
thf(106,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)],[17]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unequally_directed_opposite_lines ) )
<=> ( B @ reverse_line @ ( A @ unequally_directed_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_defns) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ unequally_directed_lines ) )
=> ( B @ ( A @ unequally_directed_opposite_lines ) ) )
& ( ( B @ ( A @ unequally_directed_opposite_lines ) )
=> ( B @ reverse_line @ ( A @ unequally_directed_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',ax2_cons_objs) ).
thf(133,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)],[23]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',a9_defns) ).
thf(116,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)],[21]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ equally_directed_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax9_cons_objs) ).
thf(176,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ distinct_points ) )
=> ( A @ ( B @ line_connecting ) @ reverse_line @ ( B @ ( A @ line_connecting ) @ equally_directed_lines ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ apart_point_and_line ) )
<=> ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_defns) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) )
=> ( B @ ( A @ apart_point_and_line ) ) )
& ( ( B @ ( A @ apart_point_and_line ) )
=> ( ( B @ ( A @ right_apart_point ) )
| ( B @ ( A @ left_apart_point ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_basics) ).
thf(103,plain,
! [A: $i] :
~ ( A @ ( A @ distinct_points ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ right_convergent_lines ) )
<=> ( B @ reverse_line @ ( A @ left_convergent_lines ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_defns) ).
thf(140,plain,
! [A: $i,B: $i] :
( ( ( B @ reverse_line @ ( A @ left_convergent_lines ) )
=> ( B @ ( A @ right_convergent_lines ) ) )
& ( ( B @ ( A @ right_convergent_lines ) )
=> ( B @ reverse_line @ ( A @ left_convergent_lines ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax8_cons_objs) ).
thf(108,plain,
! [A: $i] :
~ ( A @ reverse_line @ ( A @ distinct_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ before_on_line ) ) )
<=> ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_defns) ).
thf(186,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) )
=> ( C @ ( B @ ( A @ before_on_line ) ) ) )
& ( ( C @ ( B @ ( A @ before_on_line ) ) )
=> ( ( C @ ( B @ line_connecting ) @ ( A @ equally_directed_lines ) )
& ( A @ ( C @ incident_point_and_line ) )
& ( A @ ( B @ incident_point_and_line ) )
& ( C @ ( B @ distinct_points ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5,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',ax4_basics) ).
thf(55,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)],[5]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ distinct_points ) )
& ( B @ point )
& ( A @ point ) )
=> ( B @ ( A @ line_connecting ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_cons_objs) ).
thf(114,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)],[20]) ).
thf(8,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/sandbox/benchmark/theBenchmark.p',ax7_basics) ).
thf(75,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)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ ( C @ divides_points ) ) )
<=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_defns) ).
thf(58,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) )
=> ( B @ ( A @ ( C @ divides_points ) ) ) )
& ( ( B @ ( A @ ( C @ divides_points ) ) )
=> ( ( ( C @ ( B @ left_apart_point ) )
& ( C @ ( A @ right_apart_point ) ) )
| ( ( C @ ( B @ right_apart_point ) )
& ( C @ ( A @ left_apart_point ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,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/sandbox/benchmark/theBenchmark.p',ax2_uniq_cons) ).
thf(82,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)],[9]) ).
thf(38,axiom,
! [A: $i] : ( A @ ( A @ equally_directed_lines ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5_basics) ).
thf(195,plain,
! [A: $i] : ( A @ ( A @ equally_directed_lines ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ left_apart_point ) )
=> ( ( C @ ( B @ left_apart_point ) )
| ( B @ ( A @ distinct_points ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1_subs) ).
thf(94,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)],[13]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( A @ line )
& ( B @ point ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_cons_objs) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( ( A @ line )
& ( B @ point ) )
=> ( B @ ( A @ parallel_through_point ) @ line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7_cons_objs) ).
thf(111,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ parallel_through_point ) @ ( A @ apart_point_and_line ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(197,plain,
$false,
inference(e,[status(thm)],[170,92,96,180,159,39,135,162,150,127,99,146,178,69,138,52,157,164,106,84,133,116,176,44,103,140,108,186,55,114,75,58,82,195,94,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO231+3 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.14/0.41 % Computer : n016.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 13:13:59 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.22 % [INFO] Parsing done (230ms).
% 1.42/1.24 % [INFO] Running in sequential loop mode.
% 2.07/1.64 % [INFO] eprover registered as external prover.
% 2.07/1.65 % [INFO] Scanning for conjecture ...
% 2.29/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 36 axioms. Running axiom selection ...
% 2.46/1.84 % [INFO] Axiom selection finished. Selected 36 axioms (removed 0 axioms).
% 2.69/1.91 % [INFO] Problem is first-order (TPTP FOF).
% 2.69/1.92 % [INFO] Type checking passed.
% 2.69/1.93 % [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 ...
% 4.97/2.88 % External prover 'e' found a proof!
% 4.97/2.88 % [INFO] Killing All external provers ...
% 4.97/2.88 % Time passed: 2329ms (effective reasoning time: 1635ms)
% 4.97/2.88 % 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)>
% 4.97/2.88 % Axioms used in derivation (36): ax3_basics, a3_defns, ax4_cons_objs, ax10_cons_objs, ax8_cons_objs, ax2_basics, ax10_basics, a8_defns, a9_defns, a4_defns, ax6_basics, a1_defns, a7_defns, ax2_uniq_cons, ax7_cons_objs, ax2_subs, ax1_subs, ax11_basics, ax2_cons_objs, ax6_cons_objs, a5_defns, ax1_cons_objs, ax3_subs, ax3_cons_objs, ax8_basics, a2_defns, ax9_basics, ax7_basics, ax4_defns, ax4_basics, ax5_basics, a6_defns, ax9_cons_objs, ax1_basics, ax1_uniq_cons, ax5_cons_objs
% 4.97/2.88 % No. of inferences in proof: 76
% 4.97/2.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2329 ms resp. 1635 ms w/o parsing
% 5.38/2.98 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.38/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------