TSTP Solution File: GEO257+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO257+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:10:15 EDT 2023
% Result : Theorem 4.00s 1.90s
% Output : Refutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 59
% Syntax : Number of formulae : 98 ( 13 unt; 22 typ; 0 def)
% Number of atoms : 271 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 873 ( 28 ~; 47 |; 78 &; 650 @)
% ( 10 <=>; 60 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 22 usr; 1 con; 0-4 aty)
% Number of variables : 177 ( 0 ^; 177 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(distinct_points_type,type,
distinct_points: $i > $i > $o ).
thf(incident_point_and_line_type,type,
incident_point_and_line: $i > $i > $o ).
thf(left_apart_point_type,type,
left_apart_point: $i > $i > $o ).
thf(before_on_line_type,type,
before_on_line: $i > $i > $i > $o ).
thf(equally_directed_opposite_lines_type,type,
equally_directed_opposite_lines: $i > $i > $o ).
thf(unequally_directed_opposite_lines_type,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(point_type,type,
point: $i > $o ).
thf(line_type,type,
line: $i > $o ).
thf(parallel_through_point_type,type,
parallel_through_point: $i > $i > $i ).
thf(reverse_line_type,type,
reverse_line: $i > $i ).
thf(unequally_directed_lines_type,type,
unequally_directed_lines: $i > $i > $o ).
thf(intersection_point_type,type,
intersection_point: $i > $i > $i ).
thf(distinct_lines_type,type,
distinct_lines: $i > $i > $o ).
thf(equally_directed_lines_type,type,
equally_directed_lines: $i > $i > $o ).
thf(left_convergent_lines_type,type,
left_convergent_lines: $i > $i > $o ).
thf(apart_point_and_line_type,type,
apart_point_and_line: $i > $i > $o ).
thf(right_convergent_lines_type,type,
right_convergent_lines: $i > $i > $o ).
thf(convergent_lines_type,type,
convergent_lines: $i > $i > $o ).
thf(right_apart_point_type,type,
right_apart_point: $i > $i > $o ).
thf(line_connecting_type,type,
line_connecting: $i > $i > $i ).
thf(divides_points_type,type,
divides_points: $i > $i > $i > $o ).
thf(between_on_line_type,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( equally_directed_lines @ A @ B )
<=> ~ ( unequally_directed_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_defns) ).
thf(69,plain,
! [A: $i,B: $i] :
( ( ( equally_directed_lines @ A @ B )
=> ~ ( unequally_directed_lines @ A @ B ) )
& ( ~ ( unequally_directed_lines @ A @ B )
=> ( equally_directed_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( line @ B )
& ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( point @ ( intersection_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2_cons_objs) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( ( line @ A )
& ( line @ B )
& ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( point @ ( intersection_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( distinct_points @ A @ B )
& ( distinct_lines @ C @ D ) )
=> ( ( left_apart_point @ A @ C )
| ( left_apart_point @ B @ C )
| ( left_apart_point @ A @ D )
| ( left_apart_point @ B @ D )
| ( left_apart_point @ A @ ( reverse_line @ C ) )
| ( left_apart_point @ B @ ( reverse_line @ C ) )
| ( left_apart_point @ A @ ( reverse_line @ D ) )
| ( left_apart_point @ B @ ( reverse_line @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_uniq_cons) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( distinct_points @ A @ B )
& ( distinct_lines @ C @ D ) )
=> ( ( left_apart_point @ A @ C )
| ( left_apart_point @ B @ C )
| ( left_apart_point @ A @ D )
| ( left_apart_point @ B @ D )
| ( left_apart_point @ A @ ( reverse_line @ C ) )
| ( left_apart_point @ B @ ( reverse_line @ C ) )
| ( left_apart_point @ A @ ( reverse_line @ D ) )
| ( left_apart_point @ B @ ( reverse_line @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ( ( unequally_directed_lines @ A @ C )
& ( unequally_directed_lines @ A @ ( reverse_line @ C ) ) )
| ( ( unequally_directed_lines @ B @ C )
& ( unequally_directed_lines @ B @ ( reverse_line @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7_basics) ).
thf(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ( ( unequally_directed_lines @ A @ C )
& ( unequally_directed_lines @ A @ ( reverse_line @ C ) ) )
| ( ( unequally_directed_lines @ B @ C )
& ( unequally_directed_lines @ B @ ( reverse_line @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9_cons_objs) ).
thf(160,plain,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( equally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( distinct_points @ B @ D )
& ( distinct_points @ C @ D )
& ( incident_point_and_line @ D @ A )
& ( left_apart_point @ E @ A ) )
=> ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
=> ( before_on_line @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( distinct_points @ B @ D )
& ( distinct_points @ C @ D )
& ( incident_point_and_line @ D @ A )
& ( left_apart_point @ E @ A ) )
=> ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
=> ( before_on_line @ A @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(39,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( distinct_points @ B @ D )
& ( distinct_points @ C @ D )
& ( incident_point_and_line @ D @ A )
& ( left_apart_point @ E @ A ) )
=> ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
=> ( before_on_line @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i,B: $i] :
~ ( ( left_convergent_lines @ A @ B )
| ( left_convergent_lines @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11_basics) ).
thf(91,plain,
! [A: $i,B: $i] :
~ ( ( left_convergent_lines @ A @ B )
| ( left_convergent_lines @ A @ ( reverse_line @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i] :
~ ( distinct_lines @ A @ ( reverse_line @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_cons_objs) ).
thf(80,plain,
! [A: $i] :
~ ( distinct_lines @ A @ ( reverse_line @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( equally_directed_opposite_lines @ A @ B )
<=> ~ ( unequally_directed_opposite_lines @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5_defns) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( equally_directed_opposite_lines @ A @ B )
=> ~ ( unequally_directed_opposite_lines @ A @ B ) )
& ( ~ ( unequally_directed_opposite_lines @ A @ B )
=> ( equally_directed_opposite_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ C ) )
=> ( ( left_apart_point @ B @ C )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2_uniq_cons) ).
thf(146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( distinct_points @ A @ B )
& ( left_apart_point @ A @ C ) )
=> ( ( left_apart_point @ B @ C )
| ( left_convergent_lines @ ( line_connecting @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ( left_convergent_lines @ A @ B )
| ( left_convergent_lines @ A @ ( reverse_line @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9_basics) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ( left_convergent_lines @ A @ B )
| ( left_convergent_lines @ A @ ( reverse_line @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7_cons_objs) ).
thf(83,plain,
! [A: $i,B: $i] :
~ ( apart_point_and_line @ A @ ( parallel_through_point @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5_cons_objs) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( distinct_points @ A @ B )
=> ( ~ ( apart_point_and_line @ A @ ( line_connecting @ A @ B ) )
& ~ ( apart_point_and_line @ B @ ( line_connecting @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( apart_point_and_line @ A @ B )
<=> ( ( left_apart_point @ A @ B )
| ( right_apart_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_defns) ).
thf(120,plain,
! [A: $i,B: $i] :
( ( ( apart_point_and_line @ A @ B )
=> ( ( left_apart_point @ A @ B )
| ( right_apart_point @ A @ B ) ) )
& ( ( ( left_apart_point @ A @ B )
| ( right_apart_point @ A @ B ) )
=> ( apart_point_and_line @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( point @ B )
& ( line @ A ) )
=> ( line @ ( parallel_through_point @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_cons_objs) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( ( point @ B )
& ( line @ A ) )
=> ( line @ ( parallel_through_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
! [A: $i,B: $i] :
~ ( ( left_apart_point @ A @ B )
| ( left_apart_point @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10_basics) ).
thf(141,plain,
! [A: $i,B: $i] :
~ ( ( left_apart_point @ A @ B )
| ( left_apart_point @ A @ ( reverse_line @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ A )
& ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_cons_objs) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
=> ( ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ A )
& ~ ( apart_point_and_line @ ( intersection_point @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ A @ B )
=> ( ( distinct_lines @ A @ C )
| ( distinct_lines @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_basics) ).
thf(96,plain,
! [A: $i,B: $i,C: $i] :
( ( distinct_lines @ A @ B )
=> ( ( distinct_lines @ A @ C )
| ( distinct_lines @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
! [A: $i] :
~ ( distinct_points @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_basics) ).
thf(173,plain,
! [A: $i] :
~ ( distinct_points @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( left_apart_point @ A @ B )
& ( unequally_directed_lines @ B @ C ) )
=> ( ( distinct_lines @ B @ C )
| ( left_apart_point @ A @ ( reverse_line @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2_subs) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( left_apart_point @ A @ B )
& ( unequally_directed_lines @ B @ C ) )
=> ( ( distinct_lines @ B @ C )
| ( left_apart_point @ A @ ( reverse_line @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( between_on_line @ A @ B @ C @ D )
<=> ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
| ( ( before_on_line @ A @ D @ C )
& ( before_on_line @ A @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9_defns) ).
thf(148,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( between_on_line @ A @ B @ C @ D )
=> ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
| ( ( before_on_line @ A @ D @ C )
& ( before_on_line @ A @ C @ B ) ) ) )
& ( ( ( ( before_on_line @ A @ B @ C )
& ( before_on_line @ A @ C @ D ) )
| ( ( before_on_line @ A @ D @ C )
& ( before_on_line @ A @ C @ B ) ) )
=> ( between_on_line @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( left_convergent_lines @ A @ B )
=> ( ( unequally_directed_lines @ B @ C )
| ( left_convergent_lines @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_subs) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( left_convergent_lines @ A @ B )
=> ( ( unequally_directed_lines @ B @ C )
| ( left_convergent_lines @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2_basics) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ( distinct_points @ A @ B )
=> ( ( distinct_points @ A @ C )
| ( distinct_points @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(7,axiom,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_basics) ).
thf(59,plain,
! [A: $i] :
~ ( distinct_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( right_apart_point @ A @ B )
<=> ( left_apart_point @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_defns) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( ( right_apart_point @ A @ B )
=> ( left_apart_point @ A @ ( reverse_line @ B ) ) )
& ( ( left_apart_point @ A @ ( reverse_line @ B ) )
=> ( right_apart_point @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( unequally_directed_opposite_lines @ A @ B )
<=> ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_defns) ).
thf(86,plain,
! [A: $i,B: $i] :
( ( ( unequally_directed_opposite_lines @ A @ B )
=> ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) )
& ( ( unequally_directed_lines @ A @ ( reverse_line @ B ) )
=> ( unequally_directed_opposite_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( before_on_line @ A @ B @ C )
<=> ( ( distinct_points @ B @ C )
& ( incident_point_and_line @ B @ A )
& ( incident_point_and_line @ C @ A )
& ( equally_directed_lines @ A @ ( line_connecting @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_defns) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( before_on_line @ A @ B @ C )
=> ( ( distinct_points @ B @ C )
& ( incident_point_and_line @ B @ A )
& ( incident_point_and_line @ C @ A )
& ( equally_directed_lines @ A @ ( line_connecting @ B @ C ) ) ) )
& ( ( ( distinct_points @ B @ C )
& ( incident_point_and_line @ B @ A )
& ( incident_point_and_line @ C @ A )
& ( equally_directed_lines @ A @ ( line_connecting @ B @ C ) ) )
=> ( before_on_line @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(22,axiom,
! [A: $i] : ( equally_directed_lines @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5_basics) ).
thf(112,plain,
! [A: $i] : ( equally_directed_lines @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( unequally_directed_lines @ A @ B )
| ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8_basics) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( unequally_directed_lines @ A @ B )
| ( unequally_directed_lines @ A @ ( reverse_line @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_cons_objs) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( point @ A )
& ( point @ B )
& ( distinct_points @ A @ B ) )
=> ( line @ ( line_connecting @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( right_convergent_lines @ A @ B )
<=> ( left_convergent_lines @ A @ ( reverse_line @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_defns) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( ( right_convergent_lines @ A @ B )
=> ( left_convergent_lines @ A @ ( reverse_line @ B ) ) )
& ( ( left_convergent_lines @ A @ ( reverse_line @ B ) )
=> ( right_convergent_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( unequally_directed_lines @ A @ B )
=> ( ( unequally_directed_lines @ A @ C )
| ( unequally_directed_lines @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6_basics) ).
thf(104,plain,
! [A: $i,B: $i,C: $i] :
( ( unequally_directed_lines @ A @ B )
=> ( ( unequally_directed_lines @ A @ C )
| ( unequally_directed_lines @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( left_apart_point @ A @ C )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1_subs) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( left_apart_point @ A @ C )
=> ( ( distinct_points @ A @ B )
| ( left_apart_point @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(5,axiom,
! [A: $i] :
( ( line @ A )
=> ( line @ ( reverse_line @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4_cons_objs) ).
thf(55,plain,
! [A: $i] :
( ( line @ A )
=> ( line @ ( reverse_line @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( convergent_lines @ A @ B )
<=> ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_opposite_lines @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a7_defns) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( ( convergent_lines @ A @ B )
=> ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_opposite_lines @ A @ B ) ) )
& ( ( ( unequally_directed_lines @ A @ B )
& ( unequally_directed_opposite_lines @ A @ B ) )
=> ( convergent_lines @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( divides_points @ C @ A @ B )
<=> ( ( ( left_apart_point @ A @ C )
& ( right_apart_point @ B @ C ) )
| ( ( right_apart_point @ A @ C )
& ( left_apart_point @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8_defns) ).
thf(131,plain,
! [A: $i,B: $i,C: $i] :
( ( ( divides_points @ C @ A @ B )
=> ( ( ( left_apart_point @ A @ C )
& ( right_apart_point @ B @ C ) )
| ( ( right_apart_point @ A @ C )
& ( left_apart_point @ B @ C ) ) ) )
& ( ( ( ( left_apart_point @ A @ C )
& ( right_apart_point @ B @ C ) )
| ( ( right_apart_point @ A @ C )
& ( left_apart_point @ B @ C ) ) )
=> ( divides_points @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i,B: $i] : ( equally_directed_lines @ ( parallel_through_point @ B @ A ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10_cons_objs) ).
thf(62,plain,
! [A: $i,B: $i] : ( equally_directed_lines @ ( parallel_through_point @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(186,plain,
$false,
inference(e,[status(thm)],[69,57,179,74,160,39,91,80,48,146,107,83,170,120,53,141,109,96,173,129,148,64,176,59,181,86,162,112,67,127,99,104,158,55,114,131,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO257+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 04:27:15 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (121ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.75/1.17 % [INFO] eprover registered as external prover.
% 1.75/1.17 % [INFO] cvc4 registered as external prover.
% 1.75/1.17 % [INFO] Scanning for conjecture ...
% 1.97/1.23 % [INFO] Found a conjecture and 36 axioms. Running axiom selection ...
% 2.14/1.28 % [INFO] Axiom selection finished. Selected 36 axioms (removed 0 axioms).
% 2.14/1.32 % [INFO] Problem is first-order (TPTP FOF).
% 2.14/1.33 % [INFO] Type checking passed.
% 2.14/1.33 % [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 ...
% 4.00/1.90 % External prover 'e' found a proof!
% 4.00/1.90 % [INFO] Killing All external provers ...
% 4.00/1.90 % Time passed: 1373ms (effective reasoning time: 917ms)
% 4.00/1.90 % 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)>
% 4.00/1.90 % 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
% 4.00/1.90 % No. of inferences in proof: 76
% 4.00/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1373 ms resp. 917 ms w/o parsing
% 4.35/1.96 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.35/1.96 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------