%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO232+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Wed Oct 7 10:18:34 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 156 ( 89 unt; 0 typ; 0 def)
% Number of atoms : 972 ( 248 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1735 ( 296 ~; 277 |; 18 &;1119 @)
% ( 3 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 3 con; 0-4 aty)
% Number of variables : 323 ( 0 ^; 323 !; 0 ?; 323 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $i > $i > $o ).
thf(tp_before_on_line,type,
before_on_line: $i > $i > $i > $o ).
thf(tp_between_on_line,type,
between_on_line: $i > $i > $i > $i > $o ).
thf(tp_convergent_lines,type,
convergent_lines: $i > $i > $o ).
thf(tp_distinct_lines,type,
distinct_lines: $i > $i > $o ).
thf(tp_distinct_points,type,
distinct_points: $i > $i > $o ).
thf(tp_divides_points,type,
divides_points: $i > $i > $i > $o ).
thf(tp_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_left_apart_point,type,
left_apart_point: $i > $i > $o ).
thf(tp_left_convergent_lines,type,
left_convergent_lines: $i > $i > $o ).
thf(tp_line,type,
line: $i > $o ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_parallel_through_point,type,
parallel_through_point: $i > $i > $i ).
thf(tp_point,type,
point: $i > $o ).
thf(tp_reverse_line,type,
reverse_line: $i > $i ).
thf(tp_sK1_L,type,
sK1_L: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(1,axiom,
! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagsub3) ).
thf(6,axiom,
! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco10) ).
thf(7,axiom,
! [A: $i,B: $i] :
~ ( unequally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco9) ).
thf(8,axiom,
! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco8) ).
thf(12,axiom,
! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oagco4) ).
thf(16,axiom,
! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag11) ).
thf(17,axiom,
! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag10) ).
thf(18,axiom,
! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag9) ).
thf(19,axiom,
! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag8) ).
thf(20,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag7) ).
thf(21,axiom,
! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag6) ).
thf(22,axiom,
! [L: $i] :
~ ( unequally_directed_lines @ L @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oag5) ).
thf(30,axiom,
! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con_def) ).
thf(32,conjecture,
! [L: $i] :
( ( line @ L )
=> ( unequally_directed_lines @ L @ ( reverse_line @ L ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(33,negated_conjecture,
( ( ! [L: $i] :
( ( line @ L )
=> ( unequally_directed_lines @ L @ ( reverse_line @ L ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,plain,
( ( ! [L: $i] :
( ( line @ L )
=> ( unequally_directed_lines @ L @ ( reverse_line @ L ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[33]) ).
thf(35,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(36,plain,
( ( ! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
~ ( unequally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(38,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(39,plain,
( ( ! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(40,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ! [L: $i] :
~ ( unequally_directed_lines @ L @ L ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(47,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(48,plain,
( ( ( line @ sK1_L )
=> ( unequally_directed_lines @ sK1_L @ ( reverse_line @ sK1_L ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[34]) ).
thf(49,plain,
( ( line @ sK1_L )
= $true ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(50,plain,
( ( unequally_directed_lines @ sK1_L @ ( reverse_line @ sK1_L ) )
= $false ),
inference(standard_cnf,[status(thm)],[48]) ).
thf(51,plain,
( ( ~ ( unequally_directed_lines @ sK1_L @ ( reverse_line @ sK1_L ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[50]) ).
thf(52,plain,
( ( ! [L: $i,M: $i] :
( ( convergent_lines @ L @ M )
<=> ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(53,plain,
( ( ! [L: $i] :
~ ( unequally_directed_lines @ L @ L ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(54,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( unequally_directed_lines @ L @ M )
=> ( ( unequally_directed_lines @ L @ N )
| ( unequally_directed_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(55,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( ( unequally_directed_lines @ L @ N )
& ( unequally_directed_lines @ L @ ( reverse_line @ N ) ) )
| ( ( unequally_directed_lines @ M @ N )
& ( unequally_directed_lines @ M @ ( reverse_line @ N ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(56,plain,
( ( ! [L: $i,M: $i] :
( ( ( line @ L )
& ( line @ M ) )
=> ( ( unequally_directed_lines @ L @ M )
| ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(57,plain,
( ( ! [L: $i,M: $i] :
( ( ( unequally_directed_lines @ L @ M )
& ( unequally_directed_lines @ L @ ( reverse_line @ M ) ) )
=> ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(58,plain,
( ( ! [A: $i,L: $i] :
~ ( ( left_apart_point @ A @ L )
| ( left_apart_point @ A @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(59,plain,
( ( ! [L: $i,M: $i] :
~ ( ( left_convergent_lines @ L @ M )
| ( left_convergent_lines @ L @ ( reverse_line @ M ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(60,plain,
( ( ! [L: $i] :
( ( line @ L )
=> ( line @ ( reverse_line @ L ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(61,plain,
( ( ! [L: $i] :
~ ( distinct_lines @ L @ ( reverse_line @ L ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(62,plain,
( ( ! [A: $i,B: $i] :
~ ( unequally_directed_lines @ ( line_connecting @ A @ B ) @ ( reverse_line @ ( line_connecting @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(63,plain,
( ( ! [A: $i,L: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ L @ A ) @ L ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(64,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( left_convergent_lines @ L @ M )
=> ( ( unequally_directed_lines @ M @ N )
| ( left_convergent_lines @ L @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(65,plain,
( ( line @ sK1_L )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(66,plain,
( ( ~ ( unequally_directed_lines @ sK1_L @ ( reverse_line @ sK1_L ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(67,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( left_convergent_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX1 @ SX2 )
| ( left_convergent_lines @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(68,plain,
( ( ! [SX0: $i] :
( ~ ( line @ SX0 )
| ( line @ ( reverse_line @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(69,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ SX2 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX2 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SX1 @ SX2 )
| ~ ( unequally_directed_lines @ SX1 @ ( reverse_line @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(70,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ( left_convergent_lines @ SX0 @ SX1 )
| ( left_convergent_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(71,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ SX2 )
| ( unequally_directed_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(72,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( line @ SX0 )
| ~ ( line @ SX1 ) )
| ( unequally_directed_lines @ SX0 @ SX1 )
| ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(73,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SX0 @ SX1 )
| ~ ( unequally_directed_lines @ SX0 @ ( reverse_line @ SX1 ) ) )
| ( convergent_lines @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(74,plain,
! [SV1: $i] :
( ( ~ ( unequally_directed_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(75,plain,
! [SV2: $i] :
( ( ! [SY27: $i] :
~ ( ( left_apart_point @ SV2 @ SY27 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(76,plain,
! [SV3: $i] :
( ( ! [SY28: $i] :
~ ( ( left_convergent_lines @ SV3 @ SY28 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(77,plain,
! [SV4: $i] :
( ( ~ ( distinct_lines @ SV4 @ ( reverse_line @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(78,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
~ ( unequally_directed_lines @ ( line_connecting @ SV5 @ SY29 ) @ ( reverse_line @ ( line_connecting @ SY29 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(79,plain,
! [SV6: $i] :
( ( ! [SY30: $i] :
~ ( unequally_directed_lines @ ( parallel_through_point @ SY30 @ SV6 ) @ SY30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(80,plain,
( ( unequally_directed_lines @ sK1_L @ ( reverse_line @ sK1_L ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(81,plain,
! [SV7: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( left_convergent_lines @ SV7 @ SY31 )
| ( unequally_directed_lines @ SY31 @ SY32 )
| ( left_convergent_lines @ SV7 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(82,plain,
! [SV8: $i] :
( ( ~ ( line @ SV8 )
| ( line @ ( reverse_line @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(83,plain,
! [SV9: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV9 @ SY33 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SY33 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV9 @ SY34 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SY34 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SY33 @ SY34 )
| ~ ( unequally_directed_lines @ SY33 @ ( reverse_line @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(84,plain,
! [SV10: $i] :
( ( ! [SY35: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV10 @ SY35 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SY35 ) ) )
| ( left_convergent_lines @ SV10 @ SY35 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(85,plain,
! [SV11: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( unequally_directed_lines @ SV11 @ SY36 )
| ( unequally_directed_lines @ SV11 @ SY37 )
| ( unequally_directed_lines @ SY36 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(86,plain,
! [SV12: $i] :
( ( ! [SY38: $i] :
( ~ ~ ( ~ ( line @ SV12 )
| ~ ( line @ SY38 ) )
| ( unequally_directed_lines @ SV12 @ SY38 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(87,plain,
! [SV13: $i] :
( ( ! [SY39: $i] :
~ ( ~ ( ~ ( convergent_lines @ SV13 @ SY39 )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SY39 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SY39 ) ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SY39 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SY39 ) ) )
| ( convergent_lines @ SV13 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(88,plain,
! [SV1: $i] :
( ( unequally_directed_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(89,plain,
! [SV14: $i,SV2: $i] :
( ( ~ ( ( left_apart_point @ SV2 @ SV14 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV15: $i,SV3: $i] :
( ( ~ ( ( left_convergent_lines @ SV3 @ SV15 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV4: $i] :
( ( distinct_lines @ SV4 @ ( reverse_line @ SV4 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(92,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( unequally_directed_lines @ ( line_connecting @ SV5 @ SV16 ) @ ( reverse_line @ ( line_connecting @ SV16 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(93,plain,
! [SV6: $i,SV17: $i] :
( ( ~ ( unequally_directed_lines @ ( parallel_through_point @ SV17 @ SV6 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(94,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY40: $i] :
( ~ ( left_convergent_lines @ SV7 @ SV18 )
| ( unequally_directed_lines @ SV18 @ SY40 )
| ( left_convergent_lines @ SV7 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(95,plain,
! [SV8: $i] :
( ( ( ~ ( line @ SV8 ) )
= $true )
| ( ( line @ ( reverse_line @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(96,plain,
! [SV19: $i,SV9: $i] :
( ( ! [SY41: $i] :
( ~ ~ ( ~ ( unequally_directed_lines @ SV9 @ SV19 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV9 @ SY41 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SY41 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SY41 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(97,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV10 @ SV20 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
| ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(98,plain,
! [SV21: $i,SV11: $i] :
( ( ! [SY42: $i] :
( ~ ( unequally_directed_lines @ SV11 @ SV21 )
| ( unequally_directed_lines @ SV11 @ SY42 )
| ( unequally_directed_lines @ SV21 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(99,plain,
! [SV22: $i,SV12: $i] :
( ( ~ ~ ( ~ ( line @ SV12 )
| ~ ( line @ SV22 ) )
| ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(100,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( ~ ( ~ ( convergent_lines @ SV13 @ SV23 )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
| ( convergent_lines @ SV13 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(101,plain,
! [SV14: $i,SV2: $i] :
( ( ( left_apart_point @ SV2 @ SV14 )
| ( left_apart_point @ SV2 @ ( reverse_line @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(102,plain,
! [SV15: $i,SV3: $i] :
( ( ( left_convergent_lines @ SV3 @ SV15 )
| ( left_convergent_lines @ SV3 @ ( reverse_line @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(103,plain,
! [SV16: $i,SV5: $i] :
( ( unequally_directed_lines @ ( line_connecting @ SV5 @ SV16 ) @ ( reverse_line @ ( line_connecting @ SV16 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV6: $i,SV17: $i] :
( ( unequally_directed_lines @ ( parallel_through_point @ SV17 @ SV6 ) @ SV17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ~ ( left_convergent_lines @ SV7 @ SV18 )
| ( unequally_directed_lines @ SV18 @ SV24 )
| ( left_convergent_lines @ SV7 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV8: $i] :
( ( ( line @ SV8 )
= $false )
| ( ( line @ ( reverse_line @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV9 @ SV19 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV10 @ SV20 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV26: $i,SV21: $i,SV11: $i] :
( ( ~ ( unequally_directed_lines @ SV11 @ SV21 )
| ( unequally_directed_lines @ SV11 @ SV26 )
| ( unequally_directed_lines @ SV21 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( line @ SV12 )
| ~ ( line @ SV22 ) ) )
= $true )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( ~ ( convergent_lines @ SV13 @ SV23 )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
| ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
| ( convergent_lines @ SV13 @ SV23 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV14: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ SV14 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(113,plain,
! [SV14: $i,SV2: $i] :
( ( left_apart_point @ SV2 @ ( reverse_line @ SV14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[101]) ).
thf(114,plain,
! [SV15: $i,SV3: $i] :
( ( left_convergent_lines @ SV3 @ SV15 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV15: $i,SV3: $i] :
( ( left_convergent_lines @ SV3 @ ( reverse_line @ SV15 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(116,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( ~ ( left_convergent_lines @ SV7 @ SV18 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV18 @ SV24 )
| ( left_convergent_lines @ SV7 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV9 @ SV19 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV10 @ SV20 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) ) )
= $false )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV26: $i,SV21: $i,SV11: $i] :
( ( ( ~ ( unequally_directed_lines @ SV11 @ SV21 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV11 @ SV26 )
| ( unequally_directed_lines @ SV21 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ( ~ ( line @ SV12 )
| ~ ( line @ SV22 ) ) )
= $false )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( ~ ( convergent_lines @ SV13 @ SV23 )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(122,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
| ( convergent_lines @ SV13 @ SV23 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[111]) ).
thf(123,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( left_convergent_lines @ SV7 @ SV18 )
= $false )
| ( ( ( unequally_directed_lines @ SV18 @ SV24 )
| ( left_convergent_lines @ SV7 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(124,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV19 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(125,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( unequally_directed_lines @ SV10 @ SV20 )
| ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(126,plain,
! [SV26: $i,SV21: $i,SV11: $i] :
( ( ( unequally_directed_lines @ SV11 @ SV21 )
= $false )
| ( ( ( unequally_directed_lines @ SV11 @ SV26 )
| ( unequally_directed_lines @ SV21 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(127,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ( line @ SV12 )
| ~ ( line @ SV22 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(128,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ( convergent_lines @ SV13 @ SV23 )
| ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(129,plain,
! [SV23: $i,SV13: $i] :
( ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
| ( convergent_lines @ SV13 @ SV23 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(130,plain,
! [SV7: $i,SV24: $i,SV18: $i] :
( ( ( unequally_directed_lines @ SV18 @ SV24 )
= $true )
| ( ( left_convergent_lines @ SV7 @ SV24 )
= $true )
| ( ( left_convergent_lines @ SV7 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(131,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( unequally_directed_lines @ SV9 @ SV19 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(132,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( unequally_directed_lines @ SV10 @ SV20 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(133,plain,
! [SV21: $i,SV26: $i,SV11: $i] :
( ( ( unequally_directed_lines @ SV11 @ SV26 )
= $true )
| ( ( unequally_directed_lines @ SV21 @ SV26 )
= $true )
| ( ( unequally_directed_lines @ SV11 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV22: $i,SV12: $i] :
( ( ( ~ ( line @ SV12 ) )
= $true )
| ( ( ~ ( line @ SV22 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(135,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( convergent_lines @ SV13 @ SV23 ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(136,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(137,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( ~ ( unequally_directed_lines @ SV9 @ SV19 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(138,plain,
! [SV20: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ SV20 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(139,plain,
! [SV22: $i,SV12: $i] :
( ( ( line @ SV12 )
= $false )
| ( ( ~ ( line @ SV22 ) )
= $true )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(140,plain,
! [SV23: $i,SV13: $i] :
( ( ( convergent_lines @ SV13 @ SV23 )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(141,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) ) )
= $false )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(142,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(143,plain,
! [SV20: $i,SV10: $i] :
( ( ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) )
= $false )
| ( ( unequally_directed_lines @ SV10 @ SV20 )
= $false )
| ( ( ( left_convergent_lines @ SV10 @ SV20 )
| ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(144,plain,
! [SV12: $i,SV22: $i] :
( ( ( line @ SV22 )
= $false )
| ( ( line @ SV12 )
= $false )
| ( ( ( unequally_directed_lines @ SV12 @ SV22 )
| ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
= $false )
| ( ( convergent_lines @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(146,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV23 )
| ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(147,plain,
! [SV25: $i,SV19: $i,SV9: $i] :
( ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
| ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(148,plain,
! [SV20: $i,SV10: $i] :
( ( ( left_convergent_lines @ SV10 @ SV20 )
= $true )
| ( ( left_convergent_lines @ SV10 @ ( reverse_line @ SV20 ) )
= $true )
| ( ( unequally_directed_lines @ SV10 @ SV20 )
= $false )
| ( ( unequally_directed_lines @ SV10 @ ( reverse_line @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(149,plain,
! [SV22: $i,SV12: $i] :
( ( ( unequally_directed_lines @ SV12 @ SV22 )
= $true )
| ( ( unequally_directed_lines @ SV12 @ ( reverse_line @ SV22 ) )
= $true )
| ( ( line @ SV12 )
= $false )
| ( ( line @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(150,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV23 ) )
= $false )
| ( ( convergent_lines @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(151,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
= $false )
| ( ( convergent_lines @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(152,plain,
! [SV23: $i,SV13: $i] :
( ( ( ~ ( unequally_directed_lines @ SV13 @ SV23 ) )
= $true )
| ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV23: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ SV23 )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(155,plain,
! [SV23: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(156,plain,
! [SV23: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ SV23 )
= $false )
| ( ( ~ ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) ) )
= $true )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(157,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( unequally_directed_lines @ SV9 @ SV25 )
| ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(158,plain,
! [SV23: $i,SV13: $i] :
( ( ( unequally_directed_lines @ SV13 @ ( reverse_line @ SV23 ) )
= $false )
| ( ( unequally_directed_lines @ SV13 @ SV23 )
= $false )
| ( ( convergent_lines @ SV13 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(159,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( unequally_directed_lines @ SV9 @ SV25 ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(160,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[157]) ).
thf(161,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(162,plain,
! [SV19: $i,SV25: $i,SV9: $i] :
( ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( ~ ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[160]) ).
thf(163,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(164,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV25 )
| ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(165,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV25 ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(166,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(167,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ SV25 ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(168,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( ~ ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) ) )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(169,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(170,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[166]) ).
thf(171,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ SV25 )
= $true )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(172,plain,
! [SV9: $i,SV25: $i,SV19: $i] :
( ( ( unequally_directed_lines @ SV19 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV25 ) )
= $true )
| ( ( unequally_directed_lines @ SV9 @ SV19 )
= $false )
| ( ( unequally_directed_lines @ SV9 @ ( reverse_line @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(173,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[65,172,171,170,169,158,155,154,149,148,133,130,115,114,113,112,106,104,103,91,88,80]) ).
thf(174,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[173]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO232+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 10:17:23 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.25
% 0.08/0.25 No.of.Axioms: 13
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ....
% 0.08/0.25
% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:173,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 156 ****
% 0.08/0.25 %**** clause counter: 173 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:14,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:173,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------