%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 10:18:43 AM UTC 2026
% Result : Theorem 0.08s 0.21s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 58 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 439 ( 107 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1113 ( 208 ~; 151 |; 6 &; 738 @)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 6 con; 0-4 aty)
% Number of variables : 190 ( 0 ^; 190 !; 0 ?; 190 :)
% 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_equally_directed_lines,type,
equally_directed_lines: $i > $i > $o ).
thf(tp_equally_directed_opposite_lines,type,
equally_directed_opposite_lines: $i > $i > $o ).
thf(tp_incident_point_and_line,type,
incident_point_and_line: $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_right_apart_point,type,
right_apart_point: $i > $i > $o ).
thf(tp_right_convergent_lines,type,
right_convergent_lines: $i > $i > $o ).
thf(tp_sK1_L,type,
sK1_L: $i ).
thf(tp_sK2_SY8,type,
sK2_SY8: $i ).
thf(tp_sK3_SY11,type,
sK3_SY11: $i ).
thf(tp_sK4_SY13,type,
sK4_SY13: $i ).
thf(tp_unequally_directed_lines,type,
unequally_directed_lines: $i > $i > $o ).
thf(tp_unequally_directed_opposite_lines,type,
unequally_directed_opposite_lines: $i > $i > $o ).
thf(27,axiom,
! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
<=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
| ( ( before_on_line @ L @ C @ B )
& ( before_on_line @ L @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a9_defns) ).
thf(37,conjecture,
! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
=> ( between_on_line @ L @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(38,negated_conjecture,
( ( ! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
=> ( between_on_line @ L @ C @ B @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[37]) ).
thf(39,plain,
( ( ! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
=> ( between_on_line @ L @ C @ B @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[38]) ).
thf(40,plain,
( ( ! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
<=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
| ( ( before_on_line @ L @ C @ B )
& ( before_on_line @ L @ B @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(41,plain,
( ( ! [SY8: $i,SY9: $i,SY10: $i] :
( ( between_on_line @ sK1_L @ SY8 @ SY9 @ SY10 )
=> ( between_on_line @ sK1_L @ SY10 @ SY9 @ SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[39]) ).
thf(42,plain,
( ( ! [SY11: $i,SY12: $i] :
( ( between_on_line @ sK1_L @ sK2_SY8 @ SY11 @ SY12 )
=> ( between_on_line @ sK1_L @ SY12 @ SY11 @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(43,plain,
( ( ! [SY13: $i] :
( ( between_on_line @ sK1_L @ sK2_SY8 @ sK3_SY11 @ SY13 )
=> ( between_on_line @ sK1_L @ SY13 @ sK3_SY11 @ sK2_SY8 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[42]) ).
thf(44,plain,
( ( ( between_on_line @ sK1_L @ sK2_SY8 @ sK3_SY11 @ sK4_SY13 )
=> ( between_on_line @ sK1_L @ sK4_SY13 @ sK3_SY11 @ sK2_SY8 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[43]) ).
thf(45,plain,
( ( between_on_line @ sK1_L @ sK2_SY8 @ sK3_SY11 @ sK4_SY13 )
= $true ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(46,plain,
( ( between_on_line @ sK1_L @ sK4_SY13 @ sK3_SY11 @ sK2_SY8 )
= $false ),
inference(standard_cnf,[status(thm)],[44]) ).
thf(47,plain,
( ( ~ ( between_on_line @ sK1_L @ sK4_SY13 @ sK3_SY11 @ sK2_SY8 ) )
= $true ),
inference(polarity_switch,[status(thm)],[46]) ).
thf(48,plain,
( ( ! [L: $i,A: $i,B: $i,C: $i] :
( ( between_on_line @ L @ A @ B @ C )
<=> ( ( ( before_on_line @ L @ A @ B )
& ( before_on_line @ L @ B @ C ) )
| ( ( before_on_line @ L @ C @ B )
& ( before_on_line @ L @ B @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(49,plain,
( ( between_on_line @ sK1_L @ sK2_SY8 @ sK3_SY11 @ sK4_SY13 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(50,plain,
( ( ~ ( between_on_line @ sK1_L @ sK4_SY13 @ sK3_SY11 @ sK2_SY8 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ( ~ ( ~ ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 )
| ~ ( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 ) )
| ~ ( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SX0 @ SX1 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX3 ) )
| ~ ( ~ ( before_on_line @ SX0 @ SX3 @ SX2 )
| ~ ( before_on_line @ SX0 @ SX2 @ SX1 ) ) )
| ( between_on_line @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(52,plain,
( ( between_on_line @ sK1_L @ sK4_SY13 @ sK3_SY11 @ sK2_SY8 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(53,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i,SY16: $i] :
~ ( ~ ( ~ ( between_on_line @ SV1 @ SY14 @ SY15 @ SY16 )
| ~ ( ~ ( before_on_line @ SV1 @ SY14 @ SY15 )
| ~ ( before_on_line @ SV1 @ SY15 @ SY16 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY16 @ SY15 )
| ~ ( before_on_line @ SV1 @ SY15 @ SY14 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SY14 @ SY15 )
| ~ ( before_on_line @ SV1 @ SY15 @ SY16 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY16 @ SY15 )
| ~ ( before_on_line @ SV1 @ SY15 @ SY14 ) ) )
| ( between_on_line @ SV1 @ SY14 @ SY15 @ SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY17: $i,SY18: $i] :
~ ( ~ ( ~ ( between_on_line @ SV1 @ SV2 @ SY17 @ SY18 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SY17 )
| ~ ( before_on_line @ SV1 @ SY17 @ SY18 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY18 @ SY17 )
| ~ ( before_on_line @ SV1 @ SY17 @ SV2 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SY17 )
| ~ ( before_on_line @ SV1 @ SY17 @ SY18 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY18 @ SY17 )
| ~ ( before_on_line @ SV1 @ SY17 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SY17 @ SY18 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(55,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY19: $i] :
~ ( ~ ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SY19 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SY19 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY19 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SY19 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SY19 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SV3 @ SY19 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(56,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(57,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(58,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(59,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(60,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
| ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(61,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
| ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(62,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(63,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
| ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $false )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(66,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) ) )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(67,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) ) )
= $false )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(68,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $false )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(69,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(71,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(72,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(73,plain,
! [SV2: $i,SV4: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
= $false )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV2 @ SV3 ) )
= $true )
| ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 ) )
= $true )
| ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV2: $i,SV4: $i,SV3: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( ~ ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $false )
| ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV4 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV4 @ SV3 )
= $false )
| ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 )
| ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV2: $i,SV4: $i,SV3: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $false )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $false )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV3 @ SV2 )
= $false )
| ( ( before_on_line @ SV1 @ SV4 @ SV3 )
= $false )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[80]) ).
thf(86,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV4 @ SV3 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(87,plain,
! [SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( before_on_line @ SV1 @ SV3 @ SV2 ) )
= $false )
| ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[81]) ).
thf(88,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV4 @ SV3 )
= $true )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV3 @ SV2 )
= $true )
| ( ( before_on_line @ SV1 @ SV2 @ SV3 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV2: $i,SV3: $i,SV4: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV4 @ SV3 )
= $true )
| ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(91,plain,
! [SV4: $i,SV2: $i,SV3: $i,SV1: $i] :
( ( ( before_on_line @ SV1 @ SV3 @ SV2 )
= $true )
| ( ( before_on_line @ SV1 @ SV3 @ SV4 )
= $true )
| ( ( between_on_line @ SV1 @ SV2 @ SV3 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(92,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[49,91,90,89,88,83,82,52]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO258+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n018.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Oct 6 10:15:21 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.21
% 0.08/0.21 No.of.Axioms: 1
% 0.08/0.21
% 0.08/0.21 Length.of.Defs: 0
% 0.08/0.21
% 0.08/0.21 Contains.Choice.Funs: false
% 0.08/0.21 ..
% 0.08/0.21
% 0.08/0.21 ********************************
% 0.08/0.21 * All subproblems solved! *
% 0.08/0.21 ********************************
% 0.08/0.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.21
% 0.08/0.21 %**** Beginning of derivation protocol ****
% 0.08/0.21 % SZS output start CNFRefutation
% See solution above
% 0.08/0.22
% 0.08/0.22 %**** End of derivation protocol ****
% 0.08/0.22 %**** no. of clauses in derivation: 58 ****
% 0.08/0.22 %**** clause counter: 92 ****
% 0.08/0.22
% 0.08/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:2,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------