%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n026.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 10:18:15 AM UTC 2026
% Result : Theorem 0.66s 0.36s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 90 ( 59 unt; 0 typ; 0 def)
% Number of atoms : 517 ( 120 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 899 ( 90 ~; 142 |; 21 &; 622 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 211 ( 0 ^; 211 !; 0 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_apart_point_and_line,type,
apart_point_and_line: $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_intersection_point,type,
intersection_point: $i > $i > $i ).
thf(tp_line_connecting,type,
line_connecting: $i > $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK2_SY21,type,
sK2_SY21: $i ).
thf(tp_sK3_SY23,type,
sK3_SY23: $i ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq2) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ceq1) ).
thf(4,axiom,
! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cu1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci2) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ci1) ).
thf(11,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart4) ).
thf(14,axiom,
! [X: $i] :
~ ( distinct_points @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apart1) ).
thf(15,conjecture,
! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_points @ X @ Z )
& ( distinct_points @ Y @ Z )
& ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) ) )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ Z @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(16,negated_conjecture,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_points @ X @ Z )
& ( distinct_points @ Y @ Z )
& ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) ) )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ Z @ Y ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_points @ X @ Z )
& ( distinct_points @ Y @ Z )
& ~ ( apart_point_and_line @ Z @ ( line_connecting @ X @ Y ) ) )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ Z @ Y ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(25,plain,
( ( ! [SY21: $i,SY22: $i] :
( ( ( distinct_points @ sK1_X @ SY21 )
& ( distinct_points @ sK1_X @ SY22 )
& ( distinct_points @ SY21 @ SY22 )
& ~ ( apart_point_and_line @ SY22 @ ( line_connecting @ sK1_X @ SY21 ) ) )
=> ~ ( apart_point_and_line @ sK1_X @ ( line_connecting @ SY22 @ SY21 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[17]) ).
thf(26,plain,
( ( ! [SY23: $i] :
( ( ( distinct_points @ sK1_X @ sK2_SY21 )
& ( distinct_points @ sK1_X @ SY23 )
& ( distinct_points @ sK2_SY21 @ SY23 )
& ~ ( apart_point_and_line @ SY23 @ ( line_connecting @ sK1_X @ sK2_SY21 ) ) )
=> ~ ( apart_point_and_line @ sK1_X @ ( line_connecting @ SY23 @ sK2_SY21 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(27,plain,
( ( ( ( distinct_points @ sK1_X @ sK2_SY21 )
& ( distinct_points @ sK1_X @ sK3_SY23 )
& ( distinct_points @ sK2_SY21 @ sK3_SY23 )
& ~ ( apart_point_and_line @ sK3_SY23 @ ( line_connecting @ sK1_X @ sK2_SY21 ) ) )
=> ~ ( apart_point_and_line @ sK1_X @ ( line_connecting @ sK3_SY23 @ sK2_SY21 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( distinct_points @ sK1_X @ sK2_SY21 )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(29,plain,
( ( distinct_points @ sK1_X @ sK3_SY23 )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(30,plain,
( ( distinct_points @ sK2_SY21 @ sK3_SY23 )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(31,plain,
( ( ~ ( apart_point_and_line @ sK3_SY23 @ ( line_connecting @ sK1_X @ sK2_SY21 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( apart_point_and_line @ sK1_X @ ( line_connecting @ sK3_SY23 @ sK2_SY21 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(33,plain,
( ( apart_point_and_line @ sK1_X @ ( line_connecting @ sK3_SY23 @ sK2_SY21 ) )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(34,plain,
( ( ! [X: $i] :
~ ( distinct_points @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( distinct_points @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( distinct_points @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ X @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( distinct_points @ X @ Y )
=> ~ ( apart_point_and_line @ Y @ ( line_connecting @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,U: $i,V: $i] :
( ( ( distinct_points @ X @ Y )
& ( distinct_lines @ U @ V ) )
=> ( ( apart_point_and_line @ X @ U )
| ( apart_point_and_line @ X @ V )
| ( apart_point_and_line @ Y @ U )
| ( apart_point_and_line @ Y @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_points @ X @ Z )
| ( apart_point_and_line @ Z @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( apart_point_and_line @ X @ Y )
=> ( ( distinct_lines @ Y @ Z )
| ( apart_point_and_line @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(41,plain,
( ( ~ ( apart_point_and_line @ sK3_SY23 @ ( line_connecting @ sK1_X @ sK2_SY21 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(42,plain,
( ( distinct_points @ sK2_SY21 @ sK3_SY23 )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(43,plain,
( ( distinct_points @ sK1_X @ sK3_SY23 )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(44,plain,
( ( distinct_points @ sK1_X @ sK2_SY21 )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(45,plain,
( ( apart_point_and_line @ sK1_X @ ( line_connecting @ sK3_SY23 @ sK2_SY21 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( distinct_points @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(47,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_points @ SX0 @ SX2 )
| ( apart_point_and_line @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(48,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX0 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( apart_point_and_line @ SX1 @ ( line_connecting @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( distinct_points @ SX0 @ SX1 )
| ~ ( distinct_lines @ SX2 @ SX3 ) )
| ( apart_point_and_line @ SX0 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX3 )
| ( apart_point_and_line @ SX1 @ SX2 )
| ( apart_point_and_line @ SX1 @ SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( apart_point_and_line @ SX0 @ SX1 )
| ( distinct_lines @ SX1 @ SX2 )
| ( apart_point_and_line @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(52,plain,
! [SV1: $i] :
( ( ~ ( distinct_points @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(53,plain,
( ( apart_point_and_line @ sK3_SY23 @ ( line_connecting @ sK1_X @ sK2_SY21 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( distinct_points @ SV2 @ SY24 )
| ( distinct_points @ SV2 @ SY25 )
| ( distinct_points @ SY24 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV3: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( apart_point_and_line @ SV3 @ SY26 )
| ( distinct_points @ SV3 @ SY27 )
| ( apart_point_and_line @ SY27 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(56,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( distinct_points @ SV4 @ SY28 )
| ~ ( apart_point_and_line @ SV4 @ ( line_connecting @ SV4 @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
( ~ ( distinct_points @ SV5 @ SY29 )
| ~ ( apart_point_and_line @ SY29 @ ( line_connecting @ SV5 @ SY29 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV6: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SY30 )
| ~ ( distinct_lines @ SY31 @ SY32 ) )
| ( apart_point_and_line @ SV6 @ SY31 )
| ( apart_point_and_line @ SV6 @ SY32 )
| ( apart_point_and_line @ SY30 @ SY31 )
| ( apart_point_and_line @ SY30 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV7: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( apart_point_and_line @ SV7 @ SY33 )
| ( distinct_lines @ SY33 @ SY34 )
| ( apart_point_and_line @ SV7 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV1: $i] :
( ( distinct_points @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY35: $i] :
( ~ ( distinct_points @ SV2 @ SV8 )
| ( distinct_points @ SV2 @ SY35 )
| ( distinct_points @ SV8 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY36: $i] :
( ~ ( apart_point_and_line @ SV3 @ SV9 )
| ( distinct_points @ SV3 @ SY36 )
| ( apart_point_and_line @ SY36 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( distinct_points @ SV4 @ SV10 )
| ~ ( apart_point_and_line @ SV4 @ ( line_connecting @ SV4 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(64,plain,
! [SV11: $i,SV5: $i] :
( ( ~ ( distinct_points @ SV5 @ SV11 )
| ~ ( apart_point_and_line @ SV11 @ ( line_connecting @ SV5 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SY37 @ SY38 ) )
| ( apart_point_and_line @ SV6 @ SY37 )
| ( apart_point_and_line @ SV6 @ SY38 )
| ( apart_point_and_line @ SV12 @ SY37 )
| ( apart_point_and_line @ SV12 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV13: $i,SV7: $i] :
( ( ! [SY39: $i] :
( ~ ( apart_point_and_line @ SV7 @ SV13 )
| ( distinct_lines @ SV13 @ SY39 )
| ( apart_point_and_line @ SV7 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( distinct_points @ SV2 @ SV8 )
| ( distinct_points @ SV2 @ SV14 )
| ( distinct_points @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ~ ( apart_point_and_line @ SV3 @ SV9 )
| ( distinct_points @ SV3 @ SV15 )
| ( apart_point_and_line @ SV15 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( distinct_points @ SV4 @ SV10 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV4 @ ( line_connecting @ SV4 @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(70,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( distinct_points @ SV5 @ SV11 ) )
= $true )
| ( ( ~ ( apart_point_and_line @ SV11 @ ( line_connecting @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV16: $i,SV12: $i,SV6: $i] :
( ( ! [SY40: $i] :
( ~ ~ ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SV16 @ SY40 ) )
| ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SY40 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV17: $i,SV13: $i,SV7: $i] :
( ( ~ ( apart_point_and_line @ SV7 @ SV13 )
| ( distinct_lines @ SV13 @ SV17 )
| ( apart_point_and_line @ SV7 @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( distinct_points @ SV2 @ SV8 ) )
= $true )
| ( ( ( distinct_points @ SV2 @ SV14 )
| ( distinct_points @ SV8 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( apart_point_and_line @ SV3 @ SV9 ) )
= $true )
| ( ( ( distinct_points @ SV3 @ SV15 )
| ( apart_point_and_line @ SV15 @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV10: $i,SV4: $i] :
( ( ( distinct_points @ SV4 @ SV10 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV4 @ ( line_connecting @ SV4 @ SV10 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV11: $i,SV5: $i] :
( ( ( distinct_points @ SV5 @ SV11 )
= $false )
| ( ( ~ ( apart_point_and_line @ SV11 @ ( line_connecting @ SV5 @ SV11 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SV16 @ SV18 ) )
| ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV17: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( apart_point_and_line @ SV7 @ SV13 ) )
= $true )
| ( ( ( distinct_lines @ SV13 @ SV17 )
| ( apart_point_and_line @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV8 )
= $false )
| ( ( ( distinct_points @ SV2 @ SV14 )
| ( distinct_points @ SV8 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ( apart_point_and_line @ SV3 @ SV9 )
= $false )
| ( ( ( distinct_points @ SV3 @ SV15 )
| ( apart_point_and_line @ SV15 @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV10: $i,SV4: $i] :
( ( ( apart_point_and_line @ SV4 @ ( line_connecting @ SV4 @ SV10 ) )
= $false )
| ( ( distinct_points @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV5: $i,SV11: $i] :
( ( ( apart_point_and_line @ SV11 @ ( line_connecting @ SV5 @ SV11 ) )
= $false )
| ( ( distinct_points @ SV5 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(83,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SV16 @ SV18 ) ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(84,plain,
! [SV17: $i,SV13: $i,SV7: $i] :
( ( ( apart_point_and_line @ SV7 @ SV13 )
= $false )
| ( ( ( distinct_lines @ SV13 @ SV17 )
| ( apart_point_and_line @ SV7 @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(85,plain,
! [SV8: $i,SV14: $i,SV2: $i] :
( ( ( distinct_points @ SV2 @ SV14 )
= $true )
| ( ( distinct_points @ SV8 @ SV14 )
= $true )
| ( ( distinct_points @ SV2 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(86,plain,
! [SV9: $i,SV15: $i,SV3: $i] :
( ( ( distinct_points @ SV3 @ SV15 )
= $true )
| ( ( apart_point_and_line @ SV15 @ SV9 )
= $true )
| ( ( apart_point_and_line @ SV3 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(87,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SV16 @ SV18 ) ) )
= $false )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV7: $i,SV17: $i,SV13: $i] :
( ( ( distinct_lines @ SV13 @ SV17 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV17 )
= $true )
| ( ( apart_point_and_line @ SV7 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(89,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV12 )
| ~ ( distinct_lines @ SV16 @ SV18 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(90,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( distinct_points @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( distinct_lines @ SV16 @ SV18 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(91,plain,
! [SV18: $i,SV16: $i,SV12: $i,SV6: $i] :
( ( ( distinct_points @ SV6 @ SV12 )
= $false )
| ( ( ~ ( distinct_lines @ SV16 @ SV18 ) )
= $true )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(92,plain,
! [SV12: $i,SV6: $i,SV18: $i,SV16: $i] :
( ( ( distinct_lines @ SV16 @ SV18 )
= $false )
| ( ( distinct_points @ SV6 @ SV12 )
= $false )
| ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 )
| ( apart_point_and_line @ SV12 @ SV18 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(93,plain,
! [SV12: $i,SV18: $i,SV16: $i,SV6: $i] :
( ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 )
| ( apart_point_and_line @ SV12 @ SV16 ) )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV18 )
= $true )
| ( ( distinct_points @ SV6 @ SV12 )
= $false )
| ( ( distinct_lines @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(94,plain,
! [SV12: $i,SV18: $i,SV16: $i,SV6: $i] :
( ( ( ( apart_point_and_line @ SV6 @ SV16 )
| ( apart_point_and_line @ SV6 @ SV18 ) )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV16 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV18 )
= $true )
| ( ( distinct_points @ SV6 @ SV12 )
= $false )
| ( ( distinct_lines @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(95,plain,
! [SV12: $i,SV18: $i,SV16: $i,SV6: $i] :
( ( ( apart_point_and_line @ SV6 @ SV16 )
= $true )
| ( ( apart_point_and_line @ SV6 @ SV18 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV16 )
= $true )
| ( ( apart_point_and_line @ SV12 @ SV18 )
= $true )
| ( ( distinct_points @ SV6 @ SV12 )
= $false )
| ( ( distinct_lines @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(96,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[42,95,88,86,85,82,81,60,53,45,44,43]) ).
thf(97,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO188+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.11/0.17 % Computer : n026.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Oct 6 10:10:17 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.66/0.36
% 0.66/0.36 No.of.Axioms: 7
% 0.66/0.36
% 0.66/0.36 Length.of.Defs: 0
% 0.66/0.36
% 0.66/0.36 Contains.Choice.Funs: false
% 0.66/0.36 ..
% 0.66/0.36
% 0.66/0.36 ********************************
% 0.66/0.36 * All subproblems solved! *
% 0.66/0.36 ********************************
% 0.66/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:96,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.66/0.36
% 0.66/0.36 %**** Beginning of derivation protocol ****
% 0.66/0.36 % SZS output start CNFRefutation
% See solution above
% 0.66/0.36
% 0.66/0.36 %**** End of derivation protocol ****
% 0.66/0.36 %**** no. of clauses in derivation: 90 ****
% 0.66/0.36 %**** clause counter: 96 ****
% 0.66/0.36
% 0.66/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,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:96,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------