%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO216+2 : 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 : n010.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 10:18:27 AM UTC 2026
% Result : Theorem 0.09s 0.21s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 76 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 589 ( 162 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 1003 ( 288 ~; 174 |; 9 &; 526 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 191 ( 0 ^; 191 !; 0 ?; 191 :)
% 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_L,type,
sK1_L: $i ).
thf(tp_unorthogonal_lines,type,
unorthogonal_lines: $i > $i > $o ).
thf(1,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',couo1) ).
thf(2,axiom,
! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cotno1) ).
thf(3,axiom,
! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',coipo1) ).
thf(16,conjecture,
! [L: $i] :
~ ~ ( unorthogonal_lines @ L @ L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(17,negated_conjecture,
( ( ! [L: $i] :
~ ~ ( unorthogonal_lines @ L @ L ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ! [L: $i] :
~ ~ ( unorthogonal_lines @ L @ L ) )
= $false ),
inference(unfold_def,[status(thm)],[17]) ).
thf(19,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ~ ~ ( unorthogonal_lines @ sK1_L @ sK1_L ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(23,plain,
( ( ~ ( unorthogonal_lines @ sK1_L @ sK1_L ) )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ( ~ ( convergent_lines @ L @ M )
| ~ ( unorthogonal_lines @ L @ M ) )
& ( ~ ( convergent_lines @ L @ N )
| ~ ( unorthogonal_lines @ L @ N ) ) )
=> ( ~ ( convergent_lines @ M @ N )
| ~ ( unorthogonal_lines @ M @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(26,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( unorthogonal_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( convergent_lines @ M @ N ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(27,plain,
( ( ~ ( unorthogonal_lines @ sK1_L @ sK1_L ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(28,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX2 ) )
| ~ ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ( unorthogonal_lines @ SX0 @ SX1 ) )
| ~ ( ~ ( convergent_lines @ SX0 @ SX2 )
| ~ ( unorthogonal_lines @ SX0 @ SX2 ) ) )
| ~ ( convergent_lines @ SX1 @ SX2 )
| ~ ( unorthogonal_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(31,plain,
( ( unorthogonal_lines @ sK1_L @ sK1_L )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV1: $i] :
( ( ! [SY9: $i,SY10: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV1 @ SY9 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SY10 ) )
| ~ ( convergent_lines @ SY9 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV2: $i] :
( ( ! [SY11: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SV2 @ SY11 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV3: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SY12 )
| ~ ( unorthogonal_lines @ SV3 @ SY12 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SY13 )
| ~ ( unorthogonal_lines @ SV3 @ SY13 ) ) )
| ~ ( convergent_lines @ SY12 @ SY13 )
| ~ ( unorthogonal_lines @ SY12 @ SY13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY14: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SY14 ) )
| ~ ( convergent_lines @ SV4 @ SY14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(36,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( convergent_lines @ SV2 @ SV5 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY15: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SY15 )
| ~ ( unorthogonal_lines @ SV3 @ SY15 ) ) )
| ~ ( convergent_lines @ SV6 @ SY15 )
| ~ ( unorthogonal_lines @ SV6 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
| ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV2 @ SV5 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
| ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ~ ( convergent_lines @ SV2 @ SV5 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ~ ( convergent_lines @ SV2 @ SV5 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(46,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 )
| ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(48,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( convergent_lines @ SV2 @ SV5 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(49,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(50,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV1 @ SV4 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(51,plain,
! [SV5: $i,SV2: $i] :
( ( ( convergent_lines @ SV2 @ SV5 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[48]) ).
thf(52,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( ~ ( unorthogonal_lines @ SV1 @ SV4 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(54,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( unorthogonal_lines @ SV2 @ SV5 ) )
= $false )
| ( ( convergent_lines @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(55,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV6 )
| ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(56,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ( unorthogonal_lines @ SV1 @ SV4 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV5: $i,SV2: $i] :
( ( ( unorthogonal_lines @ SV2 @ SV5 )
= $true )
| ( ( convergent_lines @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(58,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( ~ ( unorthogonal_lines @ SV1 @ SV7 ) )
= $false )
| ( ( unorthogonal_lines @ SV1 @ SV4 )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(62,plain,
! [SV8: $i,SV6: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(63,plain,
! [SV4: $i,SV7: $i,SV1: $i] :
( ( ( unorthogonal_lines @ SV1 @ SV7 )
= $true )
| ( ( unorthogonal_lines @ SV1 @ SV4 )
= $true )
| ( ( ~ ( convergent_lines @ SV4 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV1: $i,SV7: $i,SV4: $i] :
( ( ( convergent_lines @ SV4 @ SV7 )
= $false )
| ( ( unorthogonal_lines @ SV1 @ SV4 )
= $true )
| ( ( unorthogonal_lines @ SV1 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(68,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(71,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(72,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[68]) ).
thf(73,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[69]) ).
thf(74,plain,
! [SV6: $i,SV8: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( ~ ( convergent_lines @ SV6 @ SV8 )
| ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(75,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(76,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(77,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV8 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(79,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV6 @ SV8 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(85,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV3: $i,SV8: $i,SV6: $i] :
( ( ( unorthogonal_lines @ SV6 @ SV8 )
= $false )
| ( ( convergent_lines @ SV6 @ SV8 )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV6 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(87,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[31,86,85,84,83,66,57]) ).
thf(88,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO216+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n010.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 10:11:14 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.21
% 0.09/0.21 No.of.Axioms: 3
% 0.09/0.21
% 0.09/0.21 Length.of.Defs: 0
% 0.09/0.21
% 0.09/0.21 Contains.Choice.Funs: false
% 0.09/0.21 .
% 0.09/0.21
% 0.09/0.21 ********************************
% 0.09/0.21 * All subproblems solved! *
% 0.09/0.21 ********************************
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:87,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.21
% 0.09/0.21 %**** Beginning of derivation protocol ****
% 0.09/0.21 % SZS output start CNFRefutation
% See solution above
% 0.09/0.21
% 0.09/0.21 %**** End of derivation protocol ****
% 0.09/0.21 %**** no. of clauses in derivation: 76 ****
% 0.09/0.21 %**** clause counter: 87 ****
% 0.09/0.21
% 0.09/0.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:3,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:87,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------