%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO218+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/sandbox/solver/bin/eprover /export/starexec/sandbox/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 10:18:28 AM UTC 2026
% Result : Theorem 0.06s 0.22s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 107 ( 51 unt; 0 typ; 0 def)
% Number of atoms : 728 ( 196 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1211 ( 314 ~; 196 |; 15 &; 668 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 251 ( 0 ^; 251 !; 0 ?; 251 :)
% 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_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $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/sandbox/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/sandbox/benchmark/theBenchmark.p',cotno1) ).
thf(3,axiom,
! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',coipo1) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).
thf(13,axiom,
! [X: $i] :
~ ( convergent_lines @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).
thf(16,conjecture,
! [L: $i,M: $i,N: $i] :
( ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( unorthogonal_lines @ M @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(17,negated_conjecture,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( unorthogonal_lines @ M @ N ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,plain,
( ( ! [L: $i,M: $i,N: $i] :
( ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ N ) )
=> ~ ( unorthogonal_lines @ M @ N ) ) )
= $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,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(24,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(25,plain,
( ( ! [SY17: $i,SY18: $i] :
( ( ~ ( convergent_lines @ sK1_L @ SY17 )
& ~ ( unorthogonal_lines @ sK1_L @ SY18 ) )
=> ~ ( unorthogonal_lines @ SY17 @ SY18 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(26,plain,
( ( ! [SY19: $i] :
( ( ~ ( convergent_lines @ sK1_L @ sK2_SY17 )
& ~ ( unorthogonal_lines @ sK1_L @ SY19 ) )
=> ~ ( unorthogonal_lines @ sK2_SY17 @ SY19 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[25]) ).
thf(27,plain,
( ( ( ~ ( convergent_lines @ sK1_L @ sK2_SY17 )
& ~ ( unorthogonal_lines @ sK1_L @ sK3_SY19 ) )
=> ~ ( unorthogonal_lines @ sK2_SY17 @ sK3_SY19 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ~ ( convergent_lines @ sK1_L @ sK2_SY17 ) )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(29,plain,
( ( ~ ( unorthogonal_lines @ sK1_L @ sK3_SY19 ) )
= $true ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ( unorthogonal_lines @ sK2_SY17 @ sK3_SY19 ) )
= $false ),
inference(standard_cnf,[status(thm)],[27]) ).
thf(31,plain,
( ( unorthogonal_lines @ sK2_SY17 @ sK3_SY19 )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(32,plain,
( ( ! [X: $i] :
~ ( convergent_lines @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( convergent_lines @ X @ Y )
=> ( ( convergent_lines @ X @ Z )
| ( convergent_lines @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ( convergent_lines @ X @ Y )
=> ( distinct_lines @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(35,plain,
( ( ! [L: $i,M: $i] :
~ ( ~ ( convergent_lines @ L @ M )
& ~ ( unorthogonal_lines @ L @ M ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(36,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(37,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(38,plain,
( ( ~ ( unorthogonal_lines @ sK1_L @ sK3_SY19 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(39,plain,
( ( ~ ( convergent_lines @ sK1_L @ sK2_SY17 ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(40,plain,
( ( unorthogonal_lines @ sK2_SY17 @ sK3_SY19 )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SX0 @ SX1 )
| ~ ~ ( unorthogonal_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(42,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)],[36]) ).
thf(43,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)],[37]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( convergent_lines @ SX0 @ SX2 )
| ( convergent_lines @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( convergent_lines @ SX0 @ SX1 )
| ( distinct_lines @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(46,plain,
! [SV1: $i] :
( ( ~ ( convergent_lines @ SV1 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
( ( unorthogonal_lines @ sK1_L @ sK3_SY19 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(48,plain,
( ( convergent_lines @ sK1_L @ sK2_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(49,plain,
! [SV2: $i] :
( ( ! [SY20: $i] :
~ ~ ( ~ ~ ( convergent_lines @ SV2 @ SY20 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV3: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SY21 )
| ~ ( unorthogonal_lines @ SV3 @ SY21 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SY22 )
| ~ ( unorthogonal_lines @ SV3 @ SY22 ) ) )
| ~ ( convergent_lines @ SY21 @ SY22 )
| ~ ( unorthogonal_lines @ SY21 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV4: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV4 @ SY23 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SY24 ) )
| ~ ( convergent_lines @ SY23 @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV5: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( convergent_lines @ SV5 @ SY25 )
| ( convergent_lines @ SV5 @ SY26 )
| ( convergent_lines @ SY25 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV6: $i] :
( ( ! [SY27: $i] :
( ~ ( convergent_lines @ SV6 @ SY27 )
| ( distinct_lines @ SV6 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV1: $i] :
( ( convergent_lines @ SV1 @ SV1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( convergent_lines @ SV2 @ SV7 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY28: $i] :
( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SY28 )
| ~ ( unorthogonal_lines @ SV3 @ SY28 ) ) )
| ~ ( convergent_lines @ SV8 @ SY28 )
| ~ ( unorthogonal_lines @ SV8 @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY29: $i] :
( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SY29 ) )
| ~ ( convergent_lines @ SV9 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY30: $i] :
( ~ ( convergent_lines @ SV5 @ SV10 )
| ( convergent_lines @ SV5 @ SY30 )
| ( convergent_lines @ SV10 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV11: $i,SV6: $i] :
( ( ~ ( convergent_lines @ SV6 @ SV11 )
| ( distinct_lines @ SV6 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ( ~ ~ ( convergent_lines @ SV2 @ SV7 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
| ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
| ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ~ ( convergent_lines @ SV5 @ SV10 )
| ( convergent_lines @ SV5 @ SV14 )
| ( convergent_lines @ SV10 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV11: $i,SV6: $i] :
( ( ( ~ ( convergent_lines @ SV6 @ SV11 ) )
= $true )
| ( ( distinct_lines @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV7: $i,SV2: $i] :
( ( ~ ~ ( convergent_lines @ SV2 @ SV7 )
| ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(66,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( convergent_lines @ SV5 @ SV10 ) )
= $true )
| ( ( ( convergent_lines @ SV5 @ SV14 )
| ( convergent_lines @ SV10 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(69,plain,
! [SV11: $i,SV6: $i] :
( ( ( convergent_lines @ SV6 @ SV11 )
= $false )
| ( ( distinct_lines @ SV6 @ SV11 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(70,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ~ ( convergent_lines @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) ) )
= $false )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(73,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( convergent_lines @ SV5 @ SV10 )
= $false )
| ( ( ( convergent_lines @ SV5 @ SV14 )
| ( convergent_lines @ SV10 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( convergent_lines @ SV2 @ SV7 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(75,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
| ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(76,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 )
| ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(77,plain,
! [SV10: $i,SV14: $i,SV5: $i] :
( ( ( convergent_lines @ SV5 @ SV14 )
= $true )
| ( ( convergent_lines @ SV10 @ SV14 )
= $true )
| ( ( convergent_lines @ SV5 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(78,plain,
! [SV7: $i,SV2: $i] :
( ( ( convergent_lines @ SV2 @ SV7 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) ) )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ~ ( unorthogonal_lines @ SV4 @ SV9 ) )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV7: $i,SV2: $i] :
( ( ( ~ ( unorthogonal_lines @ SV2 @ SV7 ) )
= $false )
| ( ( convergent_lines @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(82,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 )
| ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(83,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( unorthogonal_lines @ SV4 @ SV9 ) )
= $false )
| ( ( ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(84,plain,
! [SV7: $i,SV2: $i] :
( ( ( unorthogonal_lines @ SV2 @ SV7 )
= $true )
| ( ( convergent_lines @ SV2 @ SV7 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(85,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV8 ) )
= $false )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( unorthogonal_lines @ SV4 @ SV9 )
= $true )
| ( ( ~ ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(89,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) ) )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
! [SV9: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( unorthogonal_lines @ SV4 @ SV13 ) )
= $false )
| ( ( unorthogonal_lines @ SV4 @ SV9 )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV12 )
| ~ ( unorthogonal_lines @ SV3 @ SV12 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV9: $i,SV13: $i,SV4: $i] :
( ( ( unorthogonal_lines @ SV4 @ SV13 )
= $true )
| ( ( unorthogonal_lines @ SV4 @ SV9 )
= $true )
| ( ( ~ ( convergent_lines @ SV9 @ SV13 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(94,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV12 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(95,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV12 ) )
= $false )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[91]) ).
thf(96,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( convergent_lines @ SV3 @ SV12 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( unorthogonal_lines @ SV3 @ SV12 ) )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(98,plain,
! [SV4: $i,SV13: $i,SV9: $i] :
( ( ( convergent_lines @ SV9 @ SV13 )
= $false )
| ( ( unorthogonal_lines @ SV4 @ SV9 )
= $true )
| ( ( unorthogonal_lines @ SV4 @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV12 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(100,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(101,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( convergent_lines @ SV3 @ SV12 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(102,plain,
! [SV8: $i,SV12: $i,SV3: $i] :
( ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( ~ ( convergent_lines @ SV8 @ SV12 )
| ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(103,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( convergent_lines @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( convergent_lines @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( convergent_lines @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( convergent_lines @ SV8 @ SV12 ) )
= $true )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(109,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( ~ ( unorthogonal_lines @ SV8 @ SV12 ) )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( convergent_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV3: $i,SV12: $i,SV8: $i] :
( ( ( unorthogonal_lines @ SV8 @ SV12 )
= $false )
| ( ( convergent_lines @ SV8 @ SV12 )
= $false )
| ( ( unorthogonal_lines @ SV3 @ SV8 )
= $true )
| ( ( unorthogonal_lines @ SV3 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(115,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,114,113,112,111,98,84,77,69,54,48,47]) ).
thf(116,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO218+2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n001.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Tue Oct 6 10:17:08 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.22
% 0.06/0.22 No.of.Axioms: 6
% 0.06/0.22
% 0.06/0.22 Length.of.Defs: 0
% 0.06/0.22
% 0.06/0.22 Contains.Choice.Funs: false
% 0.06/0.22 ..
% 0.06/0.22
% 0.06/0.22 ********************************
% 0.06/0.22 * All subproblems solved! *
% 0.06/0.22 ********************************
% 0.06/0.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:115,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.06/0.22
% 0.06/0.22 %**** Beginning of derivation protocol ****
% 0.06/0.22 % SZS output start CNFRefutation
% See solution above
% 0.06/0.23
% 0.06/0.23 %**** End of derivation protocol ****
% 0.06/0.23 %**** no. of clauses in derivation: 107 ****
% 0.06/0.23 %**** clause counter: 115 ****
% 0.06/0.23
% 0.06/0.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,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:115,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------