%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO080+1 : TPTP v9.3.1. Released v2.4.0.
% 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 : n006.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 10:17:50 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 4
% Syntax : Number of formulae : 82 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 1057 ( 252 equ; 0 cnn)
% Maximal formula atoms : 12 ( 12 avg)
% Number of connectives : 2025 ( 403 ~; 467 |; 18 &;1125 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 285 ( 0 ^; 282 !; 3 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_closed,type,
closed: $i > $o ).
thf(tp_end_point,type,
end_point: $i > $i > $o ).
thf(tp_incident_c,type,
incident_c: $i > $i > $o ).
thf(tp_inner_point,type,
inner_point: $i > $i > $o ).
thf(tp_meet,type,
meet: $i > $i > $i > $o ).
thf(tp_open,type,
open: $i > $o ).
thf(tp_part_of,type,
part_of: $i > $i > $o ).
thf(tp_sK1_C,type,
sK1_C: $i ).
thf(tp_sK2_SY23,type,
sK2_SY23: $i > $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i ).
thf(8,axiom,
! [C: $i,C1: $i,C2: $i,C3: $i] :
( ( ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( part_of @ C3 @ C )
& ? [P: $i] :
( ( end_point @ P @ C1 )
& ( end_point @ P @ C2 )
& ( end_point @ P @ C3 ) ) )
=> ( ( part_of @ C2 @ C3 )
| ( part_of @ C3 @ C2 )
| ( part_of @ C1 @ C2 )
| ( part_of @ C2 @ C1 )
| ( part_of @ C1 @ C3 )
| ( part_of @ C3 @ C1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2) ).
thf(9,axiom,
! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c1) ).
thf(16,axiom,
! [C: $i,C1: $i] :
( ( part_of @ C1 @ C )
<=> ! [P: $i] :
( ( incident_c @ P @ C1 )
=> ( incident_c @ P @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_of_defn) ).
thf(17,conjecture,
! [C: $i] : ( part_of @ C @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_reflexivity) ).
thf(18,negated_conjecture,
( ( ! [C: $i] : ( part_of @ C @ C ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [C: $i] : ( part_of @ C @ C ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [C: $i,C1: $i,C2: $i,C3: $i] :
( ( ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( part_of @ C3 @ C )
& ? [P: $i] :
( ( end_point @ P @ C1 )
& ( end_point @ P @ C2 )
& ( end_point @ P @ C3 ) ) )
=> ( ( part_of @ C2 @ C3 )
| ( part_of @ C3 @ C2 )
| ( part_of @ C1 @ C2 )
| ( part_of @ C2 @ C1 )
| ( part_of @ C1 @ C3 )
| ( part_of @ C3 @ C1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( ! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( ! [C: $i,C1: $i] :
( ( part_of @ C1 @ C )
<=> ! [P: $i] :
( ( incident_c @ P @ C1 )
=> ( incident_c @ P @ C ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(23,plain,
( ( part_of @ sK1_C @ sK1_C )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(24,plain,
( ( ~ ( part_of @ sK1_C @ sK1_C ) )
= $true ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(25,plain,
( ( ! [C: $i,C1: $i] :
( ( part_of @ C1 @ C )
<=> ! [P: $i] :
( ( incident_c @ P @ C1 )
=> ( incident_c @ P @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(26,plain,
( ( ! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [C: $i,C1: $i,C2: $i,C3: $i] :
( ( ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( part_of @ C3 @ C )
& ? [P: $i] :
( ( end_point @ P @ C1 )
& ( end_point @ P @ C2 )
& ( end_point @ P @ C3 ) ) )
=> ( ( part_of @ C2 @ C3 )
| ( part_of @ C3 @ C2 )
| ( part_of @ C1 @ C2 )
| ( part_of @ C2 @ C1 )
| ( part_of @ C1 @ C3 )
| ( part_of @ C3 @ C1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ~ ( part_of @ sK1_C @ sK1_C ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( part_of @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) ) )
| ( open @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SX1 @ SX0 )
| ~ ( part_of @ SX2 @ SX0 ) )
| ~ ( part_of @ SX3 @ SX0 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SX4 @ SX1 )
| ~ ( end_point @ SX4 @ SX2 ) )
| ~ ( end_point @ SX4 @ SX3 ) ) )
| ( part_of @ SX2 @ SX3 )
| ( part_of @ SX3 @ SX2 )
| ( part_of @ SX1 @ SX2 )
| ( part_of @ SX2 @ SX1 )
| ( part_of @ SX1 @ SX3 )
| ( part_of @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(31,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( part_of @ SX1 @ SX0 )
| ! [SX2: $i] :
( ~ ( incident_c @ SX2 @ SX1 )
| ( incident_c @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( incident_c @ SX2 @ SX1 )
| ( incident_c @ SX2 @ SX0 ) )
| ( part_of @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(32,plain,
( ( part_of @ sK1_C @ sK1_C )
= $false ),
inference(extcnf_not_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ~ ~ ( ~ ( part_of @ SY11 @ SV1 )
| ~ ( ( SY11 != SV1 ) ) )
| ( open @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i,SY14: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SY12 @ SV2 )
| ~ ( part_of @ SY13 @ SV2 ) )
| ~ ( part_of @ SY14 @ SV2 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SX4 @ SY12 )
| ~ ( end_point @ SX4 @ SY13 ) )
| ~ ( end_point @ SX4 @ SY14 ) ) )
| ( part_of @ SY13 @ SY14 )
| ( part_of @ SY14 @ SY13 )
| ( part_of @ SY12 @ SY13 )
| ( part_of @ SY13 @ SY12 )
| ( part_of @ SY12 @ SY14 )
| ( part_of @ SY14 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i] :
( ( ! [SY16: $i] :
~ ( ~ ( ~ ( part_of @ SY16 @ SV3 )
| ! [SY17: $i] :
( ~ ( incident_c @ SY17 @ SY16 )
| ( incident_c @ SY17 @ SV3 ) ) )
| ~ ( ~ ! [SY18: $i] :
( ~ ( incident_c @ SY18 @ SY16 )
| ( incident_c @ SY18 @ SV3 ) )
| ( part_of @ SY16 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i,SV4: $i] :
( ( ~ ~ ( ~ ( part_of @ SV4 @ SV1 )
| ~ ( ( SV4 != SV1 ) ) )
| ( open @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV2: $i,SV5: $i] :
( ( ! [SY19: $i,SY20: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SY19 @ SV2 ) )
| ~ ( part_of @ SY20 @ SV2 ) )
| ~ ~ ! [SY21: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY21 @ SV5 )
| ~ ( end_point @ SY21 @ SY19 ) )
| ~ ( end_point @ SY21 @ SY20 ) ) )
| ( part_of @ SY19 @ SY20 )
| ( part_of @ SY20 @ SY19 )
| ( part_of @ SV5 @ SY19 )
| ( part_of @ SY19 @ SV5 )
| ( part_of @ SV5 @ SY20 )
| ( part_of @ SY20 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(38,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( part_of @ SV6 @ SV3 )
| ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) )
| ~ ( ~ ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) )
| ( part_of @ SV6 @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(39,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV4 @ SV1 )
| ~ ( ( SV4 != SV1 ) ) ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV7: $i,SV2: $i,SV5: $i] :
( ( ! [SY24: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SY24 @ SV2 ) )
| ~ ~ ! [SY25: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY25 @ SV5 )
| ~ ( end_point @ SY25 @ SV7 ) )
| ~ ( end_point @ SY25 @ SY24 ) ) )
| ( part_of @ SV7 @ SY24 )
| ( part_of @ SY24 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SY24 )
| ( part_of @ SY24 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( part_of @ SV6 @ SV3 )
| ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) )
| ~ ( ~ ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) )
| ( part_of @ SV6 @ SV3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( ~ ( part_of @ SV4 @ SV1 )
| ~ ( ( SV4 != SV1 ) ) ) )
= $false )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) )
| ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
| ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( part_of @ SV6 @ SV3 )
| ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) )
| ( part_of @ SV6 @ SV3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(46,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( part_of @ SV4 @ SV1 )
| ~ ( ( SV4 != SV1 ) ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) )
| ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( part_of @ SV6 @ SV3 )
| ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) )
| ( part_of @ SV6 @ SV3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( part_of @ SV4 @ SV1 ) )
= $true )
| ( ( ~ ( ( SV4 != SV1 ) ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) )
| ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) ) )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ( part_of @ SV6 @ SV3 ) )
= $true )
| ( ( ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) ) )
= $true )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV1: $i,SV4: $i] :
( ( ( part_of @ SV4 @ SV1 )
= $false )
| ( ( ~ ( ( SV4 != SV1 ) ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(55,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) )
| ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV3: $i,SV6: $i] :
( ( ( part_of @ SV6 @ SV3 )
= $false )
| ( ( ! [SY22: $i] :
( ~ ( incident_c @ SY22 @ SV6 )
| ( incident_c @ SY22 @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(57,plain,
! [SV3: $i,SV6: $i] :
( ( ( ! [SY23: $i] :
( ~ ( incident_c @ SY23 @ SV6 )
| ( incident_c @ SY23 @ SV3 ) ) )
= $false )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV1: $i,SV4: $i] :
( ( ( SV4 != SV1 )
= $false )
| ( ( part_of @ SV4 @ SV1 )
= $false )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(59,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(60,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( incident_c @ SV9 @ SV6 )
| ( incident_c @ SV9 @ SV3 ) )
= $true )
| ( ( part_of @ SV6 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( incident_c @ ( sK2_SY23 @ SV3 @ SV6 ) @ SV6 )
| ( incident_c @ ( sK2_SY23 @ SV3 @ SV6 ) @ SV3 ) )
= $false )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(62,plain,
! [SV1: $i,SV4: $i] :
( ( ( SV4 = SV1 )
= $true )
| ( ( part_of @ SV4 @ SV1 )
= $false )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) ) )
= $false )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( incident_c @ SV9 @ SV6 ) )
= $true )
| ( ( incident_c @ SV9 @ SV3 )
= $true )
| ( ( part_of @ SV6 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( incident_c @ ( sK2_SY23 @ SV3 @ SV6 ) @ SV6 ) )
= $false )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(66,plain,
! [SV6: $i,SV3: $i] :
( ( ( incident_c @ ( sK2_SY23 @ SV3 @ SV6 ) @ SV3 )
= $false )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[61]) ).
thf(67,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
| ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( incident_c @ SV9 @ SV6 )
= $false )
| ( ( incident_c @ SV9 @ SV3 )
= $true )
| ( ( part_of @ SV6 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV6: $i,SV3: $i] :
( ( ( incident_c @ ( sK2_SY23 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( part_of @ SV6 @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(70,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) ) )
= $true )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) ) )
= $false )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(72,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( part_of @ SV5 @ SV2 )
| ~ ( part_of @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(73,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( ~ ( part_of @ SV5 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(74,plain,
! [SV8: $i,SV7: $i,SV2: $i,SV5: $i] :
( ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( ~ ( part_of @ SV7 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(75,plain,
! [SV8: $i,SV5: $i,SV2: $i,SV7: $i] :
( ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(76,plain,
! [SV7: $i,SV5: $i,SV2: $i,SV8: $i] :
( ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( ~ ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(77,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i] :
( ( ( ~ ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(78,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i] :
( ( ( ! [SY26: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY26 @ SV5 )
| ~ ( end_point @ SY26 @ SV7 ) )
| ~ ( end_point @ SY26 @ SV8 ) ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(79,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) )
| ~ ( end_point @ SV10 @ SV8 ) ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(80,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) )
| ~ ( end_point @ SV10 @ SV8 ) ) )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(81,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) )
| ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(82,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) ) )
= $true )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(83,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) ) )
= $false )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(84,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ( end_point @ SV10 @ SV5 )
| ~ ( end_point @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(85,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( ~ ( end_point @ SV10 @ SV5 ) )
= $true )
| ( ( ~ ( end_point @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(86,plain,
! [SV2: $i,SV8: $i,SV7: $i,SV5: $i,SV10: $i] :
( ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( ~ ( end_point @ SV10 @ SV7 ) )
= $true )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(87,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV7: $i,SV10: $i] :
( ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( ~ ( end_point @ SV10 @ SV8 ) )
= $true )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(88,plain,
! [SV2: $i,SV7: $i,SV5: $i,SV8: $i,SV10: $i] :
( ( ( end_point @ SV10 @ SV8 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 )
| ( part_of @ SV8 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(89,plain,
! [SV10: $i,SV2: $i,SV5: $i,SV8: $i,SV7: $i] :
( ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 )
| ( part_of @ SV5 @ SV8 ) )
= $true )
| ( ( part_of @ SV8 @ SV5 )
= $true )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(90,plain,
! [SV10: $i,SV2: $i,SV5: $i,SV8: $i,SV7: $i] :
( ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 )
| ( part_of @ SV7 @ SV5 ) )
= $true )
| ( ( part_of @ SV5 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV5 )
= $true )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(91,plain,
! [SV10: $i,SV2: $i,SV5: $i,SV8: $i,SV7: $i] :
( ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 )
| ( part_of @ SV5 @ SV7 ) )
= $true )
| ( ( part_of @ SV7 @ SV5 )
= $true )
| ( ( part_of @ SV5 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV5 )
= $true )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(92,plain,
! [SV10: $i,SV2: $i,SV5: $i,SV8: $i,SV7: $i] :
( ( ( ( part_of @ SV7 @ SV8 )
| ( part_of @ SV8 @ SV7 ) )
= $true )
| ( ( part_of @ SV5 @ SV7 )
= $true )
| ( ( part_of @ SV7 @ SV5 )
= $true )
| ( ( part_of @ SV5 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV5 )
= $true )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(93,plain,
! [SV10: $i,SV2: $i,SV5: $i,SV8: $i,SV7: $i] :
( ( ( part_of @ SV7 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV7 )
= $true )
| ( ( part_of @ SV5 @ SV7 )
= $true )
| ( ( part_of @ SV7 @ SV5 )
= $true )
| ( ( part_of @ SV5 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV5 )
= $true )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV5 @ SV2 )
= $false )
| ( ( part_of @ SV7 @ SV2 )
= $false )
| ( ( end_point @ SV10 @ SV7 )
= $false )
| ( ( end_point @ SV10 @ SV5 )
= $false )
| ( ( end_point @ SV10 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(94,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[32,93,69,68,66,62]) ).
thf(95,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO080+1 : TPTP v9.3.1. Released v2.4.0.
% 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
% 0.08/0.17 % Computer : n006.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 10:02:07 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
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% 0.08/0.25 No.of.Axioms: 3
% 0.08/0.25
% 0.08/0.25 Length.of.Defs: 0
% 0.08/0.25
% 0.08/0.25 Contains.Choice.Funs: false
% 0.08/0.25 ...
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% 0.08/0.25 ********************************
% 0.08/0.25 * All subproblems solved! *
% 0.08/0.25 ********************************
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/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:94,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.25
% 0.08/0.25 %**** Beginning of derivation protocol ****
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
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% 0.08/0.25 %**** End of derivation protocol ****
% 0.08/0.25 %**** no. of clauses in derivation: 82 ****
% 0.08/0.25 %**** clause counter: 94 ****
% 0.08/0.25
% 0.08/0.25 % SZS status Theorem for /export/starexec/sandbox/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:94,loop_count:0,foatp_calls:1,translation:fof_full)
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