%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO085+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:52 AM UTC 2026
% Result : Theorem 0.08s 0.30s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 7
% Syntax : Number of formulae : 158 ( 61 unt; 0 typ; 0 def)
% Number of atoms : 1587 ( 487 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 2811 ( 727 ~; 616 |; 41 &;1405 @)
% ( 6 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 476 ( 0 ^; 450 !; 26 ?; 476 :)
% 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_SY37,type,
sK2_SY37: $i > $i > $i ).
thf(tp_sK3_SY32,type,
sK3_SY32: $i > $i ).
thf(tp_sK4_SY35,type,
sK4_SY35: $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i ).
thf(4,axiom,
! [C: $i,P: $i] :
( ( end_point @ P @ C )
=> ? [Q: $i] :
( ( end_point @ Q @ C )
& ( P != Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c6) ).
thf(5,axiom,
! [C: $i,P: $i,Q: $i,R: $i] :
( ( ( end_point @ P @ C )
& ( end_point @ Q @ C )
& ( end_point @ R @ C ) )
=> ( ( P = Q )
| ( P = R )
| ( Q = R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c5) ).
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(10,axiom,
! [C: $i] :
( ( open @ C )
<=> ? [P: $i] : ( end_point @ P @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',open_defn) ).
thf(11,axiom,
! [C: $i] :
( ( closed @ C )
<=> ~ ? [P: $i] : ( end_point @ P @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closed_defn) ).
thf(17,conjecture,
! [C: $i] :
( ( open @ C )
=> ? [P: $i,Q: $i] :
( ( P != Q )
& ( end_point @ P @ C )
& ( end_point @ Q @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_2_7_1) ).
thf(18,negated_conjecture,
( ( ! [C: $i] :
( ( open @ C )
=> ? [P: $i,Q: $i] :
( ( P != Q )
& ( end_point @ P @ C )
& ( end_point @ Q @ C ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [C: $i] :
( ( open @ C )
=> ? [P: $i,Q: $i] :
( ( P != Q )
& ( end_point @ P @ C )
& ( end_point @ Q @ C ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [C: $i,P: $i] :
( ( end_point @ P @ C )
=> ? [Q: $i] :
( ( end_point @ Q @ C )
& ( P != Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [C: $i,P: $i,Q: $i,R: $i] :
( ( ( end_point @ P @ C )
& ( end_point @ Q @ C )
& ( end_point @ R @ C ) )
=> ( ( P = Q )
| ( P = R )
| ( Q = R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,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(23,plain,
( ( ! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [C: $i] :
( ( open @ C )
<=> ? [P: $i] : ( end_point @ P @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [C: $i] :
( ( closed @ C )
<=> ~ ? [P: $i] : ( end_point @ P @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ( open @ sK1_C )
=> ? [SY21: $i,SY22: $i] :
( ( SY21 != SY22 )
& ( end_point @ SY21 @ sK1_C )
& ( end_point @ SY22 @ sK1_C ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(27,plain,
( ( open @ sK1_C )
= $true ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(28,plain,
( ( ? [SY21: $i,SY22: $i] :
( ( SY21 != SY22 )
& ( end_point @ SY21 @ sK1_C )
& ( end_point @ SY22 @ sK1_C ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ? [SY21: $i,SY22: $i] :
( ( SY21 != SY22 )
& ( end_point @ SY21 @ sK1_C )
& ( end_point @ SY22 @ sK1_C ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[28]) ).
thf(30,plain,
( ( ! [C: $i] :
( ( closed @ C )
<=> ~ ? [P: $i] : ( end_point @ P @ C ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [C: $i] :
( ( open @ C )
<=> ? [P: $i] : ( end_point @ P @ C ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(33,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)],[22]) ).
thf(34,plain,
( ( ! [C: $i,P: $i,Q: $i,R: $i] :
( ( ( end_point @ P @ C )
& ( end_point @ Q @ C )
& ( end_point @ R @ C ) )
=> ( ( P = Q )
| ( P = R )
| ( Q = R ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(35,plain,
( ( ! [C: $i,P: $i] :
( ( end_point @ P @ C )
=> ? [Q: $i] :
( ( end_point @ Q @ C )
& ( P != Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(36,plain,
( ( open @ sK1_C )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(37,plain,
( ( ~ ? [SY21: $i,SY22: $i] :
( ( SY21 != SY22 )
& ( end_point @ SY21 @ sK1_C )
& ( end_point @ SY22 @ sK1_C ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(38,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( end_point @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( end_point @ SX2 @ SX0 )
| ~ ( ( SX1 != SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(39,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)],[33]) ).
thf(40,plain,
( ( ~ ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( end_point @ SX0 @ sK1_C ) )
| ~ ( end_point @ SX1 @ sK1_C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ( end_point @ SX1 @ SX0 )
| ~ ( end_point @ SX2 @ SX0 ) )
| ~ ( end_point @ SX3 @ SX0 ) )
| ( SX1 = SX2 )
| ( SX1 = SX3 )
| ( SX2 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(42,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( open @ SX0 )
| ~ ! [SX1: $i] :
~ ( end_point @ SX1 @ SX0 ) )
| ~ ( ~ ~ ! [SX1: $i] :
~ ( end_point @ SX1 @ SX0 )
| ( open @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( closed @ SX0 )
| ~ ~ ! [SX1: $i] :
~ ( end_point @ SX1 @ SX0 ) )
| ~ ( ~ ~ ~ ! [SX1: $i] :
~ ( end_point @ SX1 @ SX0 )
| ( closed @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( part_of @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) ) )
| ( open @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( end_point @ SY23 @ SV1 )
| ~ ! [SY24: $i] :
~ ~ ( ~ ( end_point @ SY24 @ SV1 )
| ~ ( ( SY23 != SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY25: $i,SY26: $i,SY27: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SY25 @ SV2 )
| ~ ( part_of @ SY26 @ SV2 ) )
| ~ ( part_of @ SY27 @ SV2 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SX4 @ SY25 )
| ~ ( end_point @ SX4 @ SY26 ) )
| ~ ( end_point @ SX4 @ SY27 ) ) )
| ( part_of @ SY26 @ SY27 )
| ( part_of @ SY27 @ SY26 )
| ( part_of @ SY25 @ SY26 )
| ( part_of @ SY26 @ SY25 )
| ( part_of @ SY25 @ SY27 )
| ( part_of @ SY27 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
( ( ~ ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( end_point @ SX0 @ sK1_C ) )
| ~ ( end_point @ SX1 @ sK1_C ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY29: $i,SY30: $i,SY31: $i] :
( ~ ~ ( ~ ~ ( ~ ( end_point @ SY29 @ SV3 )
| ~ ( end_point @ SY30 @ SV3 ) )
| ~ ( end_point @ SY31 @ SV3 ) )
| ( SY29 = SY30 )
| ( SY29 = SY31 )
| ( SY30 = SY31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV4: $i] :
( ( ~ ( ~ ( ~ ( open @ SV4 )
| ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
| ~ ( ~ ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 )
| ( open @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV5: $i] :
( ( ~ ( ~ ( ~ ( closed @ SV5 )
| ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
| ~ ( ~ ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 )
| ( closed @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV6: $i] :
( ( ! [SY36: $i] :
( ~ ~ ( ~ ( part_of @ SY36 @ SV6 )
| ~ ( ( SY36 != SV6 ) ) )
| ( open @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV1: $i,SV7: $i] :
( ( ~ ( end_point @ SV7 @ SV1 )
| ~ ! [SY37: $i] :
~ ~ ( ~ ( end_point @ SY37 @ SV1 )
| ~ ( ( SV7 != SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV2: $i,SV8: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SY38 @ SV2 ) )
| ~ ( part_of @ SY39 @ SV2 ) )
| ~ ~ ! [SY40: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY40 @ SV8 )
| ~ ( end_point @ SY40 @ SY38 ) )
| ~ ( end_point @ SY40 @ SY39 ) ) )
| ( part_of @ SY38 @ SY39 )
| ( part_of @ SY39 @ SY38 )
| ( part_of @ SV8 @ SY38 )
| ( part_of @ SY38 @ SV8 )
| ( part_of @ SV8 @ SY39 )
| ( part_of @ SY39 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
( ( ! [SX0: $i] :
~ ~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ( ( SX0 != SX1 ) )
| ~ ( end_point @ SX0 @ sK1_C ) )
| ~ ( end_point @ SX1 @ sK1_C ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(55,plain,
! [SV3: $i,SV9: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ~ ~ ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SY41 @ SV3 ) )
| ~ ( end_point @ SY42 @ SV3 ) )
| ( SV9 = SY41 )
| ( SV9 = SY42 )
| ( SY41 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV4: $i] :
( ( ~ ( ~ ( open @ SV4 )
| ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
| ~ ( ~ ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 )
| ( open @ SV4 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(57,plain,
! [SV5: $i] :
( ( ~ ( ~ ( closed @ SV5 )
| ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
| ~ ( ~ ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 )
| ( closed @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(58,plain,
! [SV6: $i,SV10: $i] :
( ( ~ ~ ( ~ ( part_of @ SV10 @ SV6 )
| ~ ( ( SV10 != SV6 ) ) )
| ( open @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( end_point @ SV7 @ SV1 ) )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( end_point @ SY37 @ SV1 )
| ~ ( ( SV7 != SY37 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[52]) ).
thf(60,plain,
! [SV11: $i,SV2: $i,SV8: $i] :
( ( ! [SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SY43 @ SV2 ) )
| ~ ~ ! [SY44: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY44 @ SV8 )
| ~ ( end_point @ SY44 @ SV11 ) )
| ~ ( end_point @ SY44 @ SY43 ) ) )
| ( part_of @ SV11 @ SY43 )
| ( part_of @ SY43 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SY43 )
| ( part_of @ SY43 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(61,plain,
! [SV12: $i] :
( ( ~ ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( ( SV12 != SY45 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SY45 @ sK1_C ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(62,plain,
! [SV13: $i,SV3: $i,SV9: $i] :
( ( ! [SY46: $i] :
( ~ ~ ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
| ~ ( end_point @ SY46 @ SV3 ) )
| ( SV9 = SV13 )
| ( SV9 = SY46 )
| ( SV13 = SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(63,plain,
! [SV4: $i] :
( ( ~ ( ~ ( open @ SV4 )
| ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(64,plain,
! [SV4: $i] :
( ( ~ ( ~ ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 )
| ( open @ SV4 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(65,plain,
! [SV5: $i] :
( ( ~ ( ~ ( closed @ SV5 )
| ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(66,plain,
! [SV5: $i] :
( ( ~ ( ~ ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 )
| ( closed @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(67,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV10 @ SV6 )
| ~ ( ( SV10 != SV6 ) ) ) )
= $true )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(68,plain,
! [SV1: $i,SV7: $i] :
( ( ( end_point @ SV7 @ SV1 )
= $false )
| ( ( ~ ! [SY37: $i] :
~ ~ ( ~ ( end_point @ SY37 @ SV1 )
| ~ ( ( SV7 != SY37 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(69,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) )
| ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
| ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(70,plain,
! [SV12: $i] :
( ( ~ ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( ( SV12 != SY45 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SY45 @ sK1_C ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
| ~ ( end_point @ SV15 @ SV3 ) )
| ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV4: $i] :
( ( ~ ( open @ SV4 )
| ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(73,plain,
! [SV4: $i] :
( ( ~ ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 )
| ( open @ SV4 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(74,plain,
! [SV5: $i] :
( ( ~ ( closed @ SV5 )
| ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[65]) ).
thf(75,plain,
! [SV5: $i] :
( ( ~ ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 )
| ( closed @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(76,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( part_of @ SV10 @ SV6 )
| ~ ( ( SV10 != SV6 ) ) ) )
= $false )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV7: $i,SV1: $i] :
( ( ( ! [SY37: $i] :
~ ~ ( ~ ( end_point @ SY37 @ SV1 )
| ~ ( ( SV7 != SY37 ) ) ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) )
| ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV12: $i] :
( ( ! [SY45: $i] :
~ ~ ( ~ ~ ( ~ ( ( SV12 != SY45 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SY45 @ sK1_C ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[70]) ).
thf(80,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
| ~ ( end_point @ SV15 @ SV3 ) ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV4: $i] :
( ( ( ~ ( open @ SV4 ) )
= $true )
| ( ( ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV4: $i] :
( ( ( ~ ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV5: $i] :
( ( ( ~ ( closed @ SV5 ) )
= $true )
| ( ( ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV5: $i] :
( ( ( ~ ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 ) )
= $true )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( part_of @ SV10 @ SV6 )
| ~ ( ( SV10 != SV6 ) ) )
= $true )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ~ ( ~ ( end_point @ ( sK2_SY37 @ SV7 @ SV1 ) @ SV1 )
| ~ ( ( SV7
!= ( sK2_SY37 @ SV7 @ SV1 ) ) ) ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[77]) ).
thf(87,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) )
| ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) ) )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SV16 @ sK1_C ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
| ~ ( end_point @ SV15 @ SV3 ) ) )
= $false )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV4: $i] :
( ( ( open @ SV4 )
= $false )
| ( ( ~ ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV4: $i] :
( ( ( ~ ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 ) )
= $false )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV5: $i] :
( ( ( closed @ SV5 )
= $false )
| ( ( ~ ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV5: $i] :
( ( ( ~ ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 ) )
= $false )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( part_of @ SV10 @ SV6 ) )
= $true )
| ( ( ~ ( ( SV10 != SV6 ) ) )
= $true )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( ~ ( end_point @ ( sK2_SY37 @ SV7 @ SV1 ) @ SV1 )
| ~ ( ( SV7
!= ( sK2_SY37 @ SV7 @ SV1 ) ) ) ) )
= $true )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(96,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) )
| ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(97,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ( ~ ~ ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SV16 @ sK1_C ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
| ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(99,plain,
! [SV4: $i] :
( ( ( ! [SY32: $i] :
~ ( end_point @ SY32 @ SV4 ) )
= $false )
| ( ( open @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV4: $i] :
( ( ( ! [SY33: $i] :
~ ( end_point @ SY33 @ SV4 ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[91]) ).
thf(101,plain,
! [SV5: $i] :
( ( ( ~ ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
= $false )
| ( ( closed @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(102,plain,
! [SV5: $i] :
( ( ( ~ ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 ) )
= $true )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[93]) ).
thf(103,plain,
! [SV6: $i,SV10: $i] :
( ( ( part_of @ SV10 @ SV6 )
= $false )
| ( ( ~ ( ( SV10 != SV6 ) ) )
= $true )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( end_point @ ( sK2_SY37 @ SV7 @ SV1 ) @ SV1 )
| ~ ( ( SV7
!= ( sK2_SY37 @ SV7 @ SV1 ) ) ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV16: $i,SV12: $i] :
( ( ~ ~ ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
| ~ ( end_point @ SV16 @ sK1_C ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[97]) ).
thf(107,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) ) )
= $true )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV4: $i] :
( ( ( ~ ( end_point @ ( sK3_SY32 @ SV4 ) @ SV4 ) )
= $false )
| ( ( open @ SV4 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(109,plain,
! [SV4: $i,SV17: $i] :
( ( ( ~ ( end_point @ SV17 @ SV4 ) )
= $true )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV5: $i] :
( ( ( ! [SY34: $i] :
~ ( end_point @ SY34 @ SV5 ) )
= $true )
| ( ( closed @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(111,plain,
! [SV5: $i] :
( ( ( ! [SY35: $i] :
~ ( end_point @ SY35 @ SV5 ) )
= $false )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV6: $i,SV10: $i] :
( ( ( SV10 != SV6 )
= $false )
| ( ( part_of @ SV10 @ SV6 )
= $false )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( end_point @ ( sK2_SY37 @ SV7 @ SV1 ) @ SV1 ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(114,plain,
! [SV1: $i,SV7: $i] :
( ( ( ~ ( ( SV7
!= ( sK2_SY37 @ SV7 @ SV1 ) ) ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[104]) ).
thf(115,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) ) )
= $false )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) ) )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) ) )
= $false )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV4: $i] :
( ( ( end_point @ ( sK3_SY32 @ SV4 ) @ SV4 )
= $true )
| ( ( open @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(119,plain,
! [SV4: $i,SV17: $i] :
( ( ( end_point @ SV17 @ SV4 )
= $false )
| ( ( open @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(120,plain,
! [SV5: $i,SV18: $i] :
( ( ( ~ ( end_point @ SV18 @ SV5 ) )
= $true )
| ( ( closed @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV5: $i] :
( ( ( ~ ( end_point @ ( sK4_SY35 @ SV5 ) @ SV5 ) )
= $false )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[111]) ).
thf(122,plain,
! [SV6: $i,SV10: $i] :
( ( ( SV10 = SV6 )
= $true )
| ( ( part_of @ SV10 @ SV6 )
= $false )
| ( ( open @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[112]) ).
thf(123,plain,
! [SV1: $i,SV7: $i] :
( ( ( end_point @ ( sK2_SY37 @ SV7 @ SV1 ) @ SV1 )
= $true )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(124,plain,
! [SV1: $i,SV7: $i] :
( ( ( SV7
!= ( sK2_SY37 @ SV7 @ SV1 ) )
= $true )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(125,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
| ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(126,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) ) )
= $false )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( end_point @ SV9 @ SV3 )
| ~ ( end_point @ SV13 @ SV3 ) )
= $true )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(128,plain,
! [SV5: $i,SV18: $i] :
( ( ( end_point @ SV18 @ SV5 )
= $false )
| ( ( closed @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(129,plain,
! [SV5: $i] :
( ( ( end_point @ ( sK4_SY35 @ SV5 ) @ SV5 )
= $true )
| ( ( closed @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(130,plain,
! [SV1: $i,SV7: $i] :
( ( ( SV7
= ( sK2_SY37 @ SV7 @ SV1 ) )
= $false )
| ( ( end_point @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(131,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) ) )
= $true )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV16 ) )
| ~ ( end_point @ SV12 @ sK1_C ) )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(133,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( end_point @ SV9 @ SV3 ) )
= $true )
| ( ( ~ ( end_point @ SV13 @ SV3 ) )
= $true )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) ) )
= $false )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(135,plain,
! [SV16: $i,SV12: $i] :
( ( ( ~ ( ( SV12 != SV16 ) ) )
= $true )
| ( ( ~ ( end_point @ SV12 @ sK1_C ) )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(136,plain,
! [SV15: $i,SV13: $i,SV3: $i,SV9: $i] :
( ( ( end_point @ SV9 @ SV3 )
= $false )
| ( ( ~ ( end_point @ SV13 @ SV3 ) )
= $true )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(137,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( part_of @ SV8 @ SV2 )
| ~ ( part_of @ SV11 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(138,plain,
! [SV16: $i,SV12: $i] :
( ( ( SV12 != SV16 )
= $false )
| ( ( ~ ( end_point @ SV12 @ sK1_C ) )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV15: $i,SV9: $i,SV3: $i,SV13: $i] :
( ( ( end_point @ SV13 @ SV3 )
= $false )
| ( ( end_point @ SV9 @ SV3 )
= $false )
| ( ( ~ ( end_point @ SV15 @ SV3 ) )
= $true )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(140,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( part_of @ SV8 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV11 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(141,plain,
! [SV16: $i,SV12: $i] :
( ( ( SV12 = SV16 )
= $true )
| ( ( ~ ( end_point @ SV12 @ sK1_C ) )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(142,plain,
! [SV13: $i,SV9: $i,SV3: $i,SV15: $i] :
( ( ( end_point @ SV15 @ SV3 )
= $false )
| ( ( end_point @ SV9 @ SV3 )
= $false )
| ( ( end_point @ SV13 @ SV3 )
= $false )
| ( ( ( SV9 = SV13 )
| ( SV9 = SV15 )
| ( SV13 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(143,plain,
! [SV14: $i,SV11: $i,SV2: $i,SV8: $i] :
( ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ~ ( part_of @ SV11 @ SV2 ) )
= $true )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(144,plain,
! [SV16: $i,SV12: $i] :
( ( ( end_point @ SV12 @ sK1_C )
= $false )
| ( ( SV12 = SV16 )
= $true )
| ( ( ~ ( end_point @ SV16 @ sK1_C ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(145,plain,
! [SV3: $i,SV15: $i,SV13: $i,SV9: $i] :
( ( ( ( SV9 = SV13 )
| ( SV9 = SV15 ) )
= $true )
| ( ( SV13 = SV15 )
= $true )
| ( ( end_point @ SV13 @ SV3 )
= $false )
| ( ( end_point @ SV9 @ SV3 )
= $false )
| ( ( end_point @ SV15 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(146,plain,
! [SV14: $i,SV8: $i,SV2: $i,SV11: $i] :
( ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( ~ ( part_of @ SV14 @ SV2 ) )
= $true )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(147,plain,
! [SV12: $i,SV16: $i] :
( ( ( end_point @ SV16 @ sK1_C )
= $false )
| ( ( SV12 = SV16 )
= $true )
| ( ( end_point @ SV12 @ sK1_C )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV3: $i,SV15: $i,SV13: $i,SV9: $i] :
( ( ( SV9 = SV13 )
= $true )
| ( ( SV9 = SV15 )
= $true )
| ( ( SV13 = SV15 )
= $true )
| ( ( end_point @ SV13 @ SV3 )
= $false )
| ( ( end_point @ SV9 @ SV3 )
= $false )
| ( ( end_point @ SV15 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(149,plain,
! [SV11: $i,SV8: $i,SV2: $i,SV14: $i] :
( ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( ~ ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(150,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i] :
( ( ( ~ ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(151,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i] :
( ( ( ! [SY47: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY47 @ SV8 )
| ~ ( end_point @ SY47 @ SV11 ) )
| ~ ( end_point @ SY47 @ SV14 ) ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(152,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) )
| ~ ( end_point @ SV19 @ SV14 ) ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(153,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( ~ ~ ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) )
| ~ ( end_point @ SV19 @ SV14 ) ) )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(154,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) )
| ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(155,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) ) )
= $true )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(156,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) ) )
= $false )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(157,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( end_point @ SV19 @ SV8 )
| ~ ( end_point @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(158,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( ~ ( end_point @ SV19 @ SV8 ) )
= $true )
| ( ( ~ ( end_point @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[157]) ).
thf(159,plain,
! [SV2: $i,SV14: $i,SV11: $i,SV8: $i,SV19: $i] :
( ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( ~ ( end_point @ SV19 @ SV11 ) )
= $true )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(160,plain,
! [SV2: $i,SV14: $i,SV8: $i,SV11: $i,SV19: $i] :
( ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( ~ ( end_point @ SV19 @ SV14 ) )
= $true )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(161,plain,
! [SV2: $i,SV11: $i,SV8: $i,SV14: $i,SV19: $i] :
( ( ( end_point @ SV19 @ SV14 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 )
| ( part_of @ SV14 @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(162,plain,
! [SV19: $i,SV2: $i,SV8: $i,SV14: $i,SV11: $i] :
( ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 )
| ( part_of @ SV8 @ SV14 ) )
= $true )
| ( ( part_of @ SV14 @ SV8 )
= $true )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(163,plain,
! [SV19: $i,SV2: $i,SV8: $i,SV14: $i,SV11: $i] :
( ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 )
| ( part_of @ SV11 @ SV8 ) )
= $true )
| ( ( part_of @ SV8 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV8 )
= $true )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(164,plain,
! [SV19: $i,SV2: $i,SV8: $i,SV14: $i,SV11: $i] :
( ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 )
| ( part_of @ SV8 @ SV11 ) )
= $true )
| ( ( part_of @ SV11 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV8 )
= $true )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(165,plain,
! [SV19: $i,SV2: $i,SV8: $i,SV14: $i,SV11: $i] :
( ( ( ( part_of @ SV11 @ SV14 )
| ( part_of @ SV14 @ SV11 ) )
= $true )
| ( ( part_of @ SV8 @ SV11 )
= $true )
| ( ( part_of @ SV11 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV8 )
= $true )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(166,plain,
! [SV19: $i,SV2: $i,SV8: $i,SV14: $i,SV11: $i] :
( ( ( part_of @ SV11 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV11 )
= $true )
| ( ( part_of @ SV8 @ SV11 )
= $true )
| ( ( part_of @ SV11 @ SV8 )
= $true )
| ( ( part_of @ SV8 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV8 )
= $true )
| ( ( part_of @ SV14 @ SV2 )
= $false )
| ( ( part_of @ SV8 @ SV2 )
= $false )
| ( ( part_of @ SV11 @ SV2 )
= $false )
| ( ( end_point @ SV19 @ SV11 )
= $false )
| ( ( end_point @ SV19 @ SV8 )
= $false )
| ( ( end_point @ SV19 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(167,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,166,148,147,130,129,128,123,122,119,118]) ).
thf(168,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO085+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
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 10:05:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.30
% 0.08/0.30 No.of.Axioms: 6
% 0.08/0.30
% 0.08/0.30 Length.of.Defs: 0
% 0.08/0.30
% 0.08/0.30 Contains.Choice.Funs: false
% 0.08/0.30 .....
% 0.08/0.30
% 0.08/0.30 ********************************
% 0.08/0.30 * All subproblems solved! *
% 0.08/0.30 ********************************
% 0.08/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:167,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.30
% 0.08/0.30 %**** Beginning of derivation protocol ****
% 0.08/0.30 % SZS output start CNFRefutation
% See solution above
% 0.08/0.30
% 0.08/0.30 %**** End of derivation protocol ****
% 0.08/0.30 %**** no. of clauses in derivation: 158 ****
% 0.08/0.30 %**** clause counter: 167 ****
% 0.08/0.30
% 0.08/0.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:7,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:167,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------