%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO093+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 10:17:53 AM UTC 2026
% Result : Theorem 231.80s 38.95s
% Output : CNFRefutation 231.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 8
% Syntax : Number of formulae : 200 ( 72 unt; 0 typ; 0 def)
% Number of atoms : 1970 ( 560 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 4012 ( 734 ~; 778 |; 42 &;2424 @)
% ( 12 <=>; 22 =>; 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 : 21 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 647 ( 0 ^; 629 !; 18 ?; 647 :)
% 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_sK10_SY69,type,
sK10_SY69: $i > $i > $i > $i ).
thf(tp_sK1_C,type,
sK1_C: $i ).
thf(tp_sK2_SY28,type,
sK2_SY28: $i ).
thf(tp_sK3_SY31,type,
sK3_SY31: $i ).
thf(tp_sK4_SY33,type,
sK4_SY33: $i ).
thf(tp_sK5_SY56,type,
sK5_SY56: $i > $i > $i ).
thf(tp_sK6_SY37,type,
sK6_SY37: $i > $i ).
thf(tp_sK7_SY62,type,
sK7_SY62: $i > $i > $i ).
thf(tp_sK8_SY55,type,
sK8_SY55: $i > $i > $i > $i ).
thf(tp_sK9_SY71,type,
sK9_SY71: $i > $i > $i ).
thf(tp_sum,type,
sum: $i > $i > $i ).
thf(2,axiom,
! [C1: $i,C2: $i] :
( ? [P: $i] : ( meet @ P @ C1 @ C2 )
=> ? [C: $i] :
( C
= ( sum @ C1 @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c8) ).
thf(6,axiom,
! [C: $i,P: $i] :
( ( inner_point @ P @ C )
=> ? [C1: $i,C2: $i] :
( ( meet @ P @ C1 @ C2 )
& ( C
= ( sum @ C1 @ C2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
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/sandbox2/benchmark/theBenchmark.p',c2) ).
thf(9,axiom,
! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c1) ).
thf(10,axiom,
! [C: $i] :
( ( open @ C )
<=> ? [P: $i] : ( end_point @ P @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',open_defn) ).
thf(15,axiom,
! [C: $i,C1: $i,C2: $i] :
( ( C
= ( sum @ C1 @ C2 ) )
<=> ! [Q: $i] :
( ( incident_c @ Q @ C )
<=> ( ( incident_c @ Q @ C1 )
| ( incident_c @ Q @ C2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_defn) ).
thf(16,axiom,
! [C: $i,C1: $i] :
( ( part_of @ C1 @ C )
<=> ! [P: $i] :
( ( incident_c @ P @ C1 )
=> ( incident_c @ P @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',part_of_defn) ).
thf(17,conjecture,
! [C: $i,C1: $i,C2: $i,P: $i] :
( ( ( open @ C )
& ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( meet @ P @ C1 @ C2 ) )
=> ( open @ ( sum @ C1 @ C2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proposition_2_14_2) ).
thf(18,negated_conjecture,
( ( ! [C: $i,C1: $i,C2: $i,P: $i] :
( ( ( open @ C )
& ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( meet @ P @ C1 @ C2 ) )
=> ( open @ ( sum @ C1 @ C2 ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[17]) ).
thf(19,plain,
( ( ! [C: $i,C1: $i,C2: $i,P: $i] :
( ( ( open @ C )
& ( part_of @ C1 @ C )
& ( part_of @ C2 @ C )
& ( meet @ P @ C1 @ C2 ) )
=> ( open @ ( sum @ C1 @ C2 ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[18]) ).
thf(20,plain,
( ( ! [C1: $i,C2: $i] :
( ? [P: $i] : ( meet @ P @ C1 @ C2 )
=> ? [C: $i] :
( C
= ( sum @ C1 @ C2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [C: $i,P: $i] :
( ( inner_point @ P @ C )
=> ? [C1: $i,C2: $i] :
( ( meet @ P @ C1 @ C2 )
& ( C
= ( sum @ C1 @ C2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
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,C1: $i,C2: $i] :
( ( C
= ( sum @ C1 @ C2 ) )
<=> ! [Q: $i] :
( ( incident_c @ Q @ C )
<=> ( ( incident_c @ Q @ C1 )
| ( incident_c @ Q @ C2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(26,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(27,plain,
( ( ! [SY28: $i,SY29: $i,SY30: $i] :
( ( ( open @ sK1_C )
& ( part_of @ SY28 @ sK1_C )
& ( part_of @ SY29 @ sK1_C )
& ( meet @ SY30 @ SY28 @ SY29 ) )
=> ( open @ ( sum @ SY28 @ SY29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(28,plain,
( ( ! [SY31: $i,SY32: $i] :
( ( ( open @ sK1_C )
& ( part_of @ sK2_SY28 @ sK1_C )
& ( part_of @ SY31 @ sK1_C )
& ( meet @ SY32 @ sK2_SY28 @ SY31 ) )
=> ( open @ ( sum @ sK2_SY28 @ SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ! [SY33: $i] :
( ( ( open @ sK1_C )
& ( part_of @ sK2_SY28 @ sK1_C )
& ( part_of @ sK3_SY31 @ sK1_C )
& ( meet @ SY33 @ sK2_SY28 @ sK3_SY31 ) )
=> ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ( ( open @ sK1_C )
& ( part_of @ sK2_SY28 @ sK1_C )
& ( part_of @ sK3_SY31 @ sK1_C )
& ( meet @ sK4_SY33 @ sK2_SY28 @ sK3_SY31 ) )
=> ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[29]) ).
thf(31,plain,
( ( open @ sK1_C )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(32,plain,
( ( part_of @ sK2_SY28 @ sK1_C )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(33,plain,
( ( part_of @ sK3_SY31 @ sK1_C )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(34,plain,
( ( meet @ sK4_SY33 @ sK2_SY28 @ sK3_SY31 )
= $true ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(35,plain,
( ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) )
= $false ),
inference(standard_cnf,[status(thm)],[30]) ).
thf(36,plain,
( ( ~ ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(37,plain,
( ( ! [C: $i,C1: $i] :
( ( part_of @ C1 @ C )
<=> ! [P: $i] :
( ( incident_c @ P @ C1 )
=> ( incident_c @ P @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(38,plain,
( ( ! [C: $i,C1: $i,C2: $i] :
( ( C
= ( sum @ C1 @ C2 ) )
<=> ! [Q: $i] :
( ( incident_c @ Q @ C )
<=> ( ( incident_c @ Q @ C1 )
| ( incident_c @ Q @ C2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(39,plain,
( ( ! [C: $i] :
( ( open @ C )
<=> ? [P: $i] : ( end_point @ P @ C ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(40,plain,
( ( ! [C: $i,C1: $i] :
( ( ( part_of @ C1 @ C )
& ( C1 != C ) )
=> ( open @ C1 ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(41,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(42,plain,
( ( ! [C: $i,P: $i] :
( ( inner_point @ P @ C )
=> ? [C1: $i,C2: $i] :
( ( meet @ P @ C1 @ C2 )
& ( C
= ( sum @ C1 @ C2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(43,plain,
( ( ! [C1: $i,C2: $i] :
( ? [P: $i] : ( meet @ P @ C1 @ C2 )
=> ? [C: $i] :
( C
= ( sum @ C1 @ C2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(44,plain,
( ( meet @ sK4_SY33 @ sK2_SY28 @ sK3_SY31 )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(45,plain,
( ( part_of @ sK3_SY31 @ sK1_C )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( part_of @ sK2_SY28 @ sK1_C )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(47,plain,
( ( open @ sK1_C )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(48,plain,
( ( ~ ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(49,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ! [SX2: $i] :
~ ( meet @ SX2 @ SX0 @ SX1 )
| ~ ! [SX2: $i] :
( SX2
!= ( sum @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(50,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)],[39]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( inner_point @ SX1 @ SX0 )
| ~ ! [SX2: $i] :
~ ~ ! [SX3: $i] :
~ ~ ( ~ ( meet @ SX1 @ SX2 @ SX3 )
| ( SX0
!= ( sum @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(52,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)],[41]) ).
thf(53,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)],[37]) ).
thf(54,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX0
!= ( sum @ SX1 @ SX2 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( incident_c @ SX3 @ SX0 )
| ( incident_c @ SX3 @ SX1 )
| ( incident_c @ SX3 @ SX2 ) )
| ~ ( ~ ( ( incident_c @ SX3 @ SX1 )
| ( incident_c @ SX3 @ SX2 ) )
| ( incident_c @ SX3 @ SX0 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( incident_c @ SX3 @ SX0 )
| ( incident_c @ SX3 @ SX1 )
| ( incident_c @ SX3 @ SX2 ) )
| ~ ( ~ ( ( incident_c @ SX3 @ SX1 )
| ( incident_c @ SX3 @ SX2 ) )
| ( incident_c @ SX3 @ SX0 ) ) )
| ( SX0
= ( sum @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( part_of @ SX1 @ SX0 )
| ~ ( ( SX1 != SX0 ) ) )
| ( open @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(56,plain,
( ( open @ ( sum @ sK2_SY28 @ sK3_SY31 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV1: $i] :
( ( ! [SY34: $i] :
( ~ ~ ! [SY35: $i] :
~ ( meet @ SY35 @ SV1 @ SY34 )
| ~ ! [SY36: $i] :
( SY36
!= ( sum @ SV1 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV2: $i] :
( ( ~ ( ~ ( ~ ( open @ SV2 )
| ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
| ~ ( ~ ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 )
| ( open @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV3: $i] :
( ( ! [SY39: $i] :
( ~ ( inner_point @ SY39 @ SV3 )
| ~ ! [SY40: $i] :
~ ~ ! [SY41: $i] :
~ ~ ( ~ ( meet @ SY39 @ SY40 @ SY41 )
| ( SV3
!= ( sum @ SY40 @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV4: $i] :
( ( ! [SY42: $i,SY43: $i,SY44: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SY42 @ SV4 )
| ~ ( part_of @ SY43 @ SV4 ) )
| ~ ( part_of @ SY44 @ SV4 ) )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SX4 @ SY42 )
| ~ ( end_point @ SX4 @ SY43 ) )
| ~ ( end_point @ SX4 @ SY44 ) ) )
| ( part_of @ SY43 @ SY44 )
| ( part_of @ SY44 @ SY43 )
| ( part_of @ SY42 @ SY43 )
| ( part_of @ SY43 @ SY42 )
| ( part_of @ SY42 @ SY44 )
| ( part_of @ SY44 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV5: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ~ ( part_of @ SY46 @ SV5 )
| ! [SY47: $i] :
( ~ ( incident_c @ SY47 @ SY46 )
| ( incident_c @ SY47 @ SV5 ) ) )
| ~ ( ~ ! [SY48: $i] :
( ~ ( incident_c @ SY48 @ SY46 )
| ( incident_c @ SY48 @ SV5 ) )
| ( part_of @ SY46 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV6: $i] :
( ( ! [SY49: $i,SY50: $i] :
~ ( ~ ( ( SV6
!= ( sum @ SY49 @ SY50 ) )
| ! [SY51: $i] :
~ ( ~ ( ~ ( incident_c @ SY51 @ SV6 )
| ( incident_c @ SY51 @ SY49 )
| ( incident_c @ SY51 @ SY50 ) )
| ~ ( ~ ( ( incident_c @ SY51 @ SY49 )
| ( incident_c @ SY51 @ SY50 ) )
| ( incident_c @ SY51 @ SV6 ) ) ) )
| ~ ( ~ ! [SY52: $i] :
~ ( ~ ( ~ ( incident_c @ SY52 @ SV6 )
| ( incident_c @ SY52 @ SY49 )
| ( incident_c @ SY52 @ SY50 ) )
| ~ ( ~ ( ( incident_c @ SY52 @ SY49 )
| ( incident_c @ SY52 @ SY50 ) )
| ( incident_c @ SY52 @ SV6 ) ) )
| ( SV6
= ( sum @ SY49 @ SY50 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
! [SV7: $i] :
( ( ! [SY53: $i] :
( ~ ~ ( ~ ( part_of @ SY53 @ SV7 )
| ~ ( ( SY53 != SV7 ) ) )
| ( open @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(64,plain,
! [SV8: $i,SV1: $i] :
( ( ~ ~ ! [SY54: $i] :
~ ( meet @ SY54 @ SV1 @ SV8 )
| ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(65,plain,
! [SV2: $i] :
( ( ~ ( ~ ( open @ SV2 )
| ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
| ~ ( ~ ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 )
| ( open @ SV2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV3: $i,SV9: $i] :
( ( ~ ( inner_point @ SV9 @ SV3 )
| ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ( meet @ SV9 @ SY56 @ SY57 )
| ( SV3
!= ( sum @ SY56 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV4: $i,SV10: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SY58 @ SV4 ) )
| ~ ( part_of @ SY59 @ SV4 ) )
| ~ ~ ! [SY60: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY60 @ SV10 )
| ~ ( end_point @ SY60 @ SY58 ) )
| ~ ( end_point @ SY60 @ SY59 ) ) )
| ( part_of @ SY58 @ SY59 )
| ( part_of @ SY59 @ SY58 )
| ( part_of @ SV10 @ SY58 )
| ( part_of @ SY58 @ SV10 )
| ( part_of @ SV10 @ SY59 )
| ( part_of @ SY59 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ( ~ ( part_of @ SV11 @ SV5 )
| ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) )
| ( part_of @ SV11 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(69,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY63: $i] :
~ ( ~ ( ( SV6
!= ( sum @ SV12 @ SY63 ) )
| ! [SY64: $i] :
~ ( ~ ( ~ ( incident_c @ SY64 @ SV6 )
| ( incident_c @ SY64 @ SV12 )
| ( incident_c @ SY64 @ SY63 ) )
| ~ ( ~ ( ( incident_c @ SY64 @ SV12 )
| ( incident_c @ SY64 @ SY63 ) )
| ( incident_c @ SY64 @ SV6 ) ) ) )
| ~ ( ~ ! [SY65: $i] :
~ ( ~ ( ~ ( incident_c @ SY65 @ SV6 )
| ( incident_c @ SY65 @ SV12 )
| ( incident_c @ SY65 @ SY63 ) )
| ~ ( ~ ( ( incident_c @ SY65 @ SV12 )
| ( incident_c @ SY65 @ SY63 ) )
| ( incident_c @ SY65 @ SV6 ) ) )
| ( SV6
= ( sum @ SV12 @ SY63 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(70,plain,
! [SV7: $i,SV13: $i] :
( ( ~ ~ ( ~ ( part_of @ SV13 @ SV7 )
| ~ ( ( SV13 != SV7 ) ) )
| ( open @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(71,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ~ ! [SY54: $i] :
~ ( meet @ SY54 @ SV1 @ SV8 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(72,plain,
! [SV2: $i] :
( ( ~ ( ~ ( open @ SV2 )
| ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(73,plain,
! [SV2: $i] :
( ( ~ ( ~ ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 )
| ( open @ SV2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[65]) ).
thf(74,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( inner_point @ SV9 @ SV3 ) )
= $true )
| ( ( ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ( meet @ SV9 @ SY56 @ SY57 )
| ( SV3
!= ( sum @ SY56 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV14: $i,SV4: $i,SV10: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SY66 @ SV4 ) )
| ~ ~ ! [SY67: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY67 @ SV10 )
| ~ ( end_point @ SY67 @ SV14 ) )
| ~ ( end_point @ SY67 @ SY66 ) ) )
| ( part_of @ SV14 @ SY66 )
| ( part_of @ SY66 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SY66 )
| ( part_of @ SY66 @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ( part_of @ SV11 @ SV5 )
| ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) )
| ~ ( ~ ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) )
| ( part_of @ SV11 @ SV5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(77,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ( SV6
!= ( sum @ SV12 @ SV15 ) )
| ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) )
| ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) )
| ( SV6
= ( sum @ SV12 @ SV15 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV13 @ SV7 )
| ~ ( ( SV13 != SV7 ) ) ) )
= $true )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV8: $i,SV1: $i] :
( ( ( ~ ! [SY54: $i] :
~ ( meet @ SY54 @ SV1 @ SV8 ) )
= $false )
| ( ( ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV2: $i] :
( ( ~ ( open @ SV2 )
| ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[72]) ).
thf(81,plain,
! [SV2: $i] :
( ( ~ ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 )
| ( open @ SV2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[73]) ).
thf(82,plain,
! [SV3: $i,SV9: $i] :
( ( ( inner_point @ SV9 @ SV3 )
= $false )
| ( ( ~ ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ( meet @ SV9 @ SY56 @ SY57 )
| ( SV3
!= ( sum @ SY56 @ SY57 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
| ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ( part_of @ SV11 @ SV5 )
| ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(85,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( ~ ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) )
| ( part_of @ SV11 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(86,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ~ ( ( SV6
!= ( sum @ SV12 @ SV15 ) )
| ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) )
| ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) )
| ( SV6
= ( sum @ SV12 @ SV15 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( ~ ( part_of @ SV13 @ SV7 )
| ~ ( ( SV13 != SV7 ) ) ) )
= $false )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV8: $i,SV1: $i] :
( ( ( ! [SY54: $i] :
~ ( meet @ SY54 @ SV1 @ SV8 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(89,plain,
! [SV2: $i] :
( ( ( ~ ( open @ SV2 ) )
= $true )
| ( ( ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV2: $i] :
( ( ( ~ ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 ) )
= $true )
| ( ( open @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV3: $i,SV9: $i] :
( ( ( ! [SY56: $i] :
~ ~ ! [SY57: $i] :
~ ~ ( ~ ( meet @ SV9 @ SY56 @ SY57 )
| ( SV3
!= ( sum @ SY56 @ SY57 ) ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ( part_of @ SV11 @ SV5 )
| ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(94,plain,
! [SV5: $i,SV11: $i] :
( ( ~ ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) )
| ( part_of @ SV11 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[85]) ).
thf(95,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ~ ( ( SV6
!= ( sum @ SV12 @ SV15 ) )
| ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(96,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) )
| ( SV6
= ( sum @ SV12 @ SV15 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[86]) ).
thf(97,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( part_of @ SV13 @ SV7 )
| ~ ( ( SV13 != SV7 ) ) )
= $true )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[87]) ).
thf(98,plain,
! [SV8: $i,SV1: $i,SV17: $i] :
( ( ( ~ ( meet @ SV17 @ SV1 @ SV8 ) )
= $true )
| ( ( ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(99,plain,
! [SV2: $i] :
( ( ( open @ SV2 )
= $false )
| ( ( ~ ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(100,plain,
! [SV2: $i] :
( ( ( ~ ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 ) )
= $false )
| ( ( open @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(101,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ~ ! [SY71: $i] :
~ ~ ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 ) ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(102,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) ) )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(103,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ( part_of @ SV11 @ SV5 ) )
= $true )
| ( ( ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(104,plain,
! [SV5: $i,SV11: $i] :
( ( ( ~ ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) ) )
= $true )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(105,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ( SV6
!= ( sum @ SV12 @ SV15 ) )
| ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(106,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) )
| ( SV6
= ( sum @ SV12 @ SV15 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(107,plain,
! [SV7: $i,SV13: $i] :
( ( ( ~ ( part_of @ SV13 @ SV7 ) )
= $true )
| ( ( ~ ( ( SV13 != SV7 ) ) )
= $true )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(108,plain,
! [SV8: $i,SV1: $i,SV17: $i] :
( ( ( meet @ SV17 @ SV1 @ SV8 )
= $false )
| ( ( ~ ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(109,plain,
! [SV2: $i] :
( ( ( ! [SY37: $i] :
~ ( end_point @ SY37 @ SV2 ) )
= $false )
| ( ( open @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(110,plain,
! [SV2: $i] :
( ( ( ! [SY38: $i] :
~ ( end_point @ SY38 @ SV2 ) )
= $true )
| ( ( open @ SV2 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(111,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ! [SY71: $i] :
~ ~ ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 ) ) ) )
= $true )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(112,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) )
| ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[102]) ).
thf(113,plain,
! [SV5: $i,SV11: $i] :
( ( ( part_of @ SV11 @ SV5 )
= $false )
| ( ( ! [SY61: $i] :
( ~ ( incident_c @ SY61 @ SV11 )
| ( incident_c @ SY61 @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(114,plain,
! [SV5: $i,SV11: $i] :
( ( ( ! [SY62: $i] :
( ~ ( incident_c @ SY62 @ SV11 )
| ( incident_c @ SY62 @ SV5 ) ) )
= $false )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(115,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ( SV6
!= ( sum @ SV12 @ SV15 ) )
= $true )
| ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(116,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ( ~ ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(117,plain,
! [SV7: $i,SV13: $i] :
( ( ( part_of @ SV13 @ SV7 )
= $false )
| ( ( ~ ( ( SV13 != SV7 ) ) )
= $true )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(118,plain,
! [SV17: $i,SV8: $i,SV1: $i] :
( ( ( ! [SY55: $i] :
( SY55
!= ( sum @ SV1 @ SV8 ) ) )
= $false )
| ( ( meet @ SV17 @ SV1 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(119,plain,
! [SV2: $i] :
( ( ( ~ ( end_point @ ( sK6_SY37 @ SV2 ) @ SV2 ) )
= $false )
| ( ( open @ SV2 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[109]) ).
thf(120,plain,
! [SV2: $i,SV18: $i] :
( ( ( ~ ( end_point @ SV18 @ SV2 ) )
= $true )
| ( ( open @ SV2 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(121,plain,
! [SV3: $i,SV9: $i] :
( ( ( ! [SY71: $i] :
~ ~ ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ SY71 ) ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV5: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( incident_c @ SV19 @ SV11 )
| ( incident_c @ SV19 @ SV5 ) )
= $true )
| ( ( part_of @ SV11 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( incident_c @ ( sK7_SY62 @ SV5 @ SV11 ) @ SV11 )
| ( incident_c @ ( sK7_SY62 @ SV5 @ SV11 ) @ SV5 ) )
= $false )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[114]) ).
thf(125,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false )
| ( ( ! [SY68: $i] :
~ ( ~ ( ~ ( incident_c @ SY68 @ SV6 )
| ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY68 @ SV12 )
| ( incident_c @ SY68 @ SV15 ) )
| ( incident_c @ SY68 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV15: $i,SV12: $i,SV6: $i] :
( ( ( ! [SY69: $i] :
~ ( ~ ( ~ ( incident_c @ SY69 @ SV6 )
| ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SY69 @ SV12 )
| ( incident_c @ SY69 @ SV15 ) )
| ( incident_c @ SY69 @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV7: $i,SV13: $i] :
( ( ( SV13 != SV7 )
= $false )
| ( ( part_of @ SV13 @ SV7 )
= $false )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV1: $i,SV8: $i,SV17: $i] :
( ( ( ( sK8_SY55 @ SV17 @ SV8 @ SV1 )
!= ( sum @ SV1 @ SV8 ) )
= $false )
| ( ( meet @ SV17 @ SV1 @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[118]) ).
thf(129,plain,
! [SV2: $i] :
( ( ( end_point @ ( sK6_SY37 @ SV2 ) @ SV2 )
= $true )
| ( ( open @ SV2 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(130,plain,
! [SV2: $i,SV18: $i] :
( ( ( end_point @ SV18 @ SV2 )
= $false )
| ( ( open @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ~ ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[121]) ).
thf(132,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) ) )
= $false )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV5: $i,SV11: $i,SV19: $i] :
( ( ( ~ ( incident_c @ SV19 @ SV11 ) )
= $true )
| ( ( incident_c @ SV19 @ SV5 )
= $true )
| ( ( part_of @ SV11 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV11: $i,SV5: $i] :
( ( ( ~ ( incident_c @ ( sK7_SY62 @ SV5 @ SV11 ) @ SV11 ) )
= $false )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(135,plain,
! [SV11: $i,SV5: $i] :
( ( ( incident_c @ ( sK7_SY62 @ SV5 @ SV11 ) @ SV5 )
= $false )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(136,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( ~ ( ~ ( incident_c @ SV20 @ SV6 )
| ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ( incident_c @ SV20 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(137,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( ~ ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[126]) ).
thf(138,plain,
! [SV7: $i,SV13: $i] :
( ( ( SV13 = SV7 )
= $true )
| ( ( part_of @ SV13 @ SV7 )
= $false )
| ( ( open @ SV13 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(139,plain,
! [SV1: $i,SV8: $i,SV17: $i] :
( ( ( ( sK8_SY55 @ SV17 @ SV8 @ SV1 )
= ( sum @ SV1 @ SV8 ) )
= $true )
| ( ( meet @ SV17 @ SV1 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(140,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) ) ) )
= $true )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(141,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
| ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(142,plain,
! [SV5: $i,SV11: $i,SV19: $i] :
( ( ( incident_c @ SV19 @ SV11 )
= $false )
| ( ( incident_c @ SV19 @ SV5 )
= $true )
| ( ( part_of @ SV11 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(143,plain,
! [SV11: $i,SV5: $i] :
( ( ( incident_c @ ( sK7_SY62 @ SV5 @ SV11 ) @ SV11 )
= $true )
| ( ( part_of @ SV11 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(144,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( ~ ( incident_c @ SV20 @ SV6 )
| ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ~ ( ~ ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ( incident_c @ SV20 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[137]) ).
thf(146,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) )
| ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(147,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) ) )
= $true )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( ~ ( incident_c @ SV20 @ SV6 )
| ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) ) )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(149,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV20: $i] :
( ( ( ~ ( ~ ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ( incident_c @ SV20 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[144]) ).
thf(150,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ~ ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) ) )
= $true )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(151,plain,
! [SV3: $i,SV9: $i] :
( ( ( ~ ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(152,plain,
! [SV9: $i,SV3: $i] :
( ( ( SV3
!= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) )
= $false )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(153,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) ) )
= $false )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( incident_c @ SV20 @ SV6 )
| ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(155,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV20: $i] :
( ( ( ~ ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
| ( incident_c @ SV20 @ SV6 ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[149]) ).
thf(156,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV3: $i,SV9: $i] :
( ( ( meet @ SV9 @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) )
= $true )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(158,plain,
! [SV9: $i,SV3: $i] :
( ( ( SV3
= ( sum @ ( sK5_SY56 @ SV3 @ SV9 ) @ ( sK9_SY71 @ SV3 @ SV9 ) ) )
= $true )
| ( ( inner_point @ SV9 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(159,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( part_of @ SV10 @ SV4 )
| ~ ( part_of @ SV14 @ SV4 ) )
= $true )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(160,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( ~ ( incident_c @ SV20 @ SV6 ) )
= $true )
| ( ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(161,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV20: $i] :
( ( ( ~ ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) ) )
= $true )
| ( ( incident_c @ SV20 @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(163,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
= $false )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[156]) ).
thf(164,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( part_of @ SV10 @ SV4 ) )
= $true )
| ( ( ~ ( part_of @ SV14 @ SV4 ) )
= $true )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(165,plain,
! [SV15: $i,SV12: $i,SV6: $i,SV20: $i] :
( ( ( incident_c @ SV20 @ SV6 )
= $false )
| ( ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(166,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV20: $i] :
( ( ( ( incident_c @ SV20 @ SV12 )
| ( incident_c @ SV20 @ SV15 ) )
= $false )
| ( ( incident_c @ SV20 @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(167,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(168,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(169,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( ~ ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV16: $i,SV14: $i,SV4: $i,SV10: $i] :
( ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( ~ ( part_of @ SV14 @ SV4 ) )
= $true )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(171,plain,
! [SV6: $i,SV15: $i,SV12: $i,SV20: $i] :
( ( ( incident_c @ SV20 @ SV12 )
= $true )
| ( ( incident_c @ SV20 @ SV15 )
= $true )
| ( ( incident_c @ SV20 @ SV6 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(172,plain,
! [SV15: $i,SV6: $i,SV12: $i,SV20: $i] :
( ( ( incident_c @ SV20 @ SV12 )
= $false )
| ( ( incident_c @ SV20 @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(173,plain,
! [SV12: $i,SV6: $i,SV15: $i,SV20: $i] :
( ( ( incident_c @ SV20 @ SV15 )
= $false )
| ( ( incident_c @ SV20 @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[166]) ).
thf(174,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(175,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(176,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(177,plain,
! [SV16: $i,SV10: $i,SV4: $i,SV14: $i] :
( ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( ~ ( part_of @ SV16 @ SV4 ) )
= $true )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(178,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(179,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(180,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(181,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(182,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ~ ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) ) )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(183,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $false )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[176]) ).
thf(184,plain,
! [SV14: $i,SV10: $i,SV4: $i,SV16: $i] :
( ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( ~ ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(185,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(186,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[180]) ).
thf(187,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
| ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 ) )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[182]) ).
thf(188,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i] :
( ( ( ~ ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(189,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(190,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(191,plain,
! [SV6: $i,SV12: $i,SV15: $i] :
( ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV12 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $true )
| ( ( incident_c @ ( sK10_SY69 @ SV15 @ SV12 @ SV6 ) @ SV15 )
= $false )
| ( ( SV6
= ( sum @ SV12 @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(192,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i] :
( ( ( ! [SY70: $i] :
~ ~ ( ~ ~ ( ~ ( end_point @ SY70 @ SV10 )
| ~ ( end_point @ SY70 @ SV14 ) )
| ~ ( end_point @ SY70 @ SV16 ) ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(193,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) )
| ~ ( end_point @ SV21 @ SV16 ) ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(194,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( ~ ~ ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) )
| ~ ( end_point @ SV21 @ SV16 ) ) )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(195,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) )
| ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[194]) ).
thf(196,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ~ ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) ) )
= $true )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(197,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) ) )
= $false )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(198,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( end_point @ SV21 @ SV10 )
| ~ ( end_point @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[197]) ).
thf(199,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( ~ ( end_point @ SV21 @ SV10 ) )
= $true )
| ( ( ~ ( end_point @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(200,plain,
! [SV4: $i,SV16: $i,SV14: $i,SV10: $i,SV21: $i] :
( ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( ~ ( end_point @ SV21 @ SV14 ) )
= $true )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(201,plain,
! [SV4: $i,SV16: $i,SV10: $i,SV14: $i,SV21: $i] :
( ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( ~ ( end_point @ SV21 @ SV16 ) )
= $true )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(202,plain,
! [SV4: $i,SV14: $i,SV10: $i,SV16: $i,SV21: $i] :
( ( ( end_point @ SV21 @ SV16 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 )
| ( part_of @ SV16 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(203,plain,
! [SV21: $i,SV4: $i,SV10: $i,SV16: $i,SV14: $i] :
( ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 )
| ( part_of @ SV10 @ SV16 ) )
= $true )
| ( ( part_of @ SV16 @ SV10 )
= $true )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(204,plain,
! [SV21: $i,SV4: $i,SV10: $i,SV16: $i,SV14: $i] :
( ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 )
| ( part_of @ SV14 @ SV10 ) )
= $true )
| ( ( part_of @ SV10 @ SV16 )
= $true )
| ( ( part_of @ SV16 @ SV10 )
= $true )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(205,plain,
! [SV21: $i,SV4: $i,SV10: $i,SV16: $i,SV14: $i] :
( ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 )
| ( part_of @ SV10 @ SV14 ) )
= $true )
| ( ( part_of @ SV14 @ SV10 )
= $true )
| ( ( part_of @ SV10 @ SV16 )
= $true )
| ( ( part_of @ SV16 @ SV10 )
= $true )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(206,plain,
! [SV21: $i,SV4: $i,SV10: $i,SV16: $i,SV14: $i] :
( ( ( ( part_of @ SV14 @ SV16 )
| ( part_of @ SV16 @ SV14 ) )
= $true )
| ( ( part_of @ SV10 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV10 )
= $true )
| ( ( part_of @ SV10 @ SV16 )
= $true )
| ( ( part_of @ SV16 @ SV10 )
= $true )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(207,plain,
! [SV21: $i,SV4: $i,SV10: $i,SV16: $i,SV14: $i] :
( ( ( part_of @ SV14 @ SV16 )
= $true )
| ( ( part_of @ SV16 @ SV14 )
= $true )
| ( ( part_of @ SV10 @ SV14 )
= $true )
| ( ( part_of @ SV14 @ SV10 )
= $true )
| ( ( part_of @ SV10 @ SV16 )
= $true )
| ( ( part_of @ SV16 @ SV10 )
= $true )
| ( ( part_of @ SV16 @ SV4 )
= $false )
| ( ( part_of @ SV10 @ SV4 )
= $false )
| ( ( part_of @ SV14 @ SV4 )
= $false )
| ( ( end_point @ SV21 @ SV14 )
= $false )
| ( ( end_point @ SV21 @ SV10 )
= $false )
| ( ( end_point @ SV21 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(208,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[44,207,191,190,189,183,181,179,173,172,171,158,157,143,142,139,138,135,130,129,56,47,46,45]) ).
thf(209,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO093+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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.18 % Computer : n004.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Oct 6 10:03:09 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 231.80/38.95
% 231.80/38.95 No.of.Axioms: 7
% 231.80/38.95
% 231.80/38.95 Length.of.Defs: 0
% 231.80/38.95
% 231.80/38.95 Contains.Choice.Funs: false
% 231.80/38.95 .......
% 231.80/38.95
% 231.80/38.95 ********************************
% 231.80/38.95 * All subproblems solved! *
% 231.80/38.95 ********************************
% 231.80/38.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:208,loop_count:0,foatp_calls:1,translation:fof_full)
% 231.80/38.95
% 231.80/38.95 %**** Beginning of derivation protocol ****
% 231.80/38.95 % SZS output start CNFRefutation
% See solution above
% 231.80/38.95
% 231.80/38.95 %**** End of derivation protocol ****
% 231.80/38.95 %**** no. of clauses in derivation: 200 ****
% 231.80/38.95 %**** clause counter: 208 ****
% 231.80/38.95
% 231.80/38.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:11,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:208,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------