%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 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 : n017.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 10:19:41 AM UTC 2026
% Result : Theorem 5.12s 1.13s
% Output : CNFRefutation 5.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 8
% Syntax : Number of formulae : 331 ( 87 unt; 0 typ; 0 def)
% Number of atoms : 3515 (1096 equ; 0 cnn)
% Maximal formula atoms : 7 ( 10 avg)
% Number of connectives : 7757 (2339 ~;1301 |; 78 &;3994 @)
% ( 9 <=>; 30 =>; 3 <=; 3 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 14 con; 0-6 aty)
% Number of variables : 1401 ( 0 ^;1383 !; 18 ?;1401 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_complete,type,
complete: $o ).
thf(tp_edge,type,
edge: $i > $o ).
thf(tp_edges,type,
edges: $i ).
thf(tp_empty,type,
empty: $i ).
thf(tp_graph,type,
graph: $i ).
thf(tp_head_of,type,
head_of: $i > $i ).
thf(tp_in_path,type,
in_path: $i > $i > $o ).
thf(tp_length_of,type,
length_of: $i > $i ).
thf(tp_less_or_equal,type,
less_or_equal: $i > $i > $o ).
thf(tp_minus,type,
minus: $i > $i > $i ).
thf(tp_n1,type,
n1: $i ).
thf(tp_number_of_in,type,
number_of_in: $i > $i > $i ).
thf(tp_on_path,type,
on_path: $i > $i > $o ).
thf(tp_path,type,
path: $i > $i > $i > $o ).
thf(tp_path_cons,type,
path_cons: $i > $i > $i ).
thf(tp_precedes,type,
precedes: $i > $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY79,type,
sK2_SY79: $i ).
thf(tp_sK3_SY96,type,
sK3_SY96: $i ).
thf(tp_sK4_SY107,type,
sK4_SY107: $i ).
thf(tp_sK5_SY115,type,
sK5_SY115: $i ).
thf(tp_sK6_SY127,type,
sK6_SY127: $i > $i > $i > $i > $i > $i ).
thf(tp_sK7_SY89,type,
sK7_SY89: $i > $i > $i > $i ).
thf(tp_sK8_SY129,type,
sK8_SY129: $i > $i > $i > $i > $i > $i ).
thf(tp_sK9_SY129,type,
sK9_SY129: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_sequential,type,
sequential: $i > $i > $o ).
thf(tp_sequential_pairs,type,
sequential_pairs: $i ).
thf(tp_shortest_path,type,
shortest_path: $i > $i > $i > $o ).
thf(tp_tail_of,type,
tail_of: $i > $i ).
thf(tp_triangle,type,
triangle: $i > $i > $i > $o ).
thf(tp_triangles,type,
triangles: $i ).
thf(tp_vertex,type,
vertex: $i > $o ).
thf(5,axiom,
! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
thf(6,axiom,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
thf(7,axiom,
! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(8,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
thf(9,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
thf(10,axiom,
! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_defn) ).
thf(18,axiom,
( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
thf(19,conjecture,
( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
thf(20,negated_conjecture,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(29,plain,
complete = $true,
inference(standard_cnf,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(31,plain,
( ( ~ ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[30]) ).
thf(32,plain,
( ( complete
=> ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ? [E3: $i] :
( ( edge @ E3 )
& ( ( tail_of @ E3 )
= ( head_of @ E2 ) )
& ( ( head_of @ E3 )
= ( tail_of @ E1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(34,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
<= ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
| ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( path @ V1 @ V2 @ P )
=> ! [E1: $i,E2: $i] :
( ( precedes @ E1 @ E2 @ P )
=> ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( ( sequential @ E1 @ E2 )
<~> ? [E3: $i] :
( ( sequential @ E1 @ E3 )
& ( precedes @ E3 @ E2 @ P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( ! [V1: $i,V2: $i,SP: $i] :
( ( shortest_path @ V1 @ V2 @ SP )
<=> ( ( path @ V1 @ V2 @ SP )
& ( V1 != V2 )
& ! [P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( tail_of @ E3 )
= ( tail_of @ E1 ) )
& ( ( head_of @ E3 )
= ( head_of @ E2 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(38,plain,
( ( ! [E1: $i,E2: $i,E3: $i] :
( ( triangle @ E1 @ E2 @ E3 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( edge @ E3 )
& ( sequential @ E1 @ E2 )
& ( sequential @ E2 @ E3 )
& ( sequential @ E3 @ E1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(39,plain,
complete = $true,
inference(copy,[status(thm)],[29]) ).
thf(40,plain,
( ( ~ ! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ~ ( precedes @ SX3 @ SX4 @ SX0 )
| ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SX3 @ SX4 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) )
| ( sequential @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(42,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SX0 @ SX1 @ SX2 )
| ~ ( ( SX0 != SX1 ) ) )
| ~ ! [SX3: $i] :
( ~ ( path @ SX0 @ SX1 @ SX3 )
| ( less_or_equal @ ( length_of @ SX2 ) @ ( length_of @ SX3 ) ) ) )
| ( shortest_path @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(43,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SX2 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SX3 ) ) )
| ~ ~ ( precedes @ SX3 @ SX2 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(44,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( sequential @ SX0 @ SX1 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( ( SX0 != SX1 ) ) )
| ( ( head_of @ SX0 )
!= ( tail_of @ SX1 ) ) )
| ( sequential @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(45,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX1 @ SX2 @ SX0 )
| ! [SX3: $i,SX4: $i] :
( ( precedes @ SX3 @ SX4 @ SX0 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( ( sequential @ SX3 @ SX4 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( sequential @ SX3 @ SX5 )
| ~ ( precedes @ SX5 @ SX4 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(46,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( triangle @ SX0 @ SX1 @ SX2 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( edge @ SX2 ) )
| ~ ( sequential @ SX0 @ SX1 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ( sequential @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SX0 )
| ~ ( edge @ SX1 ) )
| ~ ( edge @ SX2 ) )
| ~ ( sequential @ SX0 @ SX1 ) )
| ~ ( sequential @ SX1 @ SX2 ) )
| ~ ( sequential @ SX2 @ SX0 ) )
| ( triangle @ SX0 @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(47,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ( sequential @ SX2 @ SX3 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX2 @ SX3 @ SX5 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(48,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX5 )
| ( ( tail_of @ SX5 )
!= ( head_of @ SX3 ) ) )
| ( ( head_of @ SX5 )
!= ( tail_of @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(49,plain,
! [SV1: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ~ ( path @ SY39 @ SY40 @ SV1 )
| ! [SY41: $i,SY42: $i] :
( ~ ( precedes @ SY41 @ SY42 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SY41 @ SV1 )
| ~ ( on_path @ SY42 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY41 @ SY42 )
| ~ ! [SY43: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY43 )
| ~ ( precedes @ SY43 @ SY42 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY44 )
| ~ ( precedes @ SY44 @ SY42 @ SV1 ) )
| ( sequential @ SY41 @ SY42 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV2: $i] :
( ( ! [SY45: $i,SY46: $i] :
~ ( ~ ( ~ ( shortest_path @ SV2 @ SY45 @ SY46 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SY45 @ SY46 )
| ~ ( ( SV2 != SY45 ) ) )
| ~ ! [SY47: $i] :
( ~ ( path @ SV2 @ SY45 @ SY47 )
| ( less_or_equal @ ( length_of @ SY46 ) @ ( length_of @ SY47 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SY45 @ SY46 )
| ~ ( ( SV2 != SY45 ) ) )
| ~ ! [SY48: $i] :
( ~ ( path @ SV2 @ SY45 @ SY48 )
| ( less_or_equal @ ( length_of @ SY46 ) @ ( length_of @ SY48 ) ) ) )
| ( shortest_path @ SV2 @ SY45 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV3: $i] :
( ( ! [SY49: $i,SY50: $i,SY51: $i,SY52: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SY49 @ SY52 )
| ~ ( precedes @ SY50 @ SY51 @ SY52 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY50 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY51 ) ) )
| ~ ~ ( precedes @ SY51 @ SY50 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV4: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( sequential @ SV4 @ SY54 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SY54 ) )
| ~ ( ( SV4 != SY54 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SY54 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SY54 ) )
| ~ ( ( SV4 != SY54 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SY54 ) ) )
| ( sequential @ SV4 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV5: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( path @ SY55 @ SY56 @ SV5 )
| ! [SY57: $i,SY58: $i] :
( ( precedes @ SY57 @ SY58 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY57 @ SV5 )
| ~ ( on_path @ SY58 @ SV5 ) )
| ~ ( ( sequential @ SY57 @ SY58 )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( sequential @ SY57 @ SY59 )
| ~ ( precedes @ SY59 @ SY58 @ SV5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV6: $i] :
( ( ! [SY60: $i,SY61: $i] :
~ ( ~ ( ~ ( triangle @ SV6 @ SY60 @ SY61 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SY60 ) )
| ~ ( edge @ SY61 ) )
| ~ ( sequential @ SV6 @ SY60 ) )
| ~ ( sequential @ SY60 @ SY61 ) )
| ~ ( sequential @ SY61 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SY60 ) )
| ~ ( edge @ SY61 ) )
| ~ ( sequential @ SV6 @ SY60 ) )
| ~ ( sequential @ SY60 @ SY61 ) )
| ~ ( sequential @ SY61 @ SV6 ) )
| ( triangle @ SV6 @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ( sequential @ SX2 @ SX3 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX2 @ SX3 @ SX5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(56,plain,
( ( ( ~ complete ) = $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX5 )
| ( ( tail_of @ SX5 )
!= ( head_of @ SX3 ) ) )
| ( ( head_of @ SX5 )
!= ( tail_of @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(57,plain,
! [SV1: $i,SV7: $i] :
( ( ! [SY62: $i] :
( ~ ( path @ SV7 @ SY62 @ SV1 )
| ! [SY41: $i,SY42: $i] :
( ~ ( precedes @ SY41 @ SY42 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SY41 @ SV1 )
| ~ ( on_path @ SY42 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY41 @ SY42 )
| ~ ! [SY43: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY43 )
| ~ ( precedes @ SY43 @ SY42 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY44 )
| ~ ( precedes @ SY44 @ SY42 @ SV1 ) )
| ( sequential @ SY41 @ SY42 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(58,plain,
! [SV8: $i,SV2: $i] :
( ( ! [SY67: $i] :
~ ( ~ ( ~ ( shortest_path @ SV2 @ SV8 @ SY67 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SY67 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY68: $i] :
( ~ ( path @ SV2 @ SV8 @ SY68 )
| ( less_or_equal @ ( length_of @ SY67 ) @ ( length_of @ SY68 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SY67 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY69: $i] :
( ~ ( path @ SV2 @ SV8 @ SY69 )
| ( less_or_equal @ ( length_of @ SY67 ) @ ( length_of @ SY69 ) ) ) )
| ( shortest_path @ SV2 @ SV8 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(59,plain,
! [SV9: $i,SV3: $i] :
( ( ! [SY70: $i,SY71: $i,SY72: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SY72 )
| ~ ( precedes @ SY70 @ SY71 @ SY72 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY70 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY71 ) ) )
| ~ ~ ( precedes @ SY71 @ SY70 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(60,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( sequential @ SV4 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
| ( sequential @ SV4 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(61,plain,
! [SV5: $i,SV11: $i] :
( ( ! [SY74: $i] :
( ~ ( path @ SV11 @ SY74 @ SV5 )
| ! [SY57: $i,SY58: $i] :
( ( precedes @ SY57 @ SY58 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY57 @ SV5 )
| ~ ( on_path @ SY58 @ SV5 ) )
| ~ ( ( sequential @ SY57 @ SY58 )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( sequential @ SY57 @ SY59 )
| ~ ( precedes @ SY59 @ SY58 @ SV5 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(62,plain,
! [SV12: $i,SV6: $i] :
( ( ! [SY78: $i] :
~ ( ~ ( ~ ( triangle @ SV6 @ SV12 @ SY78 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SY78 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SY78 ) )
| ~ ( sequential @ SY78 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SY78 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SY78 ) )
| ~ ( sequential @ SY78 @ SV6 ) )
| ( triangle @ SV6 @ SV12 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(63,plain,
( ( ! [SY79: $i,SY80: $i,SY81: $i,SY82: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ SY79 @ SY82 )
| ~ ( precedes @ SY80 @ SY81 @ SY82 ) )
| ~ ( sequential @ SY80 @ SY81 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY80 @ SY81 @ SX5 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[55]) ).
thf(64,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ~ ~ ( ~ ( shortest_path @ SX0 @ SX1 @ SX4 )
| ~ ( precedes @ SX2 @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX5 )
| ( ( tail_of @ SX5 )
!= ( head_of @ SX3 ) ) )
| ( ( head_of @ SX5 )
!= ( tail_of @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(65,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ~ ( path @ SV7 @ SV13 @ SV1 )
| ! [SY41: $i,SY42: $i] :
( ~ ( precedes @ SY41 @ SY42 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SY41 @ SV1 )
| ~ ( on_path @ SY42 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY41 @ SY42 )
| ~ ! [SY43: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY43 )
| ~ ( precedes @ SY43 @ SY42 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY44 )
| ~ ( precedes @ SY44 @ SY42 @ SV1 ) )
| ( sequential @ SY41 @ SY42 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(66,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( shortest_path @ SV2 @ SV8 @ SV14 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
| ( shortest_path @ SV2 @ SV8 @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(67,plain,
! [SV15: $i,SV9: $i,SV3: $i] :
( ( ! [SY90: $i,SY91: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SY91 )
| ~ ( precedes @ SV15 @ SY90 @ SY91 ) )
| ~ ( ~ ~ ~ ! [SY92: $i] :
~ ~ ( ( ( tail_of @ SY92 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY92 )
!= ( head_of @ SY90 ) ) )
| ~ ~ ( precedes @ SY90 @ SV15 @ SY91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(68,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( sequential @ SV4 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
| ( sequential @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(69,plain,
! [SV5: $i,SV16: $i,SV11: $i] :
( ( ~ ( path @ SV11 @ SV16 @ SV5 )
| ! [SY57: $i,SY58: $i] :
( ( precedes @ SY57 @ SY58 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY57 @ SV5 )
| ~ ( on_path @ SY58 @ SV5 ) )
| ~ ( ( sequential @ SY57 @ SY58 )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( sequential @ SY57 @ SY59 )
| ~ ( precedes @ SY59 @ SY58 @ SV5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(70,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( ~ ( triangle @ SV6 @ SV12 @ SV17 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
| ( triangle @ SV6 @ SV12 @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(71,plain,
( ( ! [SY96: $i,SY97: $i,SY98: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ SY98 )
| ~ ( precedes @ SY96 @ SY97 @ SY98 ) )
| ~ ( sequential @ SY96 @ SY97 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY96 @ SY97 @ SX5 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(72,plain,
! [SV18: $i] :
( ( ( ! [SY100: $i,SY101: $i,SY102: $i,SY103: $i] :
( ~ ~ ( ~ ( shortest_path @ SV18 @ SY100 @ SY103 )
| ~ ( precedes @ SY101 @ SY102 @ SY103 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX5 )
| ( ( tail_of @ SX5 )
!= ( head_of @ SY102 ) ) )
| ( ( head_of @ SX5 )
!= ( tail_of @ SY101 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV13 @ SV1 ) )
= $true )
| ( ( ! [SY41: $i,SY42: $i] :
( ~ ( precedes @ SY41 @ SY42 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SY41 @ SV1 )
| ~ ( on_path @ SY42 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY41 @ SY42 )
| ~ ! [SY43: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY43 )
| ~ ( precedes @ SY43 @ SY42 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY44 )
| ~ ( precedes @ SY44 @ SY42 @ SV1 ) )
| ( sequential @ SY41 @ SY42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( ~ ( shortest_path @ SV2 @ SV8 @ SV14 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
| ( shortest_path @ SV2 @ SV8 @ SV14 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(75,plain,
! [SV19: $i,SV15: $i,SV9: $i,SV3: $i] :
( ( ! [SY105: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SY105 )
| ~ ( precedes @ SV15 @ SV19 @ SY105 ) )
| ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(76,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ( sequential @ SV4 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(77,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
| ( sequential @ SV4 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[68]) ).
thf(78,plain,
! [SV5: $i,SV16: $i,SV11: $i] :
( ( ( ~ ( path @ SV11 @ SV16 @ SV5 ) )
= $true )
| ( ( ! [SY57: $i,SY58: $i] :
( ( precedes @ SY57 @ SY58 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY57 @ SV5 )
| ~ ( on_path @ SY58 @ SV5 ) )
| ~ ( ( sequential @ SY57 @ SY58 )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( sequential @ SY57 @ SY59 )
| ~ ( precedes @ SY59 @ SY58 @ SV5 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( triangle @ SV6 @ SV12 @ SV17 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
| ( triangle @ SV6 @ SV12 @ SV17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(80,plain,
( ( ! [SY107: $i,SY108: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ SY108 )
| ~ ( precedes @ sK3_SY96 @ SY107 @ SY108 ) )
| ~ ( sequential @ sK3_SY96 @ SY107 ) )
| ~ ! [SY109: $i] :
~ ( triangle @ sK3_SY96 @ SY107 @ SY109 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[71]) ).
thf(81,plain,
! [SV20: $i,SV18: $i] :
( ( ( ! [SY110: $i,SY111: $i,SY112: $i] :
( ~ ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SY112 )
| ~ ( precedes @ SY110 @ SY111 @ SY112 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SX5 )
| ( ( tail_of @ SX5 )
!= ( head_of @ SY111 ) ) )
| ( ( head_of @ SX5 )
!= ( tail_of @ SY110 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV1: $i,SV13: $i,SV7: $i] :
( ( ( path @ SV7 @ SV13 @ SV1 )
= $false )
| ( ( ! [SY41: $i,SY42: $i] :
( ~ ( precedes @ SY41 @ SY42 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SY41 @ SV1 )
| ~ ( on_path @ SY42 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY41 @ SY42 )
| ~ ! [SY43: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY43 )
| ~ ( precedes @ SY43 @ SY42 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY44: $i] :
~ ~ ( ~ ( sequential @ SY41 @ SY44 )
| ~ ( precedes @ SY44 @ SY42 @ SV1 ) )
| ( sequential @ SY41 @ SY42 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( ~ ( shortest_path @ SV2 @ SV8 @ SV14 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(84,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
| ( shortest_path @ SV2 @ SV8 @ SV14 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(85,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ~ ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SV21 )
| ~ ( precedes @ SV15 @ SV19 @ SV21 ) )
| ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ( sequential @ SV4 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(87,plain,
! [SV10: $i,SV4: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
| ( sequential @ SV4 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(88,plain,
! [SV5: $i,SV16: $i,SV11: $i] :
( ( ( path @ SV11 @ SV16 @ SV5 )
= $false )
| ( ( ! [SY57: $i,SY58: $i] :
( ( precedes @ SY57 @ SY58 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY57 @ SV5 )
| ~ ( on_path @ SY58 @ SV5 ) )
| ~ ( ( sequential @ SY57 @ SY58 )
| ~ ! [SY59: $i] :
~ ~ ( ~ ( sequential @ SY57 @ SY59 )
| ~ ( precedes @ SY59 @ SY58 @ SV5 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ( triangle @ SV6 @ SV12 @ SV17 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(90,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
| ( triangle @ SV6 @ SV12 @ SV17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[79]) ).
thf(91,plain,
( ( ! [SY115: $i] :
( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ SY115 ) )
| ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) )
| ~ ! [SY116: $i] :
~ ( triangle @ sK3_SY96 @ sK4_SY107 @ SY116 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[80]) ).
thf(92,plain,
! [SV22: $i,SV20: $i,SV18: $i] :
( ( ( ! [SY117: $i,SY118: $i] :
( ~ ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SY118 )
| ~ ( precedes @ SV22 @ SY117 @ SY118 ) )
| ~ ! [SY119: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY119 )
| ( ( tail_of @ SY119 )
!= ( head_of @ SY117 ) ) )
| ( ( head_of @ SY119 )
!= ( tail_of @ SV22 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(93,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV23: $i] :
( ( ( ! [SY120: $i] :
( ~ ( precedes @ SV23 @ SY120 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SY120 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SY120 )
| ~ ! [SY121: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY121 )
| ~ ( precedes @ SY121 @ SY120 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY122: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY122 )
| ~ ( precedes @ SY122 @ SY120 @ SV1 ) )
| ( sequential @ SV23 @ SY120 ) ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(94,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ( shortest_path @ SV2 @ SV8 @ SV14 )
| ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(95,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
| ( shortest_path @ SV2 @ SV8 @ SV14 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(96,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SV21 )
| ~ ( precedes @ SV15 @ SV19 @ SV21 ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(97,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( sequential @ SV4 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV24: $i] :
( ( ( ! [SY123: $i] :
( ( precedes @ SV24 @ SY123 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SY123 @ SV5 ) )
| ~ ( ( sequential @ SV24 @ SY123 )
| ~ ! [SY124: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY124 )
| ~ ( precedes @ SY124 @ SY123 @ SV5 ) ) ) ) ) )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ( triangle @ SV6 @ SV12 @ SV17 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[89]) ).
thf(101,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
| ( triangle @ SV6 @ SV12 @ SV17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(102,plain,
( ( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
| ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) )
| ~ ! [SY116: $i] :
~ ( triangle @ sK3_SY96 @ sK4_SY107 @ SY116 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[91]) ).
thf(103,plain,
! [SV25: $i,SV22: $i,SV20: $i,SV18: $i] :
( ( ( ! [SY126: $i] :
( ~ ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SY126 )
| ~ ( precedes @ SV22 @ SV25 @ SY126 ) )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(104,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( precedes @ SV23 @ SV26 @ SV1 )
| ~ ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(105,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( shortest_path @ SV2 @ SV8 @ SV14 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(106,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(107,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( ~ ( shortest_path @ SV3 @ SV9 @ SV21 )
| ~ ( precedes @ SV15 @ SV19 @ SV21 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(108,plain,
! [SV10: $i,SV4: $i] :
( ( ( sequential @ SV4 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(109,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(110,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( ( precedes @ SV24 @ SV27 @ SV5 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) )
| ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) ) )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(111,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( triangle @ SV6 @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(112,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(113,plain,
( ( ~ ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
| ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(114,plain,
( ( ~ ! [SY116: $i] :
~ ( triangle @ sK3_SY96 @ sK4_SY107 @ SY116 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(115,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SV28 )
| ~ ( precedes @ SV22 @ SV25 @ SV28 ) )
| ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(116,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( precedes @ SV23 @ SV26 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(117,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(118,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(119,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( shortest_path @ SV3 @ SV9 @ SV21 )
| ~ ( precedes @ SV15 @ SV19 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(120,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(121,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
| ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(122,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) )
| ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) ) )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[110]) ).
thf(123,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(124,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(125,plain,
( ( ~ ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
| ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[113]) ).
thf(126,plain,
( ( ! [SY116: $i] :
~ ( triangle @ sK3_SY96 @ sK4_SY107 @ SY116 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(127,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( ~ ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SV28 )
| ~ ( precedes @ SV22 @ SV25 @ SV28 ) ) )
= $true )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
| ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(131,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ( ~ ( shortest_path @ SV3 @ SV9 @ SV21 ) )
= $true )
| ( ( ~ ( precedes @ SV15 @ SV19 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(133,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[120]) ).
thf(134,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[121]) ).
thf(135,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) )
| ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) ) )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(136,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(137,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
| ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[124]) ).
thf(138,plain,
( ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
| ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(139,plain,
! [SV29: $i] :
( ( ~ ( triangle @ sK3_SY96 @ sK4_SY107 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(140,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( ~ ( ~ ( shortest_path @ SV18 @ SV20 @ SV28 )
| ~ ( precedes @ SV22 @ SV25 @ SV28 ) ) )
= $false )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(141,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(142,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(143,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[129]) ).
thf(144,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV9: $i,SV3: $i] :
( ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( ~ ( precedes @ SV15 @ SV19 @ SV21 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[132]) ).
thf(147,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( head_of @ SV4 )
= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(148,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) ) )
= $false )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(149,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) )
| ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[135]) ).
thf(150,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(151,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[136]) ).
thf(152,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(153,plain,
( ( ~ ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(154,plain,
( ( ~ ( sequential @ sK3_SY96 @ sK4_SY107 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(155,plain,
! [SV29: $i] :
( ( triangle @ sK3_SY96 @ sK4_SY107 @ SV29 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(156,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( ~ ( shortest_path @ SV18 @ SV20 @ SV28 )
| ~ ( precedes @ SV22 @ SV25 @ SV28 ) )
= $true )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(157,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(158,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[141]) ).
thf(159,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(160,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ! [SY88: $i] :
( ~ ( path @ SV2 @ SV8 @ SY88 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY88 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(161,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) ) )
= $false )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(162,plain,
! [SV9: $i,SV3: $i,SV21: $i,SV19: $i,SV15: $i] :
( ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(163,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(164,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
| ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(165,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) ) )
= $true )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[149]) ).
thf(166,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[150]) ).
thf(167,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( sequential @ SV17 @ SV6 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[151]) ).
thf(168,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) ) )
= $false )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(169,plain,
( ( ~ ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[153]) ).
thf(170,plain,
( ( sequential @ sK3_SY96 @ sK4_SY107 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[154]) ).
thf(171,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( ~ ( shortest_path @ SV18 @ SV20 @ SV28 ) )
= $true )
| ( ( ~ ( precedes @ SV22 @ SV25 @ SV28 ) )
= $true )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(173,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(174,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV14: $i,SV30: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV30 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SV30 ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV14 )
| ~ ( ( SV2 != SV8 ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(177,plain,
! [SV9: $i,SV3: $i,SV21: $i,SV19: $i,SV15: $i] :
( ( ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) )
| ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(179,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ( SV4 != SV10 ) ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(180,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) ) )
= $true )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(181,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) ) )
= $false )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(182,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(183,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
| ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(184,plain,
( ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
| ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[169]) ).
thf(185,plain,
! [SV25: $i,SV22: $i,SV28: $i,SV20: $i,SV18: $i] :
( ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( ~ ( precedes @ SV22 @ SV25 @ SV28 ) )
= $true )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(186,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( on_path @ SV23 @ SV1 )
| ~ ( on_path @ SV26 @ SV1 ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(187,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[173]) ).
thf(188,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV14 ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(189,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV8 ) ) )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[174]) ).
thf(190,plain,
! [SV14: $i,SV30: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV30 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SV30 ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(191,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ SV14 ) )
= $true )
| ( ( ~ ( ( SV2 != SV8 ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(192,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i] :
( ( ( ~ ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(193,plain,
! [SV9: $i,SV3: $i,SV21: $i,SV15: $i,SV19: $i] :
( ( ( ~ ~ ( precedes @ SV19 @ SV15 @ SV21 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[177]) ).
thf(194,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[178]) ).
thf(195,plain,
! [SV10: $i,SV4: $i] :
( ( ( SV4 != SV10 )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[179]) ).
thf(196,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) ) )
= $false )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(197,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( on_path @ SV24 @ SV5 )
| ~ ( on_path @ SV27 @ SV5 ) )
= $true )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[181]) ).
thf(198,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(199,plain,
! [SV6: $i,SV17: $i,SV12: $i] :
( ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[182]) ).
thf(200,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(201,plain,
( ( ~ ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(202,plain,
( ( ~ ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[184]) ).
thf(203,plain,
! [SV20: $i,SV18: $i,SV28: $i,SV25: $i,SV22: $i] :
( ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( ~ ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(204,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( ~ ( on_path @ SV23 @ SV1 ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(205,plain,
! [SV13: $i,SV7: $i,SV23: $i,SV1: $i,SV26: $i] :
( ( ( ~ ( on_path @ SV26 @ SV1 ) )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[186]) ).
thf(206,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
| ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(207,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( path @ SV2 @ SV8 @ SV14 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[188]) ).
thf(208,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( SV2 != SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[189]) ).
thf(209,plain,
! [SV14: $i,SV30: $i,SV8: $i,SV2: $i] :
( ( ( path @ SV2 @ SV8 @ SV30 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SV30 ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(210,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( ~ ( ( SV2 != SV8 ) ) )
= $true )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(211,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i] :
( ( ( ~ ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[192]) ).
thf(212,plain,
! [SV9: $i,SV3: $i,SV21: $i,SV15: $i,SV19: $i] :
( ( ( ~ ( precedes @ SV19 @ SV15 @ SV21 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[193]) ).
thf(213,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(214,plain,
! [SV10: $i,SV4: $i] :
( ( ( SV4 = SV10 )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(215,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( edge @ SV4 )
| ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(216,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( ~ ( on_path @ SV24 @ SV5 ) )
= $true )
| ( ( ~ ( on_path @ SV27 @ SV5 ) )
= $true )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[198]) ).
thf(218,plain,
! [SV6: $i,SV17: $i,SV12: $i] :
( ( ( sequential @ SV12 @ SV17 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[199]) ).
thf(219,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) ) )
= $false )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(220,plain,
( ( shortest_path @ sK1_SX0 @ sK2_SY79 @ sK5_SY115 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(221,plain,
( ( precedes @ sK3_SY96 @ sK4_SY107 @ sK5_SY115 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(222,plain,
! [SV28: $i,SV20: $i,SV18: $i,SV22: $i,SV25: $i] :
( ( ( ! [SY127: $i] :
~ ~ ( ~ ~ ( ~ ( edge @ SY127 )
| ( ( tail_of @ SY127 )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ SY127 )
!= ( tail_of @ SV22 ) ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(223,plain,
! [SV13: $i,SV7: $i,SV26: $i,SV1: $i,SV23: $i] :
( ( ( on_path @ SV23 @ SV1 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[204]) ).
thf(224,plain,
! [SV13: $i,SV7: $i,SV23: $i,SV1: $i,SV26: $i] :
( ( ( on_path @ SV26 @ SV1 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(225,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(226,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( SV2 = SV8 )
= $false )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( SV2 != SV8 )
= $false )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(228,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i] :
( ( ( ~ ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(229,plain,
! [SV9: $i,SV3: $i,SV21: $i,SV15: $i,SV19: $i] :
( ( ( precedes @ SV19 @ SV15 @ SV21 )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(230,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( edge @ SV4 ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(231,plain,
! [SV4: $i,SV10: $i] :
( ( ( ~ ( edge @ SV10 ) )
= $false )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[213]) ).
thf(232,plain,
! [SV10: $i,SV4: $i] :
( ( ( ~ ( edge @ SV4 ) )
= $true )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(233,plain,
! [SV16: $i,SV11: $i,SV27: $i,SV5: $i,SV24: $i] :
( ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( ~ ( on_path @ SV27 @ SV5 ) )
= $true )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(234,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(235,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
| ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(236,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( tail_of @ SV22 ) ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_forall_neg,[status(esa)],[222]) ).
thf(237,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ SV26 )
| ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(238,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( SV2 = SV8 )
= $true )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( ~ ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(239,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i] :
( ( ( ! [SY106: $i] :
~ ~ ( ( ( tail_of @ SY106 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SY106 )
!= ( head_of @ SV19 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(240,plain,
! [SV10: $i,SV4: $i] :
( ( ( edge @ SV4 )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(241,plain,
! [SV4: $i,SV10: $i] :
( ( ( edge @ SV10 )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(242,plain,
! [SV10: $i,SV4: $i] :
( ( ( edge @ SV4 )
= $false )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(243,plain,
! [SV16: $i,SV11: $i,SV24: $i,SV5: $i,SV27: $i] :
( ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( ~ ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) ) )
= $true )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(244,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(245,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(246,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(247,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( tail_of @ SV22 ) ) ) )
= $true )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(248,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ SV26 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(249,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(250,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ! [SY89: $i] :
( ~ ( path @ SV2 @ SV8 @ SY89 )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ SY89 ) ) ) )
= $false )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( SV2 = SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(251,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i,SV31: $i] :
( ( ( ~ ~ ( ( ( tail_of @ SV31 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SV31 )
!= ( head_of @ SV19 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(252,plain,
! [SV4: $i,SV10: $i] :
( ( ( edge @ SV10 )
= $false )
| ( ( edge @ SV4 )
= $false )
| ( ( ~ ( ( SV4 != SV10 ) ) )
= $true )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(253,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( ( sequential @ SV24 @ SV27 )
| ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(254,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[244]) ).
thf(255,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( sequential @ SV6 @ SV12 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[245]) ).
thf(256,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) ) )
= $false )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(257,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) )
| ( ( head_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( tail_of @ SV22 ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(258,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[248]) ).
thf(259,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY128 )
| ~ ( precedes @ SY128 @ SV26 @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[249]) ).
thf(260,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ ( sK7_SY89 @ SV14 @ SV8 @ SV2 ) )
| ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ ( sK7_SY89 @ SV14 @ SV8 @ SV2 ) ) ) )
= $false )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( SV2 = SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[250]) ).
thf(261,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i,SV31: $i] :
( ( ( ~ ( ( ( tail_of @ SV31 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SV31 )
!= ( head_of @ SV19 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[251]) ).
thf(262,plain,
! [SV10: $i,SV4: $i] :
( ( ( SV4 != SV10 )
= $false )
| ( ( edge @ SV4 )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[252]) ).
thf(263,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( sequential @ SV24 @ SV27 )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(264,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( ~ ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[253]) ).
thf(265,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
| ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(267,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ~ ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(268,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ( head_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( tail_of @ SV22 ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[257]) ).
thf(269,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV32: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV23 @ SV32 )
| ~ ( precedes @ SV32 @ SV26 @ SV1 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV8 @ ( sK7_SY89 @ SV14 @ SV8 @ SV2 ) ) )
= $false )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( SV2 = SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(272,plain,
! [SV2: $i,SV8: $i,SV14: $i] :
( ( ( less_or_equal @ ( length_of @ SV14 ) @ ( length_of @ ( sK7_SY89 @ SV14 @ SV8 @ SV2 ) ) )
= $false )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( SV2 = SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[260]) ).
thf(273,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i,SV31: $i] :
( ( ( ( ( tail_of @ SV31 )
!= ( tail_of @ SV15 ) )
| ( ( head_of @ SV31 )
!= ( head_of @ SV19 ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(274,plain,
! [SV10: $i,SV4: $i] :
( ( ( SV4 = SV10 )
= $true )
| ( ( edge @ SV4 )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( ( head_of @ SV4 )
!= ( tail_of @ SV10 ) )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(275,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV24: $i] :
( ( ( ! [SY130: $i] :
~ ~ ( ~ ( sequential @ SV24 @ SY130 )
| ~ ( precedes @ SY130 @ SV27 @ SV5 ) ) )
= $true )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(276,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(277,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( ~ ( edge @ SV17 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[265]) ).
thf(278,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) ) )
= $true )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(279,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) ) )
= $true )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[267]) ).
thf(280,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ( head_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
= ( tail_of @ SV22 ) )
= $true )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(281,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(282,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( sequential @ SV23 @ SV26 )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[269]) ).
thf(283,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV32: $i,SV23: $i] :
( ( ( ~ ( ~ ( sequential @ SV23 @ SV32 )
| ~ ( precedes @ SV32 @ SV26 @ SV1 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(284,plain,
! [SV14: $i,SV8: $i,SV2: $i] :
( ( ( path @ SV2 @ SV8 @ ( sK7_SY89 @ SV14 @ SV8 @ SV2 ) )
= $true )
| ( ( path @ SV2 @ SV8 @ SV14 )
= $false )
| ( ( SV2 = SV8 )
= $true )
| ( ( shortest_path @ SV2 @ SV8 @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[271]) ).
thf(285,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i,SV31: $i] :
( ( ( ( tail_of @ SV31 )
!= ( tail_of @ SV15 ) )
= $true )
| ( ( ( head_of @ SV31 )
!= ( head_of @ SV19 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(286,plain,
! [SV10: $i,SV4: $i] :
( ( ( ( head_of @ SV4 )
= ( tail_of @ SV10 ) )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( edge @ SV4 )
= $false )
| ( ( SV4 = SV10 )
= $true )
| ( ( sequential @ SV4 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[274]) ).
thf(287,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV33: $i,SV24: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV24 @ SV33 )
| ~ ( precedes @ SV33 @ SV27 @ SV5 ) ) )
= $true )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(288,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(289,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( edge @ SV17 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[277]) ).
thf(290,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) ) )
= $false )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(291,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
| ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(292,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $true )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(293,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV32: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ SV32 )
| ~ ( precedes @ SV32 @ SV26 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(294,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV19: $i,SV15: $i,SV31: $i] :
( ( ( ( tail_of @ SV31 )
= ( tail_of @ SV15 ) )
= $false )
| ( ( ( head_of @ SV31 )
!= ( head_of @ SV19 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(295,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV33: $i,SV24: $i] :
( ( ( ~ ( ~ ( sequential @ SV24 @ SV33 )
| ~ ( precedes @ SV33 @ SV27 @ SV5 ) ) )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(296,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[288]) ).
thf(297,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 )
| ~ ( edge @ SV12 ) )
= $true )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(298,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ~ ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(299,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
!= ( head_of @ SV25 ) )
= $false )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_or_neg,[status(thm)],[291]) ).
thf(300,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(301,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV32: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ SV32 ) )
= $true )
| ( ( ~ ( precedes @ SV32 @ SV26 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(302,plain,
! [SV21: $i,SV9: $i,SV3: $i,SV15: $i,SV19: $i,SV31: $i] :
( ( ( ( head_of @ SV31 )
= ( head_of @ SV19 ) )
= $false )
| ( ( ( tail_of @ SV31 )
= ( tail_of @ SV15 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV9 @ SV21 )
= $false )
| ( ( precedes @ SV15 @ SV19 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(303,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV33: $i,SV24: $i] :
( ( ( ~ ( sequential @ SV24 @ SV33 )
| ~ ( precedes @ SV33 @ SV27 @ SV5 ) )
= $true )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(304,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(305,plain,
! [SV17: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( edge @ SV12 ) )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[296]) ).
thf(306,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 ) )
= $true )
| ( ( ~ ( edge @ SV12 ) )
= $true )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(307,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( edge @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
= $true )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(308,plain,
! [SV25: $i,SV22: $i,SV18: $i,SV20: $i,SV28: $i] :
( ( ( ( tail_of @ ( sK6_SY127 @ SV28 @ SV20 @ SV18 @ SV22 @ SV25 ) )
= ( head_of @ SV25 ) )
= $true )
| ( ( shortest_path @ SV18 @ SV20 @ SV28 )
= $false )
| ( ( precedes @ SV22 @ SV25 @ SV28 )
= $false )
| ( complete = $false ) ),
inference(extcnf_not_neg,[status(thm)],[299]) ).
thf(309,plain,
! [SV26: $i,SV1: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV23 @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[300]) ).
thf(310,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV26: $i,SV32: $i,SV23: $i] :
( ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( ~ ( precedes @ SV32 @ SV26 @ SV1 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(311,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV33: $i,SV24: $i] :
( ( ( ~ ( sequential @ SV24 @ SV33 ) )
= $true )
| ( ( ~ ( precedes @ SV33 @ SV27 @ SV5 ) )
= $true )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[303]) ).
thf(312,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( edge @ SV6 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(313,plain,
! [SV17: $i,SV6: $i,SV12: $i] :
( ( ( edge @ SV12 )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(314,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( edge @ SV6 )
= $false )
| ( ( ~ ( edge @ SV12 ) )
= $true )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(315,plain,
! [SV26: $i,SV1: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( ~ ( sequential @ SV23 @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) ) )
= $true )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[309]) ).
thf(316,plain,
! [SV13: $i,SV7: $i,SV23: $i,SV1: $i,SV26: $i,SV32: $i] :
( ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( ~ ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) ) )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(317,plain,
! [SV16: $i,SV11: $i,SV5: $i,SV27: $i,SV33: $i,SV24: $i] :
( ( ( sequential @ SV24 @ SV33 )
= $false )
| ( ( ~ ( precedes @ SV33 @ SV27 @ SV5 ) )
= $true )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(318,plain,
! [SV17: $i,SV6: $i,SV12: $i] :
( ( ( edge @ SV12 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( ~ ( edge @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(319,plain,
! [SV26: $i,SV1: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(320,plain,
! [SV13: $i,SV7: $i,SV32: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) )
| ( sequential @ SV23 @ SV26 ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(321,plain,
! [SV16: $i,SV11: $i,SV24: $i,SV5: $i,SV27: $i,SV33: $i] :
( ( ( precedes @ SV33 @ SV27 @ SV5 )
= $false )
| ( ( sequential @ SV24 @ SV33 )
= $false )
| ( ( on_path @ SV24 @ SV5 )
= $false )
| ( ( on_path @ SV27 @ SV5 )
= $false )
| ( ( precedes @ SV24 @ SV27 @ SV5 )
= $true )
| ( ( path @ SV11 @ SV16 @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(322,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( edge @ SV17 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV12 )
= $false )
| ( ( ~ ( sequential @ SV6 @ SV12 ) )
= $true )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(323,plain,
! [SV26: $i,SV1: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(324,plain,
! [SV23: $i,SV26: $i,SV1: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( precedes @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) )
= $false )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[319]) ).
thf(325,plain,
! [SV13: $i,SV7: $i,SV32: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(326,plain,
! [SV13: $i,SV7: $i,SV1: $i,SV32: $i,SV26: $i,SV23: $i] :
( ( ( sequential @ SV23 @ SV26 )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[320]) ).
thf(327,plain,
! [SV17: $i,SV12: $i,SV6: $i] :
( ( ( sequential @ SV6 @ SV12 )
= $false )
| ( ( edge @ SV12 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV17 )
= $false )
| ( ( ~ ( sequential @ SV12 @ SV17 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[322]) ).
thf(328,plain,
! [SV26: $i,SV1: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( sequential @ SV23 @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) )
= $true )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[323]) ).
thf(329,plain,
! [SV23: $i,SV26: $i,SV1: $i,SV7: $i,SV13: $i] :
( ( ( precedes @ ( sK8_SY129 @ SV13 @ SV7 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 )
= $true )
| ( ( sequential @ SV23 @ SV26 )
= $true )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[324]) ).
thf(330,plain,
! [SV13: $i,SV7: $i,SV32: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ~ ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $true )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[325]) ).
thf(331,plain,
! [SV6: $i,SV17: $i,SV12: $i] :
( ( ( sequential @ SV12 @ SV17 )
= $false )
| ( ( edge @ SV17 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV12 )
= $false )
| ( ( sequential @ SV6 @ SV12 )
= $false )
| ( ( ~ ( sequential @ SV17 @ SV6 ) )
= $true )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(332,plain,
! [SV13: $i,SV7: $i,SV32: $i,SV1: $i,SV26: $i,SV23: $i] :
( ( ( ! [SY129: $i] :
~ ~ ( ~ ( sequential @ SV23 @ SY129 )
| ~ ( precedes @ SY129 @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(333,plain,
! [SV12: $i,SV6: $i,SV17: $i] :
( ( ( sequential @ SV17 @ SV6 )
= $false )
| ( ( sequential @ SV6 @ SV12 )
= $false )
| ( ( edge @ SV12 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV17 )
= $false )
| ( ( sequential @ SV12 @ SV17 )
= $false )
| ( ( triangle @ SV6 @ SV12 @ SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(334,plain,
! [SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV23 @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[332]) ).
thf(335,plain,
! [SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( ~ ( sequential @ SV23 @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) ) )
= $true )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[334]) ).
thf(336,plain,
! [SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) )
| ~ ( precedes @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(337,plain,
! [SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( ~ ( sequential @ SV23 @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(338,plain,
! [SV23: $i,SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i] :
( ( ( ~ ( precedes @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 ) )
= $false )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[336]) ).
thf(339,plain,
! [SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i,SV23: $i] :
( ( ( sequential @ SV23 @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) )
= $true )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[337]) ).
thf(340,plain,
! [SV23: $i,SV26: $i,SV1: $i,SV32: $i,SV7: $i,SV13: $i] :
( ( ( precedes @ ( sK9_SY129 @ SV13 @ SV7 @ SV32 @ SV1 @ SV26 @ SV23 ) @ SV26 @ SV1 )
= $true )
| ( ( sequential @ SV23 @ SV32 )
= $false )
| ( ( precedes @ SV32 @ SV26 @ SV1 )
= $false )
| ( ( precedes @ SV23 @ SV26 @ SV1 )
= $false )
| ( ( path @ SV7 @ SV13 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[338]) ).
thf(341,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,340,339,333,329,328,326,321,313,312,308,307,302,289,286,284,282,280,272,263,255,241,240,229,226,224,223,221,220,218,214,209,207,170,167,155,147]) ).
thf(342,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA008+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 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 : n017.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
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:17:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.12/1.13
% 5.12/1.13 No.of.Axioms: 7
% 5.12/1.13
% 5.12/1.13 Length.of.Defs: 0
% 5.12/1.13
% 5.12/1.13 Contains.Choice.Funs: false
% 5.12/1.13 ............
% 5.12/1.13
% 5.12/1.13 ********************************
% 5.12/1.13 * All subproblems solved! *
% 5.12/1.13 ********************************
% 5.12/1.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:341,loop_count:0,foatp_calls:1,translation:fof_full)
% 5.12/1.13
% 5.12/1.13 %**** Beginning of derivation protocol ****
% 5.12/1.13 % SZS output start CNFRefutation
% See solution above
% 5.12/1.14
% 5.12/1.14 %**** End of derivation protocol ****
% 5.12/1.14 %**** no. of clauses in derivation: 331 ****
% 5.12/1.14 %**** clause counter: 341 ****
% 5.12/1.14
% 5.12/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:8,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:341,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------