%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRA010+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 : n014.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 10:19:42 AM UTC 2026
% Result : Theorem 0.55s 0.35s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 221 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 2539 ( 676 equ; 0 cnn)
% Maximal formula atoms : 7 ( 11 avg)
% Number of connectives : 5863 (1656 ~; 953 |; 60 &;3155 @)
% ( 3 <=>; 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 : 34 ( 31 usr; 12 con; 0-6 aty)
% Number of variables : 999 ( 0 ^; 984 !; 15 ?; 999 :)
% 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_SY49,type,
sK2_SY49: $i ).
thf(tp_sK3_SY67,type,
sK3_SY67: $i ).
thf(tp_sK4_SY42,type,
sK4_SY42: $i > $i > $i > $i ).
thf(tp_sK5_SY91,type,
sK5_SY91: $i > $i > $i > $i ).
thf(tp_sK6_SY93,type,
sK6_SY93: $i > $i > $i ).
thf(tp_sK7_SY88,type,
sK7_SY88: $i > $i > $i > $i > $i > $i ).
thf(tp_sK8_SY88,type,
sK8_SY88: $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(2,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
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(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(19,conjecture,
( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
thf(20,negated_conjecture,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(23,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(24,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(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)],[9]) ).
thf(26,plain,
complete = $true,
inference(standard_cnf,[status(thm)],[21]) ).
thf(27,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(28,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(29,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(30,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)],[24]) ).
thf(31,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)],[23]) ).
thf(32,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(33,plain,
complete = $true,
inference(copy,[status(thm)],[26]) ).
thf(34,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( ( path @ V1 @ V2 @ P )
& ! [E1: $i,E2: $i] :
( ( ( on_path @ E1 @ P )
& ( on_path @ E2 @ P )
& ( sequential @ E1 @ E2 ) )
=> ? [E3: $i] : ( triangle @ E1 @ E2 @ E3 ) ) )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(35,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)],[29]) ).
thf(36,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(37,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)],[31]) ).
thf(38,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)],[30]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(40,plain,
! [SV1: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( path @ SY27 @ SY28 @ SV1 )
| ! [SY29: $i,SY30: $i] :
( ( precedes @ SY29 @ SY30 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY29 @ SV1 )
| ~ ( on_path @ SY30 @ SV1 ) )
| ~ ( ( sequential @ SY29 @ SY30 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( sequential @ SY29 @ SY31 )
| ~ ( precedes @ SY31 @ SY30 @ SV1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( path @ SX1 @ SX2 @ SX0 )
| ~ ! [SX3: $i,SX4: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SX3 @ SX0 )
| ~ ( on_path @ SX4 @ SX0 ) )
| ~ ( sequential @ SX3 @ SX4 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SX3 @ SX4 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY32: $i,SY33: $i] :
~ ( ~ ( ~ ( triangle @ SV2 @ SY32 @ SY33 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SY32 ) )
| ~ ( edge @ SY33 ) )
| ~ ( sequential @ SV2 @ SY32 ) )
| ~ ( sequential @ SY32 @ SY33 ) )
| ~ ( sequential @ SY33 @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SY32 ) )
| ~ ( edge @ SY33 ) )
| ~ ( sequential @ SV2 @ SY32 ) )
| ~ ( sequential @ SY32 @ SY33 ) )
| ~ ( sequential @ SY33 @ SV2 ) )
| ( triangle @ SV2 @ SY32 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY34: $i,SY35: $i] :
( ~ ( path @ SY34 @ SY35 @ SV3 )
| ! [SY36: $i,SY37: $i] :
( ~ ( precedes @ SY36 @ SY37 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SY36 @ SV3 )
| ~ ( on_path @ SY37 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY36 @ SY37 )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY38 )
| ~ ( precedes @ SY38 @ SY37 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY39 )
| ~ ( precedes @ SY39 @ SY37 @ SV3 ) )
| ( sequential @ SY36 @ SY37 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( path @ SY40 @ SY41 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(45,plain,
! [SV1: $i,SV5: $i] :
( ( ! [SY45: $i] :
( ~ ( path @ SV5 @ SY45 @ SV1 )
| ! [SY29: $i,SY30: $i] :
( ( precedes @ SY29 @ SY30 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY29 @ SV1 )
| ~ ( on_path @ SY30 @ SV1 ) )
| ~ ( ( sequential @ SY29 @ SY30 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( sequential @ SY29 @ SY31 )
| ~ ( precedes @ SY31 @ SY30 @ SV1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(46,plain,
( ( ! [SY49: $i,SY50: $i] :
( ~ ~ ( ~ ( path @ SY49 @ SY50 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ sK1_SX0 )
= ( number_of_in @ triangles @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[41]) ).
thf(47,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY54: $i] :
~ ( ~ ( ~ ( triangle @ SV2 @ SV6 @ SY54 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SY54 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SY54 ) )
| ~ ( sequential @ SY54 @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SY54 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SY54 ) )
| ~ ( sequential @ SY54 @ SV2 ) )
| ( triangle @ SV2 @ SV6 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV3: $i,SV7: $i] :
( ( ! [SY55: $i] :
( ~ ( path @ SV7 @ SY55 @ SV3 )
| ! [SY36: $i,SY37: $i] :
( ~ ( precedes @ SY36 @ SY37 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SY36 @ SV3 )
| ~ ( on_path @ SY37 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY36 @ SY37 )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY38 )
| ~ ( precedes @ SY38 @ SY37 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY39 )
| ~ ( precedes @ SY39 @ SY37 @ SV3 ) )
| ( sequential @ SY36 @ SY37 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV4: $i,SV8: $i] :
( ( ! [SY60: $i] :
( ~ ~ ( ~ ( path @ SV8 @ SY60 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(50,plain,
! [SV1: $i,SV9: $i,SV5: $i] :
( ( ~ ( path @ SV5 @ SV9 @ SV1 )
| ! [SY29: $i,SY30: $i] :
( ( precedes @ SY29 @ SY30 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY29 @ SV1 )
| ~ ( on_path @ SY30 @ SV1 ) )
| ~ ( ( sequential @ SY29 @ SY30 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( sequential @ SY29 @ SY31 )
| ~ ( precedes @ SY31 @ SY30 @ SV1 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
( ( ! [SY67: $i] :
( ~ ~ ( ~ ( path @ sK2_SY49 @ SY67 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ sK1_SX0 )
= ( number_of_in @ triangles @ sK1_SX0 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( ~ ( ~ ( triangle @ SV2 @ SV6 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
| ( triangle @ SV2 @ SV6 @ SV10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV3: $i,SV11: $i,SV7: $i] :
( ( ~ ( path @ SV7 @ SV11 @ SV3 )
| ! [SY36: $i,SY37: $i] :
( ~ ( precedes @ SY36 @ SY37 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SY36 @ SV3 )
| ~ ( on_path @ SY37 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY36 @ SY37 )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY38 )
| ~ ( precedes @ SY38 @ SY37 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY39 )
| ~ ( precedes @ SY39 @ SY37 @ SV3 ) )
| ( sequential @ SY36 @ SY37 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ~ ~ ( ~ ( path @ SV8 @ SV12 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV1: $i,SV9: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV9 @ SV1 ) )
= $true )
| ( ( ! [SY29: $i,SY30: $i] :
( ( precedes @ SY29 @ SY30 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY29 @ SV1 )
| ~ ( on_path @ SY30 @ SV1 ) )
| ~ ( ( sequential @ SY29 @ SY30 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( sequential @ SY29 @ SY31 )
| ~ ( precedes @ SY31 @ SY30 @ SV1 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(56,plain,
( ( ~ ~ ( ~ ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
| ( ( number_of_in @ sequential_pairs @ sK1_SX0 )
= ( number_of_in @ triangles @ sK1_SX0 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[51]) ).
thf(57,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( ~ ( triangle @ SV2 @ SV6 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
| ( triangle @ SV2 @ SV6 @ SV10 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV3: $i,SV11: $i,SV7: $i] :
( ( ( ~ ( path @ SV7 @ SV11 @ SV3 ) )
= $true )
| ( ( ! [SY36: $i,SY37: $i] :
( ~ ( precedes @ SY36 @ SY37 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SY36 @ SV3 )
| ~ ( on_path @ SY37 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY36 @ SY37 )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY38 )
| ~ ( precedes @ SY38 @ SY37 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY39 )
| ~ ( precedes @ SY39 @ SY37 @ SV3 ) )
| ( sequential @ SY36 @ SY37 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ~ ( ~ ( path @ SV8 @ SV12 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV1: $i,SV9: $i,SV5: $i] :
( ( ( path @ SV5 @ SV9 @ SV1 )
= $false )
| ( ( ! [SY29: $i,SY30: $i] :
( ( precedes @ SY29 @ SY30 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SY29 @ SV1 )
| ~ ( on_path @ SY30 @ SV1 ) )
| ~ ( ( sequential @ SY29 @ SY30 )
| ~ ! [SY31: $i] :
~ ~ ( ~ ( sequential @ SY29 @ SY31 )
| ~ ( precedes @ SY31 @ SY30 @ SV1 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(61,plain,
( ( ~ ~ ( ~ ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(62,plain,
( ( ( number_of_in @ sequential_pairs @ sK1_SX0 )
= ( number_of_in @ triangles @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[56]) ).
thf(63,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( ~ ( triangle @ SV2 @ SV6 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
| ( triangle @ SV2 @ SV6 @ SV10 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(65,plain,
! [SV3: $i,SV11: $i,SV7: $i] :
( ( ( path @ SV7 @ SV11 @ SV3 )
= $false )
| ( ( ! [SY36: $i,SY37: $i] :
( ~ ( precedes @ SY36 @ SY37 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SY36 @ SV3 )
| ~ ( on_path @ SY37 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SY36 @ SY37 )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY38 )
| ~ ( precedes @ SY38 @ SY37 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY39: $i] :
~ ~ ( ~ ( sequential @ SY36 @ SY39 )
| ~ ( precedes @ SY39 @ SY37 @ SV3 ) )
| ( sequential @ SY36 @ SY37 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(66,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( ~ ( path @ SV8 @ SV12 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) ) )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(67,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV13: $i] :
( ( ( ! [SY81: $i] :
( ( precedes @ SV13 @ SY81 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SY81 @ SV1 ) )
| ~ ( ( sequential @ SV13 @ SY81 )
| ~ ! [SY82: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY82 )
| ~ ( precedes @ SY82 @ SY81 @ SV1 ) ) ) ) ) )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(68,plain,
( ( ~ ( ~ ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(69,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ( triangle @ SV2 @ SV6 @ SV10 )
| ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
| ( triangle @ SV2 @ SV6 @ SV10 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(71,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV14: $i] :
( ( ( ! [SY83: $i] :
( ~ ( precedes @ SV14 @ SY83 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SY83 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SY83 )
| ~ ! [SY84: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY84 )
| ~ ( precedes @ SY84 @ SY83 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY85: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY85 )
| ~ ( precedes @ SY85 @ SY83 @ SV3 ) )
| ( sequential @ SV14 @ SY83 ) ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( path @ SV8 @ SV12 @ SV4 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( ( precedes @ SV13 @ SV15 @ SV1 )
| ~ ~ ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) )
| ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) ) )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(74,plain,
( ( ~ ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 )
| ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( triangle @ SV2 @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( precedes @ SV14 @ SV16 @ SV3 )
| ~ ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( ~ ( path @ SV8 @ SV12 @ SV4 ) )
= $true )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) )
| ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) ) )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(80,plain,
( ( ~ ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(81,plain,
( ( ~ ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(82,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(83,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(84,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( precedes @ SV14 @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(85,plain,
! [SV4: $i,SV12: $i,SV8: $i] :
( ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) )
| ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) ) )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(87,plain,
( ( path @ sK2_SY49 @ sK3_SY67 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(88,plain,
( ( ! [SY51: $i,SY52: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY51 @ sK1_SX0 )
| ~ ( on_path @ SY52 @ sK1_SX0 ) )
| ~ ( sequential @ SY51 @ SY52 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY51 @ SY52 @ SX5 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[81]) ).
thf(89,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(90,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
| ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[83]) ).
thf(91,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) ) )
= $true )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ! [SY42: $i,SY43: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SY42 @ SV4 )
| ~ ( on_path @ SY43 @ SV4 ) )
| ~ ( sequential @ SY42 @ SY43 ) )
| ~ ! [SX5: $i] :
~ ( triangle @ SY42 @ SY43 @ SX5 ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) )
| ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(94,plain,
! [SV17: $i] :
( ( ! [SY89: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SY89 @ sK1_SX0 ) )
| ~ ( sequential @ SV17 @ SY89 ) )
| ~ ! [SY90: $i] :
~ ( triangle @ SV17 @ SY89 @ SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(96,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[89]) ).
thf(97,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) )
| ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY91: $i] :
( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ SY91 @ SV4 ) )
| ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SY91 ) )
| ~ ! [SY92: $i] :
~ ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SY91 @ SY92 ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[92]) ).
thf(100,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) ) )
= $true )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV18: $i,SV17: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) )
| ~ ( sequential @ SV17 @ SV18 ) )
| ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(103,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( sequential @ SV10 @ SV2 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(104,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) ) )
= $false )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(106,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[98]) ).
thf(107,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
| ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) ) )
| ~ ! [SY94: $i] :
~ ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SY94 ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[99]) ).
thf(108,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) ) )
= $false )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(109,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) )
| ~ ( sequential @ SV17 @ SV18 ) ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(110,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(111,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
| ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(112,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[105]) ).
thf(113,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(114,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
| ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(115,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ! [SY94: $i] :
~ ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SY94 ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[107]) ).
thf(116,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( on_path @ SV13 @ SV1 )
| ~ ( on_path @ SV15 @ SV1 ) )
= $true )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(117,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) )
| ~ ( sequential @ SV17 @ SV18 ) ) )
= $false )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(119,plain,
! [SV2: $i,SV10: $i,SV6: $i] :
( ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[110]) ).
thf(120,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(121,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( on_path @ SV14 @ SV3 )
| ~ ( on_path @ SV16 @ SV3 ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(122,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(123,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
| ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) ) ) )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(124,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ! [SY94: $i] :
~ ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SY94 ) )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[115]) ).
thf(125,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( ~ ( on_path @ SV13 @ SV1 ) )
= $true )
| ( ( ~ ( on_path @ SV15 @ SV1 ) )
= $true )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[116]) ).
thf(126,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) )
| ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[117]) ).
thf(127,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(128,plain,
! [SV2: $i,SV10: $i,SV6: $i] :
( ( ( sequential @ SV6 @ SV10 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[119]) ).
thf(129,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) ) )
= $false )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(130,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( ~ ( on_path @ SV14 @ SV3 ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(131,plain,
! [SV11: $i,SV7: $i,SV14: $i,SV3: $i,SV16: $i] :
( ( ( ~ ( on_path @ SV16 @ SV3 ) )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[121]) ).
thf(132,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
| ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(133,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
| ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV19: $i,SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV19 ) )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV9: $i,SV5: $i,SV15: $i,SV1: $i,SV13: $i] :
( ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( ~ ( on_path @ SV15 @ SV1 ) )
= $true )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(138,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
| ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(139,plain,
! [SV11: $i,SV7: $i,SV16: $i,SV3: $i,SV14: $i] :
( ( ( on_path @ SV14 @ SV3 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(140,plain,
! [SV11: $i,SV7: $i,SV14: $i,SV3: $i,SV16: $i] :
( ( ( on_path @ SV16 @ SV3 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[131]) ).
thf(141,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(142,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(143,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[133]) ).
thf(144,plain,
! [SV19: $i,SV4: $i,SV8: $i,SV12: $i] :
( ( ( triangle @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV19 )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(145,plain,
! [SV9: $i,SV5: $i,SV13: $i,SV1: $i,SV15: $i] :
( ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( ~ ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) ) )
= $true )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) ) )
= $false )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(147,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(148,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[137]) ).
thf(149,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ SV16 )
| ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(151,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) ) )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[142]) ).
thf(152,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( sequential @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(153,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( ( sequential @ SV13 @ SV15 )
| ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(154,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ( on_path @ SV17 @ sK1_SX0 )
| ~ ( on_path @ SV18 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( sequential @ SV2 @ SV6 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(157,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) ) )
= $false )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(158,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ SV16 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(159,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[150]) ).
thf(160,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
| ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(161,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( sequential @ SV13 @ SV15 )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(162,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( ~ ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(163,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ( on_path @ SV17 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( on_path @ SV18 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(165,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
| ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[157]) ).
thf(166,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(167,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ! [SY87: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY87 )
| ~ ( precedes @ SY87 @ SV16 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[159]) ).
thf(168,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( ~ ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(169,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( ~ ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 ) )
= $false )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[160]) ).
thf(170,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV13: $i] :
( ( ( ! [SY86: $i] :
~ ~ ( ~ ( sequential @ SV13 @ SY86 )
| ~ ( precedes @ SY86 @ SV15 @ SV1 ) ) )
= $true )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[162]) ).
thf(171,plain,
! [SV18: $i,SV17: $i] :
( ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( ~ ( on_path @ SV18 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(172,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(173,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( edge @ SV10 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[164]) ).
thf(174,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) ) )
= $true )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[165]) ).
thf(175,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(176,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV20: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV14 @ SV20 )
| ~ ( precedes @ SV20 @ SV16 @ SV3 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(177,plain,
! [SV4: $i,SV8: $i,SV12: $i] :
( ( ( on_path @ ( sK4_SY42 @ SV12 @ SV8 @ SV4 ) @ SV4 )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[168]) ).
thf(178,plain,
! [SV12: $i,SV8: $i,SV4: $i] :
( ( ( on_path @ ( sK5_SY91 @ SV4 @ SV8 @ SV12 ) @ SV4 )
= $true )
| ( ( path @ SV8 @ SV12 @ SV4 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV4 )
= ( number_of_in @ triangles @ SV4 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(179,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV21: $i,SV13: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV13 @ SV21 )
| ~ ( precedes @ SV21 @ SV15 @ SV1 ) ) )
= $true )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(180,plain,
! [SV17: $i,SV18: $i] :
( ( ( on_path @ SV18 @ sK1_SX0 )
= $false )
| ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( ~ ( sequential @ SV17 @ SV18 ) )
= $true )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(181,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[172]) ).
thf(182,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( edge @ SV10 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[173]) ).
thf(183,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) ) )
= $false )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(184,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(185,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( sequential @ SV14 @ SV16 )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[175]) ).
thf(186,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV20: $i,SV14: $i] :
( ( ( ~ ( ~ ( sequential @ SV14 @ SV20 )
| ~ ( precedes @ SV20 @ SV16 @ SV3 ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( ~ ( sequential @ SV13 @ SV21 )
| ~ ( precedes @ SV21 @ SV15 @ SV1 ) ) )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(188,plain,
! [SV18: $i,SV17: $i] :
( ( ( sequential @ SV17 @ SV18 )
= $false )
| ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( on_path @ SV18 @ sK1_SX0 )
= $false )
| ( ( ~ ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(189,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(190,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( edge @ SV2 )
| ~ ( edge @ SV6 ) )
= $true )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[183]) ).
thf(191,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $true )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[184]) ).
thf(192,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV20: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ SV20 )
| ~ ( precedes @ SV20 @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[186]) ).
thf(193,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( sequential @ SV13 @ SV21 )
| ~ ( precedes @ SV21 @ SV15 @ SV1 ) )
= $true )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[187]) ).
thf(194,plain,
! [SV18: $i,SV17: $i] :
( ( ( ! [SY93: $i] :
~ ( triangle @ SV17 @ SV18 @ SY93 ) )
= $false )
| ( ( on_path @ SV18 @ sK1_SX0 )
= $false )
| ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( sequential @ SV17 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(195,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( edge @ SV2 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(196,plain,
! [SV10: $i,SV2: $i,SV6: $i] :
( ( ( ~ ( edge @ SV6 ) )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[189]) ).
thf(197,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( ~ ( edge @ SV2 ) )
= $true )
| ( ( ~ ( edge @ SV6 ) )
= $true )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[190]) ).
thf(198,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[191]) ).
thf(199,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV20: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ SV20 ) )
= $true )
| ( ( ~ ( precedes @ SV20 @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(200,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV21: $i,SV13: $i] :
( ( ( ~ ( sequential @ SV13 @ SV21 ) )
= $true )
| ( ( ~ ( precedes @ SV21 @ SV15 @ SV1 ) )
= $true )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(201,plain,
! [SV18: $i,SV17: $i] :
( ( ( ~ ( triangle @ SV17 @ SV18 @ ( sK6_SY93 @ SV18 @ SV17 ) ) )
= $false )
| ( ( on_path @ SV18 @ sK1_SX0 )
= $false )
| ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( sequential @ SV17 @ SV18 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[194]) ).
thf(202,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( edge @ SV2 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(203,plain,
! [SV10: $i,SV2: $i,SV6: $i] :
( ( ( edge @ SV6 )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[196]) ).
thf(204,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( edge @ SV2 )
= $false )
| ( ( ~ ( edge @ SV6 ) )
= $true )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(205,plain,
! [SV16: $i,SV3: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV14 @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[198]) ).
thf(206,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV16: $i,SV20: $i,SV14: $i] :
( ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( ~ ( precedes @ SV20 @ SV16 @ SV3 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(207,plain,
! [SV9: $i,SV5: $i,SV1: $i,SV15: $i,SV21: $i,SV13: $i] :
( ( ( sequential @ SV13 @ SV21 )
= $false )
| ( ( ~ ( precedes @ SV21 @ SV15 @ SV1 ) )
= $true )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(208,plain,
! [SV18: $i,SV17: $i] :
( ( ( triangle @ SV17 @ SV18 @ ( sK6_SY93 @ SV18 @ SV17 ) )
= $true )
| ( ( on_path @ SV18 @ sK1_SX0 )
= $false )
| ( ( on_path @ SV17 @ sK1_SX0 )
= $false )
| ( ( sequential @ SV17 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[201]) ).
thf(209,plain,
! [SV10: $i,SV2: $i,SV6: $i] :
( ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV2 )
= $false )
| ( ( ~ ( edge @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(210,plain,
! [SV16: $i,SV3: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ( sequential @ SV14 @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) ) )
= $true )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[205]) ).
thf(211,plain,
! [SV11: $i,SV7: $i,SV14: $i,SV3: $i,SV16: $i,SV20: $i] :
( ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( ~ ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) ) )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(212,plain,
! [SV9: $i,SV5: $i,SV13: $i,SV1: $i,SV15: $i,SV21: $i] :
( ( ( precedes @ SV21 @ SV15 @ SV1 )
= $false )
| ( ( sequential @ SV13 @ SV21 )
= $false )
| ( ( on_path @ SV13 @ SV1 )
= $false )
| ( ( on_path @ SV15 @ SV1 )
= $false )
| ( ( precedes @ SV13 @ SV15 @ SV1 )
= $true )
| ( ( path @ SV5 @ SV9 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(213,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( edge @ SV10 )
= $false )
| ( ( edge @ SV2 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( ~ ( sequential @ SV2 @ SV6 ) )
= $true )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(214,plain,
! [SV16: $i,SV3: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV11: $i,SV7: $i,SV20: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) )
| ( sequential @ SV14 @ SV16 ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV10: $i,SV6: $i,SV2: $i] :
( ( ( sequential @ SV2 @ SV6 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV2 )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( ~ ( sequential @ SV6 @ SV10 ) )
= $true )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(217,plain,
! [SV16: $i,SV3: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(218,plain,
! [SV14: $i,SV16: $i,SV3: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( precedes @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) )
= $false )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[214]) ).
thf(219,plain,
! [SV11: $i,SV7: $i,SV20: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(220,plain,
! [SV11: $i,SV7: $i,SV3: $i,SV20: $i,SV16: $i,SV14: $i] :
( ( ( sequential @ SV14 @ SV16 )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[215]) ).
thf(221,plain,
! [SV2: $i,SV10: $i,SV6: $i] :
( ( ( sequential @ SV6 @ SV10 )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( edge @ SV2 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( sequential @ SV2 @ SV6 )
= $false )
| ( ( ~ ( sequential @ SV10 @ SV2 ) )
= $true )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(222,plain,
! [SV16: $i,SV3: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( sequential @ SV14 @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) )
= $true )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[217]) ).
thf(223,plain,
! [SV14: $i,SV16: $i,SV3: $i,SV7: $i,SV11: $i] :
( ( ( precedes @ ( sK7_SY88 @ SV11 @ SV7 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 )
= $true )
| ( ( sequential @ SV14 @ SV16 )
= $true )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[218]) ).
thf(224,plain,
! [SV11: $i,SV7: $i,SV20: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ~ ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $true )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(225,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( sequential @ SV10 @ SV2 )
= $false )
| ( ( sequential @ SV2 @ SV6 )
= $false )
| ( ( edge @ SV6 )
= $false )
| ( ( edge @ SV2 )
= $false )
| ( ( edge @ SV10 )
= $false )
| ( ( sequential @ SV6 @ SV10 )
= $false )
| ( ( triangle @ SV2 @ SV6 @ SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV11: $i,SV7: $i,SV20: $i,SV3: $i,SV16: $i,SV14: $i] :
( ( ( ! [SY88: $i] :
~ ~ ( ~ ( sequential @ SV14 @ SY88 )
| ~ ( precedes @ SY88 @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(227,plain,
! [SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ~ ( ~ ( sequential @ SV14 @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[226]) ).
thf(228,plain,
! [SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( ~ ( sequential @ SV14 @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) ) )
= $true )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[227]) ).
thf(229,plain,
! [SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) )
| ~ ( precedes @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(230,plain,
! [SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( ~ ( sequential @ SV14 @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(231,plain,
! [SV14: $i,SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( precedes @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 ) )
= $false )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(232,plain,
! [SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i,SV14: $i] :
( ( ( sequential @ SV14 @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) )
= $true )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[230]) ).
thf(233,plain,
! [SV14: $i,SV16: $i,SV3: $i,SV20: $i,SV7: $i,SV11: $i] :
( ( ( precedes @ ( sK8_SY88 @ SV11 @ SV7 @ SV20 @ SV3 @ SV16 @ SV14 ) @ SV16 @ SV3 )
= $true )
| ( ( sequential @ SV14 @ SV20 )
= $false )
| ( ( precedes @ SV20 @ SV16 @ SV3 )
= $false )
| ( ( precedes @ SV14 @ SV16 @ SV3 )
= $false )
| ( ( path @ SV7 @ SV11 @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[231]) ).
thf(234,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,233,232,225,223,222,220,212,208,203,202,185,182,178,177,161,156,152,144,140,139,128,103,87,62]) ).
thf(235,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+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 : n014.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 10:21:56 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
% 0.55/0.35
% 0.55/0.35 No.of.Axioms: 4
% 0.55/0.35
% 0.55/0.35 Length.of.Defs: 0
% 0.55/0.35
% 0.55/0.35 Contains.Choice.Funs: false
% 0.55/0.35 ........
% 0.55/0.35
% 0.55/0.35 ********************************
% 0.55/0.35 * All subproblems solved! *
% 0.55/0.35 ********************************
% 0.55/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:234,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.35
% 0.55/0.35 %**** Beginning of derivation protocol ****
% 0.55/0.35 % SZS output start CNFRefutation
% See solution above
% 0.55/0.35
% 0.55/0.35 %**** End of derivation protocol ****
% 0.55/0.35 %**** no. of clauses in derivation: 221 ****
% 0.55/0.35 %**** clause counter: 234 ****
% 0.55/0.35
% 0.55/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:234,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------