%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GRA002+4 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:19:38 AM UTC 2026
% Result : Theorem 0.57s 0.31s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of formulae : 124 ( 56 unt; 0 typ; 0 def)
% Number of atoms : 887 ( 345 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 2041 ( 485 ~; 272 |; 15 &;1239 @)
% ( 3 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 12 con; 0-3 aty)
% Number of variables : 460 ( 0 ^; 457 !; 3 ?; 460 :)
% 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_SY44,type,
sK2_SY44: $i ).
thf(tp_sK3_SY54,type,
sK3_SY54: $i ).
thf(tp_sK4_SY56,type,
sK4_SY56: $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(1,axiom,
! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
thf(3,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
thf(4,axiom,
! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',length_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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
thf(18,axiom,
( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
thf(19,conjecture,
( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
thf(20,negated_conjecture,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,plain,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[20]) ).
thf(22,plain,
( ( ! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(23,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(25,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(26,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(27,plain,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(28,plain,
complete = $true,
inference(standard_cnf,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[21]) ).
thf(30,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(31,plain,
( ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( number_of_in @ triangles @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(32,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)],[26]) ).
thf(33,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)],[25]) ).
thf(34,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( length_of @ P )
= ( number_of_in @ edges @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(35,plain,
( ( ! [V1: $i,V2: $i,P: $i] :
( ( path @ V1 @ V2 @ P )
=> ( ( number_of_in @ sequential_pairs @ P )
= ( minus @ ( length_of @ P ) @ n1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(36,plain,
( ( ! [Things: $i,InThese: $i] : ( less_or_equal @ ( number_of_in @ Things @ InThese ) @ ( number_of_in @ Things @ graph ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
complete = $true,
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ~ ! [P: $i,V1: $i,V2: $i] :
( ( shortest_path @ V1 @ V2 @ P )
=> ( less_or_equal @ ( minus @ ( length_of @ P ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(39,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ( ( number_of_in @ sequential_pairs @ SX2 )
= ( minus @ ( length_of @ SX2 ) @ n1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(40,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)],[33]) ).
thf(41,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( path @ SX0 @ SX1 @ SX2 )
| ( ( length_of @ SX2 )
= ( number_of_in @ edges @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(42,plain,
( ( ~ complete
| ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(43,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ( less_or_equal @ ( minus @ ( length_of @ SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(44,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)],[32]) ).
thf(45,plain,
! [SV1: $i] :
( ( ! [SY24: $i] : ( less_or_equal @ ( number_of_in @ SV1 @ SY24 ) @ ( number_of_in @ SV1 @ graph ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV2: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( path @ SV2 @ SY25 @ SY26 )
| ( ( number_of_in @ sequential_pairs @ SY26 )
= ( minus @ ( length_of @ SY26 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV3: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i,SY30: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SY27 @ SY30 )
| ~ ( precedes @ SY28 @ SY29 @ SY30 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY28 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY29 ) ) )
| ~ ~ ( precedes @ SY29 @ SY28 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV4: $i] :
( ( ! [SY32: $i,SY33: $i] :
( ~ ( path @ SV4 @ SY32 @ SY33 )
| ( ( length_of @ SY33 )
= ( number_of_in @ edges @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
( ( ( ~ complete ) = $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ( less_or_equal @ ( minus @ ( length_of @ SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV5: $i] :
( ( ! [SY34: $i,SY35: $i] :
~ ( ~ ( ~ ( shortest_path @ SV5 @ SY34 @ SY35 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SY34 @ SY35 )
| ~ ( ( SV5 != SY34 ) ) )
| ~ ! [SY36: $i] :
( ~ ( path @ SV5 @ SY34 @ SY36 )
| ( less_or_equal @ ( length_of @ SY35 ) @ ( length_of @ SY36 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SY34 @ SY35 )
| ~ ( ( SV5 != SY34 ) ) )
| ~ ! [SY37: $i] :
( ~ ( path @ SV5 @ SY34 @ SY37 )
| ( less_or_equal @ ( length_of @ SY35 ) @ ( length_of @ SY37 ) ) ) )
| ( shortest_path @ SV5 @ SY34 @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV6: $i,SV1: $i] :
( ( less_or_equal @ ( number_of_in @ SV1 @ SV6 ) @ ( number_of_in @ SV1 @ graph ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY38: $i] :
( ~ ( path @ SV2 @ SV7 @ SY38 )
| ( ( number_of_in @ sequential_pairs @ SY38 )
= ( minus @ ( length_of @ SY38 ) @ n1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(54,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SY41 )
| ~ ( precedes @ SY39 @ SY40 @ SY41 ) )
| ~ ( ~ ~ ~ ! [SX5: $i] :
~ ~ ( ( ( tail_of @ SX5 )
!= ( tail_of @ SY39 ) )
| ( ( head_of @ SX5 )
!= ( head_of @ SY40 ) ) )
| ~ ~ ( precedes @ SY40 @ SY39 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(55,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY43: $i] :
( ~ ( path @ SV4 @ SV9 @ SY43 )
| ( ( length_of @ SY43 )
= ( number_of_in @ edges @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
( ( complete = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( shortest_path @ SX1 @ SX2 @ SX0 )
| ( ( number_of_in @ sequential_pairs @ SX0 )
= ( number_of_in @ triangles @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(57,plain,
( ( ! [SY44: $i,SY45: $i] :
( ~ ( shortest_path @ SY44 @ SY45 @ sK1_SX0 )
| ( less_or_equal @ ( minus @ ( length_of @ sK1_SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(58,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY46: $i] :
~ ( ~ ( ~ ( shortest_path @ SV5 @ SV10 @ SY46 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SY46 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY47: $i] :
( ~ ( path @ SV5 @ SV10 @ SY47 )
| ( less_or_equal @ ( length_of @ SY46 ) @ ( length_of @ SY47 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SY46 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY48: $i] :
( ~ ( path @ SV5 @ SV10 @ SY48 )
| ( less_or_equal @ ( length_of @ SY46 ) @ ( length_of @ SY48 ) ) ) )
| ( shortest_path @ SV5 @ SV10 @ SY46 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(59,plain,
! [SV11: $i,SV7: $i,SV2: $i] :
( ( ~ ( path @ SV2 @ SV7 @ SV11 )
| ( ( number_of_in @ sequential_pairs @ SV11 )
= ( minus @ ( length_of @ SV11 ) @ n1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SY50 )
| ~ ( precedes @ SV12 @ SY49 @ SY50 ) )
| ~ ( ~ ~ ~ ! [SY51: $i] :
~ ~ ( ( ( tail_of @ SY51 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY51 )
!= ( head_of @ SY49 ) ) )
| ~ ~ ( precedes @ SY49 @ SV12 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ~ ( path @ SV4 @ SV9 @ SV13 )
| ( ( length_of @ SV13 )
= ( number_of_in @ edges @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV14: $i] :
( ( ( ! [SY52: $i,SY53: $i] :
( ~ ( shortest_path @ SY52 @ SY53 @ SV14 )
| ( ( number_of_in @ sequential_pairs @ SV14 )
= ( number_of_in @ triangles @ SV14 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(63,plain,
( ( ! [SY54: $i] :
( ~ ( shortest_path @ sK2_SY44 @ SY54 @ sK1_SX0 )
| ( less_or_equal @ ( minus @ ( length_of @ sK1_SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(64,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( ~ ( shortest_path @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
| ( shortest_path @ SV5 @ SV10 @ SV15 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV11: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( path @ SV2 @ SV7 @ SV11 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV11 )
= ( minus @ ( length_of @ SV11 ) @ n1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(66,plain,
! [SV16: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY57: $i] :
( ~ ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SY57 )
| ~ ( precedes @ SV12 @ SV16 @ SY57 ) )
| ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(67,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( ~ ( path @ SV4 @ SV9 @ SV13 ) )
= $true )
| ( ( ( length_of @ SV13 )
= ( number_of_in @ edges @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV14: $i,SV17: $i] :
( ( ( ! [SY59: $i] :
( ~ ( shortest_path @ SV17 @ SY59 @ SV14 )
| ( ( number_of_in @ sequential_pairs @ SV14 )
= ( number_of_in @ triangles @ SV14 ) ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(69,plain,
( ( ~ ( shortest_path @ sK2_SY44 @ sK3_SY54 @ sK1_SX0 )
| ( less_or_equal @ ( minus @ ( length_of @ sK1_SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[63]) ).
thf(70,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( shortest_path @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
| ( shortest_path @ SV5 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV11: $i,SV7: $i,SV2: $i] :
( ( ( path @ SV2 @ SV7 @ SV11 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV11 )
= ( minus @ ( length_of @ SV11 ) @ n1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ~ ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SV18 )
| ~ ( precedes @ SV12 @ SV16 @ SV18 ) )
| ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ( path @ SV4 @ SV9 @ SV13 )
= $false )
| ( ( ( length_of @ SV13 )
= ( number_of_in @ edges @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV14: $i,SV19: $i,SV17: $i] :
( ( ( ~ ( shortest_path @ SV17 @ SV19 @ SV14 )
| ( ( number_of_in @ sequential_pairs @ SV14 )
= ( number_of_in @ triangles @ SV14 ) ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(75,plain,
( ( ~ ( shortest_path @ sK2_SY44 @ sK3_SY54 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(76,plain,
( ( less_or_equal @ ( minus @ ( length_of @ sK1_SX0 ) @ n1 ) @ ( number_of_in @ triangles @ graph ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[69]) ).
thf(77,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ( shortest_path @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
| ( shortest_path @ SV5 @ SV10 @ SV15 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(79,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( ~ ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SV18 )
| ~ ( precedes @ SV12 @ SV16 @ SV18 ) ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV14: $i,SV19: $i,SV17: $i] :
( ( ( ~ ( shortest_path @ SV17 @ SV19 @ SV14 ) )
= $true )
| ( ( ( number_of_in @ sequential_pairs @ SV14 )
= ( number_of_in @ triangles @ SV14 ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(81,plain,
( ( shortest_path @ sK2_SY44 @ sK3_SY54 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ( shortest_path @ SV5 @ SV10 @ SV15 )
| ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[77]) ).
thf(83,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
| ( shortest_path @ SV5 @ SV10 @ SV15 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( ~ ( shortest_path @ SV3 @ SV8 @ SV18 )
| ~ ( precedes @ SV12 @ SV16 @ SV18 ) ) )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV14: $i,SV19: $i,SV17: $i] :
( ( ( shortest_path @ SV17 @ SV19 @ SV14 )
= $false )
| ( ( ( number_of_in @ sequential_pairs @ SV14 )
= ( number_of_in @ triangles @ SV14 ) )
= $true )
| ( complete = $false ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( shortest_path @ SV5 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(87,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(88,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( shortest_path @ SV3 @ SV8 @ SV18 )
| ~ ( precedes @ SV12 @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(90,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(91,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( ~ ( shortest_path @ SV3 @ SV8 @ SV18 ) )
= $true )
| ( ( ~ ( precedes @ SV12 @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(92,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(93,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
| ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(94,plain,
! [SV16: $i,SV12: $i,SV18: $i,SV8: $i,SV3: $i] :
( ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( ~ ( precedes @ SV12 @ SV16 @ SV18 ) )
= $true )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(96,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[92]) ).
thf(97,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV16: $i,SV12: $i] :
( ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( ~ ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[95]) ).
thf(100,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ! [SY55: $i] :
( ~ ( path @ SV5 @ SV10 @ SY55 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY55 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[96]) ).
thf(101,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) ) )
= $false )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV16: $i,SV12: $i] :
( ( ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) )
| ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV15: $i,SV20: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV20 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SV20 ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV15 )
| ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[101]) ).
thf(106,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i] :
( ( ( ~ ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(107,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ~ ( precedes @ SV16 @ SV12 @ SV18 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[102]) ).
thf(108,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV15 ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(109,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( ( SV5 != SV10 ) ) )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[103]) ).
thf(110,plain,
! [SV15: $i,SV20: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV20 ) )
= $true )
| ( ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SV20 ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(111,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ SV15 ) )
= $true )
| ( ( ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(112,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i] :
( ( ( ~ ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[106]) ).
thf(113,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( ~ ( precedes @ SV16 @ SV12 @ SV18 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[107]) ).
thf(114,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( path @ SV5 @ SV10 @ SV15 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[108]) ).
thf(115,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 != SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[109]) ).
thf(116,plain,
! [SV15: $i,SV20: $i,SV10: $i,SV5: $i] :
( ( ( path @ SV5 @ SV10 @ SV20 )
= $false )
| ( ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SV20 ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(117,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ( ( SV5 != SV10 ) ) )
= $true )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(118,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i] :
( ( ( ~ ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(119,plain,
! [SV8: $i,SV3: $i,SV18: $i,SV12: $i,SV16: $i] :
( ( ( precedes @ SV16 @ SV12 @ SV18 )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(120,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
= $false )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 != SV10 )
= $false )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(122,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i] :
( ( ( ! [SY58: $i] :
~ ~ ( ( ( tail_of @ SY58 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SY58 )
!= ( head_of @ SV16 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[118]) ).
thf(123,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( SV5 = SV10 )
= $true )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( ~ ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(124,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i,SV21: $i] :
( ( ( ~ ~ ( ( ( tail_of @ SV21 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SV21 )
!= ( head_of @ SV16 ) ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(125,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ! [SY56: $i] :
( ~ ( path @ SV5 @ SV10 @ SY56 )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ SY56 ) ) ) )
= $false )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(126,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i,SV21: $i] :
( ( ( ~ ( ( ( tail_of @ SV21 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SV21 )
!= ( head_of @ SV16 ) ) ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ ( sK4_SY56 @ SV15 @ SV10 @ SV5 ) )
| ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ ( sK4_SY56 @ SV15 @ SV10 @ SV5 ) ) ) )
= $false )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(128,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i,SV21: $i] :
( ( ( ( ( tail_of @ SV21 )
!= ( tail_of @ SV12 ) )
| ( ( head_of @ SV21 )
!= ( head_of @ SV16 ) ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[126]) ).
thf(129,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( path @ SV5 @ SV10 @ ( sK4_SY56 @ SV15 @ SV10 @ SV5 ) ) )
= $false )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(130,plain,
! [SV5: $i,SV10: $i,SV15: $i] :
( ( ( less_or_equal @ ( length_of @ SV15 ) @ ( length_of @ ( sK4_SY56 @ SV15 @ SV10 @ SV5 ) ) )
= $false )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[127]) ).
thf(131,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i,SV21: $i] :
( ( ( ( tail_of @ SV21 )
!= ( tail_of @ SV12 ) )
= $true )
| ( ( ( head_of @ SV21 )
!= ( head_of @ SV16 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV15: $i,SV10: $i,SV5: $i] :
( ( ( path @ SV5 @ SV10 @ ( sK4_SY56 @ SV15 @ SV10 @ SV5 ) )
= $true )
| ( ( path @ SV5 @ SV10 @ SV15 )
= $false )
| ( ( SV5 = SV10 )
= $true )
| ( ( shortest_path @ SV5 @ SV10 @ SV15 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(133,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV16: $i,SV12: $i,SV21: $i] :
( ( ( ( tail_of @ SV21 )
= ( tail_of @ SV12 ) )
= $false )
| ( ( ( head_of @ SV21 )
!= ( head_of @ SV16 ) )
= $true )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(134,plain,
! [SV18: $i,SV8: $i,SV3: $i,SV12: $i,SV16: $i,SV21: $i] :
( ( ( ( head_of @ SV21 )
= ( head_of @ SV16 ) )
= $false )
| ( ( ( tail_of @ SV21 )
= ( tail_of @ SV12 ) )
= $false )
| ( ( shortest_path @ SV3 @ SV8 @ SV18 )
= $false )
| ( ( precedes @ SV12 @ SV16 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(135,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,134,132,130,120,119,116,114,85,81,76,73,71,52]) ).
thf(136,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA002+4 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n006.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 10:20:37 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.31
% 0.57/0.31 No.of.Axioms: 6
% 0.57/0.31
% 0.57/0.31 Length.of.Defs: 0
% 0.57/0.31
% 0.57/0.31 Contains.Choice.Funs: false
% 0.57/0.31 ....
% 0.57/0.31
% 0.57/0.31 ********************************
% 0.57/0.31 * All subproblems solved! *
% 0.57/0.31 ********************************
% 0.57/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.31
% 0.57/0.31 %**** Beginning of derivation protocol ****
% 0.57/0.31 % SZS output start CNFRefutation
% See solution above
% 0.57/0.31
% 0.57/0.31 %**** End of derivation protocol ****
% 0.57/0.31 %**** no. of clauses in derivation: 124 ****
% 0.57/0.31 %**** clause counter: 135 ****
% 0.57/0.31
% 0.57/0.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:7,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------