TSTP Solution File: GRA009+2 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRA009+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mLY6AjaaGo true
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:10:11 EDT 2023
% Result : Theorem 103.73s 15.45s
% Output : Refutation 103.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 31
% Syntax : Number of formulae : 179 ( 43 unt; 20 typ; 0 def)
% Number of atoms : 569 ( 226 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1828 ( 232 ~; 358 |; 32 &;1186 @)
% ( 3 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 232 ( 0 ^; 226 !; 6 ?; 232 :)
% Comments :
%------------------------------------------------------------------------------
thf(edge_type,type,
edge: $i > $o ).
thf(sequential_type,type,
sequential: $i > $i > $o ).
thf(length_of_type,type,
length_of: $i > $i ).
thf(sk__9_type,type,
sk__9: $i ).
thf(sk__11_type,type,
sk__11: $i ).
thf(in_path_type,type,
in_path: $i > $i > $o ).
thf(vertex_type,type,
vertex: $i > $o ).
thf(precedes_type,type,
precedes: $i > $i > $i > $o ).
thf(head_of_type,type,
head_of: $i > $i ).
thf(sk__type,type,
sk_: $i > $i > $i ).
thf(on_path_type,type,
on_path: $i > $i > $o ).
thf(sk__8_type,type,
sk__8: $i ).
thf(triangle_type,type,
triangle: $i > $i > $i > $o ).
thf(shortest_path_type,type,
shortest_path: $i > $i > $i > $o ).
thf(less_or_equal_type,type,
less_or_equal: $i > $i > $o ).
thf(tail_of_type,type,
tail_of: $i > $i ).
thf(sk__10_type,type,
sk__10: $i ).
thf(path_type,type,
path: $i > $i > $i > $o ).
thf(sk__12_type,type,
sk__12: $i ).
thf(complete_type,type,
complete: $o ).
thf(complete_means_path_means_stuff_means_triangles,conjecture,
( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_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 ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( shortest_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 ) ) ) ),
inference('cnf.neg',[status(esa)],[complete_means_path_means_stuff_means_triangles]) ).
thf(zip_derived_cl61,plain,
sequential @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl64,plain,
shortest_path @ sk__9 @ sk__12 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(complete_properties,axiom,
( complete
=> ! [V1: $i,V2: $i] :
( ( ( vertex @ V1 )
& ( vertex @ V2 )
& ( V1 != V2 ) )
=> ? [E: $i] :
( ( ( ( V1
= ( head_of @ E ) )
& ( V2
= ( tail_of @ E ) ) )
<~> ( ( V2
= ( head_of @ E ) )
& ( V1
= ( tail_of @ E ) ) ) )
& ( edge @ E ) ) ) ) ).
thf(zip_derived_cl8,plain,
! [X0: $i,X1: $i] :
( ( edge @ ( sk_ @ X0 @ X1 ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ~ complete ),
inference(cnf,[status(esa)],[complete_properties]) ).
thf(zip_derived_cl59,plain,
complete,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl96,plain,
! [X0: $i,X1: $i] :
( ( edge @ ( sk_ @ X0 @ X1 ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).
thf(zip_derived_cl6,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X0
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ~ complete ),
inference(cnf,[status(esa)],[complete_properties]) ).
thf(zip_derived_cl59_001,plain,
complete,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl113,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X0
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl59]) ).
thf(sequential_defn,axiom,
! [E1: $i,E2: $i] :
( ( sequential @ E1 @ E2 )
<=> ( ( edge @ E1 )
& ( edge @ E2 )
& ( E1 != E2 )
& ( ( head_of @ E1 )
= ( tail_of @ E2 ) ) ) ) ).
thf(zip_derived_cl30,plain,
! [X0: $i,X1: $i] :
( ( sequential @ X0 @ X1 )
| ( ( head_of @ X0 )
!= ( tail_of @ X1 ) )
| ( X0 = X1 )
| ~ ( edge @ X1 )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
!= ( tail_of @ X1 ) )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X2 )
| ( X0 = X2 )
| ( X2
= ( head_of @ ( sk_ @ X2 @ X0 ) ) )
| ~ ( edge @ ( sk_ @ X2 @ X0 ) )
| ~ ( edge @ X1 )
| ( ( sk_ @ X2 @ X0 )
= X1 )
| ( sequential @ ( sk_ @ X2 @ X0 ) @ X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl113,zip_derived_cl30]) ).
thf(zip_derived_cl3550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ( X0 = X1 )
| ( sequential @ ( sk_ @ X1 @ X0 ) @ X2 )
| ( ( sk_ @ X1 @ X0 )
= X2 )
| ~ ( edge @ X2 )
| ( X1
= ( head_of @ ( sk_ @ X1 @ X0 ) ) )
| ( X0 = X1 )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 )
| ( X0
!= ( tail_of @ X2 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl96,zip_derived_cl170]) ).
thf(zip_derived_cl3551,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
!= ( tail_of @ X2 ) )
| ( X1
= ( head_of @ ( sk_ @ X1 @ X0 ) ) )
| ~ ( edge @ X2 )
| ( ( sk_ @ X1 @ X0 )
= X2 )
| ( sequential @ ( sk_ @ X1 @ X0 ) @ X2 )
| ( X0 = X1 )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3550]) ).
thf(zip_derived_cl15982,plain,
! [X0: $i,X1: $i] :
( ~ ( vertex @ ( tail_of @ X0 ) )
| ~ ( vertex @ X1 )
| ( ( tail_of @ X0 )
= X1 )
| ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
| ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
= X0 )
| ~ ( edge @ X0 )
| ( X1
= ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl3551]) ).
thf(edge_ends_are_vertices,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( vertex @ ( head_of @ E ) )
& ( vertex @ ( tail_of @ E ) ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i] :
( ( vertex @ ( tail_of @ X0 ) )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[edge_ends_are_vertices]) ).
thf(zip_derived_cl33548,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
| ~ ( edge @ X0 )
| ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
= X0 )
| ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
| ( ( tail_of @ X0 )
= X1 )
| ~ ( vertex @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl15982,zip_derived_cl2]) ).
thf(zip_derived_cl26,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl33881,plain,
! [X0: $i,X1: $i] :
( ~ ( vertex @ X1 )
| ( ( tail_of @ X0 )
= X1 )
| ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
= X0 )
| ~ ( edge @ X0 )
| ( X1
= ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
| ( edge @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl33548,zip_derived_cl26]) ).
thf(zip_derived_cl64_002,plain,
shortest_path @ sk__9 @ sk__12 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl61_003,plain,
sequential @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl63,plain,
on_path @ sk__10 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl64_004,plain,
shortest_path @ sk__9 @ sk__12 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(shortest_path_defn,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 ) ) ) ) ) ).
thf(zip_derived_cl38,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( path @ X0 @ X1 @ X2 )
| ~ ( shortest_path @ X0 @ X1 @ X2 ) ),
inference(cnf,[status(esa)],[shortest_path_defn]) ).
thf(zip_derived_cl87,plain,
path @ sk__9 @ sk__12 @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl38]) ).
thf(precedes_defn,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] :
( ( precedes @ E3 @ E2 @ P )
& ( sequential @ E1 @ E3 ) ) ) )
=> ( precedes @ E1 @ E2 @ P ) ) ) ).
thf(zip_derived_cl32,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( precedes @ X0 @ X1 @ X2 )
| ~ ( sequential @ X0 @ X1 )
| ~ ( on_path @ X1 @ X2 )
| ~ ( on_path @ X0 @ X2 )
| ~ ( path @ X3 @ X4 @ X2 ) ),
inference(cnf,[status(esa)],[precedes_defn]) ).
thf(zip_derived_cl585,plain,
! [X0: $i,X1: $i] :
( ~ ( on_path @ X0 @ sk__8 )
| ~ ( on_path @ X1 @ sk__8 )
| ~ ( sequential @ X0 @ X1 )
| ( precedes @ X0 @ X1 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl32]) ).
thf(zip_derived_cl636,plain,
! [X0: $i] :
( ( precedes @ sk__10 @ X0 @ sk__8 )
| ~ ( sequential @ sk__10 @ X0 )
| ~ ( on_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl585]) ).
thf(zip_derived_cl638,plain,
( ~ ( on_path @ sk__11 @ sk__8 )
| ( precedes @ sk__10 @ sk__11 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl636]) ).
thf(zip_derived_cl62,plain,
on_path @ sk__11 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl639,plain,
precedes @ sk__10 @ sk__11 @ sk__8,
inference(demod,[status(thm)],[zip_derived_cl638,zip_derived_cl62]) ).
thf(zip_derived_cl63_005,plain,
on_path @ sk__10 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl87_006,plain,
path @ sk__9 @ sk__12 @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl38]) ).
thf(on_path_properties,axiom,
! [V1: $i,V2: $i,P: $i,E: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( on_path @ E @ P ) )
=> ( ( edge @ E )
& ( in_path @ ( head_of @ E ) @ P )
& ( in_path @ ( tail_of @ E ) @ P ) ) ) ).
thf(zip_derived_cl20,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( path @ X0 @ X1 @ X2 )
| ~ ( on_path @ X3 @ X2 )
| ( in_path @ ( tail_of @ X3 ) @ X2 ) ),
inference(cnf,[status(esa)],[on_path_properties]) ).
thf(zip_derived_cl106,plain,
! [X0: $i] :
( ( in_path @ ( tail_of @ X0 ) @ sk__8 )
| ~ ( on_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl20]) ).
thf(zip_derived_cl107,plain,
in_path @ ( tail_of @ sk__10 ) @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl63,zip_derived_cl106]) ).
thf(zip_derived_cl87_007,plain,
path @ sk__9 @ sk__12 @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl38]) ).
thf(in_path_properties,axiom,
! [V1: $i,V2: $i,P: $i,V: $i] :
( ( ( path @ V1 @ V2 @ P )
& ( in_path @ V @ P ) )
=> ( ( vertex @ V )
& ? [E: $i] :
( ( ( V
= ( tail_of @ E ) )
| ( V
= ( head_of @ E ) ) )
& ( on_path @ E @ P ) ) ) ) ).
thf(zip_derived_cl25,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( path @ X0 @ X1 @ X2 )
| ~ ( in_path @ X3 @ X2 )
| ( vertex @ X3 ) ),
inference(cnf,[status(esa)],[in_path_properties]) ).
thf(zip_derived_cl92,plain,
! [X0: $i] :
( ( vertex @ X0 )
| ~ ( in_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl25]) ).
thf(zip_derived_cl109,plain,
vertex @ ( tail_of @ sk__10 ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl92]) ).
thf(zip_derived_cl5,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X0
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ~ complete ),
inference(cnf,[status(esa)],[complete_properties]) ).
thf(zip_derived_cl59_008,plain,
complete,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl100,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X0
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl59]) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ~ complete ),
inference(cnf,[status(esa)],[complete_properties]) ).
thf(zip_derived_cl59_009,plain,
complete,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl74,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl59]) ).
thf(shortest_path_properties,axiom,
! [V1: $i,V2: $i,E1: $i,E2: $i,P: $i] :
( ( ( shortest_path @ V1 @ V2 @ P )
& ( precedes @ E1 @ E2 @ P ) )
=> ( ~ ? [E3: $i] :
( ( ( head_of @ E3 )
= ( head_of @ E2 ) )
& ( ( tail_of @ E3 )
= ( tail_of @ E1 ) ) )
& ~ ( precedes @ E2 @ E1 @ P ) ) ) ).
thf(zip_derived_cl43,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( ( tail_of @ X1 )
!= ( tail_of @ X0 ) )
| ( ( head_of @ X1 )
!= ( head_of @ X2 ) )
| ~ ( precedes @ X0 @ X2 @ X3 )
| ~ ( shortest_path @ X4 @ X5 @ X3 ) ),
inference(cnf,[status(esa)],[shortest_path_properties]) ).
thf(zip_derived_cl186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X0
!= ( tail_of @ X1 ) )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X2 )
| ( X0 = X2 )
| ( X2
= ( tail_of @ ( sk_ @ X2 @ X0 ) ) )
| ~ ( shortest_path @ X5 @ X4 @ X3 )
| ~ ( precedes @ X1 @ X6 @ X3 )
| ( ( head_of @ ( sk_ @ X2 @ X0 ) )
!= ( head_of @ X6 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl43]) ).
thf(zip_derived_cl4849,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X0
!= ( head_of @ X1 ) )
| ~ ( vertex @ X2 )
| ~ ( vertex @ X0 )
| ( X2 = X0 )
| ( X0
= ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
| ~ ( precedes @ X4 @ X1 @ X3 )
| ~ ( shortest_path @ X6 @ X5 @ X3 )
| ( X0
= ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
| ( X2 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X2 )
| ( X2
!= ( tail_of @ X4 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl100,zip_derived_cl186]) ).
thf(zip_derived_cl4864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( X2
!= ( tail_of @ X4 ) )
| ~ ( shortest_path @ X6 @ X5 @ X3 )
| ~ ( precedes @ X4 @ X1 @ X3 )
| ( X0
= ( tail_of @ ( sk_ @ X0 @ X2 ) ) )
| ( X2 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X2 )
| ( X0
!= ( head_of @ X1 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl4849]) ).
thf(zip_derived_cl5097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( X0
!= ( head_of @ X1 ) )
| ~ ( vertex @ ( tail_of @ X2 ) )
| ~ ( vertex @ X0 )
| ( ( tail_of @ X2 )
= X0 )
| ( X0
= ( tail_of @ ( sk_ @ X0 @ ( tail_of @ X2 ) ) ) )
| ~ ( precedes @ X2 @ X1 @ X3 )
| ~ ( shortest_path @ X5 @ X4 @ X3 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl4864]) ).
thf(zip_derived_cl9100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( shortest_path @ X2 @ X1 @ X0 )
| ~ ( precedes @ sk__10 @ X3 @ X0 )
| ( X4
= ( tail_of @ ( sk_ @ X4 @ ( tail_of @ sk__10 ) ) ) )
| ( ( tail_of @ sk__10 )
= X4 )
| ~ ( vertex @ X4 )
| ( X4
!= ( head_of @ X3 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl109,zip_derived_cl5097]) ).
thf(zip_derived_cl9121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0
!= ( head_of @ sk__11 ) )
| ~ ( vertex @ X0 )
| ( ( tail_of @ sk__10 )
= X0 )
| ( X0
= ( tail_of @ ( sk_ @ X0 @ ( tail_of @ sk__10 ) ) ) )
| ~ ( shortest_path @ X2 @ X1 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl639,zip_derived_cl9100]) ).
thf(zip_derived_cl9303,plain,
! [X0: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ ( tail_of @ sk__10 ) ) ) )
| ( ( tail_of @ sk__10 )
= X0 )
| ~ ( vertex @ X0 )
| ( X0
!= ( head_of @ sk__11 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl9121]) ).
thf(zip_derived_cl9944,plain,
( ~ ( vertex @ ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl9303]) ).
thf(zip_derived_cl62_010,plain,
on_path @ sk__11 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl87_011,plain,
path @ sk__9 @ sk__12 @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl38]) ).
thf(zip_derived_cl21,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( path @ X0 @ X1 @ X2 )
| ~ ( on_path @ X3 @ X2 )
| ( in_path @ ( head_of @ X3 ) @ X2 ) ),
inference(cnf,[status(esa)],[on_path_properties]) ).
thf(zip_derived_cl134,plain,
! [X0: $i] :
( ( in_path @ ( head_of @ X0 ) @ sk__8 )
| ~ ( on_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl21]) ).
thf(zip_derived_cl136,plain,
in_path @ ( head_of @ sk__11 ) @ sk__8,
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl134]) ).
thf(zip_derived_cl92_012,plain,
! [X0: $i] :
( ( vertex @ X0 )
| ~ ( in_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl25]) ).
thf(zip_derived_cl138,plain,
vertex @ ( head_of @ sk__11 ),
inference('sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl92]) ).
thf(zip_derived_cl9945,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9944,zip_derived_cl138]) ).
thf(zip_derived_cl113_013,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X0
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl59]) ).
thf(no_loops,axiom,
! [E: $i] :
( ( edge @ E )
=> ( ( head_of @ E )
!= ( tail_of @ E ) ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i] :
( ( ( head_of @ X0 )
!= ( tail_of @ X0 ) )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[no_loops]) ).
thf(zip_derived_cl118,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 )
| ( X1 = X0 )
| ( X1
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ~ ( edge @ ( sk_ @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl113,zip_derived_cl0]) ).
thf(zip_derived_cl96_014,plain,
! [X0: $i,X1: $i] :
( ( edge @ ( sk_ @ X0 @ X1 ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).
thf(zip_derived_cl2215,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ( X0
!= ( tail_of @ ( sk_ @ X0 @ X1 ) ) ) ),
inference(clc,[status(thm)],[zip_derived_cl118,zip_derived_cl96]) ).
thf(zip_derived_cl10103,plain,
( ( ( head_of @ sk__11 )
!= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ~ ( vertex @ ( tail_of @ sk__10 ) )
| ~ ( vertex @ ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl9945,zip_derived_cl2215]) ).
thf(zip_derived_cl109_015,plain,
vertex @ ( tail_of @ sk__10 ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl92]) ).
thf(zip_derived_cl138_016,plain,
vertex @ ( head_of @ sk__11 ),
inference('sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl92]) ).
thf(zip_derived_cl10117,plain,
( ( ( head_of @ sk__11 )
!= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl10103,zip_derived_cl109,zip_derived_cl138]) ).
thf(zip_derived_cl10118,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl10117]) ).
thf(zip_derived_cl34280,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ~ ( edge @ sk__10 )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ~ ( vertex @ ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl33881,zip_derived_cl10118]) ).
thf(zip_derived_cl61_017,plain,
sequential @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl26_018,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl67,plain,
edge @ sk__10,
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).
thf(zip_derived_cl138_019,plain,
vertex @ ( head_of @ sk__11 ),
inference('sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl92]) ).
thf(zip_derived_cl34339,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl34280,zip_derived_cl67,zip_derived_cl138]) ).
thf(zip_derived_cl34340,plain,
( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( edge @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl34339]) ).
thf(zip_derived_cl33548_020,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( head_of @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) ) )
| ~ ( edge @ X0 )
| ( ( sk_ @ X1 @ ( tail_of @ X0 ) )
= X0 )
| ( sequential @ ( sk_ @ X1 @ ( tail_of @ X0 ) ) @ X0 )
| ( ( tail_of @ X0 )
= X1 )
| ~ ( vertex @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl15982,zip_derived_cl2]) ).
thf(zip_derived_cl0_021,plain,
! [X0: $i] :
( ( ( head_of @ X0 )
!= ( tail_of @ X0 ) )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[no_loops]) ).
thf(zip_derived_cl33549,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( tail_of @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) ) )
| ~ ( vertex @ X0 )
| ( ( tail_of @ X1 )
= X0 )
| ( sequential @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) @ X1 )
| ( ( sk_ @ X0 @ ( tail_of @ X1 ) )
= X1 )
| ~ ( edge @ X1 )
| ~ ( edge @ ( sk_ @ X0 @ ( tail_of @ X1 ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl33548,zip_derived_cl0]) ).
thf(zip_derived_cl47325,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ~ ( edge @ sk__10 )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ~ ( vertex @ ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
!= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl34340,zip_derived_cl33549]) ).
thf(zip_derived_cl67_022,plain,
edge @ sk__10,
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).
thf(zip_derived_cl138_023,plain,
vertex @ ( head_of @ sk__11 ),
inference('sup-',[status(thm)],[zip_derived_cl136,zip_derived_cl92]) ).
thf(zip_derived_cl47362,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
!= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl47325,zip_derived_cl67,zip_derived_cl138]) ).
thf(zip_derived_cl47363,plain,
( ( ( head_of @ sk__11 )
!= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl47362]) ).
thf(zip_derived_cl9945_024,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9944,zip_derived_cl138]) ).
thf(zip_derived_cl49028,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) @ sk__10 ) ),
inference(clc,[status(thm)],[zip_derived_cl47363,zip_derived_cl9945]) ).
thf(zip_derived_cl96_025,plain,
! [X0: $i,X1: $i] :
( ( edge @ ( sk_ @ X0 @ X1 ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl59]) ).
thf(zip_derived_cl74_026,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ( X1 = X0 )
| ~ ( vertex @ X0 )
| ~ ( vertex @ X1 ) ),
inference(demod,[status(thm)],[zip_derived_cl3,zip_derived_cl59]) ).
thf(zip_derived_cl30_027,plain,
! [X0: $i,X1: $i] :
( ( sequential @ X0 @ X1 )
| ( ( head_of @ X0 )
!= ( tail_of @ X1 ) )
| ( X0 = X1 )
| ~ ( edge @ X1 )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( head_of @ X2 )
!= X0 )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 )
| ( X1 = X0 )
| ( X1
= ( tail_of @ ( sk_ @ X0 @ X1 ) ) )
| ~ ( edge @ X2 )
| ~ ( edge @ ( sk_ @ X0 @ X1 ) )
| ( X2
= ( sk_ @ X0 @ X1 ) )
| ( sequential @ X2 @ ( sk_ @ X0 @ X1 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl74,zip_derived_cl30]) ).
thf(zip_derived_cl3856,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( vertex @ X0 )
| ~ ( vertex @ X1 )
| ( X0 = X1 )
| ( sequential @ X2 @ ( sk_ @ X1 @ X0 ) )
| ( X2
= ( sk_ @ X1 @ X0 ) )
| ~ ( edge @ X2 )
| ( X0
= ( tail_of @ ( sk_ @ X1 @ X0 ) ) )
| ( X0 = X1 )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 )
| ( ( head_of @ X2 )
!= X1 ) ),
inference('sup-',[status(thm)],[zip_derived_cl96,zip_derived_cl173]) ).
thf(zip_derived_cl3857,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( head_of @ X2 )
!= X1 )
| ( X0
= ( tail_of @ ( sk_ @ X1 @ X0 ) ) )
| ~ ( edge @ X2 )
| ( X2
= ( sk_ @ X1 @ X0 ) )
| ( sequential @ X2 @ ( sk_ @ X1 @ X0 ) )
| ( X0 = X1 )
| ~ ( vertex @ X1 )
| ~ ( vertex @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl3856]) ).
thf(zip_derived_cl16027,plain,
! [X0: $i,X1: $i] :
( ~ ( vertex @ X0 )
| ~ ( vertex @ ( head_of @ X1 ) )
| ( X0
= ( head_of @ X1 ) )
| ( sequential @ X1 @ ( sk_ @ ( head_of @ X1 ) @ X0 ) )
| ( X1
= ( sk_ @ ( head_of @ X1 ) @ X0 ) )
| ~ ( edge @ X1 )
| ( X0
= ( tail_of @ ( sk_ @ ( head_of @ X1 ) @ X0 ) ) ) ),
inference(eq_res,[status(thm)],[zip_derived_cl3857]) ).
thf(zip_derived_cl1,plain,
! [X0: $i] :
( ( vertex @ ( head_of @ X0 ) )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[edge_ends_are_vertices]) ).
thf(zip_derived_cl44745,plain,
! [X0: $i,X1: $i] :
( ( X0
= ( tail_of @ ( sk_ @ ( head_of @ X1 ) @ X0 ) ) )
| ~ ( edge @ X1 )
| ( X1
= ( sk_ @ ( head_of @ X1 ) @ X0 ) )
| ( sequential @ X1 @ ( sk_ @ ( head_of @ X1 ) @ X0 ) )
| ( X0
= ( head_of @ X1 ) )
| ~ ( vertex @ X0 ) ),
inference(clc,[status(thm)],[zip_derived_cl16027,zip_derived_cl1]) ).
thf(zip_derived_cl61_028,plain,
sequential @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(triangle_defn,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 ) ) ) ).
thf(zip_derived_cl51,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( triangle @ X0 @ X1 @ X2 )
| ~ ( sequential @ X2 @ X0 )
| ~ ( sequential @ X1 @ X2 )
| ~ ( sequential @ X0 @ X1 )
| ~ ( edge @ X2 )
| ~ ( edge @ X1 )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[triangle_defn]) ).
thf(zip_derived_cl26_029,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl455,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( edge @ X0 )
| ~ ( edge @ X1 )
| ~ ( sequential @ X0 @ X1 )
| ~ ( sequential @ X1 @ X2 )
| ~ ( sequential @ X2 @ X0 )
| ( triangle @ X0 @ X1 @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl51,zip_derived_cl26]) ).
thf(zip_derived_cl26_030,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl456,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( triangle @ X0 @ X1 @ X2 )
| ~ ( sequential @ X2 @ X0 )
| ~ ( sequential @ X1 @ X2 )
| ~ ( sequential @ X0 @ X1 )
| ~ ( edge @ X1 ) ),
inference(clc,[status(thm)],[zip_derived_cl455,zip_derived_cl26]) ).
thf(zip_derived_cl26_031,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X0 @ X1 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl457,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( sequential @ X0 @ X1 )
| ~ ( sequential @ X1 @ X2 )
| ~ ( sequential @ X2 @ X0 )
| ( triangle @ X0 @ X1 @ X2 ) ),
inference(clc,[status(thm)],[zip_derived_cl456,zip_derived_cl26]) ).
thf(zip_derived_cl458,plain,
! [X0: $i] :
( ( triangle @ sk__10 @ sk__11 @ X0 )
| ~ ( sequential @ X0 @ sk__10 )
| ~ ( sequential @ sk__11 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl457]) ).
thf(zip_derived_cl60,plain,
! [X0: $i] :
~ ( triangle @ sk__10 @ sk__11 @ X0 ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl463,plain,
! [X0: $i] :
( ~ ( sequential @ sk__11 @ X0 )
| ~ ( sequential @ X0 @ sk__10 ) ),
inference(clc,[status(thm)],[zip_derived_cl458,zip_derived_cl60]) ).
thf(zip_derived_cl44821,plain,
! [X0: $i] :
( ~ ( vertex @ X0 )
| ( X0
= ( head_of @ sk__11 ) )
| ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ X0 ) )
| ~ ( edge @ sk__11 )
| ( X0
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) ) )
| ~ ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) @ sk__10 ) ),
inference('sup-',[status(thm)],[zip_derived_cl44745,zip_derived_cl463]) ).
thf(zip_derived_cl61_032,plain,
sequential @ sk__10 @ sk__11,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl27,plain,
! [X0: $i,X1: $i] :
( ( edge @ X0 )
| ~ ( sequential @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl68,plain,
edge @ sk__11,
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl27]) ).
thf(zip_derived_cl44892,plain,
! [X0: $i] :
( ~ ( vertex @ X0 )
| ( X0
= ( head_of @ sk__11 ) )
| ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ X0 ) )
| ( X0
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) ) )
| ~ ( sequential @ ( sk_ @ ( head_of @ sk__11 ) @ X0 ) @ sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl44821,zip_derived_cl68]) ).
thf(zip_derived_cl49033,plain,
( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ~ ( vertex @ ( tail_of @ sk__10 ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl49028,zip_derived_cl44892]) ).
thf(zip_derived_cl109_033,plain,
vertex @ ( tail_of @ sk__10 ),
inference('sup-',[status(thm)],[zip_derived_cl107,zip_derived_cl92]) ).
thf(zip_derived_cl49035,plain,
( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl49033,zip_derived_cl109]) ).
thf(zip_derived_cl49036,plain,
( ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( tail_of @ sk__10 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 ) ),
inference(simplify,[status(thm)],[zip_derived_cl49035]) ).
thf(zip_derived_cl9945_034,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9944,zip_derived_cl138]) ).
thf(zip_derived_cl49560,plain,
( ( ( head_of @ sk__11 )
= ( tail_of @ sk__10 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl49036,zip_derived_cl9945]) ).
thf(zip_derived_cl49694,plain,
( ( sk__11
= ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( head_of @ sk__11 )
= ( tail_of @ sk__10 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl49560]) ).
thf(zip_derived_cl10118_035,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl10117]) ).
thf(zip_derived_cl49914,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ sk__10 ) )
| ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl49694,zip_derived_cl10118]) ).
thf(zip_derived_cl50358,plain,
( ( ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) )
= sk__10 )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl49914]) ).
thf(zip_derived_cl9945_036,plain,
( ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( head_of @ sk__11 )
= ( tail_of @ ( sk_ @ ( head_of @ sk__11 ) @ ( tail_of @ sk__10 ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl9944,zip_derived_cl138]) ).
thf(zip_derived_cl50857,plain,
( ( ( head_of @ sk__11 )
= ( tail_of @ sk__10 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) )
| ( ( tail_of @ sk__10 )
= ( head_of @ sk__11 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl50358,zip_derived_cl9945]) ).
thf(zip_derived_cl51309,plain,
( ( head_of @ sk__11 )
= ( tail_of @ sk__10 ) ),
inference(simplify,[status(thm)],[zip_derived_cl50857]) ).
thf(zip_derived_cl30_037,plain,
! [X0: $i,X1: $i] :
( ( sequential @ X0 @ X1 )
| ( ( head_of @ X0 )
!= ( tail_of @ X1 ) )
| ( X0 = X1 )
| ~ ( edge @ X1 )
| ~ ( edge @ X0 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl51476,plain,
! [X0: $i] :
( ( ( tail_of @ sk__10 )
!= ( tail_of @ X0 ) )
| ~ ( edge @ sk__11 )
| ~ ( edge @ X0 )
| ( sk__11 = X0 )
| ( sequential @ sk__11 @ X0 ) ),
inference('sup-',[status(thm)],[zip_derived_cl51309,zip_derived_cl30]) ).
thf(zip_derived_cl68_038,plain,
edge @ sk__11,
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl27]) ).
thf(zip_derived_cl51838,plain,
! [X0: $i] :
( ( ( tail_of @ sk__10 )
!= ( tail_of @ X0 ) )
| ~ ( edge @ X0 )
| ( sk__11 = X0 )
| ( sequential @ sk__11 @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl51476,zip_derived_cl68]) ).
thf(zip_derived_cl56552,plain,
( ( sequential @ sk__11 @ sk__10 )
| ( sk__11 = sk__10 )
| ~ ( edge @ sk__10 ) ),
inference(eq_res,[status(thm)],[zip_derived_cl51838]) ).
thf(zip_derived_cl67_039,plain,
edge @ sk__10,
inference('sup-',[status(thm)],[zip_derived_cl61,zip_derived_cl26]) ).
thf(zip_derived_cl56553,plain,
( ( sequential @ sk__11 @ sk__10 )
| ( sk__11 = sk__10 ) ),
inference(demod,[status(thm)],[zip_derived_cl56552,zip_derived_cl67]) ).
thf(zip_derived_cl62_040,plain,
on_path @ sk__11 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl585_041,plain,
! [X0: $i,X1: $i] :
( ~ ( on_path @ X0 @ sk__8 )
| ~ ( on_path @ X1 @ sk__8 )
| ~ ( sequential @ X0 @ X1 )
| ( precedes @ X0 @ X1 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl87,zip_derived_cl32]) ).
thf(zip_derived_cl637,plain,
! [X0: $i] :
( ( precedes @ sk__11 @ X0 @ sk__8 )
| ~ ( sequential @ sk__11 @ X0 )
| ~ ( on_path @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl62,zip_derived_cl585]) ).
thf(zip_derived_cl56563,plain,
( ( sk__11 = sk__10 )
| ~ ( on_path @ sk__10 @ sk__8 )
| ( precedes @ sk__11 @ sk__10 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl56553,zip_derived_cl637]) ).
thf(zip_derived_cl63_042,plain,
on_path @ sk__10 @ sk__8,
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl56565,plain,
( ( sk__11 = sk__10 )
| ( precedes @ sk__11 @ sk__10 @ sk__8 ) ),
inference(demod,[status(thm)],[zip_derived_cl56563,zip_derived_cl63]) ).
thf(zip_derived_cl639_043,plain,
precedes @ sk__10 @ sk__11 @ sk__8,
inference(demod,[status(thm)],[zip_derived_cl638,zip_derived_cl62]) ).
thf(zip_derived_cl44,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( precedes @ X0 @ X1 @ X2 )
| ~ ( precedes @ X1 @ X0 @ X2 )
| ~ ( shortest_path @ X3 @ X4 @ X2 ) ),
inference(cnf,[status(esa)],[shortest_path_properties]) ).
thf(zip_derived_cl643,plain,
! [X0: $i,X1: $i] :
( ~ ( shortest_path @ X1 @ X0 @ sk__8 )
| ~ ( precedes @ sk__11 @ sk__10 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl639,zip_derived_cl44]) ).
thf(zip_derived_cl56586,plain,
! [X0: $i,X1: $i] :
( ( sk__11 = sk__10 )
| ~ ( shortest_path @ X1 @ X0 @ sk__8 ) ),
inference('sup-',[status(thm)],[zip_derived_cl56565,zip_derived_cl643]) ).
thf(zip_derived_cl56647,plain,
sk__11 = sk__10,
inference('sup-',[status(thm)],[zip_derived_cl64,zip_derived_cl56586]) ).
thf(zip_derived_cl28,plain,
! [X0: $i,X1: $i] :
( ( X1 != X0 )
| ~ ( sequential @ X1 @ X0 ) ),
inference(cnf,[status(esa)],[sequential_defn]) ).
thf(zip_derived_cl65,plain,
! [X0: $i] :
~ ( sequential @ X0 @ X0 ),
inference(eq_res,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl56649,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl61,zip_derived_cl56647,zip_derived_cl65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRA009+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.13/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.mLY6AjaaGo true
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 03:06:07 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Number of cores: 8
% 0.14/0.36 % Python version: Python 3.6.8
% 0.14/0.36 % Running in FO mode
% 0.22/0.65 % Total configuration time : 435
% 0.22/0.65 % Estimated wc time : 1092
% 0.22/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.74 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.75 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.76 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.72/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.72/0.78 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.14/0.81 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 103.73/15.45 % Solved by fo/fo5.sh.
% 103.73/15.45 % done 2720 iterations in 14.639s
% 103.73/15.45 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 103.73/15.45 % SZS output start Refutation
% See solution above
% 103.73/15.45
% 103.73/15.45
% 103.73/15.45 % Terminating...
% 104.30/15.55 % Runner terminated.
% 104.30/15.56 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------