%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA007+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.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 : Fri Sep 25 01:23:34 PM UTC 2026
% Result : Theorem 10.51s 2.34s
% Output : CNFRefutation 10.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 164 ( 18 unt; 0 def)
% Number of atoms : 714 ( 254 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 922 ( 372 ~; 418 |; 110 &)
% ( 3 <=>; 14 =>; 0 <=; 5 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 5 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 376 ( 0 sgn 349 !; 27 ?; 164 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(f3,axiom,
( complete
=> ! [X0,X1] :
( ( X0 != X1
& vertex(X1)
& vertex(X0) )
=> ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',on_path_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',back_edge) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( head_of(X5) = tail_of(X2)
& tail_of(X5) = head_of(X3)
& edge(X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f22,plain,
! [X0] :
( ~ edge(X0)
| ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f23,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f24,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(flattening,[],[f23]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(flattening,[],[f28]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f36,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) ) ),
inference(flattening,[],[f36]) ).
fof(f44,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f45,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) ) ) ),
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f47,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ( ( ( tail_of(sK0(X0,X1)) = X1
& head_of(sK0(X0,X1)) = X0 )
| ( tail_of(sK0(X0,X1)) = X0
& head_of(sK0(X0,X1)) = X1 ) )
& ( tail_of(sK0(X0,X1)) != X1
| head_of(sK0(X0,X1)) != X0
| tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X1 )
& edge(sK0(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f47]) ).
fof(f54,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0,X1] :
( ( ~ sequential(X0,X1)
| ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) )
& ( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(X0,X3,X4)) ) )
& ( ~ sequential(X3,X4)
| ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X6,sK4(X0,X3,X4))],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( ~ shortest_path(X0,X1,X2)
| ( ! [X4] :
( ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) )
& X0 != X1
& path(X0,X1,X2) ) )
& ( ( path(X0,X1,sK5(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f62]) ).
fof(f65,plain,
( complete
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12)
& ! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10),skolemize(X3,sK11),skolemize(X4,sK12)],[f45]) ).
fof(f67,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f69,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f48]) ).
fof(f70,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X1
| head_of(sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f72,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X3,X2)
| ~ path(X0,X1,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f96,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f102,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f103,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f109,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f37]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ),
inference(cnf_transformation,[],[f37]) ).
fof(f119,plain,
complete,
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_50,plain,
! [X0: $i] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_51,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X3,X4,X2)
| ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ shortest_path(X4,X5,X3)
| ~ precedes(X2,X0,X3)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,X0,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_102,negated_conjecture,
! [X0: $i] :
( ~ edge(X0)
| ( tail_of(X0) != head_of(sK11) )
| ( head_of(X0) != tail_of(sK10) ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_103,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f121]) ).
tcf(c_104,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f120]) ).
tcf(c_105,negated_conjecture,
complete,
inference(cnf_transformation,[],[f119]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_105,c_52]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( edge(sK0(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_143]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_105,c_57]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_156]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_105,c_56]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X0 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_159]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_105,c_55]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_161]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_54,c_105,c_54]) ).
tcf(c_164,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK0(X0,X1)) = X1 )
| ( head_of(sK0(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_163]) ).
tcf(c_859,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ( X2 != sK12 )
| ( X1 != sK9 )
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_89,c_103]) ).
tcf(c_860,plain,
path(sK8,sK9,sK12),
inference(unflattening,[status(thm)],[c_859]) ).
tcf(c_1663,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_164]) ).
tcf(c_1664,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_162]) ).
tcf(c_1665,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_160]) ).
tcf(c_1666,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X1_iProver_shortest_path_2 )
| ( tail_of(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_157]) ).
tcf(c_1669,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( edge(sK0(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2))
| ( X0_iProver_shortest_path_2 = X1_iProver_shortest_path_2 )
| ~ vertex(X1_iProver_shortest_path_2)
| ~ vertex(X0_iProver_shortest_path_2) ),
inference(subtyping,[status(esa)],[c_144]) ).
tcf(c_1670,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(subtyping,[status(esa)],[c_104]) ).
tcf(c_1671,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_1672,negated_conjecture,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ~ edge(X0_iProver_sequential_1)
| ( tail_of(X0_iProver_sequential_1) != head_of(sK11) )
| ( head_of(X0_iProver_sequential_1) != tail_of(sK10) ) ),
inference(subtyping,[status(esa)],[c_102]) ).
tcf(c_1679,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1)
| ~ precedes(X1_iProver_sequential_1,X0_iProver_sequential_1,X0_iProver_sK7_1)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_93]) ).
tcf(c_1680,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_1: iProver_sequential_1,X2_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1)
| ~ precedes(X2_iProver_sequential_1,X0_iProver_sequential_1,X0_iProver_sK7_1)
| ( tail_of(X1_iProver_sequential_1) != tail_of(X2_iProver_sequential_1) )
| ( head_of(X0_iProver_sequential_1) != head_of(X1_iProver_sequential_1) ) ),
inference(subtyping,[status(esa)],[c_92]) ).
tcf(c_1683,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1)
| ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_89]) ).
tcf(c_1689,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_1: iProver_sequential_1] :
( on_path(X1_iProver_sequential_1,X0_iProver_sK7_1)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,X0_iProver_sK7_1)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_83]) ).
tcf(c_1690,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_1: iProver_sequential_1] :
( on_path(X0_iProver_sequential_1,X0_iProver_sK7_1)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,X0_iProver_sK7_1)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_82]) ).
tcf(c_1691,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_sequential_1: iProver_sequential_1] :
( precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,X0_iProver_sK7_1)
| ~ sequential(X0_iProver_sequential_1,X1_iProver_sequential_1)
| ~ on_path(X1_iProver_sequential_1,X0_iProver_sK7_1)
| ~ on_path(X0_iProver_sequential_1,X0_iProver_sK7_1)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_80]) ).
tcf(c_1696,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( sequential(X0_iProver_sequential_1,X1_iProver_sequential_1)
| ( X0_iProver_sequential_1 = X1_iProver_sequential_1 )
| ~ edge(X1_iProver_sequential_1)
| ~ edge(X0_iProver_sequential_1)
| ( head_of(X0_iProver_sequential_1) != tail_of(X1_iProver_sequential_1) ) ),
inference(subtyping,[status(esa)],[c_75]) ).
tcf(c_1702,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sK7_1: iProver_sK7_1,X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( edge(X0_iProver_sequential_1)
| ~ on_path(X0_iProver_sequential_1,X0_iProver_sK7_1)
| ~ path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,X0_iProver_sK7_1) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_1712,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( vertex(tail_of(X0_iProver_sequential_1))
| ~ edge(X0_iProver_sequential_1) ),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_1713,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( vertex(head_of(X0_iProver_sequential_1))
| ~ edge(X0_iProver_sequential_1) ),
inference(subtyping,[status(esa)],[c_50]) ).
tcf(c_1718,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] : X0_iProver_sequential_1 = X0_iProver_sequential_1,
theory(equality) ).
tcf(c_1720,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2,X2_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( X2_iProver_shortest_path_2 = X0_iProver_shortest_path_2 )
| ( X2_iProver_shortest_path_2 != X1_iProver_shortest_path_2 )
| ( X0_iProver_shortest_path_2 != X1_iProver_shortest_path_2 ) ),
theory(equality) ).
tcf(c_1724,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(X0_iProver_sequential_1) = head_of(X1_iProver_sequential_1) )
| ( X0_iProver_sequential_1 != X1_iProver_sequential_1 ) ),
theory(equality) ).
tcf(c_1725,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( ( tail_of(X0_iProver_sequential_1) = tail_of(X1_iProver_sequential_1) )
| ( X0_iProver_sequential_1 != X1_iProver_sequential_1 ) ),
theory(equality) ).
tcf(c_1740,plain,
( ( tail_of(sK10) = tail_of(sK10) )
| ( sK10 != sK10 ) ),
inference(instantiation,[status(thm)],[c_1725]) ).
tcf(c_1748,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_1718]) ).
tcf(c_1784,plain,
( vertex(tail_of(sK10))
| ~ edge(sK10) ),
inference(instantiation,[status(thm)],[c_1712]) ).
tcf(c_2738,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1,X2_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(X2_iProver_sequential_1,X0_iProver_sequential_1,sK12)
| ( tail_of(X1_iProver_sequential_1) != tail_of(X2_iProver_sequential_1) )
| ( head_of(X0_iProver_sequential_1) != head_of(X1_iProver_sequential_1) ) ),
inference(instantiation,[status(thm)],[c_1680]) ).
tcf(c_2739,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(X1_iProver_sequential_1,X0_iProver_sequential_1,sK12)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,sK12) ),
inference(instantiation,[status(thm)],[c_1679]) ).
tcf(c_2758,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = head_of(X0_iProver_sequential_1) )
| ( sK11 != X0_iProver_sequential_1 ) ),
inference(instantiation,[status(thm)],[c_1724]) ).
tcf(c_2759,plain,
( ( head_of(sK11) = head_of(sK10) )
| ( sK11 != sK10 ) ),
inference(instantiation,[status(thm)],[c_2758]) ).
tcf(c_2764,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(X0_iProver_sequential_1) )
| ( tail_of(X0_iProver_sequential_1) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_2738]) ).
tcf(c_2765,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( tail_of(sK10) != tail_of(sK10) )
| ( head_of(sK11) != head_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_2764]) ).
tcf(c_2781,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ~ precedes(sK11,sK10,sK12) ),
inference(instantiation,[status(thm)],[c_2739]) ).
tcf(c_2791,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( sequential(sK11,X0_iProver_sequential_1)
| ( sK11 = X0_iProver_sequential_1 )
| ~ edge(sK11)
| ~ edge(X0_iProver_sequential_1)
| ( head_of(sK11) != tail_of(X0_iProver_sequential_1) ) ),
inference(instantiation,[status(thm)],[c_1696]) ).
tcf(c_2792,plain,
( sequential(sK11,sK10)
| ( sK11 = sK10 )
| ~ edge(sK10)
| ~ edge(sK11)
| ( head_of(sK11) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_2791]) ).
tcf(c_2793,plain,
( ( head_of(sK11) = head_of(sK11) )
| ( sK11 != sK11 ) ),
inference(instantiation,[status(thm)],[c_2758]) ).
tcf(c_2796,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = head_of(sK11) )
| ~ vertex(X0_iProver_shortest_path_2)
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1663]) ).
tcf(c_2797,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( tail_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( head_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ~ vertex(X0_iProver_shortest_path_2)
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1664]) ).
tcf(c_2798,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( tail_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = head_of(sK11) )
| ( head_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = head_of(sK11) )
| ~ vertex(X0_iProver_shortest_path_2)
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1665]) ).
tcf(c_2799,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( tail_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = X0_iProver_shortest_path_2 )
| ( tail_of(sK0(head_of(sK11),X0_iProver_shortest_path_2)) = head_of(sK11) )
| ~ vertex(X0_iProver_shortest_path_2)
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1666]) ).
tcf(c_2802,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( edge(sK0(head_of(sK11),X0_iProver_shortest_path_2))
| ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ~ vertex(X0_iProver_shortest_path_2)
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1669]) ).
tcf(c_2815,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X1_iProver_shortest_path_2 )
| ( X1_iProver_shortest_path_2 != X0_iProver_shortest_path_2 )
| ( head_of(sK11) != X0_iProver_shortest_path_2 ) ),
inference(instantiation,[status(thm)],[c_1720]) ).
tcf(c_2858,plain,
( vertex(head_of(sK11))
| ~ edge(sK11) ),
inference(instantiation,[status(thm)],[c_1713]) ).
tcf(c_2909,plain,
sK11 = sK11,
inference(instantiation,[status(thm)],[c_1718]) ).
tcf(c_2945,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( X0_iProver_shortest_path_2 != head_of(X0_iProver_sequential_1) )
| ( head_of(sK11) != head_of(X0_iProver_sequential_1) ) ),
inference(instantiation,[status(thm)],[c_2815]) ).
tcf(c_3017,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = tail_of(X0_iProver_sequential_1) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = tail_of(X0_iProver_sequential_1) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_1)) ),
inference(instantiation,[status(thm)],[c_2796]) ).
tcf(c_3018,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_3017]) ).
tcf(c_3020,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = tail_of(X0_iProver_sequential_1) )
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = tail_of(X0_iProver_sequential_1) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = tail_of(X0_iProver_sequential_1) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_1)) ),
inference(instantiation,[status(thm)],[c_2797]) ).
tcf(c_3021,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_3020]) ).
tcf(c_3040,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = tail_of(X0_iProver_sequential_1) )
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = head_of(sK11) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_1)) ),
inference(instantiation,[status(thm)],[c_2798]) ).
tcf(c_3041,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_3040]) ).
tcf(c_3043,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = tail_of(X0_iProver_sequential_1) )
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = head_of(sK11) )
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) = tail_of(X0_iProver_sequential_1) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_1)) ),
inference(instantiation,[status(thm)],[c_2799]) ).
tcf(c_3044,plain,
( ( head_of(sK11) = tail_of(sK10) )
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) )
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_3043]) ).
tcf(c_3046,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( edge(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1)))
| ( head_of(sK11) = tail_of(X0_iProver_sequential_1) )
| ~ vertex(head_of(sK11))
| ~ vertex(tail_of(X0_iProver_sequential_1)) ),
inference(instantiation,[status(thm)],[c_2802]) ).
tcf(c_3047,plain,
( edge(sK0(head_of(sK11),tail_of(sK10)))
| ( head_of(sK11) = tail_of(sK10) )
| ~ vertex(tail_of(sK10))
| ~ vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_3046]) ).
tcf(c_3225,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( on_path(X0_iProver_sequential_1,sK12)
| ~ path(sK8,sK9,sK12)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,sK12) ),
inference(instantiation,[status(thm)],[c_1690]) ).
tcf(c_3227,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( on_path(X1_iProver_sequential_1,sK12)
| ~ path(sK8,sK9,sK12)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,sK12) ),
inference(instantiation,[status(thm)],[c_1689]) ).
tcf(c_3419,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_1671,c_1683]) ).
tcf(c_3480,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( edge(X0_iProver_sequential_1)
| ~ on_path(X0_iProver_sequential_1,sK12) ),
inference(superposition,[status(thm)],[c_3419,c_1702]) ).
tcf(c_3482,plain,
( edge(sK10)
| ~ on_path(sK10,sK12) ),
inference(instantiation,[status(thm)],[c_3480]) ).
tcf(c_3561,plain,
( on_path(sK10,sK12)
| ~ precedes(sK10,sK11,sK12)
| ~ path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_3225]) ).
tcf(c_3565,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( on_path(X1_iProver_sequential_1,sK12)
| ~ precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,sK12) ),
inference(superposition,[status(thm)],[c_3419,c_1689]) ).
tcf(c_3572,plain,
( on_path(sK11,sK12)
| ~ precedes(sK10,sK11,sK12)
| ~ path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_3227]) ).
tcf(c_3654,plain,
on_path(sK11,sK12),
inference(superposition,[status(thm)],[c_1670,c_3565]) ).
tcf(c_3655,plain,
edge(sK11),
inference(superposition,[status(thm)],[c_3654,c_3480]) ).
tcf(c_3843,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2] :
( ( head_of(sK11) = X0_iProver_shortest_path_2 )
| ( X0_iProver_shortest_path_2 != head_of(sK11) )
| ( head_of(sK11) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_2945]) ).
tcf(c_4302,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_1671,c_1683]) ).
tcf(c_4352,plain,
! [X0_iProver_shortest_path_2: iProver_shortest_path_2,X1_iProver_shortest_path_2: iProver_shortest_path_2] :
( ~ precedes(sK11,sK10,sK12)
| ~ shortest_path(X0_iProver_shortest_path_2,X1_iProver_shortest_path_2,sK12) ),
inference(superposition,[status(thm)],[c_1670,c_1679]) ).
tcf(c_4451,plain,
~ precedes(sK11,sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_4352,c_104,c_103,c_2781]) ).
tcf(c_5514,plain,
! [X0_iProver_sequential_1: iProver_sequential_1,X1_iProver_sequential_1: iProver_sequential_1] :
( precedes(X0_iProver_sequential_1,X1_iProver_sequential_1,sK12)
| ~ on_path(X1_iProver_sequential_1,sK12)
| ~ on_path(X0_iProver_sequential_1,sK12)
| ~ sequential(X0_iProver_sequential_1,X1_iProver_sequential_1) ),
inference(superposition,[status(thm)],[c_4302,c_1691]) ).
tcf(c_5688,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ( head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) )
| ( head_of(sK11) != head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_3843]) ).
tcf(c_5689,plain,
( ( head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10))) )
| ( head_of(sK11) != head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11) ) ),
inference(instantiation,[status(thm)],[c_5688]) ).
tcf(c_6170,plain,
( ~ sequential(sK11,sK10)
| ~ on_path(sK10,sK12)
| ~ on_path(sK11,sK12) ),
inference(superposition,[status(thm)],[c_5514,c_4451]) ).
tcf(c_15720,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) )
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_2764]) ).
tcf(c_15723,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ precedes(sK10,sK11,sK12)
| ( head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(sK10))) )
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_15720]) ).
tcf(c_20944,plain,
! [X0_iProver_sequential_1: iProver_sequential_1] :
( ~ edge(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1)))
| ( tail_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) != head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(X0_iProver_sequential_1))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_1672]) ).
tcf(c_20946,plain,
( ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| ( tail_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11) )
| ( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10) ) ),
inference(instantiation,[status(thm)],[c_20944]) ).
tcf(c_20947,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_20946,c_15723,c_6170,c_5689,c_3655,c_3572,c_3561,c_3482,c_3047,c_3044,c_3041,c_3021,c_3018,c_2909,c_2858,c_2793,c_2792,c_2765,c_2759,c_1784,c_1748,c_1740,c_860,c_103,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA007+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n009.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Sep 23 12:43:28 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.44
% 0.11/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.44
% 0.11/0.44 % Detected problem language: tptp
% 0.11/0.46 % Proving...
% 10.51/2.34 % SZS status Started for theBenchmark.p
% 10.51/2.34 % SZS status Theorem for theBenchmark.p
% 10.51/2.34
% 10.51/2.34 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.51/2.34
% 10.51/2.34 % ------ iProver source info
% 10.51/2.34
% 10.51/2.34 % git: date: 2026-07-19 20:42:38 +0200
% 10.51/2.34 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.51/2.34 % git: non_committed_changes: false
% 10.51/2.34
% 10.51/2.34 % ------ Parsing...
% 10.51/2.34 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.51/2.34
% 10.51/2.34 % ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 10.51/2.34
% 10.51/2.34 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.51/2.34
% 10.51/2.34 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.51/2.34 % ------ Proving...
% 10.51/2.34 % ------ Problem Properties
% 10.51/2.34
% 10.51/2.34 %
% 10.51/2.34 % clauses 55
% 10.51/2.34 % conjectures 3
% 10.51/2.34 % EPR 17
% 10.51/2.34 % Horn 37
% 10.51/2.34 % unary 5
% 10.51/2.34 % binary 14
% 10.51/2.34 % lits 171
% 10.51/2.34 % lits eq 46
% 10.51/2.34 % fd_pure 0
% 10.51/2.34 % fd_pseudo 0
% 10.51/2.34 % fd_cond 0
% 10.51/2.34 % fd_pseudo_cond 5
% 10.51/2.34 % AC symbols 0
% 10.51/2.34
% 10.51/2.34 % ------ Input Options Time Limit: Unbounded
% 10.51/2.34
% 10.51/2.34
% 10.51/2.34 % ------
% 10.51/2.34 % Current options:
% 10.51/2.34 % ------
% 10.51/2.34
% 10.51/2.34
% 10.51/2.34 %
% 10.51/2.34
% 10.51/2.34 % ------ Proving...
% 10.51/2.34 %
% 10.51/2.34
% 10.51/2.34 % SZS status Theorem for theBenchmark.p
% 10.51/2.34
% 10.51/2.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.51/2.35
% 10.51/2.35
%------------------------------------------------------------------------------