%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA009+2 : 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 : n008.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 01:23:36 PM UTC 2026
% Result : Theorem 26.31s 9.33s
% Output : CNFRefutation 26.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 13
% Syntax : Number of formulae : 3083 ( 46 unt; 0 def)
% Number of atoms : 16756 (9264 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 21571 (7898 ~;13530 |; 117 &)
% ( 4 <=>; 17 =>; 0 <=; 5 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 6661 ( 0 sgn6634 !; 27 ?;6399 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
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(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(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_path_means_stuff_means_triangles) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f21,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) ) ) ),
inference(flattening,[],[f21]) ).
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(f25,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(f26,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,[],[f25]) ).
fof(f27,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(f28,plain,
! [X0,X1,X2] :
( ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| triangle(X0,X1,X2) ),
inference(ennf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| triangle(X0,X1,X2) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f31,plain,
! [X0] :
( ~ edge(X0)
| ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f32,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(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(ennf_transformation,[],[f9]) ).
fof(f34,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,[],[f33]) ).
fof(f35,plain,
( complete
& shortest_path(sK1,sK2,sK0)
& sequential(sK3,sK4)
& on_path(sK4,sK0)
& on_path(sK3,sK0)
& ! [X5] : ~ triangle(sK3,sK4,X5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f22]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f38,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ( ( ( tail_of(sK5(X0,X1)) = X1
& head_of(sK5(X0,X1)) = X0 )
| ( tail_of(sK5(X0,X1)) = X0
& head_of(sK5(X0,X1)) = X1 ) )
& ( tail_of(sK5(X0,X1)) != X1
| head_of(sK5(X0,X1)) != X0
| tail_of(sK5(X0,X1)) != X0
| head_of(sK5(X0,X1)) != X1 )
& edge(sK5(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f37]) ).
fof(f39,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(f40,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,[],[f39]) ).
fof(f41,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,[],[f27]) ).
fof(f42,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,[],[f41]) ).
fof(f43,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,[],[f42]) ).
fof(f44,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,sK6(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK6(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X3,sK6(X0,X1,X2))],[f43]) ).
fof(f45,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,[],[f32]) ).
fof(f46,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,[],[f45]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK7(X0,X3,X4),X4,X0)
& sequential(X3,sK7(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,[sK7]),skolemize(X6,sK7(X0,X3,X4))],[f47]) ).
fof(f49,plain,
complete,
inference(cnf_transformation,[],[f35]) ).
fof(f50,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f51,plain,
sequential(sK3,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
on_path(sK4,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
on_path(sK3,sK0),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X5] : ~ triangle(sK3,sK4,X5),
inference(cnf_transformation,[],[f35]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK5(X0,X1)) = X1
| tail_of(sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK5(X0,X1)) = X0
| tail_of(sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK5(X0,X1)) = X1
| head_of(sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f58,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK5(X0,X1)) = X0
| head_of(sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK5(X0,X1)) != X1
| head_of(sK5(X0,X1)) != X0
| tail_of(sK5(X0,X1)) != X0
| head_of(sK5(X0,X1)) != X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f60,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK5(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f64,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f66,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f26]) ).
fof(f67,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,[],[f26]) ).
fof(f68,plain,
! [X2,X0,X1,X4] :
( ~ shortest_path(X0,X1,X2)
| ~ path(X0,X1,X4)
| less_or_equal(length_of(X2),length_of(X4)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| X0 != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f71,plain,
! [X2,X0,X1] :
( path(X0,X1,sK6(X0,X1,X2))
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f72,plain,
! [X2,X0,X1] :
( ~ less_or_equal(length_of(X2),length_of(sK6(X0,X1,X2)))
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f73,plain,
! [X2,X0,X1] :
( ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| triangle(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f74,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f76,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f77,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| sequential(X3,X4)
| precedes(sK7(X0,X3,X4),X4,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f78,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| sequential(X3,X4)
| sequential(X3,sK7(X0,X3,X4)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ),
inference(cnf_transformation,[],[f48]) ).
fof(f80,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f81,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f82,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f83,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,[],[f34]) ).
fof(f84,plain,
! [X1] : ~ sequential(X1,X1),
inference(equality_resolution,[],[f62]) ).
fof(f85,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f69]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : ~ triangle(sK3,sK4,X0),
inference(cnf_transformation,[],[f54]) ).
tcf(c_50,negated_conjecture,
on_path(sK3,sK0),
inference(cnf_transformation,[],[f53]) ).
tcf(c_51,negated_conjecture,
on_path(sK4,sK0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_52,negated_conjecture,
sequential(sK3,sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,negated_conjecture,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f50]) ).
tcf(c_54,negated_conjecture,
complete,
inference(cnf_transformation,[],[f49]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0)
| ( tail_of(sK5(X0,X1)) != X1 )
| ( tail_of(sK5(X0,X1)) != X0 )
| ( head_of(sK5(X0,X1)) != X1 )
| ( head_of(sK5(X0,X1)) != X0 ) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_64,plain,
! [X0: $i] : ~ sequential(X0,X0),
inference(cnf_transformation,[],[f84]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ precedes(X2,X0,X5)
| ~ shortest_path(X3,X4,X5)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X4,X3,X2)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( shortest_path(X1,X2,X0)
| ( X1 = X2 )
| ~ path(X1,X2,X0)
| ~ less_or_equal(length_of(X0),length_of(sK6(X1,X2,X0))) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( shortest_path(X0,X1,X2)
| path(X0,X1,sK6(X0,X1,X2))
| ( X0 = X1 )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] : ~ shortest_path(X0,X0,X1),
inference(cnf_transformation,[],[f85]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X0,X1,X2)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_74,plain,
! [X0: $i] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_75,plain,
! [X0: $i] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_76,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X0,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X1,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ sequential(X3,X1)
| ~ sequential(X3,X0)
| ~ path(X4,X5,X2)
| ~ precedes(X3,X1,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| sequential(X0,sK7(X2,X0,X1))
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| precedes(sK7(X2,X0,X1),X1,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_82,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,[],[f83]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X1,X2)
| ~ sequential(X5,X0)
| ~ on_path(X5,X2)
| ~ on_path(X1,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_54,c_55]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_99]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X0,X1,X2)
| ~ edge(X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_63,c_62,c_73]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X1,X2)
| ~ sequential(X5,X0)
| ~ on_path(X5,X2)
| ~ precedes(X0,X1,X2)
| ~ path(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_78,c_83]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X1,X2)
| ~ sequential(X5,X0)
| ~ on_path(X5,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_104]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_54,c_60]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_106]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_54,c_59]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_109]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_54,c_58]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_111]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_54,c_57]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_113]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) != X0 )
| ( head_of(sK5(X0,X1)) != X1 )
| ( tail_of(sK5(X0,X1)) != X0 )
| ( tail_of(sK5(X0,X1)) != X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_54,c_56]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0)
| ( tail_of(sK5(X0,X1)) != X1 )
| ( tail_of(sK5(X0,X1)) != X0 )
| ( head_of(sK5(X0,X1)) != X1 )
| ( head_of(sK5(X0,X1)) != X0 ) ),
inference(renaming,[status(thm)],[c_116]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i,X2: $i] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_102,c_62]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ( X3 != sK4 )
| ( X2 != sK3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_139]) ).
tcf(c_554,plain,
! [X0: $i] :
( ~ sequential(sK3,sK4)
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(unflattening,[status(thm)],[c_553]) ).
tcf(c_556,plain,
! [X0: $i] :
( ~ sequential(X0,sK3)
| ~ sequential(sK4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_554,c_52,c_554]) ).
tcf(c_557,plain,
! [X0: $i] :
( ~ sequential(sK4,X0)
| ~ sequential(X0,sK3) ),
inference(renaming,[status(thm)],[c_556]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X1,X2,X0)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_70]) ).
tcf(c_656,plain,
path(sK1,sK2,sK0),
inference(unflattening,[status(thm)],[c_655]) ).
tcf(c_1439,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2042,plain,
edge(sK3),
inference(superposition,[status(thm)],[c_52,c_62]) ).
tcf(c_2047,plain,
head_of(sK3) = tail_of(sK4),
inference(superposition,[status(thm)],[c_52,c_65]) ).
tcf(c_2052,plain,
edge(sK4),
inference(superposition,[status(thm)],[c_52,c_63]) ).
tcf(c_2065,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_53,c_70]) ).
tcf(c_2066,plain,
( vertex(head_of(sK3))
| ~ edge(sK4) ),
inference(superposition,[status(thm)],[c_2047,c_76]) ).
tcf(c_2067,plain,
vertex(head_of(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2066,c_2052]) ).
tcf(c_2072,plain,
( ~ edge(sK4)
| ( head_of(sK3) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2047,c_74]) ).
tcf(c_2073,plain,
head_of(sK3) != head_of(sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_2072,c_2052]) ).
tcf(c_2100,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_53,c_67]) ).
tcf(c_2123,plain,
! [X0: $i] :
( less_or_equal(length_of(sK0),length_of(X0))
| ~ path(sK1,sK2,X0) ),
inference(superposition,[status(thm)],[c_53,c_72]) ).
tcf(c_2134,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(X0,sK7(sK0,X0,X1))
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2065,c_80]) ).
tcf(c_2148,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( X0 = sK4 )
| ~ edge(sK4)
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_61]) ).
tcf(c_2149,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( X0 = sK4 )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2148,c_2052]) ).
tcf(c_2163,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| sequential(X0,sK7(sK6(X2,X3,X4),X0,X1))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_69,c_80]) ).
tcf(c_2180,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2134,c_63]) ).
tcf(c_2181,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(X0) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2134,c_65]) ).
tcf(c_2182,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| sequential(X0,X1)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2134,c_62]) ).
tcf(c_2192,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2182,c_62,c_2182]) ).
tcf(c_2227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| precedes(sK7(sK6(X2,X3,X4),X0,X1),X1,sK6(X2,X3,X4))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_69,c_81]) ).
tcf(c_2228,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2065,c_81]) ).
tcf(c_2244,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| ~ sequential(X0,X2)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2228,c_79]) ).
tcf(c_2245,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on_path(X1,sK0)
| sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_78]) ).
tcf(c_2246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| on_path(sK7(sK0,X0,X1),sK0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_77]) ).
tcf(c_2247,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_2181]) ).
tcf(c_2249,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ precedes(X1,X0,sK0)
| ~ precedes(X0,sK7(sK0,X1,X0),sK0) ),
inference(superposition,[status(thm)],[c_2228,c_2100]) ).
tcf(c_2285,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| on_path(sK7(sK0,X0,X1),sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2065,c_2246]) ).
tcf(c_2308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X1,X2,X3)
| precedes(X0,X4,sK6(X1,X2,X3))
| ( X1 = X2 )
| ~ sequential(X0,X4)
| ~ path(X1,X2,X3)
| ~ on_path(X4,sK6(X1,X2,X3))
| ~ on_path(X0,sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_69,c_82]) ).
tcf(c_2309,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2065,c_82]) ).
tcf(c_2329,plain,
! [X0: $i,X1: $i] :
( shortest_path(X0,X1,sK0)
| ( X0 = X1 )
| ~ path(X0,X1,sK0)
| ~ path(sK1,sK2,sK6(X0,X1,sK0)) ),
inference(superposition,[status(thm)],[c_2123,c_68]) ).
tcf(c_2342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) ) ),
inference(equality_resolution,[status(thm)],[c_66]) ).
tcf(c_2354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK0)
| ~ on_path(X1,sK0)
| ~ sequential(X4,X1)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2309,c_79]) ).
tcf(c_2358,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_2192]) ).
tcf(c_2359,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2309,c_2100]) ).
tcf(c_2360,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X1,X0,sK0)
| ~ on_path(sK7(sK0,X1,X0),sK0)
| ~ sequential(X0,sK7(sK0,X1,X0)) ),
inference(superposition,[status(thm)],[c_2309,c_2249]) ).
tcf(c_2387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(X0,sK4,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_2342]) ).
tcf(c_2388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(sK4,X0,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_2342]) ).
tcf(c_2389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(X3,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_2342]) ).
tcf(c_2402,plain,
! [X0: $i] : ~ precedes(X0,X0,sK0),
inference(superposition,[status(thm)],[c_53,c_2389]) ).
tcf(c_2414,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_2359]) ).
tcf(c_2426,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ precedes(sK4,sK4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_2047,c_2387]) ).
tcf(c_2453,plain,
( ~ sequential(sK4,sK3)
| ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0) ),
inference(superposition,[status(thm)],[c_52,c_2414]) ).
tcf(c_2454,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ sequential(sK7(sK0,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_2134,c_2414]) ).
tcf(c_2455,plain,
~ sequential(sK4,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2453,c_51,c_50]) ).
tcf(c_2466,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X1,X0,sK0)
| ~ sequential(X0,sK7(sK0,X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2360,c_2285]) ).
tcf(c_2480,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2454,c_2285,c_2454]) ).
tcf(c_2500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X4,X3,sK0)
| ~ on_path(X4,sK0)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X4,X2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2309,c_105]) ).
tcf(c_2501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK0)
| ~ on_path(X0,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2228,c_105]) ).
tcf(c_2525,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_107]) ).
tcf(c_2526,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK5(X1,tail_of(X0))) = X1 )
| ( tail_of(sK5(X1,tail_of(X0))) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_107]) ).
tcf(c_2527,plain,
! [X0: $i] :
( ( head_of(sK3) = X0 )
| ( tail_of(sK5(X0,head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK3))) = head_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2067,c_107]) ).
tcf(c_2555,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = X1 )
| ( head_of(sK5(X1,head_of(X0))) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_110]) ).
tcf(c_2556,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK5(X1,tail_of(X0))) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_110]) ).
tcf(c_2557,plain,
! [X0: $i] :
( ( head_of(sK3) = X0 )
| ( tail_of(sK5(X0,head_of(sK3))) = X0 )
| ( head_of(sK5(X0,head_of(sK3))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2067,c_110]) ).
tcf(c_2586,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ( head_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_112]) ).
tcf(c_2587,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK5(X1,tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(X1,tail_of(X0))) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_112]) ).
tcf(c_2588,plain,
! [X0: $i] :
( ( head_of(sK3) = X0 )
| ( tail_of(sK5(X0,head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(X0,head_of(sK3))) = head_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2067,c_112]) ).
tcf(c_2618,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( head_of(sK5(X1,head_of(X0))) = X1 )
| ( head_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_114]) ).
tcf(c_2619,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_114]) ).
tcf(c_2620,plain,
! [X0: $i] :
( ( head_of(sK3) = X0 )
| ( head_of(sK5(X0,head_of(sK3))) = X0 )
| ( head_of(sK5(X0,head_of(sK3))) = head_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2067,c_114]) ).
tcf(c_2647,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(X0),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2557]) ).
tcf(c_2648,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2557]) ).
tcf(c_2672,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(X0),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(X0),head_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2527]) ).
tcf(c_2673,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2527]) ).
tcf(c_2687,plain,
! [X0: $i,X1: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_2696,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( head_of(sK5(head_of(X0),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(X0),head_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2620]) ).
tcf(c_2697,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2620]) ).
tcf(c_2709,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(X2,X0,sK0)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2718,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(X0),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(X0),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2588]) ).
tcf(c_2719,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2588]) ).
tcf(c_2731,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(sK3,X2,sK0)
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X2)
| ~ on_path(X2,sK0)
| ~ path(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2769,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X0),X0)) = head_of(sK7(sK0,X1,X0)) )
| ~ on_path(X0,sK0)
| ~ precedes(X1,X0,sK0)
| ~ on_path(sK7(sK0,X1,X0),sK0)
| ~ sequential(X0,sK7(sK0,X1,X0)) ),
inference(superposition,[status(thm)],[c_2247,c_2414]) ).
tcf(c_2770,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_63]) ).
tcf(c_2771,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(X1) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_65]) ).
tcf(c_2772,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_62]) ).
tcf(c_2773,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ precedes(X0,sK3,sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK3)) ),
inference(superposition,[status(thm)],[c_2247,c_557]) ).
tcf(c_2774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ~ precedes(sK7(sK0,X0,sK7(sK0,X1,X2)),X2,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_2244]) ).
tcf(c_2775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| precedes(sK7(sK0,X0,sK7(sK0,X1,X2)),X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,X2)),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_2501]) ).
tcf(c_2830,plain,
( sequential(sK4,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK4,sK3),sK3)) = head_of(sK7(sK0,sK4,sK3)) )
| ~ precedes(sK4,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2134,c_2773]) ).
tcf(c_2831,plain,
( ( tail_of(sK7(sK0,sK7(sK0,sK4,sK3),sK3)) = head_of(sK7(sK0,sK4,sK3)) )
| ~ precedes(sK4,sK3,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2830,c_2455]) ).
tcf(c_2853,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2065,c_2500]) ).
tcf(c_2878,plain,
! [X0: $i] :
( precedes(X0,sK4,sK0)
| ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_52,c_2853]) ).
tcf(c_2879,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_2853]) ).
tcf(c_2880,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X2),X2)) = head_of(sK7(sK0,X1,X2)) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X1,X2,sK0)
| ~ on_path(sK7(sK0,X1,X2),sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2247,c_2853]) ).
tcf(c_2881,plain,
! [X0: $i] :
( precedes(X0,sK4,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2878,c_51,c_50]) ).
tcf(c_2905,plain,
( ~ edge(sK3)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_2906,plain,
( vertex(tail_of(sK3))
| ~ edge(sK3) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK4,sK0)
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_105]) ).
tcf(c_2915,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,sK3)
| ~ sequential(X2,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X2,X3)
| ~ precedes(X2,sK4,sK0)
| ~ path(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_79]) ).
tcf(c_2919,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK0,X0,sK4)) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_2181]) ).
tcf(c_2920,plain,
! [X0: $i] :
( edge(X0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_2192]) ).
tcf(c_2921,plain,
! [X0: $i] :
( ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ precedes(sK4,X0,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_2100]) ).
tcf(c_2952,plain,
( vertex(head_of(sK4))
| ~ edge(sK4) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_2965,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| precedes(X5,sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_2853]) ).
tcf(c_2966,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X3) ),
inference(superposition,[status(thm)],[c_2163,c_2414]) ).
tcf(c_2967,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| edge(sK7(sK6(X2,X3,X4),X0,X1))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2163,c_63]) ).
tcf(c_2968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X0) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2163,c_65]) ).
tcf(c_2969,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(X0)
| sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2163,c_62]) ).
tcf(c_3006,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2770,c_63,c_2770]) ).
tcf(c_3007,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_3006]) ).
tcf(c_3014,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_3007]) ).
tcf(c_3015,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_3007]) ).
tcf(c_3036,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( X0 = sK3 )
| ~ edge(sK3)
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_3046,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_3061,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ sequential(X0,X1)
| ~ precedes(X0,sK4,sK0) ),
inference(superposition,[status(thm)],[c_2065,c_2915]) ).
tcf(c_3072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(X0)
| ~ precedes(X0,X1,sK6(X2,X3,X4))
| ~ path(X2,X3,X4)
| ( X2 = X3 )
| shortest_path(X2,X3,X4) ),
inference(global_subsumption_just,[status(thm)],[c_2969,c_62,c_2969]) ).
tcf(c_3073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(X0)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(renaming,[status(thm)],[c_3072]) ).
tcf(c_3094,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( tail_of(sK5(head_of(X0),head_of(X1))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2555]) ).
tcf(c_3095,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2555]) ).
tcf(c_3096,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(X0))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(X0))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2555]) ).
tcf(c_3132,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),sK4)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_2285,c_2919]) ).
tcf(c_3148,plain,
! [X0: $i,X1: $i] :
( ~ on_path(sK4,sK0)
| ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_3061]) ).
tcf(c_3149,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK4)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,sK4,sK0)
| ~ sequential(sK7(sK0,X0,sK4),sK4)
| ~ sequential(sK7(sK0,X0,sK4),X1) ),
inference(superposition,[status(thm)],[c_2228,c_3061]) ).
tcf(c_3157,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3148,c_51]) ).
tcf(c_3181,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_3157]) ).
tcf(c_3182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_3157]) ).
tcf(c_3183,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_3157]) ).
tcf(c_3218,plain,
! [X0: $i,X1: $i] :
( precedes(X0,sK4,sK0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2065,c_2914]) ).
tcf(c_3240,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(X0,sK4,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_3218]) ).
tcf(c_3241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| precedes(X3,sK4,sK0)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_3218]) ).
tcf(c_3242,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_3218]) ).
tcf(c_3265,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_3181,c_2285,c_3181]) ).
tcf(c_3277,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ precedes(X0,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_3265]) ).
tcf(c_3284,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_3183,c_2285,c_3183]) ).
tcf(c_3327,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3096]) ).
tcf(c_3329,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_3096]) ).
tcf(c_3330,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3096]) ).
tcf(c_3331,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3329,c_2073]) ).
tcf(c_3364,plain,
sK4 = sK4,
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_3371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_2342]) ).
tcf(c_3372,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_61]) ).
tcf(c_3373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_3331,c_2388]) ).
tcf(c_3374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK4,X0) ),
inference(superposition,[status(thm)],[c_3331,c_2387]) ).
tcf(c_3375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_2342]) ).
tcf(c_3409,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ( tail_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2556]) ).
tcf(c_3410,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( tail_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2556]) ).
tcf(c_3411,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(X0))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(X0))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2556]) ).
tcf(c_3451,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( tail_of(sK5(head_of(X0),head_of(X1))) = head_of(X1) )
| ( tail_of(sK5(head_of(X0),head_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2525]) ).
tcf(c_3452,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2525]) ).
tcf(c_3453,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(X0))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2525]) ).
tcf(c_3486,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ( tail_of(sK5(head_of(X0),tail_of(X1))) = tail_of(X1) )
| ( tail_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2526]) ).
tcf(c_3487,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( tail_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X1) )
| ( tail_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2526]) ).
tcf(c_3488,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(X0))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2526]) ).
tcf(c_3529,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( head_of(sK5(head_of(X0),head_of(X1))) = head_of(X1) )
| ( head_of(sK5(head_of(X0),head_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2618]) ).
tcf(c_3530,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2618]) ).
tcf(c_3531,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(X0))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2618]) ).
tcf(c_3557,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_3373]) ).
tcf(c_3558,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3557,c_51]) ).
tcf(c_3569,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_3374]) ).
tcf(c_3570,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_3374]) ).
tcf(c_3575,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3569,c_51]) ).
tcf(c_3600,plain,
! [X0: $i,X1: $i] :
( precedes(sK3,sK4,sK0)
| ~ sequential(sK3,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0)
| ~ path(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_2731]) ).
tcf(c_3612,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ( head_of(sK5(head_of(X0),tail_of(X1))) = tail_of(X1) )
| ( head_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2619]) ).
tcf(c_3613,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( head_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X1) )
| ( head_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2619]) ).
tcf(c_3614,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(X0))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2619]) ).
tcf(c_3698,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = head_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3411]) ).
tcf(c_3699,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2042,c_3411]) ).
tcf(c_3701,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3411]) ).
tcf(c_3739,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_3699,c_2042,c_2905,c_3699]) ).
tcf(c_3740,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_3739]) ).
tcf(c_3745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_2342]) ).
tcf(c_3746,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_61]) ).
tcf(c_3747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_3740,c_2388]) ).
tcf(c_3748,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,X0) ),
inference(superposition,[status(thm)],[c_3740,c_2387]) ).
tcf(c_3749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_2342]) ).
tcf(c_3779,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_3747]) ).
tcf(c_3780,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3779,c_51]) ).
tcf(c_3799,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_3748]) ).
tcf(c_3800,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_3748]) ).
tcf(c_3805,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3799,c_51]) ).
tcf(c_3826,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( sequential(X4,X5)
| shortest_path(X1,X2,X3)
| precedes(X0,X5,sK6(X1,X2,X3))
| ( X1 = X2 )
| ~ path(X1,X2,X3)
| ~ on_path(X0,sK6(X1,X2,X3))
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2227,c_105]) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( sequential(X4,X5)
| shortest_path(X1,X2,X3)
| ( X1 = X2 )
| ~ sequential(X0,X5)
| ~ path(X1,X2,X3)
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ precedes(X0,X5,sK6(X1,X2,X3))
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2227,c_79]) ).
tcf(c_3828,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| on_path(X1,sK6(X2,X3,X4))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ path(X5,X6,sK6(X2,X3,X4))
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2227,c_78]) ).
tcf(c_3829,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| on_path(sK7(sK6(X2,X3,X4),X0,X1),sK6(X2,X3,X4))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ path(X5,X6,sK6(X2,X3,X4))
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2227,c_77]) ).
tcf(c_3920,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( tail_of(sK5(head_of(X0),head_of(X1))) = head_of(X1) )
| ( head_of(sK5(head_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2586]) ).
tcf(c_3921,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2586]) ).
tcf(c_3922,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2586]) ).
tcf(c_3964,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ( tail_of(sK5(head_of(X0),tail_of(X1))) = tail_of(X1) )
| ( head_of(sK5(head_of(X0),tail_of(X1))) = tail_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_2587]) ).
tcf(c_3965,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( tail_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X1) )
| ( head_of(sK5(tail_of(X0),tail_of(X1))) = tail_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_2587]) ).
tcf(c_3966,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2067,c_2587]) ).
tcf(c_4015,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2647]) ).
tcf(c_4017,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_2647]) ).
tcf(c_4018,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2647]) ).
tcf(c_4019,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4017,c_2073]) ).
tcf(c_4043,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2648]) ).
tcf(c_4044,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2042,c_2648]) ).
tcf(c_4046,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2648]) ).
tcf(c_4090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_2342]) ).
tcf(c_4091,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_61]) ).
tcf(c_4094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_2342]) ).
tcf(c_4096,plain,
( vertex(head_of(sK4))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4019,c_76]) ).
tcf(c_4115,plain,
vertex(head_of(sK4)),
inference(global_subsumption_just,[status(thm)],[c_4096,c_2052,c_2952]) ).
tcf(c_4117,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2587]) ).
tcf(c_4118,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2586]) ).
tcf(c_4119,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(X0))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2619]) ).
tcf(c_4120,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(X0))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2618]) ).
tcf(c_4121,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(X0))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2526]) ).
tcf(c_4122,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(X0))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2525]) ).
tcf(c_4123,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(X0))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(X0))) = head_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2556]) ).
tcf(c_4124,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(X0))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(X0))) = head_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4115,c_2555]) ).
tcf(c_4125,plain,
! [X0: $i] :
( ( head_of(sK4) = X0 )
| ( head_of(sK5(X0,head_of(sK4))) = X0 )
| ( head_of(sK5(X0,head_of(sK4))) = head_of(sK4) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4115,c_114]) ).
tcf(c_4126,plain,
! [X0: $i] :
( ( head_of(sK4) = X0 )
| ( tail_of(sK5(X0,head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(X0,head_of(sK4))) = head_of(sK4) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4115,c_112]) ).
tcf(c_4127,plain,
! [X0: $i] :
( ( head_of(sK4) = X0 )
| ( tail_of(sK5(X0,head_of(sK4))) = X0 )
| ( head_of(sK5(X0,head_of(sK4))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4115,c_110]) ).
tcf(c_4128,plain,
! [X0: $i] :
( ( head_of(sK4) = X0 )
| ( tail_of(sK5(X0,head_of(sK4))) = X0 )
| ( tail_of(sK5(X0,head_of(sK4))) = head_of(sK4) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4115,c_107]) ).
tcf(c_4129,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4115,c_2588]) ).
tcf(c_4130,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4115,c_2620]) ).
tcf(c_4131,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4115,c_2527]) ).
tcf(c_4145,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4131,c_2073]) ).
tcf(c_4148,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4130,c_2073]) ).
tcf(c_4151,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4129,c_2073]) ).
tcf(c_4296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_2342]) ).
tcf(c_4297,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_61]) ).
tcf(c_4300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_2342]) ).
tcf(c_4301,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_74]) ).
tcf(c_4325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_4148,c_66]) ).
tcf(c_4326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),head_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4148,c_66]) ).
tcf(c_4328,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4148,c_61]) ).
tcf(c_4353,plain,
! [X0: $i] :
( ~ precedes(sK3,sK4,sK0)
| ~ shortest_path(sK1,sK2,sK0)
| ( head_of(sK4) != head_of(X0) )
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_2709]) ).
tcf(c_4355,plain,
( ~ precedes(sK4,sK3,sK0)
| ~ precedes(sK3,sK4,sK0)
| ~ shortest_path(sK1,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_2687]) ).
tcf(c_4364,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4044,c_2042,c_2905,c_4044]) ).
tcf(c_4365,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(renaming,[status(thm)],[c_4364]) ).
tcf(c_4370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_2342]) ).
tcf(c_4371,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_61]) ).
tcf(c_4372,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_2388]) ).
tcf(c_4373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_2387]) ).
tcf(c_4374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_2342]) ).
tcf(c_4376,plain,
( vertex(tail_of(sK3))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4365,c_76]) ).
tcf(c_4418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_2342]) ).
tcf(c_4419,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_61]) ).
tcf(c_4420,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_2388]) ).
tcf(c_4421,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK4,X0) ),
inference(superposition,[status(thm)],[c_4151,c_2387]) ).
tcf(c_4422,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_2342]) ).
tcf(c_4452,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_4455,plain,
( edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK3) = tail_of(sK3) )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_4459,plain,
! [X0: $i] :
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK3) != X0 )
| ( head_of(sK3) != X0 ) ),
inference(instantiation,[status(thm)],[c_1441]) ).
tcf(c_4461,plain,
vertex(tail_of(sK3)),
inference(global_subsumption_just,[status(thm)],[c_4376,c_2042,c_2906]) ).
tcf(c_4463,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2587]) ).
tcf(c_4464,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2586]) ).
tcf(c_4465,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2619]) ).
tcf(c_4466,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(X0))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2618]) ).
tcf(c_4467,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2526]) ).
tcf(c_4468,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(X0))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2525]) ).
tcf(c_4469,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(X0))) = tail_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2556]) ).
tcf(c_4470,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(X0))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(X0))) = tail_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4461,c_2555]) ).
tcf(c_4471,plain,
! [X0: $i] :
( ( tail_of(sK3) = X0 )
| ( head_of(sK5(X0,tail_of(sK3))) = X0 )
| ( head_of(sK5(X0,tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4461,c_114]) ).
tcf(c_4472,plain,
! [X0: $i] :
( ( tail_of(sK3) = X0 )
| ( tail_of(sK5(X0,tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(X0,tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4461,c_112]) ).
tcf(c_4473,plain,
! [X0: $i] :
( ( tail_of(sK3) = X0 )
| ( tail_of(sK5(X0,tail_of(sK3))) = X0 )
| ( head_of(sK5(X0,tail_of(sK3))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4461,c_110]) ).
tcf(c_4474,plain,
! [X0: $i] :
( ( tail_of(sK3) = X0 )
| ( tail_of(sK5(X0,tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_4461,c_107]) ).
tcf(c_4475,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4461,c_2588]) ).
tcf(c_4476,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4461,c_2620]) ).
tcf(c_4477,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4461,c_2527]) ).
tcf(c_4646,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_4420]) ).
tcf(c_4647,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4646,c_51]) ).
tcf(c_4666,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_4421]) ).
tcf(c_4667,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_4421]) ).
tcf(c_4672,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4666,c_51]) ).
tcf(c_4677,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4475,c_2042,c_2905,c_4475]) ).
tcf(c_4678,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_4677]) ).
tcf(c_4684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_2342]) ).
tcf(c_4685,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_61]) ).
tcf(c_4686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_2388]) ).
tcf(c_4687,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK4,X0) ),
inference(superposition,[status(thm)],[c_4678,c_2387]) ).
tcf(c_4688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_2342]) ).
tcf(c_4763,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2672]) ).
tcf(c_4766,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2672]) ).
tcf(c_4786,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2673]) ).
tcf(c_4789,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2673]) ).
tcf(c_4809,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2696]) ).
tcf(c_4812,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2696]) ).
tcf(c_4851,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(X0),head_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4127]) ).
tcf(c_4852,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(tail_of(X0),head_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4127]) ).
tcf(c_4854,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4461,c_4127]) ).
tcf(c_4879,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4473]) ).
tcf(c_4880,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4473]) ).
tcf(c_4883,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4115,c_4473]) ).
tcf(c_4935,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_4686]) ).
tcf(c_4936,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4935,c_51]) ).
tcf(c_4951,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_4687]) ).
tcf(c_4952,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_4687]) ).
tcf(c_4957,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4951,c_51]) ).
tcf(c_5010,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3453]) ).
tcf(c_5012,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_3453]) ).
tcf(c_5013,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3453]) ).
tcf(c_5014,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5012,c_2073]) ).
tcf(c_5037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_2342]) ).
tcf(c_5038,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_61]) ).
tcf(c_5041,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_2342]) ).
tcf(c_5042,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_74]) ).
tcf(c_5084,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3488]) ).
tcf(c_5085,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2042,c_3488]) ).
tcf(c_5087,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3488]) ).
tcf(c_5103,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4476,c_2042,c_2905,c_4476]) ).
tcf(c_5104,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_5103]) ).
tcf(c_5109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_5104,c_66]) ).
tcf(c_5110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5104,c_66]) ).
tcf(c_5111,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5104,c_2149]) ).
tcf(c_5112,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK3)),X0)
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5104,c_61]) ).
tcf(c_5162,plain,
( sequential(sK4,sK3)
| ( sK4 = sK3 )
| ~ edge(sK4)
| ~ edge(sK3)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_3036]) ).
tcf(c_5179,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2697]) ).
tcf(c_5182,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2697]) ).
tcf(c_5230,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2718]) ).
tcf(c_5233,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2718]) ).
tcf(c_5253,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_2719]) ).
tcf(c_5256,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_2719]) ).
tcf(c_5285,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( head_of(sK5(head_of(X0),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(X0),head_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4125]) ).
tcf(c_5286,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( head_of(sK5(tail_of(X0),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(X0),head_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4125]) ).
tcf(c_5287,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2067,c_4125]) ).
tcf(c_5288,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4461,c_4125]) ).
tcf(c_5293,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5287,c_2073]) ).
tcf(c_5326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_5293,c_66]) ).
tcf(c_5327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK3),head_of(sK4)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5293,c_66]) ).
tcf(c_5329,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK3),head_of(sK4)),X0)
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5293,c_61]) ).
tcf(c_5411,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(X0),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(X0),head_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4128]) ).
tcf(c_5412,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(tail_of(X0),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(X0),head_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4128]) ).
tcf(c_5414,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4461,c_4128]) ).
tcf(c_5437,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( head_of(sK5(head_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4471]) ).
tcf(c_5438,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( head_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4471]) ).
tcf(c_5439,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2067,c_4471]) ).
tcf(c_5441,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4115,c_4471]) ).
tcf(c_5489,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5085,c_2042,c_2905,c_5085]) ).
tcf(c_5490,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_5489]) ).
tcf(c_5496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_2342]) ).
tcf(c_5497,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_61]) ).
tcf(c_5498,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_2388]) ).
tcf(c_5499,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_2387]) ).
tcf(c_5500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_2342]) ).
tcf(c_5501,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_74]) ).
tcf(c_5551,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5439,c_2042,c_2905,c_5439]) ).
tcf(c_5552,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_5551]) ).
tcf(c_5557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_5552,c_66]) ).
tcf(c_5558,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK3),tail_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5552,c_66]) ).
tcf(c_5559,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5552,c_2149]) ).
tcf(c_5560,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK3),tail_of(sK3)),X0)
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5552,c_61]) ).
tcf(c_5584,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5501,c_2042,c_2067,c_2906,c_2905,c_4455,c_5501]) ).
tcf(c_5599,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3531]) ).
tcf(c_5602,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3531]) ).
tcf(c_5649,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3614]) ).
tcf(c_5652,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3614]) ).
tcf(c_5672,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3922]) ).
tcf(c_5674,plain,
( ( head_of(sK3) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_3922]) ).
tcf(c_5675,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3922]) ).
tcf(c_5676,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5674,c_2073]) ).
tcf(c_5717,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_2342]) ).
tcf(c_5718,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_61]) ).
tcf(c_5721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_2342]) ).
tcf(c_5748,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_3966]) ).
tcf(c_5749,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2042,c_3966]) ).
tcf(c_5751,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3966]) ).
tcf(c_5766,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4477,c_2042,c_2905,c_4477]) ).
tcf(c_5767,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_5766]) ).
tcf(c_5773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_2342]) ).
tcf(c_5774,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_61]) ).
tcf(c_5775,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_2388]) ).
tcf(c_5776,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_2387]) ).
tcf(c_5777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_2342]) ).
tcf(c_5778,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_74]) ).
tcf(c_5849,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4851]) ).
tcf(c_5852,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4851]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4852]) ).
tcf(c_5874,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),head_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),head_of(sK4))) = tail_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4852]) ).
tcf(c_5875,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4852]) ).
tcf(c_5924,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4879]) ).
tcf(c_5927,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4879]) ).
tcf(c_5968,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(head_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4474]) ).
tcf(c_5969,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4474]) ).
tcf(c_5972,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4115,c_4474]) ).
tcf(c_5994,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4) )
| ( tail_of(sK5(head_of(X0),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(X0),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4126]) ).
tcf(c_5995,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK4) )
| ( tail_of(sK5(tail_of(X0),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(X0),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4126]) ).
tcf(c_5997,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4461,c_4126]) ).
tcf(c_6020,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(head_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_4472]) ).
tcf(c_6021,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(X0),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_4472]) ).
tcf(c_6024,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4115,c_4472]) ).
tcf(c_6044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_2342]) ).
tcf(c_6045,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_61]) ).
tcf(c_6046,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_2388]) ).
tcf(c_6047,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_2387]) ).
tcf(c_6048,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_2342]) ).
tcf(c_6098,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5749,c_2042,c_2067,c_2906,c_2905,c_4452]) ).
tcf(c_6099,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(renaming,[status(thm)],[c_6098]) ).
tcf(c_6105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_2342]) ).
tcf(c_6106,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_61]) ).
tcf(c_6107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_2388]) ).
tcf(c_6108,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_2387]) ).
tcf(c_6109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_2342]) ).
tcf(c_6165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK0)
| ~ sequential(X4,X1)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2354,c_78]) ).
tcf(c_6184,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK0)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X4,X3)
| ~ sequential(X2,X4)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2309,c_6165]) ).
tcf(c_6185,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X1)
| ~ path(X3,X4,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),X2)
| ~ sequential(sK7(sK0,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_2228,c_6165]) ).
tcf(c_6186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,sK4)
| ~ sequential(X2,sK4)
| ~ sequential(X2,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_6165]) ).
tcf(c_6222,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK4)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2065,c_6186]) ).
tcf(c_6247,plain,
( ~ sequential(sK4,sK4)
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0) ),
inference(superposition,[status(thm)],[c_52,c_6222]) ).
tcf(c_6248,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_6222]) ).
tcf(c_6249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ sequential(X3,sK4)
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_6222]) ).
tcf(c_6250,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK4)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_6222]) ).
tcf(c_6309,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X1)
| ~ sequential(X0,X2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2065,c_6184]) ).
tcf(c_6334,plain,
! [X0: $i] :
( ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_52,c_6309]) ).
tcf(c_6335,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ precedes(X1,X2,sK0)
| ~ on_path(sK7(sK0,X1,X2),sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2134,c_6309]) ).
tcf(c_6336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X4,X5)
| shortest_path(X1,X2,X3)
| ( X1 = X2 )
| ~ on_path(X4,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X4,X0)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK0)
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2163,c_6309]) ).
tcf(c_6337,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ sequential(X2,X1)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2247,c_6309]) ).
tcf(c_6338,plain,
! [X0: $i] :
( ~ sequential(sK3,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6334,c_51,c_50]) ).
tcf(c_6393,plain,
( ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0) ),
inference(superposition,[status(thm)],[c_52,c_6338]) ).
tcf(c_6394,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK4),sK4)) = head_of(sK7(sK0,X0,sK4)) )
| ~ precedes(X0,sK4,sK0)
| ~ sequential(sK3,sK7(sK0,X0,sK4))
| ~ on_path(sK7(sK0,X0,sK4),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_6338]) ).
tcf(c_6406,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK4),sK4)) = head_of(sK7(sK0,X0,sK4)) )
| ~ precedes(X0,sK4,sK0)
| ~ sequential(sK3,sK7(sK0,X0,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6394,c_2285]) ).
tcf(c_6426,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_2342]) ).
tcf(c_6427,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_61]) ).
tcf(c_6430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_2342]) ).
tcf(c_6467,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4880]) ).
tcf(c_6469,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4880]) ).
tcf(c_6470,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4880]) ).
tcf(c_6510,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5285]) ).
tcf(c_6513,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5285]) ).
tcf(c_6533,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5286]) ).
tcf(c_6535,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),head_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_5286]) ).
tcf(c_6536,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5286]) ).
tcf(c_6558,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5411]) ).
tcf(c_6561,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5411]) ).
tcf(c_6596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_5288,c_66]) ).
tcf(c_6597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK4)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5288,c_66]) ).
tcf(c_6598,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5288,c_2149]) ).
tcf(c_6599,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5288,c_61]) ).
tcf(c_6714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_2342]) ).
tcf(c_6715,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_61]) ).
tcf(c_6716,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_2388]) ).
tcf(c_6717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_2387]) ).
tcf(c_6718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_2342]) ).
tcf(c_6719,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_74]) ).
tcf(c_6767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_5441,c_66]) ).
tcf(c_6768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),tail_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5441,c_66]) ).
tcf(c_6769,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5441,c_2149]) ).
tcf(c_6770,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5441,c_61]) ).
tcf(c_6813,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_2342]) ).
tcf(c_6814,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_61]) ).
tcf(c_6815,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_2388]) ).
tcf(c_6816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_2387]) ).
tcf(c_6817,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_2342]) ).
tcf(c_6818,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_74]) ).
tcf(c_6873,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK4)
| sequential(sK7(sK0,X0,sK4),X1)
| ~ precedes(X0,sK4,sK0)
| ~ sequential(sK7(sK0,X0,sK4),sK4)
| ~ precedes(sK7(sK0,X0,sK4),X1,sK0)
| ~ sequential(sK7(sK0,sK7(sK0,X0,sK4),X1),sK3)
| ~ on_path(sK7(sK0,sK7(sK0,X0,sK4),X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_3149]) ).
tcf(c_6874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,sK4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK0,X3,sK4),X4)
| ( X0 = X1 )
| ~ precedes(X3,sK4,sK0)
| ~ path(X0,X1,X2)
| ~ sequential(sK7(sK0,X3,sK4),sK4)
| ~ precedes(sK7(sK0,X3,sK4),X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK7(sK0,X3,sK4),X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK0,X3,sK4),X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_3149]) ).
tcf(c_6894,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(X0,sK4,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_3240,c_2285,c_3240]) ).
tcf(c_6906,plain,
! [X0: $i] :
( sequential(X0,sK3)
| precedes(X0,sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_6894]) ).
tcf(c_6913,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3015,c_63,c_3015]) ).
tcf(c_6914,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_6913]) ).
tcf(c_6921,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_6914]) ).
tcf(c_6922,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_6914]) ).
tcf(c_6952,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK0,X0,sK3),sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK0)
| ~ sequential(sK7(sK0,X0,sK3),sK4)
| ~ on_path(sK7(sK0,X0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_2228,c_3277]) ).
tcf(c_6983,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_3331,c_3745]) ).
tcf(c_6986,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_3740,c_3745]) ).
tcf(c_6987,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_3745]) ).
tcf(c_6990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_3745]) ).
tcf(c_6991,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_3745]) ).
tcf(c_6992,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_3745]) ).
tcf(c_6993,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_3745]) ).
tcf(c_6994,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_3745]) ).
tcf(c_6995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_3745]) ).
tcf(c_7116,plain,
( precedes(sK3,sK4,sK0)
| ~ sequential(sK3,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK3,sK0)
| ~ path(sK1,sK2,sK0) ),
inference(instantiation,[status(thm)],[c_3600]) ).
tcf(c_7128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_3331,c_3749]) ).
tcf(c_7132,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_3749]) ).
tcf(c_7135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_3749]) ).
tcf(c_7136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_3749]) ).
tcf(c_7137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_3749]) ).
tcf(c_7138,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_3749]) ).
tcf(c_7139,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_3749]) ).
tcf(c_7140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_3749]) ).
tcf(c_7189,plain,
( edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK4)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_7193,plain,
! [X0: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK3) != X0 )
| ( head_of(sK4) != X0 ) ),
inference(instantiation,[status(thm)],[c_1441]) ).
tcf(c_7204,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_4370]) ).
tcf(c_7205,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_4370]) ).
tcf(c_7206,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_4370]) ).
tcf(c_7207,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6099,c_4370]) ).
tcf(c_7208,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5490,c_4370]) ).
tcf(c_7210,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_4370]) ).
tcf(c_7211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_4370]) ).
tcf(c_7212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_4370]) ).
tcf(c_7215,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4365,c_4370]) ).
tcf(c_7216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_4370]) ).
tcf(c_7217,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_4370]) ).
tcf(c_7218,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_4370]) ).
tcf(c_7220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK3,X0) ),
inference(equality_resolution,[status(thm)],[c_4370]) ).
tcf(c_7351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_2342]) ).
tcf(c_7352,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_61]) ).
tcf(c_7358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_2342]) ).
tcf(c_7389,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5412]) ).
tcf(c_7391,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),head_of(sK4))) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_5412]) ).
tcf(c_7392,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5412]) ).
tcf(c_7414,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5437]) ).
tcf(c_7417,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5437]) ).
tcf(c_7490,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5438]) ).
tcf(c_7492,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_5438]) ).
tcf(c_7493,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5438]) ).
tcf(c_7514,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5968]) ).
tcf(c_7517,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5968]) ).
tcf(c_7546,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_7220]) ).
tcf(c_7547,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7546,c_50]) ).
tcf(c_7559,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_2342]) ).
tcf(c_7560,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_61]) ).
tcf(c_7561,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_4370]) ).
tcf(c_7562,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_3749]) ).
tcf(c_7563,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_3745]) ).
tcf(c_7564,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_2388]) ).
tcf(c_7565,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK4,X0)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_2387]) ).
tcf(c_7566,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_2342]) ).
tcf(c_7636,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4117]) ).
tcf(c_7638,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK4))) = tail_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4117]) ).
tcf(c_7639,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4117]) ).
tcf(c_7653,plain,
head_of(sK3) != tail_of(sK3),
inference(global_subsumption_just,[status(thm)],[c_4372,c_2042,c_2905]) ).
tcf(c_7664,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_4374]) ).
tcf(c_7665,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_4374]) ).
tcf(c_7667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6099,c_4374]) ).
tcf(c_7668,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5490,c_4374]) ).
tcf(c_7671,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_4374]) ).
tcf(c_7672,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_4374]) ).
tcf(c_7673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_4374]) ).
tcf(c_7677,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_4374]) ).
tcf(c_7678,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_4374]) ).
tcf(c_7679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_4374]) ).
tcf(c_7680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_4374]) ).
tcf(c_7682,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK3,sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(equality_resolution,[status(thm)],[c_4374]) ).
tcf(c_7747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5496]) ).
tcf(c_7748,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5496]) ).
tcf(c_7750,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6099,c_5496]) ).
tcf(c_7751,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5490,c_5496]) ).
tcf(c_7754,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5496]) ).
tcf(c_7755,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5496]) ).
tcf(c_7756,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_5496]) ).
tcf(c_7760,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_5496]) ).
tcf(c_7761,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_5496]) ).
tcf(c_7762,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_5496]) ).
tcf(c_7763,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_5496]) ).
tcf(c_7765,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK3,X0) ),
inference(equality_resolution,[status(thm)],[c_5496]) ).
tcf(c_7834,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( shortest_path(X2,X3,X4)
| precedes(X7,X6,sK6(X2,X3,X4))
| ( X2 = X3 )
| ~ sequential(X7,X5)
| ~ sequential(X5,X6)
| ~ path(X2,X3,X4)
| ~ on_path(X7,sK6(X2,X3,X4))
| ~ on_path(X6,sK6(X2,X3,X4))
| ~ on_path(X5,sK6(X2,X3,X4))
| ~ path(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2308,c_105]) ).
tcf(c_7835,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i] :
( shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ~ sequential(X7,X1)
| ~ sequential(X0,X7)
| ~ sequential(X0,X1)
| ~ path(X2,X3,X4)
| ~ on_path(X7,sK6(X2,X3,X4))
| ~ on_path(X1,sK6(X2,X3,X4))
| ~ path(X5,X6,sK6(X2,X3,X4))
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2308,c_79]) ).
tcf(c_7838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( edge(X0)
| shortest_path(X1,X2,X3)
| ( X1 = X2 )
| ~ sequential(X0,X4)
| ~ path(X1,X2,X3)
| ~ on_path(X4,sK6(X1,X2,X3))
| ~ on_path(X0,sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_2308,c_3073]) ).
tcf(c_7839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_3373]) ).
tcf(c_7840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_3374]) ).
tcf(c_7841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_3747]) ).
tcf(c_7842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_3748]) ).
tcf(c_7843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_4420]) ).
tcf(c_7844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_4421]) ).
tcf(c_7845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_4686]) ).
tcf(c_7846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_4687]) ).
tcf(c_7847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_7220]) ).
tcf(c_7955,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5969]) ).
tcf(c_7957,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_5969]) ).
tcf(c_7958,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5969]) ).
tcf(c_7980,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5994]) ).
tcf(c_7983,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5994]) ).
tcf(c_8003,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_5995]) ).
tcf(c_8005,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK4),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_5995]) ).
tcf(c_8006,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_5995]) ).
tcf(c_8048,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_6020]) ).
tcf(c_8051,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_6020]) ).
tcf(c_8069,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_7682]) ).
tcf(c_8070,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_7682]) ).
tcf(c_8071,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8069,c_50]) ).
tcf(c_8090,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_7765]) ).
tcf(c_8091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_7765]) ).
tcf(c_8092,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8090,c_50]) ).
tcf(c_8109,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ~ edge(sK3)
| ~ edge(sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_3036]) ).
tcf(c_8111,plain,
( vertex(tail_of(sK5(head_of(sK3),tail_of(sK3))))
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_8112,plain,
( vertex(head_of(sK5(head_of(sK3),tail_of(sK3))))
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_8122,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4118]) ).
tcf(c_8125,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4118]) ).
tcf(c_8145,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4119]) ).
tcf(c_8147,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4119]) ).
tcf(c_8148,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4119]) ).
tcf(c_8222,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5500]) ).
tcf(c_8223,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5500]) ).
tcf(c_8229,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5500]) ).
tcf(c_8230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5500]) ).
tcf(c_8231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_5500]) ).
tcf(c_8235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_5500]) ).
tcf(c_8236,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_5500]) ).
tcf(c_8237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_5500]) ).
tcf(c_8238,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_5500]) ).
tcf(c_8240,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK3,sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(equality_resolution,[status(thm)],[c_5500]) ).
tcf(c_8337,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_6105]) ).
tcf(c_8338,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_6105]) ).
tcf(c_8340,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6099,c_6105]) ).
tcf(c_8344,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_6105]) ).
tcf(c_8345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_6105]) ).
tcf(c_8346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_6105]) ).
tcf(c_8350,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_6105]) ).
tcf(c_8351,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_6105]) ).
tcf(c_8352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_6105]) ).
tcf(c_8353,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_6105]) ).
tcf(c_8355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK3,X0) ),
inference(equality_resolution,[status(thm)],[c_6105]) ).
tcf(c_8471,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_6021]) ).
tcf(c_8473,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_6021]) ).
tcf(c_8474,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK0,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_6021]) ).
tcf(c_8497,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X1)
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_2771]) ).
tcf(c_8498,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK0,X0,sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK4),sK4)) = head_of(sK7(sK0,X0,sK4)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_2881,c_2771]) ).
tcf(c_8499,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK0,X0,sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK4),sK4)) = head_of(sK7(sK0,X0,sK4)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(light_normalisation,[status(thm)],[c_8498,c_2047]) ).
tcf(c_8523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_6021]) ).
tcf(c_8524,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4119]) ).
tcf(c_8525,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4118]) ).
tcf(c_8526,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_6020]) ).
tcf(c_8527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5995]) ).
tcf(c_8528,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5994]) ).
tcf(c_8529,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5969]) ).
tcf(c_8530,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4117]) ).
tcf(c_8531,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5968]) ).
tcf(c_8532,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5438]) ).
tcf(c_8533,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5437]) ).
tcf(c_8534,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5412]) ).
tcf(c_8535,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5411]) ).
tcf(c_8536,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5286]) ).
tcf(c_8537,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_5285]) ).
tcf(c_8538,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4880]) ).
tcf(c_8539,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),tail_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4879]) ).
tcf(c_8540,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4852]) ).
tcf(c_8541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK4))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4851]) ).
tcf(c_8542,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3966]) ).
tcf(c_8543,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3922]) ).
tcf(c_8544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3614]) ).
tcf(c_8545,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3531]) ).
tcf(c_8546,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2719]) ).
tcf(c_8547,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2718]) ).
tcf(c_8548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2697]) ).
tcf(c_8549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3488]) ).
tcf(c_8550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3453]) ).
tcf(c_8551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2696]) ).
tcf(c_8552,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2673]) ).
tcf(c_8553,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2672]) ).
tcf(c_8554,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2648]) ).
tcf(c_8555,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK6(X2,X3,X4),X0,X1)),head_of(sK3))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_2647]) ).
tcf(c_8556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3411]) ).
tcf(c_8557,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3096]) ).
tcf(c_8854,plain,
! [X0: $i] :
( edge(sK5(head_of(sK3),X0))
| ( head_of(sK3) = X0 )
| ~ vertex(X0)
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_8865,plain,
! [X0: $i] :
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK3) != head_of(X0) )
| ( head_of(sK3) != head_of(X0) ) ),
inference(instantiation,[status(thm)],[c_4459]) ).
tcf(c_8866,plain,
! [X0: $i] :
( ( head_of(sK3) = head_of(X0) )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_9021,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(X0) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3094]) ).
tcf(c_9024,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3094]) ).
tcf(c_9025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( head_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3094]) ).
tcf(c_9054,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_8240]) ).
tcf(c_9055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_8240]) ).
tcf(c_9056,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9054,c_50]) ).
tcf(c_9090,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_8355]) ).
tcf(c_9091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_8355]) ).
tcf(c_9092,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9090,c_50]) ).
tcf(c_9113,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4120]) ).
tcf(c_9116,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4120]) ).
tcf(c_9117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4120]) ).
tcf(c_9191,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4121]) ).
tcf(c_9193,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK4))) = tail_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4121]) ).
tcf(c_9194,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4121]) ).
tcf(c_9195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4121]) ).
tcf(c_9237,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),sK4)
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) )
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_2285,c_8499]) ).
tcf(c_9253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_6109]) ).
tcf(c_9254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_6109]) ).
tcf(c_9260,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_6109]) ).
tcf(c_9261,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_6109]) ).
tcf(c_9262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_6109]) ).
tcf(c_9266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5414,c_6109]) ).
tcf(c_9267,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4854,c_6109]) ).
tcf(c_9268,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_6024,c_6109]) ).
tcf(c_9269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5972,c_6109]) ).
tcf(c_9271,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK3,sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(equality_resolution,[status(thm)],[c_6109]) ).
tcf(c_9326,plain,
! [X0: $i] :
( edge(sK5(X0,head_of(sK3)))
| ( X0 = head_of(sK3) )
| ~ vertex(X0)
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_9338,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_9376,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2879,c_2285,c_2879]) ).
tcf(c_9390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| precedes(X5,sK7(sK0,X0,X1),sK0)
| ~ on_path(X5,sK0)
| ~ on_path(X4,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X5,X4)
| ~ sequential(X4,X0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_105]) ).
tcf(c_9391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK0)
| ~ on_path(X1,sK0)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2))
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_9376,c_79]) ).
tcf(c_9392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(X4,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X4,X0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_78]) ).
tcf(c_9394,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK0,X0,X1))
| ( head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) = tail_of(sK7(sK0,X0,X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_2771]) ).
tcf(c_9395,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_6914]) ).
tcf(c_9396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X3,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X3)
| ~ sequential(X0,X1)
| ~ path(X4,X5,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X3,sK7(sK0,X1,X2))
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_9376,c_6165]) ).
tcf(c_9397,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_3007]) ).
tcf(c_9398,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_9376,c_2359]) ).
tcf(c_9399,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,X2,sK7(sK0,X0,X1))) = head_of(X2) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_2181]) ).
tcf(c_9400,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_2192]) ).
tcf(c_9401,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ precedes(sK7(sK0,X0,X1),X2,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_2100]) ).
tcf(c_9404,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_9376,c_2921]) ).
tcf(c_9424,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9404,c_51]) ).
tcf(c_9563,plain,
! [X0: $i] :
( ( head_of(sK4) = head_of(X0) )
| ( sK4 != X0 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_9568,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_9424,c_2285,c_9424]) ).
tcf(c_9580,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_9568]) ).
tcf(c_9602,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X2,X3)
| sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X2,X3,sK0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X2,X3),sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ sequential(sK7(sK0,X2,X3),X0)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_9376,c_9401]) ).
tcf(c_9629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ on_path(X2,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,X2)),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_2309,c_2774]) ).
tcf(c_9630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK0,X1,sK4))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK4)),sK7(sK0,X1,sK4))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK4))) )
| ~ precedes(X1,sK4,sK0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK4),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK4)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK3)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_2774]) ).
tcf(c_9631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK0,X2,X3))
| sequential(X0,sK7(sK0,X1,sK7(sK0,X2,X3)))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),sK7(sK0,X1,sK7(sK0,X2,X3)))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3)))) )
| ~ on_path(X2,sK0)
| ~ path(X4,X5,sK0)
| ~ precedes(X2,X3,sK0)
| ~ precedes(X1,sK7(sK0,X2,X3),sK0)
| ~ precedes(X0,sK7(sK0,X1,sK7(sK0,X2,X3)),sK0)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),X2)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),sK7(sK0,X2,X3)) ),
inference(superposition,[status(thm)],[c_9376,c_2774]) ).
tcf(c_9675,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = tail_of(X0) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3095]) ).
tcf(c_9678,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3095]) ).
tcf(c_9679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3095]) ).
tcf(c_9712,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = head_of(X0) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3409]) ).
tcf(c_9714,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(head_of(X0),tail_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3409]) ).
tcf(c_9715,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3409]) ).
tcf(c_9716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( head_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3409]) ).
tcf(c_9750,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(X0) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3410]) ).
tcf(c_9752,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3410]) ).
tcf(c_9753,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3410]) ).
tcf(c_9754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3410]) ).
tcf(c_9784,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_9271]) ).
tcf(c_9785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_9271]) ).
tcf(c_9786,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9784,c_50]) ).
tcf(c_9834,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4122]) ).
tcf(c_9837,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4122]) ).
tcf(c_9838,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4122]) ).
tcf(c_9893,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(X0,X1)))) = head_of(sK4) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4123]) ).
tcf(c_9895,plain,
( ( head_of(sK4) = tail_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4123]) ).
tcf(c_9896,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4123]) ).
tcf(c_9897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4123]) ).
tcf(c_9927,plain,
! [X0: $i] :
( ~ precedes(X0,sK3,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(sK4,X0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) ) ),
inference(global_subsumption_just,[status(thm)],[c_9580,c_52,c_554,c_9580]) ).
tcf(c_9928,plain,
! [X0: $i] :
( ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,sK3,sK0) ),
inference(renaming,[status(thm)],[c_9927]) ).
tcf(c_9939,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK3))
| ~ on_path(sK7(sK0,X0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_2228,c_9928]) ).
tcf(c_9955,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK0,X1,sK4))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK4)),sK7(sK0,X1,sK4))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK4))) )
| ~ precedes(X1,sK4,sK0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK4),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK4)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9630,c_2285]) ).
tcf(c_9980,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_6248,c_2285,c_6248]) ).
tcf(c_10002,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6335,c_2285]) ).
tcf(c_10022,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X2)
| sequential(X1,sK7(sK0,X0,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X0,X2)),sK7(sK0,X0,X2))) = head_of(sK7(sK0,X1,sK7(sK0,X0,X2))) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X2,sK0)
| ~ precedes(X1,sK7(sK0,X0,X2),sK0)
| ~ on_path(sK7(sK0,X1,sK7(sK0,X0,X2)),sK0)
| ~ sequential(X0,sK7(sK0,X1,sK7(sK0,X0,X2))) ),
inference(superposition,[status(thm)],[c_2247,c_10002]) ).
tcf(c_10031,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_9398,c_2285,c_9398]) ).
tcf(c_10045,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X2)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ precedes(sK7(sK0,X0,X1),X2,sK0)
| ~ on_path(sK7(sK0,sK7(sK0,X0,X1),X2),sK0)
| ~ sequential(sK7(sK0,sK7(sK0,X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_2134,c_10031]) ).
tcf(c_10046,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK0,X3,X4),X5)
| ( X0 = X1 )
| ~ on_path(X3,sK0)
| ~ precedes(X3,X4,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(sK7(sK0,X3,X4),X5,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK0,X3,X4),X5),sK0)
| ~ sequential(sK7(sK6(X0,X1,X2),sK7(sK0,X3,X4),X5),X3) ),
inference(superposition,[status(thm)],[c_2163,c_10031]) ).
tcf(c_10079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ on_path(X2,sK0)
| ~ sequential(X2,X1)
| ~ path(X3,X4,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2247,c_6185]) ).
tcf(c_10097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| precedes(sK7(sK0,X0,sK7(sK0,X1,X2)),X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2775,c_2285]) ).
tcf(c_10119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2774,c_10097]) ).
tcf(c_10127,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| precedes(sK7(sK0,X0,sK7(sK0,X1,X2)),X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_2065,c_10097]) ).
tcf(c_10150,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3451]) ).
tcf(c_10153,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3451]) ).
tcf(c_10154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3451]) ).
tcf(c_10214,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3452]) ).
tcf(c_10217,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3452]) ).
tcf(c_10218,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3452]) ).
tcf(c_10251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3486]) ).
tcf(c_10253,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(head_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( tail_of(sK5(head_of(X0),tail_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3486]) ).
tcf(c_10254,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3486]) ).
tcf(c_10255,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3486]) ).
tcf(c_10289,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3487]) ).
tcf(c_10291,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3487]) ).
tcf(c_10292,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3487]) ).
tcf(c_10293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3487]) ).
tcf(c_10351,plain,
! [X0: $i] :
( edge(sK5(X0,head_of(sK4)))
| ( X0 = head_of(sK4) )
| ~ vertex(X0)
| ~ vertex(head_of(sK4)) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_10378,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(X0,X1)))) = head_of(sK4) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4124]) ).
tcf(c_10381,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK0,X0,X1)))) = head_of(sK4) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4124]) ).
tcf(c_10382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK4) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4124]) ).
tcf(c_10410,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4463]) ).
tcf(c_10412,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2052,c_4463]) ).
tcf(c_10413,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4463]) ).
tcf(c_10414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4463]) ).
tcf(c_10444,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4464]) ).
tcf(c_10447,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4464]) ).
tcf(c_10448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4464]) ).
tcf(c_10476,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4465]) ).
tcf(c_10478,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_4465]) ).
tcf(c_10479,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4465]) ).
tcf(c_10480,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4465]) ).
tcf(c_10514,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| precedes(X0,X3,sK0)
| sequential(X1,sK7(sK0,X2,X3))
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X2,X3)),sK7(sK0,X2,X3))) = head_of(sK7(sK0,X1,sK7(sK0,X2,X3))) )
| ~ on_path(X0,sK0)
| ~ path(X4,X5,sK0)
| ~ precedes(X2,X3,sK0)
| ~ precedes(X1,sK7(sK0,X2,X3),sK0)
| ~ sequential(X0,sK7(sK0,X1,sK7(sK0,X2,X3))) ),
inference(superposition,[status(thm)],[c_10127,c_105]) ).
tcf(c_10515,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK0,X2,X3))
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X2,X3)),sK7(sK0,X2,X3))) = head_of(sK7(sK0,X1,sK7(sK0,X2,X3))) )
| ~ sequential(X0,X3)
| ~ path(X4,X5,sK0)
| ~ precedes(X2,X3,sK0)
| ~ precedes(X0,X3,sK0)
| ~ precedes(X1,sK7(sK0,X2,X3),sK0)
| ~ sequential(X0,sK7(sK0,X1,sK7(sK0,X2,X3))) ),
inference(superposition,[status(thm)],[c_10127,c_79]) ).
tcf(c_10516,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X2,sK0)
| sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_78]) ).
tcf(c_10517,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| on_path(sK7(sK0,X0,sK7(sK0,X1,X2)),sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_77]) ).
tcf(c_10518,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ( head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) = tail_of(X2) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_2771]) ).
tcf(c_10519,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2),X2)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_6914]) ).
tcf(c_10520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ on_path(X3,sK0)
| ~ sequential(X3,X2)
| ~ path(X4,X5,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X3)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_10127,c_6165]) ).
tcf(c_10521,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_3007]) ).
tcf(c_10522,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X1,sK7(sK0,X2,X0))
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X2,X0)),sK7(sK0,X2,X0))) = head_of(sK7(sK0,X1,sK7(sK0,X2,X0))) )
| ~ on_path(X0,sK0)
| ~ precedes(X2,X0,sK0)
| ~ precedes(X1,sK7(sK0,X2,X0),sK0)
| ~ on_path(sK7(sK0,X1,sK7(sK0,X2,X0)),sK0)
| ~ sequential(X0,sK7(sK0,X1,sK7(sK0,X2,X0))) ),
inference(superposition,[status(thm)],[c_10127,c_2359]) ).
tcf(c_10523,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_2181]) ).
tcf(c_10524,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| edge(sK7(sK0,X0,sK7(sK0,X1,X2)))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_2192]) ).
tcf(c_10525,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X1,sK7(sK0,X2,X0))
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X2,X0)),sK7(sK0,X2,X0))) = head_of(sK7(sK0,X1,sK7(sK0,X2,X0))) )
| ~ precedes(X2,X0,sK0)
| ~ precedes(X1,sK7(sK0,X2,X0),sK0)
| ~ precedes(X0,sK7(sK0,X1,sK7(sK0,X2,X0)),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_2100]) ).
tcf(c_10526,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK0,X1,sK3))
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK7(sK0,X1,sK3))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK3))) )
| ~ precedes(X1,sK3,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK3),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK7(sK0,X1,sK3)))
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_9928]) ).
tcf(c_10527,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK0,X1,sK3))
| sequential(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK7(sK0,X1,sK3))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK3))) )
| ~ precedes(X1,sK3,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK3),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK4)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_3277]) ).
tcf(c_10528,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK0,X1,sK4))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK4)),sK7(sK0,X1,sK4))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK4))) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ precedes(X1,sK4,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK4),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),sK4)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK4)),X2) ),
inference(superposition,[status(thm)],[c_10127,c_3061]) ).
tcf(c_10529,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_9401]) ).
tcf(c_10764,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK0,X0,sK3),sK4)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK4)) = head_of(sK7(sK0,X0,sK3)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ precedes(X0,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_3132]) ).
tcf(c_10779,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X2),X2)) = head_of(sK7(sK0,X1,X2)) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2880,c_2285]) ).
tcf(c_10802,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| precedes(sK7(sK0,X0,sK7(sK0,X1,X2)),X2,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X2),X2)) = head_of(sK7(sK0,X1,X2)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ~ on_path(X2,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,X2)),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_10779]) ).
tcf(c_10836,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3529]) ).
tcf(c_10839,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3529]) ).
tcf(c_10840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( head_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( head_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3529]) ).
tcf(c_10894,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3530]) ).
tcf(c_10897,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3530]) ).
tcf(c_10898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3530]) ).
tcf(c_10931,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3612]) ).
tcf(c_10933,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK4) )
| ( head_of(sK5(head_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(head_of(X0),tail_of(sK4))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3612]) ).
tcf(c_10934,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3612]) ).
tcf(c_10935,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( head_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(X5) )
| ( head_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3612]) ).
tcf(c_10996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3613]) ).
tcf(c_10998,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK4) )
| ( head_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3613]) ).
tcf(c_10999,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3613]) ).
tcf(c_11000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(X5) )
| ( head_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3613]) ).
tcf(c_11032,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4466]) ).
tcf(c_11035,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4466]) ).
tcf(c_11036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4466]) ).
tcf(c_11064,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4467]) ).
tcf(c_11066,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_4467]) ).
tcf(c_11067,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4467]) ).
tcf(c_11068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4467]) ).
tcf(c_11120,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = head_of(sK5(X0,X1)) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4468]) ).
tcf(c_11123,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4468]) ).
tcf(c_11124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4468]) ).
tcf(c_11200,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(X0,X1)))) = tail_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4469]) ).
tcf(c_11202,plain,
( ( tail_of(sK3) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK4))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2052,c_4469]) ).
tcf(c_11203,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4469]) ).
tcf(c_11204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4469]) ).
tcf(c_11254,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_6922,c_63,c_6922]) ).
tcf(c_11255,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_11254]) ).
tcf(c_11262,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) )
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_11255]) ).
tcf(c_11263,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_11255]) ).
tcf(c_11264,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2),X2),X2)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2),X2)) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_11255]) ).
tcf(c_11266,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_11255]) ).
tcf(c_11348,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2309,c_7207]) ).
tcf(c_11349,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2308,c_7207]) ).
tcf(c_11385,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2309,c_7208]) ).
tcf(c_11386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2308,c_7208]) ).
tcf(c_11410,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2309,c_7667]) ).
tcf(c_11411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2308,c_7667]) ).
tcf(c_11435,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2309,c_7668]) ).
tcf(c_11436,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2308,c_7668]) ).
tcf(c_11486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| precedes(X8,sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ( X0 = X1 )
| ~ on_path(X8,sK0)
| ~ on_path(X7,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X8,X7)
| ~ sequential(X7,X3)
| ~ path(X5,X6,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_105]) ).
tcf(c_11487,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( sequential(X4,X5)
| shortest_path(X1,X2,X3)
| ( X1 = X2 )
| ~ on_path(X8,sK0)
| ~ on_path(X4,sK0)
| ~ sequential(X8,X4)
| ~ sequential(X0,X8)
| ~ path(X6,X7,sK0)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK0)
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_79]) ).
tcf(c_11490,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| edge(sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_11255]) ).
tcf(c_11491,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(X5,sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( head_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) = tail_of(sK7(sK6(X0,X1,X2),X3,X4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_2771]) ).
tcf(c_11492,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| edge(sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_6914]) ).
tcf(c_11493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i] :
( sequential(X4,X5)
| shortest_path(X1,X2,X3)
| ( X1 = X2 )
| ~ on_path(X6,sK0)
| ~ on_path(X4,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X6)
| ~ sequential(X0,X4)
| ~ path(X7,X8,sK0)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK0)
| ~ sequential(X6,sK7(sK6(X1,X2,X3),X4,X5))
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2965,c_6165]) ).
tcf(c_11494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| edge(sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_3007]) ).
tcf(c_11495,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2965,c_2359]) ).
tcf(c_11496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(X5,sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) = head_of(X5) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_2181]) ).
tcf(c_11497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( edge(X5)
| sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_2192]) ).
tcf(c_11498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ~ precedes(sK7(sK6(X0,X1,X2),X3,X4),X5,sK0) ),
inference(superposition,[status(thm)],[c_2965,c_2100]) ).
tcf(c_11500,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X3)
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_2921]) ).
tcf(c_11501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X5,X6)
| sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ precedes(X5,X6,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK7(sK0,X5,X6),sK0)
| ~ sequential(sK7(sK0,X5,X6),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2965,c_9401]) ).
tcf(c_11512,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ sequential(sK4,X3)
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11500,c_51]) ).
tcf(c_11693,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ( head_of(sK5(head_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3920]) ).
tcf(c_11696,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3920]) ).
tcf(c_11697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3920]) ).
tcf(c_11746,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( head_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(X1,X2)))) = head_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3921]) ).
tcf(c_11749,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK0,X0,X1)))) = head_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3921]) ).
tcf(c_11750,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(X5),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3921]) ).
tcf(c_11800,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3964]) ).
tcf(c_11802,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(head_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(head_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3964]) ).
tcf(c_11803,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3964]) ).
tcf(c_11804,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = head_of(X5) )
| ( tail_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(head_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3964]) ).
tcf(c_11838,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( tail_of(sK5(X1,X2)) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(X1,X2)))) = tail_of(sK5(X1,X2)) )
| ~ vertex(X2)
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_100,c_3965]) ).
tcf(c_11840,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK4) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ( head_of(sK5(tail_of(X0),tail_of(sK4))) = tail_of(sK4) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2052,c_3965]) ).
tcf(c_11841,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK0,X0,X1)))) = tail_of(sK7(sK0,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_3965]) ).
tcf(c_11842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(X5) )
| ( tail_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ( head_of(sK5(tail_of(X5),tail_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ edge(X5)
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_3965]) ).
tcf(c_11964,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(X0,X1)))) = tail_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_100,c_4470]) ).
tcf(c_11967,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK0,X0,X1)))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2180,c_4470]) ).
tcf(c_11968,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| ( X2 = X3 )
| ( head_of(sK7(sK6(X2,X3,X4),X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK6(X2,X3,X4),X0,X1)))) = tail_of(sK3) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2967,c_4470]) ).
tcf(c_11999,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_3331,c_3371]) ).
tcf(c_12003,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_3371]) ).
tcf(c_12007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_3371]) ).
tcf(c_12049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_3375]) ).
tcf(c_12053,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_3375]) ).
tcf(c_12110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i,X7: $i,X8: $i,X9: $i] :
( sequential(X5,X9)
| sequential(X3,X4)
| shortest_path(X6,X7,X8)
| shortest_path(X0,X1,X2)
| ( X6 = X7 )
| ( X0 = X1 )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ path(X6,X7,X8)
| ~ path(X0,X1,X2)
| ~ precedes(X5,X9,sK6(X6,X7,X8))
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X6,X7,X8),X5,X9),sK0)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0)
| ~ sequential(sK7(sK6(X6,X7,X8),X5,X9),X3)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2965,c_11498]) ).
tcf(c_12129,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_3746,c_2042,c_2067,c_2906,c_2905,c_3746,c_4455]) ).
tcf(c_12148,plain,
( sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_12129]) ).
tcf(c_12149,plain,
( sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12148,c_2042]) ).
tcf(c_12159,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_12149,c_6309]) ).
tcf(c_12160,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_6222]) ).
tcf(c_12161,plain,
( precedes(sK3,sK4,sK0)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_3218]) ).
tcf(c_12162,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_3157]) ).
tcf(c_12163,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),tail_of(sK3)),sK0)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_2853]) ).
tcf(c_12164,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_2414]) ).
tcf(c_12165,plain,
( edge(sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12149,c_63]) ).
tcf(c_12171,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12164,c_50]) ).
tcf(c_12178,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),tail_of(sK3)),sK0)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12163,c_50]) ).
tcf(c_12185,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12159,c_50]) ).
tcf(c_12218,plain,
edge(sK5(head_of(sK3),tail_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_12165,c_2042,c_2067,c_2906,c_2905,c_4455]) ).
tcf(c_12220,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3965]) ).
tcf(c_12221,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3964]) ).
tcf(c_12222,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3921]) ).
tcf(c_12223,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3920]) ).
tcf(c_12224,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3613]) ).
tcf(c_12225,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3612]) ).
tcf(c_12226,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3530]) ).
tcf(c_12227,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3529]) ).
tcf(c_12228,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3487]) ).
tcf(c_12229,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3486]) ).
tcf(c_12230,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3452]) ).
tcf(c_12231,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3451]) ).
tcf(c_12232,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3410]) ).
tcf(c_12233,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3409]) ).
tcf(c_12234,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3095]) ).
tcf(c_12235,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_12218,c_3094]) ).
tcf(c_12236,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_4470]) ).
tcf(c_12237,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_4469]) ).
tcf(c_12238,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4468]) ).
tcf(c_12239,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4467]) ).
tcf(c_12240,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4466]) ).
tcf(c_12241,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4465]) ).
tcf(c_12242,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4464]) ).
tcf(c_12243,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4463]) ).
tcf(c_12244,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12218,c_4124]) ).
tcf(c_12245,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12218,c_4123]) ).
tcf(c_12246,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4122]) ).
tcf(c_12247,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4121]) ).
tcf(c_12248,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4120]) ).
tcf(c_12249,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_6021]) ).
tcf(c_12250,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4119]) ).
tcf(c_12251,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4118]) ).
tcf(c_12252,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_6020]) ).
tcf(c_12253,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12218,c_5995]) ).
tcf(c_12254,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12218,c_5994]) ).
tcf(c_12255,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5969]) ).
tcf(c_12256,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4117]) ).
tcf(c_12257,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5968]) ).
tcf(c_12258,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5438]) ).
tcf(c_12259,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5437]) ).
tcf(c_12260,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5412]) ).
tcf(c_12261,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5411]) ).
tcf(c_12262,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5286]) ).
tcf(c_12263,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_5285]) ).
tcf(c_12264,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4880]) ).
tcf(c_12265,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4879]) ).
tcf(c_12266,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4852]) ).
tcf(c_12267,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_4851]) ).
tcf(c_12268,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3966]) ).
tcf(c_12269,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3922]) ).
tcf(c_12270,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3614]) ).
tcf(c_12271,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3531]) ).
tcf(c_12272,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_2719]) ).
tcf(c_12273,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_2718]) ).
tcf(c_12274,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2697]) ).
tcf(c_12275,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3488]) ).
tcf(c_12276,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_3453]) ).
tcf(c_12277,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2696]) ).
tcf(c_12278,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2673]) ).
tcf(c_12279,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2672]) ).
tcf(c_12280,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2648]) ).
tcf(c_12281,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12218,c_2647]) ).
tcf(c_12282,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_3411]) ).
tcf(c_12283,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12218,c_3096]) ).
tcf(c_12567,plain,
( ~ precedes(sK3,sK4,sK0)
| ~ shortest_path(sK1,sK2,sK0)
| ( tail_of(sK3) != tail_of(sK3) )
| ( head_of(sK4) != head_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_4353]) ).
tcf(c_12568,plain,
tail_of(sK3) = tail_of(sK3),
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_12837,plain,
( ( head_of(sK3) = head_of(sK3) )
| ( sK3 != sK3 ) ),
inference(instantiation,[status(thm)],[c_8866]) ).
tcf(c_12893,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_6818,c_2042,c_2052,c_2906,c_2952,c_6818,c_7189]) ).
tcf(c_12914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| sequential(sK7(sK6(X2,X3,X4),X0,X1),X1)
| ( X2 = X3 )
| ( tail_of(sK7(sK6(X2,X3,X4),sK7(sK6(X2,X3,X4),X0,X1),X1)) = head_of(sK7(sK6(X2,X3,X4),X0,X1)) )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_2227,c_2968]) ).
tcf(c_12932,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_4090]) ).
tcf(c_12933,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5014,c_4090]) ).
tcf(c_12940,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4019,c_4090]) ).
tcf(c_12941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_4090]) ).
tcf(c_12944,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5997,c_4090]) ).
tcf(c_12949,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4883,c_4090]) ).
tcf(c_12997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_4094]) ).
tcf(c_12998,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5014,c_4094]) ).
tcf(c_13004,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4145,c_4094]) ).
tcf(c_13006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_4094]) ).
tcf(c_13009,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5997,c_4094]) ).
tcf(c_13014,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4883,c_4094]) ).
tcf(c_13128,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_4296]) ).
tcf(c_13129,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5014,c_4296]) ).
tcf(c_13135,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4145,c_4296]) ).
tcf(c_13137,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_4296]) ).
tcf(c_13140,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5997,c_4296]) ).
tcf(c_13145,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4883,c_4296]) ).
tcf(c_13250,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_12171,c_2042,c_2067,c_2906,c_2905,c_4455,c_5439,c_8109,c_12171]) ).
tcf(c_13290,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5293,c_4371]) ).
tcf(c_13291,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_4371]) ).
tcf(c_13292,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4148,c_4371]) ).
tcf(c_13294,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5288,c_4371]) ).
tcf(c_13295,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5441,c_4371]) ).
tcf(c_13296,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13291,c_12218]) ).
tcf(c_13342,plain,
( ( head_of(sK4) = head_of(sK3) )
| ( sK4 != sK3 ) ),
inference(instantiation,[status(thm)],[c_9338]) ).
tcf(c_13367,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5497,c_2042,c_2067,c_2906,c_2905,c_4455,c_5497]) ).
tcf(c_13380,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK3),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5293,c_13367]) ).
tcf(c_13382,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4148,c_13367]) ).
tcf(c_13383,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_13367]) ).
tcf(c_13384,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5288,c_13367]) ).
tcf(c_13385,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5441,c_13367]) ).
tcf(c_13447,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_6106,c_2042,c_2067,c_2906,c_2905,c_4455,c_6106]) ).
tcf(c_13460,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5293,c_13447]) ).
tcf(c_13462,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4148,c_13447]) ).
tcf(c_13463,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_13447]) ).
tcf(c_13464,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5288,c_13447]) ).
tcf(c_13465,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5441,c_13447]) ).
tcf(c_13500,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9939,c_2285]) ).
tcf(c_13513,plain,
( sequential(sK4,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK4,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,sK4,sK3),sK3)) )
| ~ precedes(sK4,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2134,c_13500]) ).
tcf(c_13514,plain,
( ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK4,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,sK4,sK3),sK3)) )
| ~ precedes(sK4,sK3,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13513,c_2455]) ).
tcf(c_13517,plain,
~ precedes(sK4,sK3,sK0),
inference(global_subsumption_just,[status(thm)],[c_13514,c_52,c_51,c_50,c_53,c_656,c_4355,c_7116]) ).
tcf(c_13527,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_2342]) ).
tcf(c_13528,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_61]) ).
tcf(c_13529,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_4296]) ).
tcf(c_13530,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_4094]) ).
tcf(c_13531,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_4090]) ).
tcf(c_13534,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12236,c_6109]) ).
tcf(c_13535,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12236,c_6105]) ).
tcf(c_13538,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12236,c_4374]) ).
tcf(c_13539,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12236,c_4370]) ).
tcf(c_13544,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_2342]) ).
tcf(c_13637,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_4325]) ).
tcf(c_13640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_4325]) ).
tcf(c_13641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_4325]) ).
tcf(c_13642,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_4325]) ).
tcf(c_13643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_4325]) ).
tcf(c_13644,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_4325]) ).
tcf(c_13645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_4325]) ).
tcf(c_13646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_4325]) ).
tcf(c_13647,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_4325]) ).
tcf(c_13648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_4325]) ).
tcf(c_13649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_4325]) ).
tcf(c_13650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_4325]) ).
tcf(c_13739,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_4326]) ).
tcf(c_13740,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_4326]) ).
tcf(c_13741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_4326]) ).
tcf(c_13742,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_4326]) ).
tcf(c_13743,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_4326]) ).
tcf(c_13747,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_4326]) ).
tcf(c_13749,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_4326]) ).
tcf(c_13751,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5414,c_4326]) ).
tcf(c_13752,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4854,c_4326]) ).
tcf(c_13753,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6024,c_4326]) ).
tcf(c_13754,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5972,c_4326]) ).
tcf(c_13756,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_4326]) ).
tcf(c_13757,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2047,c_4326]) ).
tcf(c_13758,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_4326]) ).
tcf(c_13759,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_4326]) ).
tcf(c_13760,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_4326]) ).
tcf(c_13761,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_4326]) ).
tcf(c_13762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_4326]) ).
tcf(c_13763,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_4326]) ).
tcf(c_13764,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_4326]) ).
tcf(c_13767,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_4326]) ).
tcf(c_13768,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_4326]) ).
tcf(c_13769,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_4326]) ).
tcf(c_13770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_4326]) ).
tcf(c_13771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5414,c_4326]) ).
tcf(c_13772,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4854,c_4326]) ).
tcf(c_13773,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6024,c_4326]) ).
tcf(c_13774,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5972,c_4326]) ).
tcf(c_13775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_4326]) ).
tcf(c_13776,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_4326]) ).
tcf(c_13777,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_4326]) ).
tcf(c_14050,plain,
( ( head_of(sK4) = head_of(sK4) )
| ( sK4 != sK4 ) ),
inference(instantiation,[status(thm)],[c_9563]) ).
tcf(c_14090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_5109]) ).
tcf(c_14092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_5109]) ).
tcf(c_14093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_5109]) ).
tcf(c_14094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_5109]) ).
tcf(c_14095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_5109]) ).
tcf(c_14096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_5109]) ).
tcf(c_14168,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_4300]) ).
tcf(c_14169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5014,c_4300]) ).
tcf(c_14177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_4300]) ).
tcf(c_14180,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5997,c_4300]) ).
tcf(c_14185,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4883,c_4300]) ).
tcf(c_14186,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_4300]) ).
tcf(c_14231,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4151,c_4418]) ).
tcf(c_14235,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_4418]) ).
tcf(c_14264,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_11263,c_63,c_11263]) ).
tcf(c_14265,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_14264]) ).
tcf(c_14272,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1)) )
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2309,c_14265]) ).
tcf(c_14273,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_14265]) ).
tcf(c_14274,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2),X2),X2),X2)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2),X2),X2)) )
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_14265]) ).
tcf(c_14276,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_9376,c_14265]) ).
tcf(c_14277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| edge(sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_14265]) ).
tcf(c_14312,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_3242,c_2285,c_3242]) ).
tcf(c_14326,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| precedes(X0,sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X2),X2)) = head_of(sK7(sK0,X1,X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_14312,c_105]) ).
tcf(c_14327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| ( tail_of(sK7(sK0,sK7(sK0,X1,X2),X2)) = head_of(sK7(sK0,X1,X2)) )
| ~ sequential(X2,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X2,sK0)
| ~ precedes(X0,sK4,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_14312,c_79]) ).
tcf(c_14329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| on_path(sK7(sK0,X0,X1),sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_14312,c_77]) ).
tcf(c_14332,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),sK4)
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_14312,c_2771]) ).
tcf(c_14334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X2,sK4)
| ~ sequential(X1,sK3)
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14312,c_6165]) ).
tcf(c_14336,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ on_path(sK4,sK0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK4,sK7(sK0,X0,X1))
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_14312,c_2359]) ).
tcf(c_14337,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),sK4)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK7(sK0,X0,X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_14312,c_2181]) ).
tcf(c_14338,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_14312,c_2192]) ).
tcf(c_14339,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ precedes(sK4,sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_14312,c_2100]) ).
tcf(c_14340,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X2,sK3)
| ~ sequential(X1,sK3)
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ sequential(sK7(sK0,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_14312,c_3061]) ).
tcf(c_14341,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_14312,c_9401]) ).
tcf(c_14361,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(sK4,X0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14341,c_51]) ).
tcf(c_14369,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK4,sK7(sK0,X0,X1))
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14336,c_51]) ).
tcf(c_14421,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),sK4)
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(light_normalisation,[status(thm)],[c_14332,c_2047]) ).
tcf(c_14517,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK4,sK7(sK0,X0,X1))
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2228,c_14361]) ).
tcf(c_14518,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK7(sK0,X1,X2)))
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,X2)),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_14361]) ).
tcf(c_14520,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) )
| ~ sequential(sK4,X2)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_9376,c_14361]) ).
tcf(c_14521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(X5,sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( tail_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ sequential(sK4,X5)
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_14361]) ).
tcf(c_14565,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK4,sK7(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_14369,c_2285,c_14369]) ).
tcf(c_14594,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK4,sK7(sK0,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_14517,c_2285,c_14517]) ).
tcf(c_14611,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK0,X0,X1))
| ( tail_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) )
| ~ sequential(sK4,X2)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_14520,c_2285,c_14520]) ).
tcf(c_14631,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK3)
| sequential(X1,sK7(sK0,X0,sK3))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ( tail_of(sK7(sK0,sK7(sK0,X1,sK7(sK0,X0,sK3)),sK7(sK0,X0,sK3))) = head_of(sK7(sK0,X1,sK7(sK0,X0,sK3))) )
| ~ sequential(sK4,X1)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ precedes(X0,sK3,sK0) ),
inference(superposition,[status(thm)],[c_2247,c_14611]) ).
tcf(c_14649,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_12237]) ).
tcf(c_14650,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_4326]) ).
tcf(c_14651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_2342]) ).
tcf(c_14652,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_61]) ).
tcf(c_14654,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_4300]) ).
tcf(c_14655,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_5109]) ).
tcf(c_14656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_4326]) ).
tcf(c_14657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_4325]) ).
tcf(c_14658,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_4296]) ).
tcf(c_14659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_4094]) ).
tcf(c_14660,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_4090]) ).
tcf(c_14667,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12237,c_4374]) ).
tcf(c_14668,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12237,c_4370]) ).
tcf(c_14673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_2342]) ).
tcf(c_14839,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(sK4) != tail_of(sK3) )
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_5110]) ).
tcf(c_14840,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5110]) ).
tcf(c_14841,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5110]) ).
tcf(c_14842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_5110]) ).
tcf(c_14844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_5110]) ).
tcf(c_14845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_5110]) ).
tcf(c_14846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_5110]) ).
tcf(c_14847,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5110]) ).
tcf(c_14848,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5110]) ).
tcf(c_14852,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5997,c_5110]) ).
tcf(c_14853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_5110]) ).
tcf(c_14856,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_5110]) ).
tcf(c_14857,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4883,c_5110]) ).
tcf(c_14860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_5110]) ).
tcf(c_14861,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5110]) ).
tcf(c_14862,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5110]) ).
tcf(c_14863,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_5110]) ).
tcf(c_14864,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_5110]) ).
tcf(c_14865,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_5110]) ).
tcf(c_14866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_5110]) ).
tcf(c_14867,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_5110]) ).
tcf(c_14868,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5110]) ).
tcf(c_14869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5110]) ).
tcf(c_14871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_5110]) ).
tcf(c_14873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5997,c_5110]) ).
tcf(c_14874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_5110]) ).
tcf(c_14875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_5110]) ).
tcf(c_14876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_5110]) ).
tcf(c_14877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_5110]) ).
tcf(c_14878,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4883,c_5110]) ).
tcf(c_14879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_5110]) ).
tcf(c_14880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_5110]) ).
tcf(c_14881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_5110]) ).
tcf(c_15195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_5326]) ).
tcf(c_15196,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_5326]) ).
tcf(c_15197,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_5326]) ).
tcf(c_15198,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_5326]) ).
tcf(c_15199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_5326]) ).
tcf(c_15200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_5326]) ).
tcf(c_15201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_5326]) ).
tcf(c_15202,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_5326]) ).
tcf(c_15203,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_5326]) ).
tcf(c_15204,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_5326]) ).
tcf(c_15205,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_5326]) ).
tcf(c_15206,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_5326]) ).
tcf(c_15207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_5326]) ).
tcf(c_15208,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_5326]) ).
tcf(c_15209,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_5326]) ).
tcf(c_15210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_5326]) ).
tcf(c_15211,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_5326]) ).
tcf(c_15212,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_5326]) ).
tcf(c_15213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_5326]) ).
tcf(c_15366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_5327]) ).
tcf(c_15367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_5327]) ).
tcf(c_15370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_5327]) ).
tcf(c_15372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_5327]) ).
tcf(c_15374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_5327]) ).
tcf(c_15376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5414,c_5327]) ).
tcf(c_15377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4854,c_5327]) ).
tcf(c_15378,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6024,c_5327]) ).
tcf(c_15379,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5972,c_5327]) ).
tcf(c_15381,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_5327]) ).
tcf(c_15382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_5327]) ).
tcf(c_15383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2047,c_5327]) ).
tcf(c_15386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_5327]) ).
tcf(c_15387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_5327]) ).
tcf(c_15388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_5327]) ).
tcf(c_15389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_5327]) ).
tcf(c_15390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_5327]) ).
tcf(c_15391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_5327]) ).
tcf(c_15392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_5327]) ).
tcf(c_15393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_5327]) ).
tcf(c_15394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_5327]) ).
tcf(c_15395,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_5327]) ).
tcf(c_15396,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_5327]) ).
tcf(c_15397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5414,c_5327]) ).
tcf(c_15398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4854,c_5327]) ).
tcf(c_15399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6024,c_5327]) ).
tcf(c_15400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5972,c_5327]) ).
tcf(c_15401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_5327]) ).
tcf(c_15402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_5327]) ).
tcf(c_15403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_5327]) ).
tcf(c_15404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_5327]) ).
tcf(c_15683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_5557]) ).
tcf(c_15684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_5557]) ).
tcf(c_15685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_5557]) ).
tcf(c_15686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_5557]) ).
tcf(c_15687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_5557]) ).
tcf(c_15688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_5557]) ).
tcf(c_15689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_5557]) ).
tcf(c_15690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5997,c_5557]) ).
tcf(c_15691,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5414,c_5557]) ).
tcf(c_15692,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4854,c_5557]) ).
tcf(c_15693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6024,c_5557]) ).
tcf(c_15694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5972,c_5557]) ).
tcf(c_15695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK4) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4883,c_5557]) ).
tcf(c_15698,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_5557]) ).
tcf(c_15874,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_4422]) ).
tcf(c_15928,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_4678,c_4684]) ).
tcf(c_15970,plain,
head_of(sK4) != tail_of(sK3),
inference(global_subsumption_just,[status(thm)],[c_14839,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_5162,c_7116,c_12567,c_12568,c_13342]) ).
tcf(c_15972,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12893,c_15970]) ).
tcf(c_15973,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6719,c_15970]) ).
tcf(c_15974,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6024,c_15970]) ).
tcf(c_15975,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5997,c_15970]) ).
tcf(c_15976,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5972,c_15970]) ).
tcf(c_15977,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5441,c_15970]) ).
tcf(c_15978,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5414,c_15970]) ).
tcf(c_15979,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5288,c_15970]) ).
tcf(c_15980,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4883,c_15970]) ).
tcf(c_15981,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4854,c_15970]) ).
tcf(c_16003,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ precedes(X0,X1,sK0)
| ~ on_path(X1,sK0)
| ~ sequential(X1,sK3)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_14421,c_3284,c_14421]) ).
tcf(c_16004,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_16003]) ).
tcf(c_16020,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK0,X0,X1),X1)
| ( head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),X1)) = head_of(sK7(sK0,sK7(sK0,X0,X1),X1)) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,X1),X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2228,c_16004]) ).
tcf(c_16021,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ( head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),sK4)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_16004]) ).
tcf(c_16023,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK0,X0,X1))
| ( head_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X2,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,X2,sK7(sK0,X0,X1))) )
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_9376,c_16004]) ).
tcf(c_16024,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(X5,sK7(sK6(X0,X1,X2),X3,X4))
| ( X0 = X1 )
| ( head_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK0,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK0)
| ~ on_path(X3,sK0)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_16004]) ).
tcf(c_16107,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X2)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2))) = head_of(sK7(sK0,X0,sK7(sK0,X1,X2))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2),X2)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,X2)),X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK7(sK0,X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14518,c_2285]) ).
tcf(c_16138,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK4,sK7(sK0,X0,X1))
| sequential(sK7(sK0,sK4,sK7(sK0,X0,X1)),X1)
| ( tail_of(sK7(sK0,sK7(sK0,sK4,sK7(sK0,X0,X1)),sK7(sK0,X0,X1))) = head_of(sK7(sK0,sK4,sK7(sK0,X0,X1))) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,sK4,sK7(sK0,X0,X1)),X1),X1)) = head_of(sK7(sK0,sK7(sK0,sK4,sK7(sK0,X0,X1)),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ precedes(sK4,sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_16107]) ).
tcf(c_16152,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_5327]) ).
tcf(c_16153,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_5110]) ).
tcf(c_16154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_4326]) ).
tcf(c_16155,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_2342]) ).
tcf(c_16156,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_61]) ).
tcf(c_16160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_5557]) ).
tcf(c_16161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_5327]) ).
tcf(c_16162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_5326]) ).
tcf(c_16166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_4326]) ).
tcf(c_16167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_4325]) ).
tcf(c_16173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_6109]) ).
tcf(c_16174,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_6105]) ).
tcf(c_16175,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_5500]) ).
tcf(c_16176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_5496]) ).
tcf(c_16177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_4374]) ).
tcf(c_16178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_4370]) ).
tcf(c_16183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_2342]) ).
tcf(c_16277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_5327]) ).
tcf(c_16278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_5110]) ).
tcf(c_16279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_4326]) ).
tcf(c_16280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_2342]) ).
tcf(c_16281,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_61]) ).
tcf(c_16285,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_5557]) ).
tcf(c_16287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_5326]) ).
tcf(c_16288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_5110]) ).
tcf(c_16290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_4300]) ).
tcf(c_16291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_5109]) ).
tcf(c_16293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_4325]) ).
tcf(c_16294,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_4296]) ).
tcf(c_16295,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_4094]) ).
tcf(c_16296,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_4090]) ).
tcf(c_16309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_2342]) ).
tcf(c_16399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_5327]) ).
tcf(c_16400,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_5110]) ).
tcf(c_16401,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_4326]) ).
tcf(c_16402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_2342]) ).
tcf(c_16403,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_61]) ).
tcf(c_16404,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_4688]) ).
tcf(c_16405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_4684]) ).
tcf(c_16406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_4422]) ).
tcf(c_16408,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_5327]) ).
tcf(c_16409,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12238,c_5326]) ).
tcf(c_16410,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_5110]) ).
tcf(c_16411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_4418]) ).
tcf(c_16412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_4300]) ).
tcf(c_16413,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12238,c_5109]) ).
tcf(c_16414,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_4326]) ).
tcf(c_16415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12238,c_4325]) ).
tcf(c_16416,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_4296]) ).
tcf(c_16417,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_4094]) ).
tcf(c_16418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_4090]) ).
tcf(c_16419,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_3375]) ).
tcf(c_16420,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_3371]) ).
tcf(c_16429,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_2388]) ).
tcf(c_16430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_2387]) ).
tcf(c_16431,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_2342]) ).
tcf(c_16432,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12238,c_74]) ).
tcf(c_16433,plain,
( vertex(head_of(sK5(head_of(sK3),tail_of(sK3))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12238,c_76]) ).
tcf(c_16605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5558]) ).
tcf(c_16606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5558]) ).
tcf(c_16607,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_5558]) ).
tcf(c_16612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5558]) ).
tcf(c_16613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5558]) ).
tcf(c_16614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_5558]) ).
tcf(c_16617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_5558]) ).
tcf(c_16622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_5558]) ).
tcf(c_16623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_5558]) ).
tcf(c_16624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_5558]) ).
tcf(c_16625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_5558]) ).
tcf(c_16628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_5558]) ).
tcf(c_16629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_5558]) ).
tcf(c_16630,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_5558]) ).
tcf(c_16631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_5558]) ).
tcf(c_16632,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_5558]) ).
tcf(c_16633,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_5558]) ).
tcf(c_16634,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_5558]) ).
tcf(c_16635,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_5558]) ).
tcf(c_16636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_5558]) ).
tcf(c_16639,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_5558]) ).
tcf(c_16640,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_5558]) ).
tcf(c_16834,plain,
( sequential(sK3,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK3)
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(equality_resolution,[status(thm)],[c_3372]) ).
tcf(c_16835,plain,
( sequential(sK3,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16834,c_2042]) ).
tcf(c_16852,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5293,c_4091]) ).
tcf(c_16856,plain,
( sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK4)
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_4091]) ).
tcf(c_16857,plain,
( sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16856,c_2052]) ).
tcf(c_16878,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK3) != head_of(sK3) )
| ( head_of(sK3) != head_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_8865]) ).
tcf(c_16885,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5558]) ).
tcf(c_16886,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_5327]) ).
tcf(c_16887,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5110]) ).
tcf(c_16888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_4326]) ).
tcf(c_16889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_2342]) ).
tcf(c_16890,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_61]) ).
tcf(c_16891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5558]) ).
tcf(c_16895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5557]) ).
tcf(c_16896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_5327]) ).
tcf(c_16897,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5326]) ).
tcf(c_16898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_5110]) ).
tcf(c_16901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_4326]) ).
tcf(c_16902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_4325]) ).
tcf(c_16908,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_6109]) ).
tcf(c_16909,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_6105]) ).
tcf(c_16910,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_5500]) ).
tcf(c_16911,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_5496]) ).
tcf(c_16912,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_4374]) ).
tcf(c_16913,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_4370]) ).
tcf(c_16918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_2342]) ).
tcf(c_16919,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_74]) ).
tcf(c_17047,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_15977,c_66]) ).
tcf(c_17050,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15977,c_13447]) ).
tcf(c_17051,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15977,c_13367]) ).
tcf(c_17052,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3)))
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15977,c_4371]) ).
tcf(c_17054,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),tail_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15977,c_66]) ).
tcf(c_17056,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15977,c_61]) ).
tcf(c_17158,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5558]) ).
tcf(c_17159,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_5327]) ).
tcf(c_17160,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5110]) ).
tcf(c_17161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_4326]) ).
tcf(c_17162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_2342]) ).
tcf(c_17163,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_61]) ).
tcf(c_17164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5558]) ).
tcf(c_17168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5557]) ).
tcf(c_17169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_5327]) ).
tcf(c_17170,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5326]) ).
tcf(c_17171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5110]) ).
tcf(c_17174,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_5109]) ).
tcf(c_17175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_4326]) ).
tcf(c_17176,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_4325]) ).
tcf(c_17182,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_6109]) ).
tcf(c_17183,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_6105]) ).
tcf(c_17184,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_5500]) ).
tcf(c_17185,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_5496]) ).
tcf(c_17186,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_4374]) ).
tcf(c_17187,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_4370]) ).
tcf(c_17192,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_2342]) ).
tcf(c_17312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_15979,c_66]) ).
tcf(c_17315,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_13447]) ).
tcf(c_17316,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_13367]) ).
tcf(c_17317,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_15979,c_4371]) ).
tcf(c_17319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK4)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15979,c_66]) ).
tcf(c_17321,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15979,c_61]) ).
tcf(c_17385,plain,
( edge(sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK3) = head_of(sK4) )
| ~ vertex(head_of(sK4))
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_8854]) ).
tcf(c_17390,plain,
( sequential(sK3,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_16835,c_2052,c_2067,c_2073,c_2952,c_16835,c_17385]) ).
tcf(c_17398,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_17390,c_6309]) ).
tcf(c_17399,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_6222]) ).
tcf(c_17400,plain,
( precedes(sK3,sK4,sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_3218]) ).
tcf(c_17401,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_3157]) ).
tcf(c_17402,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_2853]) ).
tcf(c_17403,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_2414]) ).
tcf(c_17404,plain,
( edge(sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_17390,c_63]) ).
tcf(c_17410,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17403,c_50]) ).
tcf(c_17417,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17402,c_50]) ).
tcf(c_17424,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17398,c_50]) ).
tcf(c_17476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_105]) ).
tcf(c_17477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_79]) ).
tcf(c_17480,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_16004]) ).
tcf(c_17484,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_2771]) ).
tcf(c_17486,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_17417,c_6165]) ).
tcf(c_17488,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_17417,c_2359]) ).
tcf(c_17489,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_2181]) ).
tcf(c_17490,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_2192]) ).
tcf(c_17491,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK0) ),
inference(superposition,[status(thm)],[c_17417,c_2100]) ).
tcf(c_17495,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_17417,c_9401]) ).
tcf(c_17496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_11498]) ).
tcf(c_17633,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK3,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_17424]) ).
tcf(c_17634,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_17424]) ).
tcf(c_17676,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_16857,c_6309]) ).
tcf(c_17678,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_3218]) ).
tcf(c_17679,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_3157]) ).
tcf(c_17680,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_2853]) ).
tcf(c_17681,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_2414]) ).
tcf(c_17685,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17681,c_51]) ).
tcf(c_17691,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17678,c_2402,c_51]) ).
tcf(c_17697,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17680,c_51]) ).
tcf(c_17705,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17676,c_51]) ).
tcf(c_17720,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17685,c_62]) ).
tcf(c_17738,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17691,c_62]) ).
tcf(c_17765,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_105]) ).
tcf(c_17766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_79]) ).
tcf(c_17769,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_16004]) ).
tcf(c_17770,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_14361]) ).
tcf(c_17773,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_2771]) ).
tcf(c_17775,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_17697,c_6165]) ).
tcf(c_17777,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_17697,c_2359]) ).
tcf(c_17778,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_2181]) ).
tcf(c_17779,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_2192]) ).
tcf(c_17780,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0) ),
inference(superposition,[status(thm)],[c_17697,c_2100]) ).
tcf(c_17784,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_17697,c_9401]) ).
tcf(c_17785,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_11498]) ).
tcf(c_17974,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_12239]) ).
tcf(c_17975,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_5558]) ).
tcf(c_17976,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_5327]) ).
tcf(c_17977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_5110]) ).
tcf(c_17978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_4326]) ).
tcf(c_17979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_2342]) ).
tcf(c_17980,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_61]) ).
tcf(c_17981,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_5558]) ).
tcf(c_17982,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_4688]) ).
tcf(c_17983,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_4684]) ).
tcf(c_17984,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_4422]) ).
tcf(c_17985,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_5557]) ).
tcf(c_17986,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_5327]) ).
tcf(c_17987,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_5326]) ).
tcf(c_17988,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_5110]) ).
tcf(c_17989,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_4418]) ).
tcf(c_17990,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_4300]) ).
tcf(c_17991,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_5109]) ).
tcf(c_17992,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_4326]) ).
tcf(c_17993,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_4325]) ).
tcf(c_17994,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_4296]) ).
tcf(c_17995,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_4094]) ).
tcf(c_17996,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_4090]) ).
tcf(c_17997,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_3375]) ).
tcf(c_17998,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_3371]) ).
tcf(c_18005,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_3749]) ).
tcf(c_18006,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_3745]) ).
tcf(c_18007,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_2388]) ).
tcf(c_18008,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_2387]) ).
tcf(c_18009,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_2342]) ).
tcf(c_18010,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_74]) ).
tcf(c_18011,plain,
( vertex(tail_of(sK5(head_of(sK3),tail_of(sK3))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12239,c_76]) ).
tcf(c_18217,plain,
( edge(sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK3) = head_of(sK3) )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_9326]) ).
tcf(c_18219,plain,
( edge(sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK4) = head_of(sK3) )
| ~ vertex(head_of(sK4))
| ~ vertex(head_of(sK3)) ),
inference(instantiation,[status(thm)],[c_9326]) ).
tcf(c_18362,plain,
edge(sK5(head_of(sK3),head_of(sK4))),
inference(global_subsumption_just,[status(thm)],[c_17404,c_2052,c_2067,c_2073,c_2952,c_17385]) ).
tcf(c_18364,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5042,c_18362]) ).
tcf(c_18365,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3372,c_18362]) ).
tcf(c_18374,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3965]) ).
tcf(c_18375,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3964]) ).
tcf(c_18376,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3921]) ).
tcf(c_18377,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3920]) ).
tcf(c_18378,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3613]) ).
tcf(c_18379,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3612]) ).
tcf(c_18380,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3530]) ).
tcf(c_18381,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3529]) ).
tcf(c_18382,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3487]) ).
tcf(c_18383,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3486]) ).
tcf(c_18384,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3452]) ).
tcf(c_18385,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3451]) ).
tcf(c_18386,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3410]) ).
tcf(c_18387,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3409]) ).
tcf(c_18388,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3095]) ).
tcf(c_18389,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_18362,c_3094]) ).
tcf(c_18390,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_4470]) ).
tcf(c_18391,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_4469]) ).
tcf(c_18392,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4468]) ).
tcf(c_18393,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4467]) ).
tcf(c_18394,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4466]) ).
tcf(c_18395,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4465]) ).
tcf(c_18396,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4464]) ).
tcf(c_18397,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4463]) ).
tcf(c_18398,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_18362,c_4124]) ).
tcf(c_18399,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_18362,c_4123]) ).
tcf(c_18400,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4122]) ).
tcf(c_18401,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4121]) ).
tcf(c_18402,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4120]) ).
tcf(c_18403,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_6021]) ).
tcf(c_18404,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4119]) ).
tcf(c_18405,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4118]) ).
tcf(c_18406,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_6020]) ).
tcf(c_18407,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_18362,c_5995]) ).
tcf(c_18408,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_18362,c_5994]) ).
tcf(c_18409,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5969]) ).
tcf(c_18410,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4117]) ).
tcf(c_18411,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5968]) ).
tcf(c_18412,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5438]) ).
tcf(c_18413,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5437]) ).
tcf(c_18414,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5412]) ).
tcf(c_18415,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5411]) ).
tcf(c_18416,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5286]) ).
tcf(c_18417,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_5285]) ).
tcf(c_18418,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4880]) ).
tcf(c_18419,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4879]) ).
tcf(c_18420,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4852]) ).
tcf(c_18421,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_4851]) ).
tcf(c_18422,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3966]) ).
tcf(c_18423,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3922]) ).
tcf(c_18424,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3614]) ).
tcf(c_18425,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3531]) ).
tcf(c_18426,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_2719]) ).
tcf(c_18427,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_2718]) ).
tcf(c_18428,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2697]) ).
tcf(c_18429,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3488]) ).
tcf(c_18430,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_3453]) ).
tcf(c_18431,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2696]) ).
tcf(c_18432,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2673]) ).
tcf(c_18433,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2672]) ).
tcf(c_18434,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2648]) ).
tcf(c_18435,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_18362,c_2647]) ).
tcf(c_18436,plain,
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_3411]) ).
tcf(c_18437,plain,
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK3),head_of(sK4))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_18362,c_3096]) ).
tcf(c_18663,plain,
( edge(sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK3) = head_of(sK4) )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK4)) ),
inference(instantiation,[status(thm)],[c_10351]) ).
tcf(c_18921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_5558]) ).
tcf(c_18922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_5327]) ).
tcf(c_18923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_5110]) ).
tcf(c_18924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_4326]) ).
tcf(c_18925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_2342]) ).
tcf(c_18926,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_61]) ).
tcf(c_18927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_5558]) ).
tcf(c_18931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_5557]) ).
tcf(c_18933,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_5326]) ).
tcf(c_18934,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_5110]) ).
tcf(c_18936,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_4300]) ).
tcf(c_18938,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_4325]) ).
tcf(c_18939,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_4296]) ).
tcf(c_18940,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_4094]) ).
tcf(c_18941,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_4090]) ).
tcf(c_18954,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_2342]) ).
tcf(c_19049,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_5558]) ).
tcf(c_19050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_5327]) ).
tcf(c_19051,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_5110]) ).
tcf(c_19052,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_4326]) ).
tcf(c_19053,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_2342]) ).
tcf(c_19054,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_61]) ).
tcf(c_19059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_5557]) ).
tcf(c_19060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_5327]) ).
tcf(c_19061,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_5326]) ).
tcf(c_19065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_5109]) ).
tcf(c_19066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_4326]) ).
tcf(c_19067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_4325]) ).
tcf(c_19073,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_6109]) ).
tcf(c_19074,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_6105]) ).
tcf(c_19075,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_5500]) ).
tcf(c_19076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_5496]) ).
tcf(c_19077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_4374]) ).
tcf(c_19078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_4370]) ).
tcf(c_19083,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_2342]) ).
tcf(c_19248,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_17705,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_7116,c_12567,c_12568,c_17705,c_18219]) ).
tcf(c_19249,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(renaming,[status(thm)],[c_19248]) ).
tcf(c_19263,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_19249]) ).
tcf(c_19264,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_19249]) ).
tcf(c_19305,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17697,c_17491]) ).
tcf(c_19315,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_17779,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_7116,c_12567,c_12568,c_17779,c_18219]) ).
tcf(c_19318,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_17777,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_7116,c_12567,c_12568,c_17777,c_18219]) ).
tcf(c_19319,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(renaming,[status(thm)],[c_19318]) ).
tcf(c_19333,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK4)
| ~ on_path(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_19319]) ).
tcf(c_19334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_19319]) ).
tcf(c_19353,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_17780,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_7116,c_12567,c_12568,c_17780,c_18219]) ).
tcf(c_19354,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0) ),
inference(renaming,[status(thm)],[c_19353]) ).
tcf(c_19369,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2881,c_19354]) ).
tcf(c_19370,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_9376,c_19354]) ).
tcf(c_19371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2965,c_19354]) ).
tcf(c_19372,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17417,c_19354]) ).
tcf(c_19411,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12240,c_66]) ).
tcf(c_19412,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12240,c_18365]) ).
tcf(c_19413,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_4091]) ).
tcf(c_19418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12240,c_66]) ).
tcf(c_19419,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK4)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12240,c_2149]) ).
tcf(c_19420,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12240,c_61]) ).
tcf(c_19421,plain,
( vertex(head_of(sK5(head_of(sK3),tail_of(sK3))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12240,c_75]) ).
tcf(c_19498,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_17047]) ).
tcf(c_19501,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_17047]) ).
tcf(c_19502,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_17047]) ).
tcf(c_19503,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_17047]) ).
tcf(c_19504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_17047]) ).
tcf(c_19505,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_17047]) ).
tcf(c_19506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_17047]) ).
tcf(c_19507,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12238,c_17047]) ).
tcf(c_19508,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_17047]) ).
tcf(c_19509,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_17047]) ).
tcf(c_19510,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_17047]) ).
tcf(c_19511,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_17047]) ).
tcf(c_19652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_17054]) ).
tcf(c_19654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_17054]) ).
tcf(c_19656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_17054]) ).
tcf(c_19657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_17054]) ).
tcf(c_19658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_17054]) ).
tcf(c_19660,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_17054]) ).
tcf(c_19661,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_17054]) ).
tcf(c_19662,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_17054]) ).
tcf(c_19665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_17054]) ).
tcf(c_19670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_17054]) ).
tcf(c_19672,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_17054]) ).
tcf(c_19674,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_17054]) ).
tcf(c_19675,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_17054]) ).
tcf(c_19676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_17054]) ).
tcf(c_19677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_17054]) ).
tcf(c_19678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_17054]) ).
tcf(c_19679,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_17054]) ).
tcf(c_19680,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_17054]) ).
tcf(c_19681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_17054]) ).
tcf(c_19682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_17054]) ).
tcf(c_19683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_17054]) ).
tcf(c_19684,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_17054]) ).
tcf(c_19685,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_17054]) ).
tcf(c_19686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_17054]) ).
tcf(c_19687,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_17054]) ).
tcf(c_19688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_17054]) ).
tcf(c_19689,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_17054]) ).
tcf(c_19690,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_17054]) ).
tcf(c_19693,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_17054]) ).
tcf(c_19694,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_17054]) ).
tcf(c_19695,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_17054]) ).
tcf(c_19696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_17054]) ).
tcf(c_19697,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_17054]) ).
tcf(c_20028,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_17312]) ).
tcf(c_20029,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12238,c_17312]) ).
tcf(c_20030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_17312]) ).
tcf(c_20031,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12239,c_17312]) ).
tcf(c_20032,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_17312]) ).
tcf(c_20033,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_17312]) ).
tcf(c_20090,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_17319]) ).
tcf(c_20092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_17319]) ).
tcf(c_20094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_17319]) ).
tcf(c_20095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_17319]) ).
tcf(c_20096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_17319]) ).
tcf(c_20098,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_17319]) ).
tcf(c_20099,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_17319]) ).
tcf(c_20100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_17319]) ).
tcf(c_20105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_17319]) ).
tcf(c_20106,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_17319]) ).
tcf(c_20108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_17319]) ).
tcf(c_20110,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_17319]) ).
tcf(c_20112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_17319]) ).
tcf(c_20113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5676,c_17319]) ).
tcf(c_20114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5014,c_17319]) ).
tcf(c_20115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_17319]) ).
tcf(c_20116,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_17319]) ).
tcf(c_20117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5490,c_17319]) ).
tcf(c_20118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_17319]) ).
tcf(c_20119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_17319]) ).
tcf(c_20120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4145,c_17319]) ).
tcf(c_20121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4019,c_17319]) ).
tcf(c_20122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_17319]) ).
tcf(c_20123,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_17319]) ).
tcf(c_20124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_17319]) ).
tcf(c_20127,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15975,c_17319]) ).
tcf(c_20128,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15980,c_17319]) ).
tcf(c_20129,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15976,c_17319]) ).
tcf(c_20130,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15974,c_17319]) ).
tcf(c_20131,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_17319]) ).
tcf(c_20132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_17319]) ).
tcf(c_20133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_17319]) ).
tcf(c_20134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_17319]) ).
tcf(c_20135,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(equality_resolution,[status(thm)],[c_17319]) ).
tcf(c_20422,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_5037]) ).
tcf(c_20423,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5014,c_5037]) ).
tcf(c_20436,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_5037]) ).
tcf(c_20437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_5037]) ).
tcf(c_20440,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_5037]) ).
tcf(c_20442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_5037]) ).
tcf(c_20517,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_5041]) ).
tcf(c_20518,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_5041]) ).
tcf(c_20521,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_5041]) ).
tcf(c_20523,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_5041]) ).
tcf(c_20585,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_5676,c_5717]) ).
tcf(c_20599,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_5717]) ).
tcf(c_20600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_5717]) ).
tcf(c_20603,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_5717]) ).
tcf(c_20605,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_5717]) ).
tcf(c_20643,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_19674]) ).
tcf(c_20646,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_19674]) ).
tcf(c_20647,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_19674]) ).
tcf(c_20651,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_19674]) ).
tcf(c_20659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_19674]) ).
tcf(c_20661,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_19674]) ).
tcf(c_20744,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3331,c_20112]) ).
tcf(c_20747,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_20112]) ).
tcf(c_20748,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4151,c_20112]) ).
tcf(c_20752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_20112]) ).
tcf(c_20760,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12238,c_20112]) ).
tcf(c_20762,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12239,c_20112]) ).
tcf(c_20838,plain,
! [X0: $i,X1: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2065,c_17476]) ).
tcf(c_20872,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_20838]) ).
tcf(c_20873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| precedes(X3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( X0 = X1 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_20838]) ).
tcf(c_20874,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,X1),X1)) = head_of(sK7(sK0,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_20838]) ).
tcf(c_20875,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_16857,c_20838]) ).
tcf(c_20876,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_12149,c_20838]) ).
tcf(c_20877,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_17390,c_20838]) ).
tcf(c_20888,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20876,c_50]) ).
tcf(c_20907,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20875,c_51]) ).
tcf(c_20977,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17477,c_78]) ).
tcf(c_21002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_2309,c_20977]) ).
tcf(c_21003,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK0)
| ~ path(X2,X3,sK0)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),X1)
| ~ sequential(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_2228,c_20977]) ).
tcf(c_21004,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| sequential(X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4))))
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4)))),sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4))))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4))))) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK0)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4))),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4)))),X2)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK5(head_of(sK3),head_of(sK4)))),sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_10127,c_20977]) ).
tcf(c_21005,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ sequential(X0,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_17417,c_20977]) ).
tcf(c_21054,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_6099,c_12241]) ).
tcf(c_21056,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_12241]) ).
tcf(c_21058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12241,c_66]) ).
tcf(c_21059,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12241,c_18365]) ).
tcf(c_21060,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_4091]) ).
tcf(c_21064,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12241,c_12129]) ).
tcf(c_21065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12241,c_66]) ).
tcf(c_21066,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK4)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK4 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12241,c_2149]) ).
tcf(c_21067,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12241,c_61]) ).
tcf(c_21068,plain,
( vertex(tail_of(sK5(head_of(sK3),tail_of(sK3))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12241,c_75]) ).
tcf(c_21163,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_4297,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_4297,c_7116,c_12567,c_12568,c_18219]) ).
tcf(c_21176,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5293,c_21163]) ).
tcf(c_21182,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_21163]) ).
tcf(c_21183,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_21163]) ).
tcf(c_21184,plain,
( sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK4) ),
inference(equality_resolution,[status(thm)],[c_21163]) ).
tcf(c_21185,plain,
( sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21184,c_2052]) ).
tcf(c_21189,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21176,c_18362]) ).
tcf(c_21216,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_4328,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_4328,c_7116,c_12567,c_12568,c_18219]) ).
tcf(c_21230,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5676,c_21216]) ).
tcf(c_21231,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5014,c_21216]) ).
tcf(c_21244,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15975,c_21216]) ).
tcf(c_21245,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15980,c_21216]) ).
tcf(c_21248,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_21216]) ).
tcf(c_21250,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_21216]) ).
tcf(c_21262,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21231,c_18362]) ).
tcf(c_21267,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21230,c_18362]) ).
tcf(c_21334,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4419,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_4419,c_7116,c_12567,c_12568,c_18219]) ).
tcf(c_21353,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12240,c_21334]) ).
tcf(c_21354,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12241,c_21334]) ).
tcf(c_21355,plain,
( sequential(sK3,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_21334]) ).
tcf(c_21356,plain,
( sequential(sK3,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21355,c_2042]) ).
tcf(c_21374,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_4685,c_2042,c_2067,c_2906,c_2905,c_3046,c_4685,c_12837,c_16878,c_18217]) ).
tcf(c_21393,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12240,c_21374]) ).
tcf(c_21394,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12241,c_21374]) ).
tcf(c_21395,plain,
( sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_21374]) ).
tcf(c_21396,plain,
( sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21395,c_2042]) ).
tcf(c_21428,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_20838]) ).
tcf(c_21429,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21185,c_6309]) ).
tcf(c_21431,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_3218]) ).
tcf(c_21432,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_3157]) ).
tcf(c_21433,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_2853]) ).
tcf(c_21434,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_2414]) ).
tcf(c_21435,plain,
( edge(sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21185,c_63]) ).
tcf(c_21438,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_19249]) ).
tcf(c_21442,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21434,c_51]) ).
tcf(c_21447,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21431,c_2402,c_51]) ).
tcf(c_21452,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21433,c_51]) ).
tcf(c_21459,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21429,c_51]) ).
tcf(c_21466,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21428,c_51]) ).
tcf(c_21485,plain,
edge(sK5(head_of(sK4),head_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_21435,c_52,c_51,c_50,c_53,c_656,c_2052,c_2067,c_2952,c_7116,c_12567,c_12568,c_18219]) ).
tcf(c_21487,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17697,c_21485]) ).
tcf(c_21488,plain,
( sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_16857,c_21485]) ).
tcf(c_21489,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4301,c_21485]) ).
tcf(c_21490,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4091,c_21485]) ).
tcf(c_21509,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3965]) ).
tcf(c_21510,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3964]) ).
tcf(c_21511,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3921]) ).
tcf(c_21512,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3920]) ).
tcf(c_21513,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3613]) ).
tcf(c_21514,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3612]) ).
tcf(c_21515,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3530]) ).
tcf(c_21516,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3529]) ).
tcf(c_21517,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3487]) ).
tcf(c_21518,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3486]) ).
tcf(c_21519,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3452]) ).
tcf(c_21520,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3451]) ).
tcf(c_21521,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3410]) ).
tcf(c_21522,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3409]) ).
tcf(c_21523,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3095]) ).
tcf(c_21524,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_21485,c_3094]) ).
tcf(c_21525,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_4470]) ).
tcf(c_21526,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_4469]) ).
tcf(c_21527,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4468]) ).
tcf(c_21528,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4467]) ).
tcf(c_21529,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4466]) ).
tcf(c_21530,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4465]) ).
tcf(c_21531,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4464]) ).
tcf(c_21532,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4463]) ).
tcf(c_21533,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_21485,c_4124]) ).
tcf(c_21534,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_21485,c_4123]) ).
tcf(c_21535,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4122]) ).
tcf(c_21536,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4121]) ).
tcf(c_21537,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4120]) ).
tcf(c_21538,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_6021]) ).
tcf(c_21539,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4119]) ).
tcf(c_21540,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4118]) ).
tcf(c_21541,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_6020]) ).
tcf(c_21542,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_21485,c_5995]) ).
tcf(c_21543,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_21485,c_5994]) ).
tcf(c_21544,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5969]) ).
tcf(c_21545,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4117]) ).
tcf(c_21546,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5968]) ).
tcf(c_21547,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5438]) ).
tcf(c_21548,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5437]) ).
tcf(c_21549,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5412]) ).
tcf(c_21550,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5411]) ).
tcf(c_21551,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5286]) ).
tcf(c_21552,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_5285]) ).
tcf(c_21553,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4880]) ).
tcf(c_21554,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4879]) ).
tcf(c_21555,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4852]) ).
tcf(c_21556,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_4851]) ).
tcf(c_21557,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3966]) ).
tcf(c_21558,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3922]) ).
tcf(c_21559,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3614]) ).
tcf(c_21560,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3531]) ).
tcf(c_21561,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_2719]) ).
tcf(c_21562,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_2718]) ).
tcf(c_21563,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2697]) ).
tcf(c_21564,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3488]) ).
tcf(c_21565,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_3453]) ).
tcf(c_21566,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2696]) ).
tcf(c_21567,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2673]) ).
tcf(c_21568,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2672]) ).
tcf(c_21569,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2648]) ).
tcf(c_21570,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_21485,c_2647]) ).
tcf(c_21571,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_3411]) ).
tcf(c_21572,plain,
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21485,c_3096]) ).
tcf(c_22027,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_20838]) ).
tcf(c_22028,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21356,c_6309]) ).
tcf(c_22029,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_6222]) ).
tcf(c_22030,plain,
( precedes(sK3,sK4,sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_3218]) ).
tcf(c_22031,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_3157]) ).
tcf(c_22032,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_2853]) ).
tcf(c_22033,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_2414]) ).
tcf(c_22038,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22033,c_50]) ).
tcf(c_22045,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22032,c_50]) ).
tcf(c_22052,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22028,c_50]) ).
tcf(c_22059,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22027,c_50]) ).
tcf(c_22114,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_105]) ).
tcf(c_22115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_79]) ).
tcf(c_22118,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_16004]) ).
tcf(c_22119,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_14361]) ).
tcf(c_22122,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_2771]) ).
tcf(c_22124,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21452,c_6165]) ).
tcf(c_22126,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_21452,c_2359]) ).
tcf(c_22127,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_2181]) ).
tcf(c_22128,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_2192]) ).
tcf(c_22129,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0) ),
inference(superposition,[status(thm)],[c_21452,c_2100]) ).
tcf(c_22133,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_21452,c_9401]) ).
tcf(c_22134,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_11498]) ).
tcf(c_22135,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_17491]) ).
tcf(c_22136,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21452,c_19354]) ).
tcf(c_22313,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_21459]) ).
tcf(c_22314,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21185,c_21459]) ).
tcf(c_22350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_105]) ).
tcf(c_22351,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_79]) ).
tcf(c_22354,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_16004]) ).
tcf(c_22358,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_2771]) ).
tcf(c_22360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_22045,c_6165]) ).
tcf(c_22362,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_22045,c_2359]) ).
tcf(c_22363,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_2181]) ).
tcf(c_22364,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_2192]) ).
tcf(c_22365,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0) ),
inference(superposition,[status(thm)],[c_22045,c_2100]) ).
tcf(c_22369,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK3)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_22045,c_9401]) ).
tcf(c_22370,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_11498]) ).
tcf(c_22371,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_22045,c_17491]) ).
tcf(c_22605,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(sK3,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_22052]) ).
tcf(c_22607,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21356,c_22052]) ).
tcf(c_22653,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_17319]) ).
tcf(c_22654,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_17054]) ).
tcf(c_22656,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_5327]) ).
tcf(c_22657,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_5110]) ).
tcf(c_22658,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_4326]) ).
tcf(c_22659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_2342]) ).
tcf(c_22660,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_61]) ).
tcf(c_22661,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_21216]) ).
tcf(c_22662,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_20112]) ).
tcf(c_22663,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_19674]) ).
tcf(c_22664,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_5717]) ).
tcf(c_22665,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_5041]) ).
tcf(c_22666,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_5037]) ).
tcf(c_22667,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_17319]) ).
tcf(c_22668,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12242,c_17312]) ).
tcf(c_22669,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_17054]) ).
tcf(c_22670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12242,c_17047]) ).
tcf(c_22672,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_4688]) ).
tcf(c_22673,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_4684]) ).
tcf(c_22674,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_4422]) ).
tcf(c_22676,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_5327]) ).
tcf(c_22677,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12242,c_5326]) ).
tcf(c_22678,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_5110]) ).
tcf(c_22679,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_4418]) ).
tcf(c_22680,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_4300]) ).
tcf(c_22681,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12242,c_5109]) ).
tcf(c_22682,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_4326]) ).
tcf(c_22683,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12242,c_4325]) ).
tcf(c_22684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_4296]) ).
tcf(c_22685,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_4094]) ).
tcf(c_22686,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_4090]) ).
tcf(c_22687,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_3375]) ).
tcf(c_22688,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_3371]) ).
tcf(c_22697,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_2388]) ).
tcf(c_22698,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12242,c_2387]) ).
tcf(c_22699,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_2342]) ).
tcf(c_22701,plain,
( vertex(head_of(sK5(head_of(sK3),tail_of(sK3))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12242,c_76]) ).
tcf(c_23000,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK3),tail_of(sK3)) != sK3 ) ),
inference(instantiation,[status(thm)],[c_9338]) ).
tcf(c_23234,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5293,c_21490]) ).
tcf(c_23240,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_21490]) ).
tcf(c_23241,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_21490]) ).
tcf(c_23243,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23234,c_18362]) ).
tcf(c_23286,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_5038,c_2052,c_2067,c_2073,c_2952,c_5042,c_5718,c_17385]) ).
tcf(c_23305,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_23286]) ).
tcf(c_23306,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_23286]) ).
tcf(c_23307,plain,
( sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK4) ),
inference(equality_resolution,[status(thm)],[c_23286]) ).
tcf(c_23308,plain,
( sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23307,c_2052]) ).
tcf(c_23326,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK3)),X0)
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5112,c_2042,c_2067,c_2906,c_2905,c_3046,c_5112,c_12837,c_16878,c_18217]) ).
tcf(c_23343,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_6099,c_23326]) ).
tcf(c_23344,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5490,c_23326]) ).
tcf(c_23352,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15981,c_23326]) ).
tcf(c_23353,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15978,c_23326]) ).
tcf(c_23356,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15976,c_23326]) ).
tcf(c_23357,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15974,c_23326]) ).
tcf(c_23360,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12236,c_23326]) ).
tcf(c_23362,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12237,c_23326]) ).
tcf(c_23363,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_23326]) ).
tcf(c_23364,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23363,c_2042]) ).
tcf(c_23388,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23344,c_12218]) ).
tcf(c_23393,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23343,c_12218]) ).
tcf(c_23472,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK3),head_of(sK4)),X0)
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(X0)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_5329,c_2052,c_2067,c_2073,c_2952,c_5329,c_17385]) ).
tcf(c_23500,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15975,c_23472]) ).
tcf(c_23501,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15980,c_23472]) ).
tcf(c_23504,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_23472]) ).
tcf(c_23505,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_23472]) ).
tcf(c_23507,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_23472]) ).
tcf(c_23605,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_20838]) ).
tcf(c_23606,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21396,c_6309]) ).
tcf(c_23607,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_6222]) ).
tcf(c_23608,plain,
( precedes(sK3,sK4,sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_3218]) ).
tcf(c_23609,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_3157]) ).
tcf(c_23610,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_2853]) ).
tcf(c_23611,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21396,c_2414]) ).
tcf(c_23612,plain,
( edge(sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_21396,c_63]) ).
tcf(c_23618,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23611,c_50]) ).
tcf(c_23625,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23610,c_50]) ).
tcf(c_23632,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23606,c_50]) ).
tcf(c_23639,plain,
( precedes(sK3,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23605,c_50]) ).
tcf(c_23669,plain,
edge(sK5(tail_of(sK3),head_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_23612,c_2042,c_2067,c_2906,c_2905,c_3046,c_12837,c_16878,c_18217]) ).
tcf(c_23671,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5778,c_23669]) ).
tcf(c_23672,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4371,c_23669]) ).
tcf(c_23681,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3965]) ).
tcf(c_23682,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3964]) ).
tcf(c_23683,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3921]) ).
tcf(c_23684,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3920]) ).
tcf(c_23685,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3613]) ).
tcf(c_23686,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3612]) ).
tcf(c_23687,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3530]) ).
tcf(c_23688,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3529]) ).
tcf(c_23689,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3487]) ).
tcf(c_23690,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3486]) ).
tcf(c_23691,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3452]) ).
tcf(c_23692,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3451]) ).
tcf(c_23693,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3410]) ).
tcf(c_23694,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3409]) ).
tcf(c_23695,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3095]) ).
tcf(c_23696,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_23669,c_3094]) ).
tcf(c_23697,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_4470]) ).
tcf(c_23698,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_4469]) ).
tcf(c_23699,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4468]) ).
tcf(c_23700,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4467]) ).
tcf(c_23701,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4466]) ).
tcf(c_23702,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4465]) ).
tcf(c_23703,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4464]) ).
tcf(c_23704,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4463]) ).
tcf(c_23705,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_23669,c_4124]) ).
tcf(c_23706,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_23669,c_4123]) ).
tcf(c_23707,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4122]) ).
tcf(c_23708,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4121]) ).
tcf(c_23709,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4120]) ).
tcf(c_23710,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_6021]) ).
tcf(c_23711,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4119]) ).
tcf(c_23712,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4118]) ).
tcf(c_23713,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_6020]) ).
tcf(c_23714,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_23669,c_5995]) ).
tcf(c_23715,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_23669,c_5994]) ).
tcf(c_23716,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5969]) ).
tcf(c_23717,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4117]) ).
tcf(c_23718,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5968]) ).
tcf(c_23719,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5438]) ).
tcf(c_23720,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5437]) ).
tcf(c_23721,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5412]) ).
tcf(c_23722,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5411]) ).
tcf(c_23723,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5286]) ).
tcf(c_23724,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_5285]) ).
tcf(c_23725,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4880]) ).
tcf(c_23726,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4879]) ).
tcf(c_23727,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4852]) ).
tcf(c_23728,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_4851]) ).
tcf(c_23729,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3966]) ).
tcf(c_23730,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3922]) ).
tcf(c_23731,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3614]) ).
tcf(c_23732,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3531]) ).
tcf(c_23733,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_2719]) ).
tcf(c_23734,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_2718]) ).
tcf(c_23735,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2697]) ).
tcf(c_23736,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3488]) ).
tcf(c_23737,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_3453]) ).
tcf(c_23738,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2696]) ).
tcf(c_23739,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2673]) ).
tcf(c_23740,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2672]) ).
tcf(c_23741,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2648]) ).
tcf(c_23742,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK3))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_23669,c_2647]) ).
tcf(c_23743,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_3411]) ).
tcf(c_23744,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_23669,c_3096]) ).
tcf(c_24194,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_21488,c_20838]) ).
tcf(c_24195,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21488,c_6309]) ).
tcf(c_24197,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21488,c_3218]) ).
tcf(c_24199,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21488,c_2853]) ).
tcf(c_24200,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21488,c_2414]) ).
tcf(c_24206,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21488,c_19249]) ).
tcf(c_24211,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24194,c_51]) ).
tcf(c_24220,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_23618,c_23364,c_23618]) ).
tcf(c_24258,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_23308,c_6309]) ).
tcf(c_24260,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23308,c_3218]) ).
tcf(c_24261,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23308,c_3157]) ).
tcf(c_24262,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23308,c_2853]) ).
tcf(c_24263,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23308,c_2414]) ).
tcf(c_24268,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24263,c_51]) ).
tcf(c_24273,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24260,c_2402,c_51]) ).
tcf(c_24278,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24262,c_51]) ).
tcf(c_24285,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24258,c_51]) ).
tcf(c_24311,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_3740,c_12243]) ).
tcf(c_24312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_17319]) ).
tcf(c_24313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_17054]) ).
tcf(c_24314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_5558]) ).
tcf(c_24315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_5327]) ).
tcf(c_24316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_5110]) ).
tcf(c_24317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_4326]) ).
tcf(c_24318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_2342]) ).
tcf(c_24319,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_61]) ).
tcf(c_24320,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_23472]) ).
tcf(c_24322,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_21216]) ).
tcf(c_24323,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_20112]) ).
tcf(c_24324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_19674]) ).
tcf(c_24325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_5717]) ).
tcf(c_24326,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_5041]) ).
tcf(c_24327,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_5037]) ).
tcf(c_24328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_17319]) ).
tcf(c_24329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12243,c_17312]) ).
tcf(c_24330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_17054]) ).
tcf(c_24331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12243,c_17047]) ).
tcf(c_24332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_5558]) ).
tcf(c_24333,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_4688]) ).
tcf(c_24334,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_4684]) ).
tcf(c_24335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_4422]) ).
tcf(c_24336,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_5557]) ).
tcf(c_24337,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_5327]) ).
tcf(c_24338,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12243,c_5326]) ).
tcf(c_24339,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_5110]) ).
tcf(c_24340,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_4418]) ).
tcf(c_24341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_4300]) ).
tcf(c_24342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12243,c_5109]) ).
tcf(c_24343,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_4326]) ).
tcf(c_24344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12243,c_4325]) ).
tcf(c_24345,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_4296]) ).
tcf(c_24346,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_4094]) ).
tcf(c_24347,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_4090]) ).
tcf(c_24348,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_3375]) ).
tcf(c_24349,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_3371]) ).
tcf(c_24356,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_3749]) ).
tcf(c_24357,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_3745]) ).
tcf(c_24358,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_2388]) ).
tcf(c_24359,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12243,c_2387]) ).
tcf(c_24360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_2342]) ).
tcf(c_24362,plain,
( vertex(tail_of(sK5(head_of(sK3),tail_of(sK3))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12243,c_76]) ).
tcf(c_24778,plain,
edge(sK3),
inference(superposition,[status(thm)],[c_52,c_62]) ).
tcf(c_24796,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_53,c_70]) ).
tcf(c_24824,plain,
head_of(sK3) = tail_of(sK4),
inference(superposition,[status(thm)],[c_52,c_65]) ).
tcf(c_24933,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_24796,c_82]) ).
tcf(c_25117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X0) != tail_of(X1) ) ),
inference(equality_resolution,[status(thm)],[c_66]) ).
tcf(c_25447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(X0,sK4,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_24824,c_25117]) ).
tcf(c_25496,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK5(X1,tail_of(X0))) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_76,c_110]) ).
tcf(c_25745,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ( tail_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(X1))) = head_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_75,c_25496]) ).
tcf(c_25882,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK3) )
| ( tail_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK3))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_24778,c_25745]) ).
tcf(c_26458,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_24778,c_25882]) ).
tcf(c_26478,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_26458,c_2042,c_2905,c_3699]) ).
tcf(c_26479,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_26478]) ).
tcf(c_26487,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,X0) ),
inference(superposition,[status(thm)],[c_26479,c_25447]) ).
tcf(c_26948,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_24933,c_26487]) ).
tcf(c_26954,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26948,c_51]) ).
tcf(c_26959,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_26954,c_13250,c_23000]) ).
tcf(c_28375,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK3) != head_of(sK4) )
| ( head_of(sK4) != head_of(sK4) ) ),
inference(instantiation,[status(thm)],[c_7193]) ).
tcf(c_28457,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_23672]) ).
tcf(c_28460,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_23672]) ).
tcf(c_28461,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15977,c_23672]) ).
tcf(c_28474,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28457,c_12218]) ).
tcf(c_28483,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK3),tail_of(sK3)),X0)
| ( sK5(head_of(sK3),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5560,c_2042,c_2067,c_2906,c_2905,c_4455,c_5560]) ).
tcf(c_28506,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5767,c_28483]) ).
tcf(c_28509,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15981,c_28483]) ).
tcf(c_28510,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15978,c_28483]) ).
tcf(c_28513,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15976,c_28483]) ).
tcf(c_28514,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15974,c_28483]) ).
tcf(c_28520,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12237,c_28483]) ).
tcf(c_28521,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_28483]) ).
tcf(c_28522,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28521,c_2042]) ).
tcf(c_28546,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28506,c_23669]) ).
tcf(c_28612,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_5718,c_2052,c_2067,c_2073,c_2952,c_5718,c_17385]) ).
tcf(c_28631,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_28612]) ).
tcf(c_28632,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_28612]) ).
tcf(c_28633,plain,
( sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK4) ),
inference(equality_resolution,[status(thm)],[c_28612]) ).
tcf(c_28634,plain,
( sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28633,c_2052]) ).
tcf(c_28724,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_5774,c_2042,c_2067,c_2906,c_2905,c_3046,c_5778,c_12837,c_16878,c_18217,c_23672]) ).
tcf(c_28741,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_28724]) ).
tcf(c_28742,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15977,c_28724]) ).
tcf(c_28883,plain,
( precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23364,c_20838]) ).
tcf(c_28884,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_23364,c_6309]) ).
tcf(c_28885,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_23364,c_6222]) ).
tcf(c_28886,plain,
( precedes(sK5(tail_of(sK3),head_of(sK3)),sK4,sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_23364,c_3218]) ).
tcf(c_28887,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_23364,c_3157]) ).
tcf(c_28888,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_23364,c_2853]) ).
tcf(c_28889,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_23364,c_2414]) ).
tcf(c_28893,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_23364,c_557]) ).
tcf(c_28897,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28889,c_50]) ).
tcf(c_28902,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28888,c_50]) ).
tcf(c_28909,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28884,c_50]) ).
tcf(c_28916,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28885,c_52,c_50]) ).
tcf(c_29006,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_28522,c_23000,c_28522]) ).
tcf(c_29012,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3800,c_29006]) ).
tcf(c_29016,plain,
( precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_29006,c_20838]) ).
tcf(c_29017,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_29006,c_6309]) ).
tcf(c_29018,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_29006,c_6222]) ).
tcf(c_29019,plain,
( precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,sK0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_29006,c_3218]) ).
tcf(c_29020,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_29006,c_3157]) ).
tcf(c_29021,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_29006,c_2853]) ).
tcf(c_29022,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_29006,c_2414]) ).
tcf(c_29026,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_29006,c_557]) ).
tcf(c_29029,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29022,c_50]) ).
tcf(c_29033,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29021,c_50]) ).
tcf(c_29039,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29017,c_50]) ).
tcf(c_29045,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29018,c_52,c_50]) ).
tcf(c_29055,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_29012,c_26959]) ).
tcf(c_29091,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_105]) ).
tcf(c_29092,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_79]) ).
tcf(c_29095,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_16004]) ).
tcf(c_29096,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_14361]) ).
tcf(c_29099,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_2771]) ).
tcf(c_29101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_24278,c_6165]) ).
tcf(c_29103,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_24278,c_2359]) ).
tcf(c_29104,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_2181]) ).
tcf(c_29105,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_2192]) ).
tcf(c_29106,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK0) ),
inference(superposition,[status(thm)],[c_24278,c_2100]) ).
tcf(c_29110,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_24278,c_9401]) ).
tcf(c_29111,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_11498]) ).
tcf(c_29114,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_19354]) ).
tcf(c_29308,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_24285]) ).
tcf(c_29309,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_23308,c_24285]) ).
tcf(c_29326,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5552,c_12244]) ).
tcf(c_29327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_17319]) ).
tcf(c_29328,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_17054]) ).
tcf(c_29329,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_5558]) ).
tcf(c_29330,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_5327]) ).
tcf(c_29331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_5110]) ).
tcf(c_29332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_4326]) ).
tcf(c_29333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_2342]) ).
tcf(c_29334,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_61]) ).
tcf(c_29336,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12244,c_23472]) ).
tcf(c_29338,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12244,c_21216]) ).
tcf(c_29341,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12244,c_5717]) ).
tcf(c_29342,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_12244,c_5041]) ).
tcf(c_29343,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12244,c_5037]) ).
tcf(c_29344,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_17319]) ).
tcf(c_29345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_17312]) ).
tcf(c_29346,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_17054]) ).
tcf(c_29347,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_17047]) ).
tcf(c_29348,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_5558]) ).
tcf(c_29352,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_5557]) ).
tcf(c_29354,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_5326]) ).
tcf(c_29355,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12244,c_5110]) ).
tcf(c_29357,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12244,c_4300]) ).
tcf(c_29358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_5109]) ).
tcf(c_29360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_4325]) ).
tcf(c_29361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12244,c_4296]) ).
tcf(c_29362,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12244,c_4094]) ).
tcf(c_29363,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12244,c_4090]) ).
tcf(c_29376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_2342]) ).
tcf(c_30107,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_16156,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_5162,c_7116,c_7189,c_7560,c_12567,c_12568,c_13342]) ).
tcf(c_30121,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_30107]) ).
tcf(c_30123,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_30107]) ).
tcf(c_30124,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_30107]) ).
tcf(c_30133,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30123,c_23669]) ).
tcf(c_30138,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30121,c_12218]) ).
tcf(c_30165,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_16281,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_3364,c_5162,c_7116,c_7352,c_12567,c_12568,c_13342,c_14050,c_18663,c_28375]) ).
tcf(c_30178,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5293,c_30165]) ).
tcf(c_30180,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4148,c_30165]) ).
tcf(c_30184,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_30165]) ).
tcf(c_30185,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_30165]) ).
tcf(c_30186,plain,
( sequential(sK4,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK4) ),
inference(equality_resolution,[status(thm)],[c_30165]) ).
tcf(c_30187,plain,
( sequential(sK4,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30186,c_2052]) ).
tcf(c_30191,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30180,c_21485]) ).
tcf(c_30196,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30178,c_18362]) ).
tcf(c_30233,plain,
vertex(head_of(sK5(head_of(sK3),tail_of(sK3)))),
inference(global_subsumption_just,[status(thm)],[c_16433,c_2042,c_2067,c_2906,c_2905,c_4455,c_8112]) ).
tcf(c_30236,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2587]) ).
tcf(c_30237,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2586]) ).
tcf(c_30238,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2619]) ).
tcf(c_30239,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2618]) ).
tcf(c_30240,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2526]) ).
tcf(c_30241,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2525]) ).
tcf(c_30242,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2556]) ).
tcf(c_30243,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30233,c_2555]) ).
tcf(c_30244,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_30233,c_114]) ).
tcf(c_30245,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_30233,c_112]) ).
tcf(c_30246,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_30233,c_110]) ).
tcf(c_30247,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_30233,c_107]) ).
tcf(c_30393,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_28634,c_6309]) ).
tcf(c_30395,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_3218]) ).
tcf(c_30396,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_3157]) ).
tcf(c_30397,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_2853]) ).
tcf(c_30398,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_2414]) ).
tcf(c_30402,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_24285]) ).
tcf(c_30404,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30398,c_51]) ).
tcf(c_30409,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30395,c_2402,c_51]) ).
tcf(c_30414,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30397,c_51]) ).
tcf(c_30421,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30393,c_51]) ).
tcf(c_30481,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_20838]) ).
tcf(c_30482,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_30187,c_6309]) ).
tcf(c_30484,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_3218]) ).
tcf(c_30485,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_3157]) ).
tcf(c_30486,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_2853]) ).
tcf(c_30487,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_2414]) ).
tcf(c_30488,plain,
( edge(sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30187,c_63]) ).
tcf(c_30494,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30487,c_51]) ).
tcf(c_30499,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30484,c_2402,c_51]) ).
tcf(c_30504,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30486,c_51]) ).
tcf(c_30511,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30482,c_51]) ).
tcf(c_30518,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30481,c_51]) ).
tcf(c_30535,plain,
edge(sK5(tail_of(sK3),head_of(sK4))),
inference(global_subsumption_just,[status(thm)],[c_30488,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_3364,c_5162,c_7116,c_12567,c_12568,c_13342,c_14050,c_18663,c_28375]) ).
tcf(c_30537,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_15973,c_30535]) ).
tcf(c_30540,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3965]) ).
tcf(c_30541,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3964]) ).
tcf(c_30542,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3921]) ).
tcf(c_30543,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3920]) ).
tcf(c_30544,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3613]) ).
tcf(c_30545,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3612]) ).
tcf(c_30546,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3530]) ).
tcf(c_30547,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3529]) ).
tcf(c_30548,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3487]) ).
tcf(c_30549,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3486]) ).
tcf(c_30550,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3452]) ).
tcf(c_30551,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3451]) ).
tcf(c_30552,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3410]) ).
tcf(c_30553,plain,
! [X0: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3409]) ).
tcf(c_30554,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3095]) ).
tcf(c_30555,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_30535,c_3094]) ).
tcf(c_30556,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_4470]) ).
tcf(c_30557,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_4469]) ).
tcf(c_30558,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4468]) ).
tcf(c_30559,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4467]) ).
tcf(c_30560,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4466]) ).
tcf(c_30561,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4465]) ).
tcf(c_30562,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4464]) ).
tcf(c_30563,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4463]) ).
tcf(c_30564,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30535,c_4124]) ).
tcf(c_30565,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30535,c_4123]) ).
tcf(c_30566,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4122]) ).
tcf(c_30567,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4121]) ).
tcf(c_30568,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4120]) ).
tcf(c_30569,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_6021]) ).
tcf(c_30570,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4119]) ).
tcf(c_30571,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4118]) ).
tcf(c_30572,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_6020]) ).
tcf(c_30573,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30535,c_5995]) ).
tcf(c_30574,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30535,c_5994]) ).
tcf(c_30575,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5969]) ).
tcf(c_30576,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4117]) ).
tcf(c_30577,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5968]) ).
tcf(c_30578,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5438]) ).
tcf(c_30579,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5437]) ).
tcf(c_30580,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5412]) ).
tcf(c_30581,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5411]) ).
tcf(c_30582,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5286]) ).
tcf(c_30583,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_5285]) ).
tcf(c_30584,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4880]) ).
tcf(c_30585,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),tail_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4879]) ).
tcf(c_30586,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4852]) ).
tcf(c_30587,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK4))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_4851]) ).
tcf(c_30588,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3966]) ).
tcf(c_30589,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3922]) ).
tcf(c_30590,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3614]) ).
tcf(c_30591,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3531]) ).
tcf(c_30592,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_2719]) ).
tcf(c_30593,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_2718]) ).
tcf(c_30594,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2697]) ).
tcf(c_30595,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3488]) ).
tcf(c_30596,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_3453]) ).
tcf(c_30597,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2696]) ).
tcf(c_30598,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2673]) ).
tcf(c_30599,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2672]) ).
tcf(c_30600,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2648]) ).
tcf(c_30601,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( head_of(sK5(head_of(sK5(tail_of(sK3),head_of(sK4))),head_of(sK3))) = head_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_30535,c_2647]) ).
tcf(c_30602,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_3411]) ).
tcf(c_30603,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(tail_of(sK3),head_of(sK4))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_30535,c_3096]) ).
tcf(c_31168,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_105]) ).
tcf(c_31169,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_79]) ).
tcf(c_31172,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_16004]) ).
tcf(c_31173,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_14361]) ).
tcf(c_31176,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_2771]) ).
tcf(c_31178,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_30414,c_6165]) ).
tcf(c_31180,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30414,c_2359]) ).
tcf(c_31181,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_2181]) ).
tcf(c_31182,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_2192]) ).
tcf(c_31183,plain,
! [X0: $i] :
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK0) ),
inference(superposition,[status(thm)],[c_30414,c_2100]) ).
tcf(c_31187,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30414,c_9401]) ).
tcf(c_31188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_11498]) ).
tcf(c_31191,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_19354]) ).
tcf(c_31368,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_12245]) ).
tcf(c_31369,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_12245]) ).
tcf(c_31370,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_12245]) ).
tcf(c_31371,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_17319]) ).
tcf(c_31372,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_17054]) ).
tcf(c_31373,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_5558]) ).
tcf(c_31374,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_5327]) ).
tcf(c_31375,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_5110]) ).
tcf(c_31376,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_4326]) ).
tcf(c_31377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_2342]) ).
tcf(c_31378,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_61]) ).
tcf(c_31380,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12245,c_23472]) ).
tcf(c_31382,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12245,c_21216]) ).
tcf(c_31385,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12245,c_5717]) ).
tcf(c_31386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_12245,c_5041]) ).
tcf(c_31387,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12245,c_5037]) ).
tcf(c_31388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_17319]) ).
tcf(c_31389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_17312]) ).
tcf(c_31390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_17054]) ).
tcf(c_31391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_17047]) ).
tcf(c_31392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_5558]) ).
tcf(c_31398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_5326]) ).
tcf(c_31399,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12245,c_5110]) ).
tcf(c_31401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12245,c_4300]) ).
tcf(c_31402,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_5109]) ).
tcf(c_31404,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_4325]) ).
tcf(c_31405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12245,c_4296]) ).
tcf(c_31406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12245,c_4094]) ).
tcf(c_31407,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12245,c_4090]) ).
tcf(c_31420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_2342]) ).
tcf(c_31731,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_16890,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_5162,c_6818,c_7116,c_7189,c_7560,c_12567,c_12568,c_13342]) ).
tcf(c_31745,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_31731]) ).
tcf(c_31747,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_31731]) ).
tcf(c_31748,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15979,c_31731]) ).
tcf(c_31752,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31748,c_30535]) ).
tcf(c_31757,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31747,c_23669]) ).
tcf(c_31762,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31745,c_12218]) ).
tcf(c_31767,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17056,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_5162,c_6770,c_7116,c_7189,c_12567,c_12568,c_13342]) ).
tcf(c_31784,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_6099,c_31767]) ).
tcf(c_31785,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5490,c_31767]) ).
tcf(c_31790,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5767,c_31767]) ).
tcf(c_31792,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4365,c_31767]) ).
tcf(c_31793,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15981,c_31767]) ).
tcf(c_31794,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_15978,c_31767]) ).
tcf(c_31801,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12236,c_31767]) ).
tcf(c_31804,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12237,c_31767]) ).
tcf(c_31807,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_31767]) ).
tcf(c_31808,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31807,c_2042]) ).
tcf(c_31812,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31794,c_30535]) ).
tcf(c_31817,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31793,c_30535]) ).
tcf(c_31822,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31792,c_23669]) ).
tcf(c_31827,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31790,c_23669]) ).
tcf(c_31832,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31785,c_12218]) ).
tcf(c_31837,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31784,c_12218]) ).
tcf(c_31867,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17163,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_3364,c_5162,c_6045,c_7116,c_12567,c_12568,c_13342,c_14050,c_15973,c_18663,c_28375]) ).
tcf(c_31881,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_31867]) ).
tcf(c_31883,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_31867]) ).
tcf(c_31888,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31883,c_23669]) ).
tcf(c_31893,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31881,c_12218]) ).
tcf(c_31921,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(X0)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_17321,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_3364,c_5162,c_7116,c_12567,c_12568,c_13342,c_14050,c_17321,c_18663,c_28375]) ).
tcf(c_31938,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_6099,c_31921]) ).
tcf(c_31939,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5490,c_31921]) ).
tcf(c_31944,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5767,c_31921]) ).
tcf(c_31946,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4365,c_31921]) ).
tcf(c_31952,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_15974,c_31921]) ).
tcf(c_31955,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12236,c_31921]) ).
tcf(c_31958,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12237,c_31921]) ).
tcf(c_31961,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK3) ),
inference(equality_resolution,[status(thm)],[c_31921]) ).
tcf(c_31962,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31961,c_2042]) ).
tcf(c_31971,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31946,c_23669]) ).
tcf(c_31976,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31944,c_23669]) ).
tcf(c_31981,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31939,c_12218]) ).
tcf(c_31986,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),tail_of(sK3)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31938,c_12218]) ).
tcf(c_32118,plain,
( precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_20838]) ).
tcf(c_32119,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_31808,c_6309]) ).
tcf(c_32120,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_6222]) ).
tcf(c_32121,plain,
( precedes(sK5(head_of(sK4),tail_of(sK3)),sK4,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_3218]) ).
tcf(c_32122,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_3157]) ).
tcf(c_32123,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_31808,c_2853]) ).
tcf(c_32124,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_2414]) ).
tcf(c_32127,plain,
( edge(sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_31808,c_62]) ).
tcf(c_32128,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_31808,c_557]) ).
tcf(c_32135,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK3,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32124,c_50]) ).
tcf(c_32140,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32123,c_50]) ).
tcf(c_32147,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32119,c_50]) ).
tcf(c_32154,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32120,c_52,c_50]) ).
tcf(c_32162,plain,
edge(sK5(head_of(sK4),tail_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_32127,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_5162,c_7116,c_7189,c_12567,c_12568,c_13342]) ).
tcf(c_32164,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3965]) ).
tcf(c_32165,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3964]) ).
tcf(c_32166,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3921]) ).
tcf(c_32167,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3920]) ).
tcf(c_32168,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3613]) ).
tcf(c_32169,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3612]) ).
tcf(c_32170,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3530]) ).
tcf(c_32171,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3529]) ).
tcf(c_32172,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3487]) ).
tcf(c_32173,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3486]) ).
tcf(c_32174,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3452]) ).
tcf(c_32175,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3451]) ).
tcf(c_32176,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3410]) ).
tcf(c_32177,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3409]) ).
tcf(c_32178,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3095]) ).
tcf(c_32179,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ( head_of(sK5(head_of(X0),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_32162,c_3094]) ).
tcf(c_32180,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_4470]) ).
tcf(c_32181,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_4469]) ).
tcf(c_32182,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4468]) ).
tcf(c_32183,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4467]) ).
tcf(c_32184,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4466]) ).
tcf(c_32185,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4465]) ).
tcf(c_32186,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4464]) ).
tcf(c_32187,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4463]) ).
tcf(c_32188,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_32162,c_4124]) ).
tcf(c_32189,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_32162,c_4123]) ).
tcf(c_32190,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4122]) ).
tcf(c_32191,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4121]) ).
tcf(c_32192,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4120]) ).
tcf(c_32193,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_6021]) ).
tcf(c_32194,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4119]) ).
tcf(c_32195,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4118]) ).
tcf(c_32196,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_6020]) ).
tcf(c_32197,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_32162,c_5995]) ).
tcf(c_32198,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_32162,c_5994]) ).
tcf(c_32199,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5969]) ).
tcf(c_32200,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4117]) ).
tcf(c_32201,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5968]) ).
tcf(c_32202,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5438]) ).
tcf(c_32203,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5437]) ).
tcf(c_32204,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5412]) ).
tcf(c_32205,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5411]) ).
tcf(c_32206,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5286]) ).
tcf(c_32207,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_5285]) ).
tcf(c_32208,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4880]) ).
tcf(c_32209,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),tail_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4879]) ).
tcf(c_32210,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4852]) ).
tcf(c_32211,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK4))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_4851]) ).
tcf(c_32212,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3966]) ).
tcf(c_32213,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3922]) ).
tcf(c_32214,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3614]) ).
tcf(c_32215,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3531]) ).
tcf(c_32216,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_2719]) ).
tcf(c_32217,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_2718]) ).
tcf(c_32218,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2697]) ).
tcf(c_32219,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3488]) ).
tcf(c_32220,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_3453]) ).
tcf(c_32221,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2696]) ).
tcf(c_32222,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2673]) ).
tcf(c_32223,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2672]) ).
tcf(c_32224,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2648]) ).
tcf(c_32225,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),tail_of(sK3))),head_of(sK3))) = head_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_32162,c_2647]) ).
tcf(c_32226,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_3411]) ).
tcf(c_32227,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK5(head_of(sK4),tail_of(sK3))))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_32162,c_3096]) ).
tcf(c_32670,plain,
( precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_20838]) ).
tcf(c_32671,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_31962,c_6309]) ).
tcf(c_32672,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_6222]) ).
tcf(c_32673,plain,
( precedes(sK5(tail_of(sK3),head_of(sK4)),sK4,sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_3218]) ).
tcf(c_32674,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_3157]) ).
tcf(c_32675,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_31962,c_2853]) ).
tcf(c_32676,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK3,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK4)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_2414]) ).
tcf(c_32680,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_31962,c_557]) ).
tcf(c_32684,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK4)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32676,c_50]) ).
tcf(c_32689,plain,
! [X0: $i] :
( precedes(X0,sK3,sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32675,c_50]) ).
tcf(c_32696,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32671,c_50]) ).
tcf(c_32703,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32672,c_52,c_50]) ).
tcf(c_32745,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK3),head_of(sK4))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_30421]) ).
tcf(c_32746,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_28634,c_30421]) ).
tcf(c_32770,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(tail_of(sK3),head_of(sK4)),sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_105]) ).
tcf(c_32771,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_79]) ).
tcf(c_32774,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_16004]) ).
tcf(c_32775,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_14361]) ).
tcf(c_32778,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_2771]) ).
tcf(c_32780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(X1,sK5(tail_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_30504,c_6165]) ).
tcf(c_32782,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30504,c_2359]) ).
tcf(c_32783,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_2181]) ).
tcf(c_32784,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_2192]) ).
tcf(c_32785,plain,
! [X0: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK0) ),
inference(superposition,[status(thm)],[c_30504,c_2100]) ).
tcf(c_32788,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30504,c_9401]) ).
tcf(c_32789,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_11498]) ).
tcf(c_32790,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_17491]) ).
tcf(c_32791,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_19354]) ).
tcf(c_32990,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_30511]) ).
tcf(c_32991,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30187,c_30511]) ).
tcf(c_33013,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| precedes(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK3,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_32140]) ).
tcf(c_33035,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(head_of(sK4),tail_of(sK3)),X0),sK3)
| ~ on_path(sK7(sK0,sK5(head_of(sK4),tail_of(sK3)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_32147]) ).
tcf(c_33036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(head_of(sK4),tail_of(sK3)),X3)
| ( X0 = X1 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),tail_of(sK3)),X3),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),tail_of(sK3)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_32147]) ).
tcf(c_33037,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_31808,c_32147]) ).
tcf(c_33056,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_32154,c_31808,c_32154]) ).
tcf(c_33073,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5552,c_12246]) ).
tcf(c_33074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_17319]) ).
tcf(c_33075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_17054]) ).
tcf(c_33076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_5558]) ).
tcf(c_33077,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_5327]) ).
tcf(c_33078,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_5110]) ).
tcf(c_33079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_4326]) ).
tcf(c_33080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_2342]) ).
tcf(c_33081,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_61]) ).
tcf(c_33082,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_31921]) ).
tcf(c_33083,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_31767]) ).
tcf(c_33084,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_28483]) ).
tcf(c_33086,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_23326]) ).
tcf(c_33088,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_20112]) ).
tcf(c_33089,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_19674]) ).
tcf(c_33093,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_17319]) ).
tcf(c_33094,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12246,c_17312]) ).
tcf(c_33095,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_17054]) ).
tcf(c_33096,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_17047]) ).
tcf(c_33097,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5558]) ).
tcf(c_33098,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4688]) ).
tcf(c_33099,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4684]) ).
tcf(c_33100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4422]) ).
tcf(c_33101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_5557]) ).
tcf(c_33102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12246,c_5327]) ).
tcf(c_33103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12246,c_5326]) ).
tcf(c_33104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5110]) ).
tcf(c_33105,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4418]) ).
tcf(c_33107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_5109]) ).
tcf(c_33108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12246,c_4326]) ).
tcf(c_33109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_4325]) ).
tcf(c_33113,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_3375]) ).
tcf(c_33114,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_3371]) ).
tcf(c_33117,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5500]) ).
tcf(c_33118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5496]) ).
tcf(c_33119,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4374]) ).
tcf(c_33120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_4370]) ).
tcf(c_33123,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_2388]) ).
tcf(c_33124,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_2387]) ).
tcf(c_33125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_2342]) ).
tcf(c_33126,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_74]) ).
tcf(c_33937,plain,
vertex(tail_of(sK5(head_of(sK3),tail_of(sK3)))),
inference(global_subsumption_just,[status(thm)],[c_18011,c_2042,c_2067,c_2906,c_2905,c_4455,c_8111]) ).
tcf(c_33942,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2587]) ).
tcf(c_33943,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2586]) ).
tcf(c_33944,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2619]) ).
tcf(c_33945,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2618]) ).
tcf(c_33946,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2526]) ).
tcf(c_33947,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2525]) ).
tcf(c_33948,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2556]) ).
tcf(c_33949,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33937,c_2555]) ).
tcf(c_33950,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33937,c_114]) ).
tcf(c_33951,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33937,c_112]) ).
tcf(c_33952,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33937,c_110]) ).
tcf(c_33953,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33937,c_107]) ).
tcf(c_34026,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK4) ) ),
inference(global_subsumption_just,[status(thm)],[c_18926,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_5162,c_6427,c_7116,c_7189,c_12567,c_12568,c_13342]) ).
tcf(c_34039,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5293,c_34026]) ).
tcf(c_34041,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4148,c_34026]) ).
tcf(c_34045,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_34026]) ).
tcf(c_34046,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_34026]) ).
tcf(c_34047,plain,
( sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK4) ),
inference(equality_resolution,[status(thm)],[c_34026]) ).
tcf(c_34048,plain,
( sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34047,c_2052]) ).
tcf(c_34052,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34041,c_21485]) ).
tcf(c_34057,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34039,c_18362]) ).
tcf(c_34076,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ edge(X0)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_19054,c_52,c_51,c_50,c_53,c_656,c_2042,c_2052,c_2455,c_2906,c_2952,c_3364,c_5162,c_6045,c_7116,c_12567,c_12568,c_13342,c_14050,c_18663,c_28375]) ).
tcf(c_34090,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_5552,c_34076]) ).
tcf(c_34092,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_5104,c_34076]) ).
tcf(c_34097,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34092,c_23669]) ).
tcf(c_34102,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK3),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34090,c_12218]) ).
tcf(c_34115,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_20838]) ).
tcf(c_34116,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34048,c_6309]) ).
tcf(c_34118,plain,
( precedes(sK4,sK4,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_3218]) ).
tcf(c_34119,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_3157]) ).
tcf(c_34120,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_2853]) ).
tcf(c_34121,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_2414]) ).
tcf(c_34125,plain,
( precedes(sK4,sK3,sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_32140]) ).
tcf(c_34126,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34121,c_51]) ).
tcf(c_34131,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34125,c_13517,c_51]) ).
tcf(c_34136,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34118,c_2402,c_51]) ).
tcf(c_34141,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34120,c_51]) ).
tcf(c_34148,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34116,c_51]) ).
tcf(c_34155,plain,
( precedes(sK4,sK5(head_of(sK3),head_of(sK4)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34115,c_51]) ).
tcf(c_34172,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_34048,c_32128]) ).
tcf(c_34195,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_30187,c_32680]) ).
tcf(c_34206,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ vertex(tail_of(sK3))
| ~ vertex(head_of(sK4))
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_34172,c_117]) ).
tcf(c_34207,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_34172,c_66]) ).
tcf(c_34212,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34172,c_30165]) ).
tcf(c_34215,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34172,c_28612]) ).
tcf(c_34217,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34172,c_23286]) ).
tcf(c_34218,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34172,c_21490]) ).
tcf(c_34221,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34172,c_21163]) ).
tcf(c_34226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),tail_of(sK3)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_34172,c_66]) ).
tcf(c_34228,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_34172,c_61]) ).
tcf(c_34244,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = X0 )
| ~ edge(X0)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34228,c_32162]) ).
tcf(c_34251,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34221,c_32162]) ).
tcf(c_34257,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34218,c_32162]) ).
tcf(c_34263,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34217,c_32162]) ).
tcf(c_34269,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34215,c_32162]) ).
tcf(c_34275,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34212,c_32162]) ).
tcf(c_34281,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34206,c_15970,c_4461,c_4115]) ).
tcf(c_34318,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| precedes(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK3,sK0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK7(sK0,X0,sK5(tail_of(sK3),head_of(sK4))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_32689]) ).
tcf(c_34341,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(tail_of(sK3),head_of(sK4)),X0),sK3)
| ~ on_path(sK7(sK0,sK5(tail_of(sK3),head_of(sK4)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_32696]) ).
tcf(c_34342,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(tail_of(sK3),head_of(sK4)),X3)
| ( X0 = X1 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(tail_of(sK3),head_of(sK4)),X3),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(tail_of(sK3),head_of(sK4)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_32696]) ).
tcf(c_34343,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK0)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_31962,c_32696]) ).
tcf(c_34362,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_32703,c_31962,c_32703]) ).
tcf(c_34384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),tail_of(sK3)),sK0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_105]) ).
tcf(c_34385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_79]) ).
tcf(c_34388,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_16004]) ).
tcf(c_34389,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_14361]) ).
tcf(c_34392,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_2771]) ).
tcf(c_34394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(X1,sK5(head_of(sK4),tail_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_34141,c_6165]) ).
tcf(c_34396,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34141,c_2359]) ).
tcf(c_34397,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_2181]) ).
tcf(c_34398,plain,
! [X0: $i] :
( edge(X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_2192]) ).
tcf(c_34399,plain,
! [X0: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK0) ),
inference(superposition,[status(thm)],[c_34141,c_2100]) ).
tcf(c_34402,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(sK7(sK0,X0,X1),sK4)
| ~ on_path(sK7(sK0,X0,X1),sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34141,c_9401]) ).
tcf(c_34403,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(X3,sK0)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_11498]) ).
tcf(c_34404,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_17491]) ).
tcf(c_34405,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_19354]) ).
tcf(c_34555,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ sequential(sK4,sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))))
| ~ on_path(sK7(sK0,X0,sK5(head_of(sK4),tail_of(sK3))),sK0) ),
inference(superposition,[status(thm)],[c_2247,c_34148]) ).
tcf(c_34556,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34048,c_34148]) ).
tcf(c_34573,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_12247]) ).
tcf(c_34574,plain,
( ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_12247]) ).
tcf(c_34575,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_12247]) ).
tcf(c_34576,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_17319]) ).
tcf(c_34577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_17054]) ).
tcf(c_34578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_5558]) ).
tcf(c_34579,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_5327]) ).
tcf(c_34580,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_5110]) ).
tcf(c_34581,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_4326]) ).
tcf(c_34582,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_2342]) ).
tcf(c_34583,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_61]) ).
tcf(c_34584,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_31921]) ).
tcf(c_34585,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_31767]) ).
tcf(c_34586,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_28483]) ).
tcf(c_34588,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_23326]) ).
tcf(c_34590,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_20112]) ).
tcf(c_34591,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_19674]) ).
tcf(c_34595,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_17319]) ).
tcf(c_34596,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12247,c_17312]) ).
tcf(c_34597,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_17054]) ).
tcf(c_34598,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_17047]) ).
tcf(c_34599,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5558]) ).
tcf(c_34600,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4688]) ).
tcf(c_34601,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4684]) ).
tcf(c_34602,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4422]) ).
tcf(c_34603,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5557]) ).
tcf(c_34604,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12247,c_5327]) ).
tcf(c_34605,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_5326]) ).
tcf(c_34606,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5110]) ).
tcf(c_34607,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4418]) ).
tcf(c_34609,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_5109]) ).
tcf(c_34610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12247,c_4326]) ).
tcf(c_34611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_4325]) ).
tcf(c_34615,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_3375]) ).
tcf(c_34616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_3371]) ).
tcf(c_34617,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_6109]) ).
tcf(c_34618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_6105]) ).
tcf(c_34619,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5500]) ).
tcf(c_34620,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5496]) ).
tcf(c_34621,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4374]) ).
tcf(c_34622,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_4370]) ).
tcf(c_34623,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_3749]) ).
tcf(c_34624,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_3745]) ).
tcf(c_34625,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_2388]) ).
tcf(c_34626,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK4,X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_2387]) ).
tcf(c_34627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_2342]) ).
tcf(c_34628,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_74]) ).
tcf(c_35136,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_34244]) ).
tcf(c_35137,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_34244]) ).
tcf(c_35139,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_34244]) ).
tcf(c_35140,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_34244]) ).
tcf(c_35143,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12244,c_34244]) ).
tcf(c_35145,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12245,c_34244]) ).
tcf(c_35225,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| shortest_path(X2,X3,X4)
| on_path(sK7(sK6(X2,X3,X4),X0,X1),sK6(X2,X3,X4))
| ( X2 = X3 )
| ~ path(X2,X3,X4)
| ~ precedes(X0,X1,sK6(X2,X3,X4)) ),
inference(superposition,[status(thm)],[c_69,c_3829]) ).
tcf(c_35258,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_34195,c_66]) ).
tcf(c_35260,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_34195,c_34026]) ).
tcf(c_35266,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_34195,c_28612]) ).
tcf(c_35268,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_34195,c_23286]) ).
tcf(c_35269,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_34195,c_21490]) ).
tcf(c_35272,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_34195,c_21163]) ).
tcf(c_35277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK4)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_34195,c_66]) ).
tcf(c_35279,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_34195,c_61]) ).
tcf(c_35295,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(tail_of(sK3),head_of(sK4)) = X0 )
| ~ edge(X0)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35279,c_30535]) ).
tcf(c_35302,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35272,c_30535]) ).
tcf(c_35308,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35269,c_30535]) ).
tcf(c_35314,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35268,c_30535]) ).
tcf(c_35320,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35266,c_30535]) ).
tcf(c_35326,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35260,c_30535]) ).
tcf(c_35356,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15975,c_5721]) ).
tcf(c_35357,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15980,c_5721]) ).
tcf(c_35360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_5721]) ).
tcf(c_35361,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_5721]) ).
tcf(c_35363,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_5721]) ).
tcf(c_35364,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_5721]) ).
tcf(c_35367,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_12244,c_5721]) ).
tcf(c_35369,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_12245,c_5721]) ).
tcf(c_35430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_5767,c_5773]) ).
tcf(c_35433,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_5773]) ).
tcf(c_35434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_5773]) ).
tcf(c_35437,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_5773]) ).
tcf(c_35438,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_5773]) ).
tcf(c_35441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12236,c_5773]) ).
tcf(c_35444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_12237,c_5773]) ).
tcf(c_35445,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5773]) ).
tcf(c_35447,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5773]) ).
tcf(c_35449,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK3,X0) ),
inference(equality_resolution,[status(thm)],[c_5773]) ).
tcf(c_35520,plain,
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5552,c_12248]) ).
tcf(c_35522,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12248,c_66]) ).
tcf(c_35523,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_34076]) ).
tcf(c_35525,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_31867]) ).
tcf(c_35526,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_31731]) ).
tcf(c_35528,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_30107]) ).
tcf(c_35529,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_28724]) ).
tcf(c_35531,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_23672]) ).
tcf(c_35534,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_21374]) ).
tcf(c_35535,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_21334]) ).
tcf(c_35537,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_18365]) ).
tcf(c_35539,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_13367]) ).
tcf(c_35541,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12248,c_66]) ).
tcf(c_35542,plain,
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK4)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_2149]) ).
tcf(c_35543,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12248,c_61]) ).
tcf(c_35703,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_35295]) ).
tcf(c_35704,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_35295]) ).
tcf(c_35706,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_35295]) ).
tcf(c_35707,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_35295]) ).
tcf(c_35710,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12244,c_35295]) ).
tcf(c_35712,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) ),
inference(superposition,[status(thm)],[c_12245,c_35295]) ).
tcf(c_35765,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_35449]) ).
tcf(c_35766,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_35449]) ).
tcf(c_35767,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35765,c_50]) ).
tcf(c_35806,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15981,c_5777]) ).
tcf(c_35807,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15978,c_5777]) ).
tcf(c_35810,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15976,c_5777]) ).
tcf(c_35811,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15974,c_5777]) ).
tcf(c_35814,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12236,c_5777]) ).
tcf(c_35817,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12237,c_5777]) ).
tcf(c_35818,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12246,c_5777]) ).
tcf(c_35820,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12247,c_5777]) ).
tcf(c_35822,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK3,sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(equality_resolution,[status(thm)],[c_5777]) ).
tcf(c_35881,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_2309,c_35822]) ).
tcf(c_35882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2308,c_35822]) ).
tcf(c_35883,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35881,c_50]) ).
tcf(c_35931,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_105]) ).
tcf(c_35932,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X3,sK4)
| ~ on_path(X3,sK0)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_79]) ).
tcf(c_35935,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_16004]) ).
tcf(c_35936,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_14361]) ).
tcf(c_35939,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_2771]) ).
tcf(c_35941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_21487,c_6165]) ).
tcf(c_35944,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK0,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_21487,c_2181]) ).
tcf(c_36043,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK4)
| ~ on_path(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_22126]) ).
tcf(c_36044,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_22126]) ).
tcf(c_36075,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),head_of(sK3)),X0)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK3)
| ~ on_path(sK7(sK0,sK5(head_of(sK4),head_of(sK3)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_22362]) ).
tcf(c_36076,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(head_of(sK4),head_of(sK3)),X3)
| ( X0 = X1 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),head_of(sK3)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_22362]) ).
tcf(c_36131,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK4)),X0)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(tail_of(sK3),head_of(sK4)),X0),sK4)
| ~ on_path(sK7(sK0,sK5(tail_of(sK3),head_of(sK4)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_32782]) ).
tcf(c_36132,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(tail_of(sK3),head_of(sK4)),X3)
| ( X0 = X1 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(tail_of(sK3),head_of(sK4)),X3),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(tail_of(sK3),head_of(sK4)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_32782]) ).
tcf(c_36160,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_3740,c_12249]) ).
tcf(c_36161,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_17319]) ).
tcf(c_36162,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_17054]) ).
tcf(c_36164,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_5327]) ).
tcf(c_36165,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_5110]) ).
tcf(c_36166,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_4326]) ).
tcf(c_36167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_2342]) ).
tcf(c_36168,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_61]) ).
tcf(c_36169,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12249,c_5777]) ).
tcf(c_36171,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12249,c_5773]) ).
tcf(c_36174,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_12249,c_31921]) ).
tcf(c_36175,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_12249,c_31767]) ).
tcf(c_36176,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_12249,c_28483]) ).
tcf(c_36178,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_12249,c_23326]) ).
tcf(c_36186,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_17312]) ).
tcf(c_36188,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_17047]) ).
tcf(c_36194,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_5327]) ).
tcf(c_36195,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_5326]) ).
tcf(c_36199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_5109]) ).
tcf(c_36200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_4326]) ).
tcf(c_36201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_4325]) ).
tcf(c_36211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12249,c_4374]) ).
tcf(c_36212,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_12249,c_4370]) ).
tcf(c_36217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_2342]) ).
tcf(c_36220,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36160,c_7653]) ).
tcf(c_36523,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK0)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2))
| ~ precedes(X0,sK7(sK0,X1,X2),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9391,c_77]) ).
tcf(c_36548,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ on_path(sK7(sK0,X1,X2),sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2309,c_36523]) ).
tcf(c_36549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK0,X1,X2))
| ~ on_path(X3,sK0)
| ~ sequential(X3,X1)
| ~ path(X4,X5,sK0)
| ~ precedes(X1,X2,sK0)
| ~ precedes(X0,sK7(sK0,X1,X2),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),X3)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,X2)),sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2228,c_36523]) ).
tcf(c_36550,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK0,X2,X3))
| sequential(X0,sK7(sK0,X1,sK7(sK0,X2,X3)))
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),sK7(sK0,X1,sK7(sK0,X2,X3)))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3)))) )
| ~ on_path(X4,sK0)
| ~ sequential(X4,X2)
| ~ path(X5,X6,sK0)
| ~ precedes(X2,X3,sK0)
| ~ precedes(X1,sK7(sK0,X2,X3),sK0)
| ~ precedes(X0,sK7(sK0,X1,sK7(sK0,X2,X3)),sK0)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),X4)
| ~ sequential(sK7(sK0,X0,sK7(sK0,X1,sK7(sK0,X2,X3))),sK7(sK0,X2,X3)) ),
inference(superposition,[status(thm)],[c_10127,c_36523]) ).
tcf(c_36551,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ sequential(X0,X1)
| ~ path(X3,X4,sK0)
| ~ precedes(X1,X2,sK0)
| ~ sequential(X0,sK7(sK0,X1,X2)) ),
inference(superposition,[status(thm)],[c_9376,c_36523]) ).
tcf(c_36610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_34207]) ).
tcf(c_36611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_34207]) ).
tcf(c_36612,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_5767,c_34207]) ).
tcf(c_36613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4678,c_34207]) ).
tcf(c_36614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4365,c_34207]) ).
tcf(c_36615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15981,c_34207]) ).
tcf(c_36616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_15978,c_34207]) ).
tcf(c_36617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_34207]) ).
tcf(c_36618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12242,c_34207]) ).
tcf(c_36619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12238,c_34207]) ).
tcf(c_36620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_34207]) ).
tcf(c_36621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12243,c_34207]) ).
tcf(c_36622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12239,c_34207]) ).
tcf(c_36623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_34207]) ).
tcf(c_36624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12246,c_34207]) ).
tcf(c_36625,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_34207]) ).
tcf(c_36626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_12247,c_34207]) ).
tcf(c_36627,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_34207]) ).
tcf(c_36628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_34207]) ).
tcf(c_36629,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_34207]) ).
tcf(c_36869,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK4) != head_of(sK4) )
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_34226]) ).
tcf(c_36871,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_34226]) ).
tcf(c_36872,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_34226]) ).
tcf(c_36873,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_34226]) ).
tcf(c_36874,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_34226]) ).
tcf(c_36875,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_34226]) ).
tcf(c_36876,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_34226]) ).
tcf(c_36877,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_34226]) ).
tcf(c_36879,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_34226]) ).
tcf(c_36880,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_34226]) ).
tcf(c_36881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_34226]) ).
tcf(c_36882,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_34226]) ).
tcf(c_36883,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_34226]) ).
tcf(c_36888,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_34226]) ).
tcf(c_36889,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_34226]) ).
tcf(c_36890,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_34226]) ).
tcf(c_36891,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_34226]) ).
tcf(c_36892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_34226]) ).
tcf(c_36893,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_34226]) ).
tcf(c_36894,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12246,c_34226]) ).
tcf(c_36896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12247,c_34226]) ).
tcf(c_36898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_34226]) ).
tcf(c_36899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2047,c_34226]) ).
tcf(c_36900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_34226]) ).
tcf(c_36901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_34226]) ).
tcf(c_36902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_34226]) ).
tcf(c_36903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_34226]) ).
tcf(c_36904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_34226]) ).
tcf(c_36905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_34226]) ).
tcf(c_36906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_34226]) ).
tcf(c_36907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_34226]) ).
tcf(c_36908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_34226]) ).
tcf(c_36909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_34226]) ).
tcf(c_36910,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_34226]) ).
tcf(c_36911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_34226]) ).
tcf(c_36912,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_34226]) ).
tcf(c_36913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_34226]) ).
tcf(c_36914,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15975,c_34226]) ).
tcf(c_36916,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_34226]) ).
tcf(c_36917,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_34226]) ).
tcf(c_36918,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_34226]) ).
tcf(c_36919,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_34226]) ).
tcf(c_36920,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_34226]) ).
tcf(c_36921,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_34226]) ).
tcf(c_36922,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_34226]) ).
tcf(c_36923,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_34226]) ).
tcf(c_36924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_34226]) ).
tcf(c_36925,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_34226]) ).
tcf(c_36926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_34226]) ).
tcf(c_36927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_34226]) ).
tcf(c_36928,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_34226]) ).
tcf(c_36929,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_34226]) ).
tcf(c_36941,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(equality_resolution_simp,[status(thm)],[c_36869]) ).
tcf(c_38199,plain,
! [X0: $i] :
( ~ precedes(X0,sK3,sK0)
| ~ on_path(X0,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| precedes(X0,sK4,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_6906,c_2881,c_6906]) ).
tcf(c_38200,plain,
! [X0: $i] :
( precedes(X0,sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ on_path(X0,sK0)
| ~ precedes(X0,sK3,sK0) ),
inference(renaming,[status(thm)],[c_38199]) ).
tcf(c_38210,plain,
! [X0: $i] :
( precedes(X0,sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ on_path(sK3,sK0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(superposition,[status(thm)],[c_2309,c_38200]) ).
tcf(c_38211,plain,
! [X0: $i] :
( sequential(X0,sK3)
| precedes(sK7(sK0,X0,sK3),sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK3),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK0)
| ~ on_path(sK7(sK0,X0,sK3),sK0) ),
inference(superposition,[status(thm)],[c_2228,c_38200]) ).
tcf(c_38212,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK0,X1,sK3))
| precedes(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3),sK3)) = head_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK7(sK0,X1,sK3)),sK7(sK0,X1,sK3))) = head_of(sK7(sK0,X0,sK7(sK0,X1,sK3))) )
| ~ precedes(X1,sK3,sK0)
| ~ precedes(X0,sK7(sK0,X1,sK3),sK0)
| ~ on_path(sK7(sK0,X0,sK7(sK0,X1,sK3)),sK0) ),
inference(superposition,[status(thm)],[c_10127,c_38200]) ).
tcf(c_38213,plain,
! [X0: $i] :
( precedes(X0,sK4,sK0)
| ( tail_of(sK7(sK0,sK7(sK0,X0,sK3),sK3)) = head_of(sK7(sK0,X0,sK3)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_38210,c_50]) ).
tcf(c_38275,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_34195,c_13650]) ).
tcf(c_38277,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34172,c_13650]) ).
tcf(c_38279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_13650]) ).
tcf(c_38280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_13650]) ).
tcf(c_38317,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34195,c_13777]) ).
tcf(c_38319,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34172,c_13777]) ).
tcf(c_38321,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_13777]) ).
tcf(c_38322,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_13777]) ).
tcf(c_38359,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK3)),X0)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK0)
| ~ sequential(sK7(sK0,sK5(head_of(sK4),tail_of(sK3)),X0),sK4)
| ~ on_path(sK7(sK0,sK5(head_of(sK4),tail_of(sK3)),X0),sK0) ),
inference(superposition,[status(thm)],[c_2134,c_34396]) ).
tcf(c_38360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( shortest_path(X0,X1,X2)
| sequential(sK5(head_of(sK4),tail_of(sK3)),X3)
| ( X0 = X1 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X3,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),tail_of(sK3)),X3),sK4)
| ~ on_path(sK7(sK6(X0,X1,X2),sK5(head_of(sK4),tail_of(sK3)),X3),sK0) ),
inference(superposition,[status(thm)],[c_2163,c_34396]) ).
tcf(c_38396,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_22129]) ).
tcf(c_38397,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_22129]) ).
tcf(c_38402,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_22129]) ).
tcf(c_38403,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_22129]) ).
tcf(c_38452,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_22365]) ).
tcf(c_38453,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_24278,c_22365]) ).
tcf(c_38458,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_22365]) ).
tcf(c_38459,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_22365]) ).
tcf(c_38529,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30414,c_29106]) ).
tcf(c_38535,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_29106]) ).
tcf(c_38536,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_29106]) ).
tcf(c_38580,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_30504,c_31183]) ).
tcf(c_38581,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_31183]) ).
tcf(c_38665,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK0)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK0) ),
inference(superposition,[status(thm)],[c_34141,c_32785]) ).
tcf(c_38706,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_12250]) ).
tcf(c_38707,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_12250]) ).
tcf(c_38708,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_12250]) ).
tcf(c_38710,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12250,c_66]) ).
tcf(c_38713,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_34076]) ).
tcf(c_38715,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_31867]) ).
tcf(c_38716,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_31731]) ).
tcf(c_38718,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_30107]) ).
tcf(c_38719,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_28724]) ).
tcf(c_38721,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_23672]) ).
tcf(c_38724,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_21374]) ).
tcf(c_38725,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_21334]) ).
tcf(c_38727,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_18365]) ).
tcf(c_38728,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_13447]) ).
tcf(c_38729,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_13367]) ).
tcf(c_38730,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_12129]) ).
tcf(c_38731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_12250,c_66]) ).
tcf(c_38732,plain,
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK4)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_2149]) ).
tcf(c_38733,plain,
! [X0: $i] :
( sequential(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))))
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12250,c_61]) ).
tcf(c_38895,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_35258]) ).
tcf(c_38896,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_35258]) ).
tcf(c_38898,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12242,c_35258]) ).
tcf(c_38899,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12238,c_35258]) ).
tcf(c_38900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12236,c_35258]) ).
tcf(c_38901,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12243,c_35258]) ).
tcf(c_38902,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12239,c_35258]) ).
tcf(c_38903,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12237,c_35258]) ).
tcf(c_38904,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12246,c_35258]) ).
tcf(c_38905,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_35258]) ).
tcf(c_38906,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_12247,c_35258]) ).
tcf(c_38907,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_35258]) ).
tcf(c_38908,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12249,c_35258]) ).
tcf(c_38909,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_35258]) ).
tcf(c_39259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK4) != head_of(sK4) )
| ( tail_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2047,c_35277]) ).
tcf(c_39261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_35277]) ).
tcf(c_39262,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_35277]) ).
tcf(c_39263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_35277]) ).
tcf(c_39264,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_35277]) ).
tcf(c_39265,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_35277]) ).
tcf(c_39266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_35277]) ).
tcf(c_39267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_35277]) ).
tcf(c_39269,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_35277]) ).
tcf(c_39270,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_35277]) ).
tcf(c_39271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_35277]) ).
tcf(c_39276,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_35277]) ).
tcf(c_39277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_35277]) ).
tcf(c_39278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12242,c_35277]) ).
tcf(c_39279,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12238,c_35277]) ).
tcf(c_39280,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_35277]) ).
tcf(c_39281,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12243,c_35277]) ).
tcf(c_39282,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12239,c_35277]) ).
tcf(c_39283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_35277]) ).
tcf(c_39284,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12246,c_35277]) ).
tcf(c_39286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12247,c_35277]) ).
tcf(c_39288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_35277]) ).
tcf(c_39289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2047,c_35277]) ).
tcf(c_39290,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5676,c_35277]) ).
tcf(c_39291,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5014,c_35277]) ).
tcf(c_39292,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3331,c_35277]) ).
tcf(c_39293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_6099,c_35277]) ).
tcf(c_39294,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5490,c_35277]) ).
tcf(c_39295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_3740,c_35277]) ).
tcf(c_39296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4151,c_35277]) ).
tcf(c_39297,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4145,c_35277]) ).
tcf(c_39298,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4019,c_35277]) ).
tcf(c_39299,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_5767,c_35277]) ).
tcf(c_39300,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4678,c_35277]) ).
tcf(c_39301,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4365,c_35277]) ).
tcf(c_39302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15981,c_35277]) ).
tcf(c_39303,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15978,c_35277]) ).
tcf(c_39305,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15980,c_35277]) ).
tcf(c_39306,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15976,c_35277]) ).
tcf(c_39307,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_15974,c_35277]) ).
tcf(c_39308,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12242,c_35277]) ).
tcf(c_39309,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12238,c_35277]) ).
tcf(c_39310,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12236,c_35277]) ).
tcf(c_39311,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK5(head_of(sK3),tail_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12243,c_35277]) ).
tcf(c_39312,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12239,c_35277]) ).
tcf(c_39313,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12237,c_35277]) ).
tcf(c_39314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12246,c_35277]) ).
tcf(c_39315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12244,c_35277]) ).
tcf(c_39316,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_12247,c_35277]) ).
tcf(c_39317,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12245,c_35277]) ).
tcf(c_39318,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK5(head_of(sK3),tail_of(sK3))),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != tail_of(sK3) )
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12249,c_35277]) ).
tcf(c_39319,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(equality_resolution,[status(thm)],[c_35277]) ).
tcf(c_39331,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(X0) != head_of(sK3) ) ),
inference(equality_resolution_simp,[status(thm)],[c_39259]) ).
tcf(c_39809,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_15979,c_14096]) ).
tcf(c_39811,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15977,c_14096]) ).
tcf(c_39814,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_14096]) ).
tcf(c_39815,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_14096]) ).
tcf(c_39849,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15979,c_14881]) ).
tcf(c_39851,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_15977,c_14881]) ).
tcf(c_39854,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12248,c_14881]) ).
tcf(c_39855,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK3),tail_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_12250,c_14881]) ).
tcf(c_39888,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_34195,c_15213]) ).
tcf(c_39890,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_34172,c_15213]) ).
tcf(c_39892,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12240,c_15213]) ).
tcf(c_39893,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK3),tail_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_12241,c_15213]) ).
tcf(c_39956,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_39893,c_39892,c_39890,c_39888,c_39855,c_39854,c_39851,c_39849,c_39815,c_39814,c_39811,c_39809,c_39331,c_39319,c_39318,c_39317,c_39316,c_39315,c_39314,c_39313,c_39312,c_39311,c_39310,c_39309,c_39308,c_39307,c_39306,c_39305,c_39303,c_39302,c_39301,c_39300,c_39299,c_39298,c_39297,c_39296,c_39295,c_39294,c_39293,c_39292,c_39291,c_39290,c_39289,c_39288,c_39286,c_39284,c_39283,c_39282,c_39281,c_39280,c_39279,c_39278,c_39277,c_39276,c_39271,c_39270,c_39269,c_39267,c_39266,c_39265,c_39264,c_39263,c_39262,c_39261,c_38909,c_38908,c_38907,c_38906,c_38905,c_38904,c_38903,c_38902,c_38901,c_38900,c_38899,c_38898,c_38896,c_38895,c_38733,c_38732,c_38731,c_38730,c_38729,c_38728,c_38727,c_38725,c_38724,c_38721,c_38719,c_38718,c_38716,c_38715,c_38713,c_38710,c_38708,c_38707,c_38706,c_38665,c_38581,c_38580,c_38536,c_38535,c_38529,c_38459,c_38458,c_38453,c_38452,c_38403,c_38402,c_38397,c_38396,c_38360,c_38359,c_38322,c_38321,c_38319,c_38317,c_38280,c_38279,c_38277,c_38275,c_38213,c_38212,c_38211,c_38210,c_38200,c_36941,c_36929,c_36928,c_36927,c_36926,c_36925,c_36924,c_36923,c_36922,c_36921,c_36920,c_36919,c_36918,c_36917,c_36916,c_36914,c_36913,c_36912,c_36911,c_36910,c_36909,c_36908,c_36907,c_36906,c_36905,c_36904,c_36903,c_36902,c_36901,c_36900,c_36899,c_36898,c_36896,c_36894,c_36893,c_36892,c_36891,c_36890,c_36889,c_36888,c_36883,c_36882,c_36881,c_36880,c_36879,c_36877,c_36876,c_36875,c_36874,c_36873,c_36872,c_36871,c_36629,c_36628,c_36627,c_36626,c_36625,c_36624,c_36623,c_36622,c_36621,c_36620,c_36619,c_36618,c_36617,c_36616,c_36615,c_36614,c_36613,c_36612,c_36611,c_36610,c_36551,c_36550,c_36549,c_36548,c_36523,c_36220,c_36217,c_36212,c_36211,c_36201,c_36200,c_36199,c_36195,c_36194,c_36188,c_36186,c_36178,c_36176,c_36175,c_36174,c_36171,c_36169,c_36168,c_36167,c_36166,c_36165,c_36164,c_36162,c_36161,c_36160,c_36132,c_36131,c_36076,c_36075,c_36044,c_36043,c_35944,c_35941,c_35939,c_35936,c_35935,c_35932,c_35931,c_35883,c_35882,c_35881,c_35822,c_35820,c_35818,c_35817,c_35814,c_35811,c_35810,c_35807,c_35806,c_35767,c_35766,c_35765,c_35712,c_35710,c_35707,c_35706,c_35704,c_35703,c_35543,c_35542,c_35541,c_35539,c_35537,c_35535,c_35534,c_35531,c_35529,c_35528,c_35526,c_35525,c_35523,c_35522,c_35520,c_35449,c_35447,c_35445,c_35444,c_35441,c_35438,c_35437,c_35434,c_35433,c_35430,c_35369,c_35367,c_35364,c_35363,c_35361,c_35360,c_35357,c_35356,c_35326,c_35320,c_35314,c_35308,c_35302,c_35295,c_35279,c_35277,c_35272,c_35269,c_35268,c_35266,c_35260,c_35258,c_35225,c_35145,c_35143,c_35140,c_35139,c_35137,c_35136,c_34628,c_34627,c_34626,c_34625,c_34624,c_34623,c_34622,c_34621,c_34620,c_34619,c_34618,c_34617,c_34616,c_34615,c_34611,c_34610,c_34609,c_34607,c_34606,c_34605,c_34604,c_34603,c_34602,c_34601,c_34600,c_34599,c_34598,c_34597,c_34596,c_34595,c_34591,c_34590,c_34588,c_34586,c_34585,c_34584,c_34583,c_34582,c_34581,c_34580,c_34579,c_34578,c_34577,c_34576,c_34575,c_34574,c_34573,c_34556,c_34555,c_34405,c_34404,c_34403,c_34402,c_34399,c_34398,c_34397,c_34396,c_34394,c_34392,c_34389,c_34388,c_34385,c_34384,c_34362,c_34343,c_34342,c_34341,c_34318,c_34281,c_34275,c_34269,c_34263,c_34257,c_34251,c_34244,c_34228,c_34226,c_34221,c_34218,c_34217,c_34215,c_34212,c_34207,c_34206,c_34195,c_34172,c_34155,c_34148,c_34141,c_34136,c_34131,c_34126,c_34125,c_34121,c_34120,c_34119,c_34118,c_34116,c_34115,c_34102,c_34097,c_34092,c_34090,c_34076,c_34057,c_34052,c_34048,c_34047,c_34046,c_34045,c_34041,c_34039,c_34026,c_33953,c_33952,c_33951,c_33950,c_33949,c_33948,c_33947,c_33946,c_33945,c_33944,c_33943,c_33942,c_33937,c_33126,c_33125,c_33124,c_33123,c_33120,c_33119,c_33118,c_33117,c_33114,c_33113,c_33109,c_33108,c_33107,c_33105,c_33104,c_33103,c_33102,c_33101,c_33100,c_33099,c_33098,c_33097,c_33096,c_33095,c_33094,c_33093,c_33089,c_33088,c_33086,c_33084,c_33083,c_33082,c_33081,c_33080,c_33079,c_33078,c_33077,c_33076,c_33075,c_33074,c_33073,c_33056,c_33037,c_33036,c_33035,c_33013,c_32991,c_32990,c_32791,c_32790,c_32789,c_32788,c_32785,c_32784,c_32783,c_32782,c_32780,c_32778,c_32775,c_32774,c_32771,c_32770,c_32746,c_32745,c_32703,c_32696,c_32689,c_32684,c_32680,c_32676,c_32675,c_32674,c_32673,c_32672,c_32671,c_32670,c_32227,c_32226,c_32225,c_32224,c_32223,c_32222,c_32221,c_32220,c_32219,c_32218,c_32217,c_32216,c_32215,c_32214,c_32213,c_32212,c_32211,c_32210,c_32209,c_32208,c_32207,c_32206,c_32205,c_32204,c_32203,c_32202,c_32201,c_32200,c_32199,c_32198,c_32197,c_32196,c_32195,c_32194,c_32193,c_32192,c_32191,c_32190,c_32189,c_32188,c_32187,c_32186,c_32185,c_32184,c_32183,c_32182,c_32181,c_32180,c_32179,c_32178,c_32177,c_32176,c_32175,c_32174,c_32173,c_32172,c_32171,c_32170,c_32169,c_32168,c_32167,c_32166,c_32165,c_32164,c_32162,c_32154,c_32147,c_32140,c_32135,c_32128,c_32127,c_32124,c_32123,c_32122,c_32121,c_32120,c_32119,c_32118,c_31986,c_31981,c_31976,c_31971,c_31962,c_31961,c_31958,c_31955,c_31952,c_31946,c_31944,c_31939,c_31938,c_31921,c_31893,c_31888,c_31883,c_31881,c_31867,c_31837,c_31832,c_31827,c_31822,c_31817,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA009+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n008.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 12:45:19 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.43 % Detected problem language: tptp
% 0.14/5.44 % Proving...
% 26.31/9.33 % SZS status Started for theBenchmark.p
% 26.31/9.33 % SZS status Theorem for theBenchmark.p
% 26.31/9.33
% 26.31/9.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 26.31/9.33
% 26.31/9.33 % ------ iProver source info
% 26.31/9.33
% 26.31/9.33 % git: date: 2026-07-19 20:42:38 +0200
% 26.31/9.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 26.31/9.33 % git: non_committed_changes: false
% 26.31/9.33
% 26.31/9.33 % ------ Parsing...
% 26.31/9.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 26.31/9.33
% 26.31/9.33 % ------ 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 %
% 26.31/9.33
% 26.31/9.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 26.31/9.33
% 26.31/9.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 26.31/9.33 % ------ Proving...
% 26.31/9.33 % ------ Problem Properties
% 26.31/9.33
% 26.31/9.33 %
% 26.31/9.33 % clauses 33
% 26.31/9.33 % conjectures 4
% 26.31/9.33 % EPR 16
% 26.31/9.33 % Horn 23
% 26.31/9.33 % unary 6
% 26.31/9.33 % binary 8
% 26.31/9.33 % lits 105
% 26.31/9.33 % lits eq 26
% 26.31/9.33 % fd_pure 0
% 26.31/9.33 % fd_pseudo 0
% 26.31/9.33 % fd_cond 0
% 26.31/9.33 % fd_pseudo_cond 5
% 26.31/9.33 % AC symbols 0
% 26.31/9.33
% 26.31/9.33 % ------ Schedule dynamic 5 is on
% 26.31/9.33
% 26.31/9.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 26.31/9.33
% 26.31/9.33
% 26.31/9.33 % ------
% 26.31/9.33 % Current options:
% 26.31/9.33 % ------
% 26.31/9.33
% 26.31/9.33
% 26.31/9.33 %
% 26.31/9.33
% 26.31/9.33 % ------ Proving...
% 26.31/9.33 %
% 26.31/9.33
% 26.31/9.33 % SZS status Theorem for theBenchmark.p
% 26.31/9.33
% 26.31/9.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 26.31/9.43
% 26.31/9.43
%------------------------------------------------------------------------------