%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA009+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n007.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 01:23:35 PM UTC 2026
% Result : Theorem 22.09s 3.81s
% Output : CNFRefutation 22.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of formulae : 3034 ( 44 unt; 0 def)
% Number of atoms : 16528 (8759 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 21361 (7867 ~;13351 |; 119 &)
% ( 4 <=>; 15 =>; 0 <=; 5 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Maximal term depth : 10 ( 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 : 6483 ( 0 sgn6456 !; 27 ?;6221 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X2)
& on_path(X3,X2)
& shortest_path(X0,X1,X2) )
=> ? [X5] : triangle(X3,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_path_and_stuff_means_triangles) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X2)
& on_path(X3,X2)
& shortest_path(X0,X1,X2) )
=> ? [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,X3,X4] :
( sequential(X3,X4)
& on_path(X4,X2)
& on_path(X3,X2)
& shortest_path(X0,X1,X2)
& ! [X5] : ~ triangle(X3,X4,X5) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( sequential(X3,X4)
& on_path(X4,X2)
& on_path(X3,X2)
& shortest_path(X0,X1,X2)
& ! [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
& sequential(sK3,sK4)
& on_path(sK4,sK2)
& on_path(sK3,sK2)
& shortest_path(sK0,sK1,sK2)
& ! [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,
sequential(sK3,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f51,plain,
on_path(sK4,sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
on_path(sK3,sK2),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
shortest_path(sK0,sK1,sK2),
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,
shortest_path(sK0,sK1,sK2),
inference(cnf_transformation,[],[f53]) ).
tcf(c_51,negated_conjecture,
on_path(sK3,sK2),
inference(cnf_transformation,[],[f52]) ).
tcf(c_52,negated_conjecture,
on_path(sK4,sK2),
inference(cnf_transformation,[],[f51]) ).
tcf(c_53,negated_conjecture,
sequential(sK3,sK4),
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_53,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(X0,X1,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_70]) ).
tcf(c_656,plain,
path(sK0,sK1,sK2),
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_1449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X0,X2,X3)
| ~ precedes(X1,X2,X3)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2042,plain,
edge(sK3),
inference(superposition,[status(thm)],[c_53,c_62]) ).
tcf(c_2051,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_2059,plain,
edge(sK4),
inference(superposition,[status(thm)],[c_53,c_63]) ).
tcf(c_2072,plain,
path(sK0,sK1,sK2),
inference(superposition,[status(thm)],[c_50,c_70]) ).
tcf(c_2077,plain,
head_of(sK3) = tail_of(sK4),
inference(superposition,[status(thm)],[c_53,c_65]) ).
tcf(c_2078,plain,
( vertex(head_of(sK3))
| ~ edge(sK4) ),
inference(superposition,[status(thm)],[c_2077,c_76]) ).
tcf(c_2079,plain,
vertex(head_of(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_2078,c_2059]) ).
tcf(c_2084,plain,
( ~ edge(sK4)
| ( head_of(sK3) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2077,c_74]) ).
tcf(c_2085,plain,
head_of(sK3) != head_of(sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_2084,c_2059]) ).
tcf(c_2112,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_50,c_67]) ).
tcf(c_2129,plain,
! [X0: $i] :
( less_or_equal(length_of(sK2),length_of(X0))
| ~ path(sK0,sK1,X0) ),
inference(superposition,[status(thm)],[c_50,c_72]) ).
tcf(c_2140,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(X0,sK7(sK2,X0,X1))
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2072,c_80]) ).
tcf(c_2154,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( X0 = sK4 )
| ~ edge(sK4)
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2077,c_61]) ).
tcf(c_2155,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( X0 = sK4 )
| ~ edge(X0)
| ( head_of(X0) != head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2154,c_2059]) ).
tcf(c_2169,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_2184,plain,
! [X0: $i,X1: $i] :
( shortest_path(X0,X1,sK2)
| ( X0 = X1 )
| ~ path(X0,X1,sK2)
| ~ path(sK0,sK1,sK6(X0,X1,sK2)) ),
inference(superposition,[status(thm)],[c_2129,c_68]) ).
tcf(c_2195,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(X0) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2140,c_65]) ).
tcf(c_2196,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2140,c_63]) ).
tcf(c_2197,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| sequential(X0,X1)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2140,c_62]) ).
tcf(c_2207,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ precedes(X0,X1,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_2197,c_62,c_2197]) ).
tcf(c_2249,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_2077,c_2051]) ).
tcf(c_2250,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_2077,c_2051]) ).
tcf(c_2251,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ precedes(X3,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_2051]) ).
tcf(c_2266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ precedes(sK4,sK4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(superposition,[status(thm)],[c_2077,c_2249]) ).
tcf(c_2273,plain,
~ precedes(sK4,sK4,sK2),
inference(superposition,[status(thm)],[c_50,c_2266]) ).
tcf(c_2292,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_2293,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK2,X0,X1),X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2072,c_81]) ).
tcf(c_2313,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_2314,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2072,c_82]) ).
tcf(c_2332,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| ~ sequential(X0,X2)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2293,c_79]) ).
tcf(c_2333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( on_path(X1,sK2)
| sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_78]) ).
tcf(c_2334,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| on_path(sK7(sK2,X0,X1),sK2)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_77]) ).
tcf(c_2335,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_2195]) ).
tcf(c_2337,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ precedes(X1,X0,sK2)
| ~ precedes(X0,sK7(sK2,X1,X0),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_2112]) ).
tcf(c_2367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X4,X1)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_79]) ).
tcf(c_2371,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_2207]) ).
tcf(c_2372,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_2112]) ).
tcf(c_2373,plain,
( ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_2273]) ).
tcf(c_2393,plain,
! [X0: $i] : ~ precedes(X0,X0,sK2),
inference(superposition,[status(thm)],[c_50,c_2251]) ).
tcf(c_2403,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X1,X0,sK2)
| ~ on_path(sK7(sK2,X1,X0),sK2)
| ~ sequential(X0,sK7(sK2,X1,X0)) ),
inference(superposition,[status(thm)],[c_2314,c_2337]) ).
tcf(c_2424,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_2372]) ).
tcf(c_2438,plain,
( ~ sequential(sK4,sK3)
| ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2) ),
inference(superposition,[status(thm)],[c_53,c_2424]) ).
tcf(c_2439,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ sequential(sK7(sK2,X0,X1),X0) ),
inference(superposition,[status(thm)],[c_2140,c_2424]) ).
tcf(c_2440,plain,
~ sequential(sK4,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2438,c_52,c_51]) ).
tcf(c_2454,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| on_path(sK7(sK2,X0,X1),sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2072,c_2334]) ).
tcf(c_2472,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X1,X0,sK2)
| ~ sequential(X0,sK7(sK2,X1,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2403,c_2454]) ).
tcf(c_2496,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X4,X3,sK2)
| ~ on_path(X4,sK2)
| ~ on_path(X3,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X4,X2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_105]) ).
tcf(c_2497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK2)
| ~ on_path(X0,sK2)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2293,c_105]) ).
tcf(c_2521,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_2522,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_2523,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_2079,c_107]) ).
tcf(c_2551,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_2552,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_2553,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_2079,c_110]) ).
tcf(c_2581,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_2582,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_2583,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_2079,c_112]) ).
tcf(c_2613,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_2614,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_2615,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_2079,c_114]) ).
tcf(c_2643,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_2553]) ).
tcf(c_2644,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_2553]) ).
tcf(c_2668,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_2523]) ).
tcf(c_2669,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_2523]) ).
tcf(c_2691,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_2615]) ).
tcf(c_2692,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_2615]) ).
tcf(c_2704,plain,
! [X0: $i,X1: $i] :
( ~ shortest_path(sK0,sK1,sK2)
| ~ precedes(X1,X0,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_2705,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2439,c_2439,c_2454]) ).
tcf(c_2715,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(sK0,sK1,sK2)
| ~ precedes(X2,X0,sK2)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2724,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_2583]) ).
tcf(c_2725,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_2583]) ).
tcf(c_2737,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(sK3,X2,sK2)
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,X2)
| ~ on_path(X2,sK2)
| ~ path(X0,X1,sK2) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_2775,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X0),X0)) = head_of(sK7(sK2,X1,X0)) )
| ~ on_path(X0,sK2)
| ~ precedes(X1,X0,sK2)
| ~ on_path(sK7(sK2,X1,X0),sK2)
| ~ sequential(X0,sK7(sK2,X1,X0)) ),
inference(superposition,[status(thm)],[c_2335,c_2424]) ).
tcf(c_2776,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_65]) ).
tcf(c_2777,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_63]) ).
tcf(c_2778,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_62]) ).
tcf(c_2779,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK3)) ),
inference(superposition,[status(thm)],[c_2335,c_557]) ).
tcf(c_2780,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ~ precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_2332]) ).
tcf(c_2781,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_2497]) ).
tcf(c_2836,plain,
( sequential(sK4,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK4,sK3),sK3)) = head_of(sK7(sK2,sK4,sK3)) )
| ~ precedes(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2140,c_2779]) ).
tcf(c_2837,plain,
( ( tail_of(sK7(sK2,sK7(sK2,sK4,sK3),sK3)) = head_of(sK7(sK2,sK4,sK3)) )
| ~ precedes(sK4,sK3,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2836,c_2440]) ).
tcf(c_2859,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK2)
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2072,c_2496]) ).
tcf(c_2884,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_53,c_2859]) ).
tcf(c_2885,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK2,X0,X1),sK2)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_2859]) ).
tcf(c_2886,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X1,X2,sK2)
| ~ on_path(sK7(sK2,X1,X2),sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2335,c_2859]) ).
tcf(c_2887,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2884,c_52,c_51]) ).
tcf(c_2911,plain,
( ~ edge(sK3)
| ( head_of(sK3) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_2912,plain,
( vertex(tail_of(sK3))
| ~ edge(sK3) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_2926,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),sK2)
| ( X0 = X1 )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_2859]) ).
tcf(c_2927,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X3,sK2)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X3) ),
inference(superposition,[status(thm)],[c_2169,c_2424]) ).
tcf(c_2928,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_2169,c_65]) ).
tcf(c_2929,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_2169,c_63]) ).
tcf(c_2930,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_2169,c_62]) ).
tcf(c_2971,plain,
( vertex(head_of(sK4))
| ~ edge(sK4) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_2978,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK4,sK2)
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_105]) ).
tcf(c_2979,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,sK3)
| ~ sequential(X2,sK4)
| ~ on_path(X3,sK2)
| ~ sequential(X2,X3)
| ~ precedes(X2,sK4,sK2)
| ~ path(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_79]) ).
tcf(c_2983,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,X0,sK4)) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_2195]) ).
tcf(c_2984,plain,
! [X0: $i] :
( edge(X0)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_2207]) ).
tcf(c_2985,plain,
! [X0: $i] :
( ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ precedes(sK4,X0,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_2112]) ).
tcf(c_3012,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2777,c_63,c_2777]) ).
tcf(c_3013,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_3012]) ).
tcf(c_3020,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_3013]) ).
tcf(c_3021,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_3013]) ).
tcf(c_3042,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_3052,plain,
sK3 = sK3,
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_3055,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_2930,c_62,c_2930]) ).
tcf(c_3056,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_3055]) ).
tcf(c_3079,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK2)
| ~ sequential(X0,X1)
| ~ precedes(X0,sK4,sK2) ),
inference(superposition,[status(thm)],[c_2072,c_2979]) ).
tcf(c_3108,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_2454,c_2983]) ).
tcf(c_3124,plain,
! [X0: $i,X1: $i] :
( ~ on_path(sK4,sK2)
| ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_3079]) ).
tcf(c_3125,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK4)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK4)
| ~ sequential(sK7(sK2,X0,sK4),X1) ),
inference(superposition,[status(thm)],[c_2293,c_3079]) ).
tcf(c_3133,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3124,c_52]) ).
tcf(c_3157,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_3133]) ).
tcf(c_3158,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,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_3133]) ).
tcf(c_3159,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3133]) ).
tcf(c_3194,plain,
! [X0: $i,X1: $i] :
( precedes(X0,sK4,sK2)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2072,c_2978]) ).
tcf(c_3216,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(X0,sK4,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_3194]) ).
tcf(c_3217,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| precedes(X3,sK4,sK2)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(X3,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_3194]) ).
tcf(c_3218,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK2,X0,X1),sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3194]) ).
tcf(c_3241,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_3157,c_2454,c_3157]) ).
tcf(c_3253,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3241]) ).
tcf(c_3260,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_3159,c_2454,c_3159]) ).
tcf(c_3302,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK2)
| ~ sequential(X4,X1)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2367,c_78]) ).
tcf(c_3321,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ on_path(X4,sK2)
| ~ on_path(X3,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X4,X3)
| ~ sequential(X2,X4)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_3302]) ).
tcf(c_3322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X1)
| ~ path(X3,X4,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2)
| ~ sequential(sK7(sK2,X0,X1),X1) ),
inference(superposition,[status(thm)],[c_2293,c_3302]) ).
tcf(c_3323,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,sK4)
| ~ sequential(X2,sK4)
| ~ sequential(X2,sK3)
| ~ on_path(X3,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_3302]) ).
tcf(c_3357,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_2292,c_105]) ).
tcf(c_3358,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_2292,c_79]) ).
tcf(c_3359,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_2292,c_78]) ).
tcf(c_3360,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_2292,c_77]) ).
tcf(c_3413,plain,
sK4 = sK4,
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_3426,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_2551]) ).
tcf(c_3427,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_2551]) ).
tcf(c_3428,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_2079,c_2551]) ).
tcf(c_3456,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_2552]) ).
tcf(c_3457,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_2552]) ).
tcf(c_3458,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_2079,c_2552]) ).
tcf(c_3486,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_2521]) ).
tcf(c_3487,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_2521]) ).
tcf(c_3488,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_2079,c_2521]) ).
tcf(c_3535,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_2522]) ).
tcf(c_3536,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_2522]) ).
tcf(c_3537,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_2079,c_2522]) ).
tcf(c_3574,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_2613]) ).
tcf(c_3575,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_2613]) ).
tcf(c_3576,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_2079,c_2613]) ).
tcf(c_3613,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_2614]) ).
tcf(c_3614,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_2614]) ).
tcf(c_3615,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_2079,c_2614]) ).
tcf(c_3652,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_2581]) ).
tcf(c_3653,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_2581]) ).
tcf(c_3654,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_2079,c_2581]) ).
tcf(c_3685,plain,
! [X0: $i,X1: $i] :
( precedes(sK3,sK4,sK2)
| ~ sequential(sK3,sK4)
| ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2)
| ~ path(X0,X1,sK2) ),
inference(instantiation,[status(thm)],[c_2737]) ).
tcf(c_3704,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,sK4)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2072,c_3323]) ).
tcf(c_3735,plain,
( ~ sequential(sK4,sK4)
| ~ sequential(sK3,sK4)
| ~ sequential(sK3,sK3)
| ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2) ),
inference(superposition,[status(thm)],[c_53,c_3704]) ).
tcf(c_3736,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_3704]) ).
tcf(c_3737,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,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_3704]) ).
tcf(c_3738,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK4)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3704]) ).
tcf(c_3801,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X1)
| ~ sequential(X0,X2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2072,c_3321]) ).
tcf(c_3826,plain,
! [X0: $i] :
( ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_53,c_3801]) ).
tcf(c_3827,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ precedes(X1,X2,sK2)
| ~ on_path(sK7(sK2,X1,X2),sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2140,c_3801]) ).
tcf(c_3828,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X4,X0)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2169,c_3801]) ).
tcf(c_3829,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X2,X1)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2335,c_3801]) ).
tcf(c_3830,plain,
! [X0: $i] :
( ~ sequential(sK3,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3826,c_52,c_51]) ).
tcf(c_3866,plain,
( ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK2) ),
inference(superposition,[status(thm)],[c_53,c_3830]) ).
tcf(c_3867,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK4))
| ~ on_path(sK7(sK2,X0,sK4),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3830]) ).
tcf(c_3879,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3867,c_2454]) ).
tcf(c_3901,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_3428]) ).
tcf(c_3903,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_2059,c_3428]) ).
tcf(c_3904,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3428]) ).
tcf(c_3905,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_3903,c_2085]) ).
tcf(c_3923,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_3905,c_2051]) ).
tcf(c_3924,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_3905,c_61]) ).
tcf(c_3925,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_3905,c_2250]) ).
tcf(c_3926,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_3905,c_2249]) ).
tcf(c_3927,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_3905,c_2051]) ).
tcf(c_4023,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_2313,c_105]) ).
tcf(c_4024,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_2313,c_79]) ).
tcf(c_4027,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_2313,c_3056]) ).
tcf(c_4081,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_2582]) ).
tcf(c_4082,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_2582]) ).
tcf(c_4083,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_2079,c_2582]) ).
tcf(c_4125,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_2643]) ).
tcf(c_4127,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_2059,c_2643]) ).
tcf(c_4128,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2643]) ).
tcf(c_4129,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_4127,c_2085]) ).
tcf(c_4165,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_2644]) ).
tcf(c_4166,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_2644]) ).
tcf(c_4168,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2644]) ).
tcf(c_4216,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_2668]) ).
tcf(c_4218,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_2059,c_2668]) ).
tcf(c_4219,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2668]) ).
tcf(c_4220,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_4218,c_2085]) ).
tcf(c_4238,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_4129,c_2051]) ).
tcf(c_4239,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_4129,c_61]) ).
tcf(c_4242,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_4129,c_2051]) ).
tcf(c_4244,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_4129,c_76]) ).
tcf(c_4285,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_4220,c_2051]) ).
tcf(c_4286,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_4220,c_61]) ).
tcf(c_4289,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_4220,c_2051]) ).
tcf(c_4290,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_4220,c_74]) ).
tcf(c_4291,plain,
( vertex(head_of(sK4))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4220,c_76]) ).
tcf(c_4313,plain,
vertex(head_of(sK4)),
inference(global_subsumption_just,[status(thm)],[c_4244,c_2059,c_2971]) ).
tcf(c_4315,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_4313,c_2582]) ).
tcf(c_4316,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_4313,c_2581]) ).
tcf(c_4317,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_4313,c_2614]) ).
tcf(c_4318,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_4313,c_2613]) ).
tcf(c_4319,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_4313,c_2522]) ).
tcf(c_4320,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_4313,c_2521]) ).
tcf(c_4321,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_4313,c_2552]) ).
tcf(c_4322,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_4313,c_2551]) ).
tcf(c_4323,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_4313,c_114]) ).
tcf(c_4324,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_4313,c_112]) ).
tcf(c_4325,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_4313,c_110]) ).
tcf(c_4326,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_4313,c_107]) ).
tcf(c_4327,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_4313,c_2583]) ).
tcf(c_4328,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_4313,c_2615]) ).
tcf(c_4343,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_4328,c_2085]) ).
tcf(c_4346,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_4327,c_2085]) ).
tcf(c_4465,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ~ precedes(sK3,sK4,sK2)
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_1449]) ).
tcf(c_4467,plain,
! [X0: $i] :
( ~ precedes(sK3,sK4,sK2)
| ~ shortest_path(sK0,sK1,sK2)
| ( head_of(sK4) != head_of(X0) )
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_2715]) ).
tcf(c_4469,plain,
( ~ precedes(sK4,sK3,sK2)
| ~ precedes(sK3,sK4,sK2)
| ~ shortest_path(sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_2704]) ).
tcf(c_4472,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_4166,c_2042,c_2911,c_4166]) ).
tcf(c_4473,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_4472]) ).
tcf(c_4478,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_4473,c_2051]) ).
tcf(c_4479,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_4473,c_61]) ).
tcf(c_4480,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_4473,c_2250]) ).
tcf(c_4481,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_4473,c_2249]) ).
tcf(c_4482,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_4473,c_2051]) ).
tcf(c_4484,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_4473,c_76]) ).
tcf(c_4530,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_4343,c_66]) ).
tcf(c_4532,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_4343,c_61]) ).
tcf(c_4534,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_4343,c_66]) ).
tcf(c_4559,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_4563,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_4571,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_4346,c_2051]) ).
tcf(c_4572,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_4346,c_61]) ).
tcf(c_4573,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_4346,c_2250]) ).
tcf(c_4574,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_4346,c_2249]) ).
tcf(c_4575,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_4346,c_2051]) ).
tcf(c_4601,plain,
vertex(tail_of(sK3)),
inference(global_subsumption_just,[status(thm)],[c_4484,c_2042,c_2912]) ).
tcf(c_4603,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_4601,c_2582]) ).
tcf(c_4604,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_4601,c_2581]) ).
tcf(c_4605,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_4601,c_2614]) ).
tcf(c_4606,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_4601,c_2613]) ).
tcf(c_4607,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_4601,c_2522]) ).
tcf(c_4608,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_4601,c_2521]) ).
tcf(c_4609,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_4601,c_2552]) ).
tcf(c_4610,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_4601,c_2551]) ).
tcf(c_4611,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_4601,c_114]) ).
tcf(c_4612,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_4601,c_112]) ).
tcf(c_4613,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_4601,c_110]) ).
tcf(c_4614,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_4601,c_107]) ).
tcf(c_4615,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_4601,c_2583]) ).
tcf(c_4616,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_4601,c_2615]) ).
tcf(c_4617,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_4601,c_2523]) ).
tcf(c_4763,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_3925]) ).
tcf(c_4764,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_2313,c_3925]) ).
tcf(c_4765,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4763,c_52]) ).
tcf(c_4825,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_3926]) ).
tcf(c_4826,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_2313,c_3926]) ).
tcf(c_4827,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_2887,c_3926]) ).
tcf(c_4832,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4825,c_52]) ).
tcf(c_4853,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_4615,c_2042,c_2911,c_4615]) ).
tcf(c_4854,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_4853]) ).
tcf(c_4860,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_4854,c_2051]) ).
tcf(c_4861,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_4854,c_61]) ).
tcf(c_4862,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_4854,c_2250]) ).
tcf(c_4863,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_4854,c_2249]) ).
tcf(c_4864,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_4854,c_2051]) ).
tcf(c_4906,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_2669]) ).
tcf(c_4909,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2669]) ).
tcf(c_4929,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_2691]) ).
tcf(c_4932,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2691]) ).
tcf(c_4957,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_2692]) ).
tcf(c_4960,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2692]) ).
tcf(c_5011,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_4325]) ).
tcf(c_5012,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_4325]) ).
tcf(c_5014,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_4601,c_4325]) ).
tcf(c_5067,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_4573]) ).
tcf(c_5068,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_2313,c_4573]) ).
tcf(c_5069,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5067,c_52]) ).
tcf(c_5088,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_4574]) ).
tcf(c_5089,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_2313,c_4574]) ).
tcf(c_5090,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2887,c_4574]) ).
tcf(c_5095,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5088,c_52]) ).
tcf(c_5120,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_4613]) ).
tcf(c_5121,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_4613]) ).
tcf(c_5122,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_2079,c_4613]) ).
tcf(c_5124,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_4313,c_4613]) ).
tcf(c_5228,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_4862]) ).
tcf(c_5229,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_2313,c_4862]) ).
tcf(c_5230,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5228,c_52]) ).
tcf(c_5273,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_4863]) ).
tcf(c_5274,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_2313,c_4863]) ).
tcf(c_5275,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2887,c_4863]) ).
tcf(c_5280,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5273,c_52]) ).
tcf(c_5301,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_4616,c_2042,c_2911,c_4616]) ).
tcf(c_5302,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_5301]) ).
tcf(c_5307,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_5302,c_66]) ).
tcf(c_5308,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_5302,c_2155]) ).
tcf(c_5309,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_5302,c_61]) ).
tcf(c_5311,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_5302,c_66]) ).
tcf(c_5335,plain,
( sequential(sK4,sK3)
| ( sK4 = sK3 )
| ~ edge(sK4)
| ~ edge(sK3)
| ( head_of(sK4) != tail_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_3042]) ).
tcf(c_5367,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_2724]) ).
tcf(c_5370,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2724]) ).
tcf(c_5390,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_2725]) ).
tcf(c_5393,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_2725]) ).
tcf(c_5421,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_5011]) ).
tcf(c_5424,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5011]) ).
tcf(c_5444,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_5012]) ).
tcf(c_5446,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_2059,c_5012]) ).
tcf(c_5447,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5012]) ).
tcf(c_5488,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_4323]) ).
tcf(c_5489,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_4323]) ).
tcf(c_5490,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_2079,c_4323]) ).
tcf(c_5491,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_4601,c_4323]) ).
tcf(c_5496,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_5490,c_2085]) ).
tcf(c_5548,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_5496,c_66]) ).
tcf(c_5550,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_5496,c_61]) ).
tcf(c_5552,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_5496,c_66]) ).
tcf(c_5605,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_4326]) ).
tcf(c_5606,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_4326]) ).
tcf(c_5607,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_2079,c_4326]) ).
tcf(c_5608,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_4601,c_4326]) ).
tcf(c_5613,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_5607,c_2085]) ).
tcf(c_5656,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_5613,c_2051]) ).
tcf(c_5657,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_5613,c_61]) ).
tcf(c_5660,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_5613,c_2051]) ).
tcf(c_5661,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_5613,c_74]) ).
tcf(c_5690,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_5122,c_2042,c_2911,c_5122]) ).
tcf(c_5691,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_5690]) ).
tcf(c_5696,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_5691,c_2051]) ).
tcf(c_5697,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_5691,c_61]) ).
tcf(c_5698,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_5691,c_2250]) ).
tcf(c_5699,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_5691,c_2249]) ).
tcf(c_5700,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_5691,c_2051]) ).
tcf(c_5730,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_5698]) ).
tcf(c_5731,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_2313,c_5698]) ).
tcf(c_5732,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5730,c_52]) ).
tcf(c_5786,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_5699]) ).
tcf(c_5787,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_2313,c_5699]) ).
tcf(c_5788,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2887,c_5699]) ).
tcf(c_5793,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5786,c_52]) ).
tcf(c_5830,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_3458]) ).
tcf(c_5833,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3458]) ).
tcf(c_5867,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_4617,c_2042,c_2911,c_4617]) ).
tcf(c_5868,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_5867]) ).
tcf(c_5874,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_5868,c_2051]) ).
tcf(c_5875,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_5868,c_61]) ).
tcf(c_5876,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_5868,c_2250]) ).
tcf(c_5877,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_5868,c_2249]) ).
tcf(c_5878,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_5868,c_2051]) ).
tcf(c_5879,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_5868,c_74]) ).
tcf(c_5930,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_5120]) ).
tcf(c_5933,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5120]) ).
tcf(c_5953,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_5121]) ).
tcf(c_5955,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_2059,c_5121]) ).
tcf(c_5956,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5121]) ).
tcf(c_6004,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_4611]) ).
tcf(c_6005,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_4611]) ).
tcf(c_6006,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_2079,c_4611]) ).
tcf(c_6008,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_4313,c_4611]) ).
tcf(c_6033,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_4614]) ).
tcf(c_6034,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_4614]) ).
tcf(c_6035,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_2079,c_4614]) ).
tcf(c_6037,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_4313,c_4614]) ).
tcf(c_6110,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_4324]) ).
tcf(c_6111,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_4324]) ).
tcf(c_6112,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_2079,c_4324]) ).
tcf(c_6113,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_4601,c_4324]) ).
tcf(c_6118,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_6112,c_2085]) ).
tcf(c_6136,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_6118,c_2051]) ).
tcf(c_6137,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_6118,c_61]) ).
tcf(c_6140,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_6118,c_2051]) ).
tcf(c_6159,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_6006,c_2042,c_2911,c_6006]) ).
tcf(c_6160,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_6159]) ).
tcf(c_6165,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_6160,c_66]) ).
tcf(c_6166,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_6160,c_2155]) ).
tcf(c_6167,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_6160,c_61]) ).
tcf(c_6169,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_6160,c_66]) ).
tcf(c_6211,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_6035,c_2042,c_2911,c_6035]) ).
tcf(c_6212,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_6211]) ).
tcf(c_6218,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_6212,c_2051]) ).
tcf(c_6219,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_6212,c_61]) ).
tcf(c_6220,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_6212,c_2250]) ).
tcf(c_6221,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_6212,c_2249]) ).
tcf(c_6222,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_6212,c_2051]) ).
tcf(c_6223,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_6212,c_74]) ).
tcf(c_6282,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_3488]) ).
tcf(c_6285,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3488]) ).
tcf(c_6305,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_3537]) ).
tcf(c_6308,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3537]) ).
tcf(c_6328,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_3576]) ).
tcf(c_6331,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3576]) ).
tcf(c_6370,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_3615]) ).
tcf(c_6373,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3615]) ).
tcf(c_6393,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_3654]) ).
tcf(c_6396,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3654]) ).
tcf(c_6416,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_4083]) ).
tcf(c_6417,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_4083]) ).
tcf(c_6419,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4083]) ).
tcf(c_6459,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_5014,c_2051]) ).
tcf(c_6460,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_5014,c_61]) ).
tcf(c_6461,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_5014,c_2250]) ).
tcf(c_6462,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_5014,c_2249]) ).
tcf(c_6463,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_5014,c_2051]) ).
tcf(c_6521,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_6223,c_2042,c_2079,c_2912,c_2911,c_4559,c_6223]) ).
tcf(c_6536,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_5488]) ).
tcf(c_6539,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5488]) ).
tcf(c_6559,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_5489]) ).
tcf(c_6561,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_2059,c_5489]) ).
tcf(c_6562,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5489]) ).
tcf(c_6588,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_5605]) ).
tcf(c_6591,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5605]) ).
tcf(c_6691,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_4612]) ).
tcf(c_6692,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_4612]) ).
tcf(c_6695,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_4313,c_4612]) ).
tcf(c_6728,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_5124,c_2051]) ).
tcf(c_6729,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_5124,c_61]) ).
tcf(c_6732,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_5124,c_2051]) ).
tcf(c_6781,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_5491,c_66]) ).
tcf(c_6782,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_5491,c_2155]) ).
tcf(c_6783,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_5491,c_61]) ).
tcf(c_6785,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_5491,c_66]) ).
tcf(c_6818,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_5608,c_2051]) ).
tcf(c_6819,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_5608,c_61]) ).
tcf(c_6820,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_5608,c_2250]) ).
tcf(c_6821,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_5608,c_2249]) ).
tcf(c_6822,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_5608,c_2051]) ).
tcf(c_6823,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_5608,c_74]) ).
tcf(c_6865,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_6417,c_2042,c_2911,c_6417]) ).
tcf(c_6866,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_6865]) ).
tcf(c_6872,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_6866,c_2051]) ).
tcf(c_6873,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_6866,c_61]) ).
tcf(c_6874,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_6866,c_2250]) ).
tcf(c_6875,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_6866,c_2249]) ).
tcf(c_6876,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_6866,c_2051]) ).
tcf(c_6923,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK4)
| sequential(sK7(sK2,X0,sK4),X1)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK4)
| ~ precedes(sK7(sK2,X0,sK4),X1,sK2)
| ~ sequential(sK7(sK2,sK7(sK2,X0,sK4),X1),sK3)
| ~ on_path(sK7(sK2,sK7(sK2,X0,sK4),X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_3125]) ).
tcf(c_6924,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,sK4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK2,X3,sK4),X4)
| ( X0 = X1 )
| ~ precedes(X3,sK4,sK2)
| ~ path(X0,X1,X2)
| ~ sequential(sK7(sK2,X3,sK4),sK4)
| ~ precedes(sK7(sK2,X3,sK4),X4,sK6(X0,X1,X2))
| ~ sequential(sK7(sK6(X0,X1,X2),sK7(sK2,X3,sK4),X4),sK3)
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK2,X3,sK4),X4),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_3125]) ).
tcf(c_6944,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(X0,sK4,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_3216,c_2454,c_3216]) ).
tcf(c_6956,plain,
! [X0: $i] :
( sequential(X0,sK3)
| precedes(X0,sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_6944]) ).
tcf(c_6971,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3021,c_63,c_3021]) ).
tcf(c_6972,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_6971]) ).
tcf(c_6979,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_6972]) ).
tcf(c_6980,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_6972]) ).
tcf(c_7014,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK2,X0,sK3),sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK7(sK2,X0,sK3),sK4)
| ~ on_path(sK7(sK2,X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_3253]) ).
tcf(c_7031,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_6118,c_4478]) ).
tcf(c_7032,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_5613,c_4478]) ).
tcf(c_7033,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_3905,c_4478]) ).
tcf(c_7034,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_4346,c_4478]) ).
tcf(c_7035,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_4220,c_4478]) ).
tcf(c_7036,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_4129,c_4478]) ).
tcf(c_7039,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_4473,c_4478]) ).
tcf(c_7040,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_6866,c_4478]) ).
tcf(c_7041,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_6212,c_4478]) ).
tcf(c_7042,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_5691,c_4478]) ).
tcf(c_7043,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_5608,c_4478]) ).
tcf(c_7044,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_5014,c_4478]) ).
tcf(c_7046,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_4478]) ).
tcf(c_7116,plain,
( precedes(sK3,sK4,sK2)
| ~ sequential(sK3,sK4)
| ~ on_path(sK4,sK2)
| ~ on_path(sK3,sK2)
| ~ path(sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_3685]) ).
tcf(c_7154,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_7158,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_7194,plain,
head_of(sK3) != tail_of(sK3),
inference(global_subsumption_just,[status(thm)],[c_4480,c_2042,c_2911]) ).
tcf(c_7202,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_6008,c_66]) ).
tcf(c_7204,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_6008,c_61]) ).
tcf(c_7206,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_6008,c_66]) ).
tcf(c_7235,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_5606]) ).
tcf(c_7237,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_2059,c_5606]) ).
tcf(c_7238,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_5606]) ).
tcf(c_7260,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_6004]) ).
tcf(c_7263,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6004]) ).
tcf(c_7283,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_6005]) ).
tcf(c_7285,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_2059,c_6005]) ).
tcf(c_7286,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6005]) ).
tcf(c_7308,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_6033]) ).
tcf(c_7311,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6033]) ).
tcf(c_7329,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_7046]) ).
tcf(c_7330,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_2313,c_7046]) ).
tcf(c_7331,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7329,c_51]) ).
tcf(c_7351,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_6037,c_2051]) ).
tcf(c_7352,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_6037,c_61]) ).
tcf(c_7353,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_6037,c_4478]) ).
tcf(c_7356,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_6037,c_2051]) ).
tcf(c_7357,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_6037,c_74]) ).
tcf(c_7395,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_6113,c_2051]) ).
tcf(c_7396,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_6113,c_61]) ).
tcf(c_7400,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_6113,c_2051]) ).
tcf(c_7430,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_6695,c_2051]) ).
tcf(c_7431,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_6695,c_61]) ).
tcf(c_7432,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_6695,c_4478]) ).
tcf(c_7435,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_6695,c_2051]) ).
tcf(c_7508,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_6118,c_4482]) ).
tcf(c_7509,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_5613,c_4482]) ).
tcf(c_7512,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_4220,c_4482]) ).
tcf(c_7513,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_4129,c_4482]) ).
tcf(c_7514,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_5868,c_4482]) ).
tcf(c_7517,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_6866,c_4482]) ).
tcf(c_7518,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_6212,c_4482]) ).
tcf(c_7521,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_5608,c_4482]) ).
tcf(c_7522,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_5014,c_4482]) ).
tcf(c_7523,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_6695,c_4482]) ).
tcf(c_7524,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_6037,c_4482]) ).
tcf(c_7526,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_4482]) ).
tcf(c_7617,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_6118,c_6872]) ).
tcf(c_7618,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_5613,c_6872]) ).
tcf(c_7621,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_4220,c_6872]) ).
tcf(c_7622,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_4129,c_6872]) ).
tcf(c_7623,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_5868,c_6872]) ).
tcf(c_7626,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_6866,c_6872]) ).
tcf(c_7630,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_5608,c_6872]) ).
tcf(c_7631,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_5014,c_6872]) ).
tcf(c_7632,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_6695,c_6872]) ).
tcf(c_7633,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_6037,c_6872]) ).
tcf(c_7635,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_6872]) ).
tcf(c_7760,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_6034]) ).
tcf(c_7762,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_2059,c_6034]) ).
tcf(c_7763,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6034]) ).
tcf(c_7785,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_6110]) ).
tcf(c_7788,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6110]) ).
tcf(c_7821,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_6111]) ).
tcf(c_7823,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_2059,c_6111]) ).
tcf(c_7824,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),head_of(sK4))) = head_of(sK4) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6111]) ).
tcf(c_7846,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_6691]) ).
tcf(c_7849,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6691]) ).
tcf(c_7867,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_7526]) ).
tcf(c_7868,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_2313,c_7526]) ).
tcf(c_7869,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7867,c_51]) ).
tcf(c_7888,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_7635]) ).
tcf(c_7889,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_2313,c_7635]) ).
tcf(c_7890,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7888,c_51]) ).
tcf(c_7911,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_4315]) ).
tcf(c_7913,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_2059,c_4315]) ).
tcf(c_7914,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4315]) ).
tcf(c_7945,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_6118,c_6876]) ).
tcf(c_7946,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_5613,c_6876]) ).
tcf(c_7949,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_4220,c_6876]) ).
tcf(c_7950,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_4129,c_6876]) ).
tcf(c_7951,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_5868,c_6876]) ).
tcf(c_7955,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_6212,c_6876]) ).
tcf(c_7958,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_5608,c_6876]) ).
tcf(c_7959,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_5014,c_6876]) ).
tcf(c_7960,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_6695,c_6876]) ).
tcf(c_7961,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_6037,c_6876]) ).
tcf(c_7963,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_6876]) ).
tcf(c_8039,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_3042]) ).
tcf(c_8044,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK2,X0,X1),sK2)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_2885,c_2454,c_2885]) ).
tcf(c_8058,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X0,X1)
| precedes(X5,sK7(sK2,X0,X1),sK2)
| ~ on_path(X5,sK2)
| ~ on_path(X4,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X5,X4)
| ~ sequential(X4,X0)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_105]) ).
tcf(c_8059,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2))
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_8044,c_79]) ).
tcf(c_8060,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(X4,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X4,X0)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_78]) ).
tcf(c_8062,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_6972]) ).
tcf(c_8063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X3,sK2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X3)
| ~ sequential(X0,X1)
| ~ path(X4,X5,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X3,sK7(sK2,X1,X2))
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_8044,c_3302]) ).
tcf(c_8064,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_3013]) ).
tcf(c_8065,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8044,c_2372]) ).
tcf(c_8066,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,X2,sK7(sK2,X0,X1))) = head_of(X2) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_2195]) ).
tcf(c_8067,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_2207]) ).
tcf(c_8068,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X2,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_2112]) ).
tcf(c_8071,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ on_path(sK4,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8044,c_2985]) ).
tcf(c_8091,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8071,c_52]) ).
tcf(c_8229,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_8091,c_2454,c_8091]) ).
tcf(c_8241,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_8229]) ).
tcf(c_8263,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X2,X3)
| sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X2,X3),sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ sequential(sK7(sK2,X2,X3),X0)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8044,c_8068]) ).
tcf(c_8283,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_2776]) ).
tcf(c_8284,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK2,X0,sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_2887,c_2776]) ).
tcf(c_8285,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK2,X0,X1))
| ( head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) = tail_of(sK7(sK2,X0,X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_2776]) ).
tcf(c_8286,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK2,X0,sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(light_normalisation,[status(thm)],[c_8284,c_2077]) ).
tcf(c_8314,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_6692]) ).
tcf(c_8316,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_2059,c_6692]) ).
tcf(c_8317,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK7(sK2,X0,X1)),tail_of(sK3))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_6692]) ).
tcf(c_8353,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_2929,c_6692]) ).
tcf(c_8354,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_2929,c_4315]) ).
tcf(c_8355,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_2929,c_6691]) ).
tcf(c_8356,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_2929,c_6111]) ).
tcf(c_8357,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_2929,c_6110]) ).
tcf(c_8358,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_2929,c_6034]) ).
tcf(c_8359,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_2929,c_6033]) ).
tcf(c_8360,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_2929,c_6005]) ).
tcf(c_8361,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_2929,c_6004]) ).
tcf(c_8362,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_2929,c_5606]) ).
tcf(c_8363,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_2929,c_5605]) ).
tcf(c_8364,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_2929,c_5489]) ).
tcf(c_8365,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_2929,c_5488]) ).
tcf(c_8366,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_2929,c_4083]) ).
tcf(c_8367,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_2929,c_3654]) ).
tcf(c_8368,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_2929,c_3615]) ).
tcf(c_8369,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_2929,c_3576]) ).
tcf(c_8370,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_2929,c_3537]) ).
tcf(c_8371,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_2929,c_3488]) ).
tcf(c_8372,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_2929,c_5121]) ).
tcf(c_8373,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_2929,c_5120]) ).
tcf(c_8374,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_2929,c_3458]) ).
tcf(c_8375,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_2929,c_5012]) ).
tcf(c_8376,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_2929,c_5011]) ).
tcf(c_8377,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_2929,c_2725]) ).
tcf(c_8378,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_2929,c_2724]) ).
tcf(c_8379,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_2929,c_2692]) ).
tcf(c_8380,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_2929,c_2691]) ).
tcf(c_8381,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_2929,c_2669]) ).
tcf(c_8382,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_2929,c_2668]) ).
tcf(c_8383,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_2929,c_2644]) ).
tcf(c_8384,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_2929,c_2643]) ).
tcf(c_8385,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_2929,c_3428]) ).
tcf(c_8713,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_8724,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_4563]) ).
tcf(c_8725,plain,
! [X0: $i] :
( ( head_of(sK3) = head_of(X0) )
| ( sK3 != X0 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_8854,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_3426]) ).
tcf(c_8857,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3426]) ).
tcf(c_8858,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_2929,c_3426]) ).
tcf(c_8913,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_7963]) ).
tcf(c_8914,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_2313,c_7963]) ).
tcf(c_8915,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8913,c_51]) ).
tcf(c_8936,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_4316]) ).
tcf(c_8939,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4316]) ).
tcf(c_8940,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_2929,c_4316]) ).
tcf(c_8968,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_4317]) ).
tcf(c_8970,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_2059,c_4317]) ).
tcf(c_8971,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4317]) ).
tcf(c_8972,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_2929,c_4317]) ).
tcf(c_9017,plain,
! [X0: $i] :
( ~ precedes(X0,sK3,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(sK4,X0)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) ) ),
inference(global_subsumption_just,[status(thm)],[c_8241,c_557,c_8241]) ).
tcf(c_9018,plain,
! [X0: $i] :
( ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(renaming,[status(thm)],[c_9017]) ).
tcf(c_9029,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK3))
| ~ on_path(sK7(sK2,X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_9018]) ).
tcf(c_9048,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) )
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(superposition,[status(thm)],[c_2454,c_8286]) ).
tcf(c_9055,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(X0,sK4)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_3736,c_2454,c_3736]) ).
tcf(c_9095,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3827,c_2454]) ).
tcf(c_9115,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X2)
| sequential(X1,sK7(sK2,X0,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,X2)),sK7(sK2,X0,X2))) = head_of(sK7(sK2,X1,sK7(sK2,X0,X2))) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,X2,sK2)
| ~ precedes(X1,sK7(sK2,X0,X2),sK2)
| ~ on_path(sK7(sK2,X1,sK7(sK2,X0,X2)),sK2)
| ~ sequential(X0,sK7(sK2,X1,sK7(sK2,X0,X2))) ),
inference(superposition,[status(thm)],[c_2335,c_9095]) ).
tcf(c_9152,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_8065,c_2454,c_8065]) ).
tcf(c_9166,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X2,sK2)
| ~ on_path(sK7(sK2,sK7(sK2,X0,X1),X2),sK2)
| ~ sequential(sK7(sK2,sK7(sK2,X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_2140,c_9152]) ).
tcf(c_9167,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK2,X3,X4),X5)
| ( X0 = X1 )
| ~ on_path(X3,sK2)
| ~ precedes(X3,X4,sK2)
| ~ path(X0,X1,X2)
| ~ precedes(sK7(sK2,X3,X4),X5,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),sK2)
| ~ sequential(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),X3) ),
inference(superposition,[status(thm)],[c_2169,c_9152]) ).
tcf(c_9200,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X2,sK2)
| ~ sequential(X2,X1)
| ~ path(X3,X4,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2335,c_3322]) ).
tcf(c_9226,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ on_path(X2,sK2)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_2314,c_2780]) ).
tcf(c_9227,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK2,X1,sK4))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK4)),sK7(sK2,X1,sK4))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK4))) )
| ~ precedes(X1,sK4,sK2)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK4),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK4)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK3)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK2) ),
inference(superposition,[status(thm)],[c_2887,c_2780]) ).
tcf(c_9228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK2,X2,X3))
| sequential(X0,sK7(sK2,X1,sK7(sK2,X2,X3)))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),sK7(sK2,X1,sK7(sK2,X2,X3)))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3)))) )
| ~ on_path(X2,sK2)
| ~ path(X4,X5,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X1,sK7(sK2,X2,X3),sK2)
| ~ precedes(X0,sK7(sK2,X1,sK7(sK2,X2,X3)),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),X2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),sK7(sK2,X2,X3)) ),
inference(superposition,[status(thm)],[c_8044,c_2780]) ).
tcf(c_9301,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_3427]) ).
tcf(c_9304,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3427]) ).
tcf(c_9305,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_2929,c_3427]) ).
tcf(c_9335,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_9347,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK3) )
| ( X0 != sK3 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_9364,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_3456]) ).
tcf(c_9366,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_2059,c_3456]) ).
tcf(c_9367,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3456]) ).
tcf(c_9368,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_2929,c_3456]) ).
tcf(c_9402,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_3457]) ).
tcf(c_9404,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_2059,c_3457]) ).
tcf(c_9405,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3457]) ).
tcf(c_9406,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_2929,c_3457]) ).
tcf(c_9440,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_3486]) ).
tcf(c_9443,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3486]) ).
tcf(c_9444,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_2929,c_3486]) ).
tcf(c_9475,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_4318]) ).
tcf(c_9478,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4318]) ).
tcf(c_9479,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_2929,c_4318]) ).
tcf(c_9507,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_4319]) ).
tcf(c_9509,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_2059,c_4319]) ).
tcf(c_9510,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4319]) ).
tcf(c_9511,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_2929,c_4319]) ).
tcf(c_9541,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_4320]) ).
tcf(c_9544,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4320]) ).
tcf(c_9545,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_2929,c_4320]) ).
tcf(c_9611,plain,
! [X0: $i] :
( ( head_of(sK4) = head_of(X0) )
| ( sK4 != X0 ) ),
inference(instantiation,[status(thm)],[c_1447]) ).
tcf(c_9624,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_4321]) ).
tcf(c_9626,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_2059,c_4321]) ).
tcf(c_9627,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4321]) ).
tcf(c_9628,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_2929,c_4321]) ).
tcf(c_9659,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK2,X1,sK4))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK4)),sK7(sK2,X1,sK4))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK4))) )
| ~ precedes(X1,sK4,sK2)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK4),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK4)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9227,c_2454]) ).
tcf(c_9694,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK2,X0,sK3),sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK4)) = head_of(sK7(sK2,X0,sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_3108]) ).
tcf(c_9701,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_6980,c_63,c_6980]) ).
tcf(c_9702,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_9701]) ).
tcf(c_9709,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) )
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_9702]) ).
tcf(c_9710,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_9702]) ).
tcf(c_9712,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_9702]) ).
tcf(c_9737,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2314,c_7040]) ).
tcf(c_9738,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_2313,c_7040]) ).
tcf(c_9762,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2781,c_2454]) ).
tcf(c_9784,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2780,c_9762]) ).
tcf(c_9792,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_2072,c_9762]) ).
tcf(c_9815,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_3487]) ).
tcf(c_9818,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3487]) ).
tcf(c_9819,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_2929,c_3487]) ).
tcf(c_9879,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_3535]) ).
tcf(c_9881,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_2059,c_3535]) ).
tcf(c_9882,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3535]) ).
tcf(c_9883,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_2929,c_3535]) ).
tcf(c_9917,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_3536]) ).
tcf(c_9919,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_2059,c_3536]) ).
tcf(c_9920,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3536]) ).
tcf(c_9921,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_2929,c_3536]) ).
tcf(c_9982,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_3574]) ).
tcf(c_9985,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3574]) ).
tcf(c_9986,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_2929,c_3574]) ).
tcf(c_10017,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_4322]) ).
tcf(c_10020,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK7(sK2,X0,X1)))) = head_of(sK4) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4322]) ).
tcf(c_10021,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_2929,c_4322]) ).
tcf(c_10049,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_4603]) ).
tcf(c_10051,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_2059,c_4603]) ).
tcf(c_10052,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4603]) ).
tcf(c_10053,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_2929,c_4603]) ).
tcf(c_10110,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_4604]) ).
tcf(c_10113,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4604]) ).
tcf(c_10114,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_2929,c_4604]) ).
tcf(c_10142,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_4605]) ).
tcf(c_10144,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_2059,c_4605]) ).
tcf(c_10145,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4605]) ).
tcf(c_10146,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_2929,c_4605]) ).
tcf(c_10180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| precedes(X0,X3,sK2)
| sequential(X1,sK7(sK2,X2,X3))
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X2,X3)),sK7(sK2,X2,X3))) = head_of(sK7(sK2,X1,sK7(sK2,X2,X3))) )
| ~ on_path(X0,sK2)
| ~ path(X4,X5,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X1,sK7(sK2,X2,X3),sK2)
| ~ sequential(X0,sK7(sK2,X1,sK7(sK2,X2,X3))) ),
inference(superposition,[status(thm)],[c_9792,c_105]) ).
tcf(c_10181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK2,X2,X3))
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X2,X3)),sK7(sK2,X2,X3))) = head_of(sK7(sK2,X1,sK7(sK2,X2,X3))) )
| ~ sequential(X0,X3)
| ~ path(X4,X5,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X0,X3,sK2)
| ~ precedes(X1,sK7(sK2,X2,X3),sK2)
| ~ sequential(X0,sK7(sK2,X1,sK7(sK2,X2,X3))) ),
inference(superposition,[status(thm)],[c_9792,c_79]) ).
tcf(c_10182,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X2,sK2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_78]) ).
tcf(c_10183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_77]) ).
tcf(c_10184,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2),X2)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_9702]) ).
tcf(c_10185,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) = tail_of(X2) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_2776]) ).
tcf(c_10186,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_6972]) ).
tcf(c_10187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ on_path(X3,sK2)
| ~ sequential(X3,X2)
| ~ path(X4,X5,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X3)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2) ),
inference(superposition,[status(thm)],[c_9792,c_3302]) ).
tcf(c_10188,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_3013]) ).
tcf(c_10189,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X1,sK7(sK2,X2,X0))
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X2,X0)),sK7(sK2,X2,X0))) = head_of(sK7(sK2,X1,sK7(sK2,X2,X0))) )
| ~ on_path(X0,sK2)
| ~ precedes(X2,X0,sK2)
| ~ precedes(X1,sK7(sK2,X2,X0),sK2)
| ~ on_path(sK7(sK2,X1,sK7(sK2,X2,X0)),sK2)
| ~ sequential(X0,sK7(sK2,X1,sK7(sK2,X2,X0))) ),
inference(superposition,[status(thm)],[c_9792,c_2372]) ).
tcf(c_10190,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_2195]) ).
tcf(c_10191,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| edge(sK7(sK2,X0,sK7(sK2,X1,X2)))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_2207]) ).
tcf(c_10192,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X1,sK7(sK2,X2,X0))
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X2,X0)),sK7(sK2,X2,X0))) = head_of(sK7(sK2,X1,sK7(sK2,X2,X0))) )
| ~ precedes(X2,X0,sK2)
| ~ precedes(X1,sK7(sK2,X2,X0),sK2)
| ~ precedes(X0,sK7(sK2,X1,sK7(sK2,X2,X0)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_2112]) ).
tcf(c_10193,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK2,X1,sK3))
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK7(sK2,X1,sK3))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK3))) )
| ~ precedes(X1,sK3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK3),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK7(sK2,X1,sK3)))
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_9018]) ).
tcf(c_10194,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK2,X1,sK3))
| sequential(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK7(sK2,X1,sK3))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK3))) )
| ~ precedes(X1,sK3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK3),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK4)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_3253]) ).
tcf(c_10195,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,sK4)
| sequential(X0,sK7(sK2,X1,sK4))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK4)),sK7(sK2,X1,sK4))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK4))) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK2)
| ~ precedes(X1,sK4,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK4),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),sK4)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK4)),X2) ),
inference(superposition,[status(thm)],[c_9792,c_3079]) ).
tcf(c_10196,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_8068]) ).
tcf(c_10339,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_10419,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2314,c_7517]) ).
tcf(c_10420,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_2313,c_7517]) ).
tcf(c_10467,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_5496,c_4479]) ).
tcf(c_10468,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_4343,c_4479]) ).
tcf(c_10470,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_6160,c_4479]) ).
tcf(c_10471,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_5491,c_4479]) ).
tcf(c_10472,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_6008,c_4479]) ).
tcf(c_10511,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_6873,c_2042,c_2079,c_2912,c_2911,c_4559,c_6873]) ).
tcf(c_10524,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_5496,c_10511]) ).
tcf(c_10525,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_4343,c_10511]) ).
tcf(c_10526,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_5302,c_10511]) ).
tcf(c_10528,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_5491,c_10511]) ).
tcf(c_10529,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_6008,c_10511]) ).
tcf(c_10594,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2886,c_2454]) ).
tcf(c_10617,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ~ on_path(X2,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_10594]) ).
tcf(c_10645,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_3575]) ).
tcf(c_10648,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3575]) ).
tcf(c_10649,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_2929,c_3575]) ).
tcf(c_10696,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_3613]) ).
tcf(c_10698,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_2059,c_3613]) ).
tcf(c_10699,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = head_of(X2) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3613]) ).
tcf(c_10700,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_2929,c_3613]) ).
tcf(c_10779,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_3614]) ).
tcf(c_10781,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_2059,c_3614]) ).
tcf(c_10782,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(X2) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3614]) ).
tcf(c_10783,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_2929,c_3614]) ).
tcf(c_10817,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_3652]) ).
tcf(c_10820,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3652]) ).
tcf(c_10821,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_2929,c_3652]) ).
tcf(c_10860,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_4606]) ).
tcf(c_10863,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4606]) ).
tcf(c_10864,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_2929,c_4606]) ).
tcf(c_10926,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_4607]) ).
tcf(c_10928,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_2059,c_4607]) ).
tcf(c_10929,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4607]) ).
tcf(c_10930,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_2929,c_4607]) ).
tcf(c_10993,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_4608]) ).
tcf(c_10996,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4608]) ).
tcf(c_10997,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_2929,c_4608]) ).
tcf(c_11025,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_4609]) ).
tcf(c_11027,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_2059,c_4609]) ).
tcf(c_11028,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4609]) ).
tcf(c_11029,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_2929,c_4609]) ).
tcf(c_11060,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9029,c_2454]) ).
tcf(c_11073,plain,
( sequential(sK4,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK4,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK4,sK3),sK3)) )
| ~ precedes(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2140,c_11060]) ).
tcf(c_11074,plain,
( ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK4,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK4,sK3),sK3)) )
| ~ precedes(sK4,sK3,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11073,c_2440]) ).
tcf(c_11077,plain,
~ precedes(sK4,sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_11074,c_53,c_52,c_51,c_50,c_656,c_4469,c_7116]) ).
tcf(c_11080,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_9710,c_63,c_9710]) ).
tcf(c_11081,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_11080]) ).
tcf(c_11088,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1)) )
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_11081]) ).
tcf(c_11089,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_11081]) ).
tcf(c_11090,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2),X2),X2)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_11081]) ).
tcf(c_11092,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_11081]) ).
tcf(c_11158,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK2,X0,X1),sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_3218,c_2454,c_3218]) ).
tcf(c_11172,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| precedes(X0,sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_11158,c_105]) ).
tcf(c_11173,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ~ sequential(X2,sK3)
| ~ sequential(X0,sK4)
| ~ on_path(X2,sK2)
| ~ precedes(X0,sK4,sK2)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_11158,c_79]) ).
tcf(c_11175,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| on_path(sK7(sK2,X0,X1),sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ path(X2,X3,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_11158,c_77]) ).
tcf(c_11178,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_11158,c_2776]) ).
tcf(c_11180,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X2,sK4)
| ~ sequential(X1,sK3)
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ path(X3,X4,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_11158,c_3302]) ).
tcf(c_11182,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(sK4,sK2)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK4,sK7(sK2,X0,X1))
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_11158,c_2372]) ).
tcf(c_11183,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK7(sK2,X0,X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_11158,c_2195]) ).
tcf(c_11184,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_11158,c_2207]) ).
tcf(c_11185,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK4,sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_11158,c_2112]) ).
tcf(c_11186,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X2,sK3)
| ~ sequential(X1,sK3)
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_11158,c_3079]) ).
tcf(c_11187,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK4,X0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_11158,c_8068]) ).
tcf(c_11207,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(sK4,X0)
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11187,c_52]) ).
tcf(c_11215,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK4,sK7(sK2,X0,X1))
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11182,c_52]) ).
tcf(c_11267,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(light_normalisation,[status(thm)],[c_11178,c_2077]) ).
tcf(c_11354,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK4,sK7(sK2,X0,X1))
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_11207]) ).
tcf(c_11355,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK7(sK2,X1,X2)))
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_11207]) ).
tcf(c_11357,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) )
| ~ sequential(sK4,X2)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8044,c_11207]) ).
tcf(c_11406,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK4,sK7(sK2,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_11215,c_2454,c_11215]) ).
tcf(c_11436,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK4,sK7(sK2,X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_11354,c_2454,c_11354]) ).
tcf(c_11481,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),sK2)
| ( X0 = X1 )
| ~ on_path(X8,sK2)
| ~ on_path(X7,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X8,X7)
| ~ sequential(X7,X3)
| ~ path(X5,X6,sK2)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_105]) ).
tcf(c_11482,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,sK2)
| ~ on_path(X4,sK2)
| ~ sequential(X8,X4)
| ~ sequential(X0,X8)
| ~ path(X6,X7,sK2)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_79]) ).
tcf(c_11485,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(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ sequential(sK4,X5)
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_11207]) ).
tcf(c_11486,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(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,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(sK2,sK7(sK2,sK7(sK2,sK7(sK2,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,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_11081]) ).
tcf(c_11487,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(sK2,sK7(sK2,sK7(sK2,sK7(sK2,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(sK2,sK7(sK2,sK7(sK2,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,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_9702]) ).
tcf(c_11488,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(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) = tail_of(sK7(sK6(X0,X1,X2),X3,X4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_2776]) ).
tcf(c_11489,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(sK2,sK7(sK2,sK7(sK2,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(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_6972]) ).
tcf(c_11490,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,sK2)
| ~ on_path(X4,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X6)
| ~ sequential(X0,X4)
| ~ path(X7,X8,sK2)
| ~ path(X1,X2,X3)
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ on_path(sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ sequential(X6,sK7(sK6(X1,X2,X3),X4,X5))
| ~ sequential(X0,sK7(sK6(X1,X2,X3),X4,X5)) ),
inference(superposition,[status(thm)],[c_2926,c_3302]) ).
tcf(c_11491,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(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_3013]) ).
tcf(c_11492,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,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2926,c_2372]) ).
tcf(c_11493,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(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) = head_of(X5) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_2195]) ).
tcf(c_11494,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,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_2207]) ).
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,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2)
| ~ precedes(sK7(sK6(X0,X1,X2),X3,X4),X5,sK2) ),
inference(superposition,[status(thm)],[c_2926,c_2112]) ).
tcf(c_11497,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ~ on_path(sK4,sK2)
| ~ sequential(sK4,X3)
| ~ on_path(X3,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_2985]) ).
tcf(c_11498,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,sK2)
| ~ on_path(X3,sK2)
| ~ precedes(X5,X6,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK7(sK2,X5,X6),sK2)
| ~ sequential(sK7(sK2,X5,X6),X3)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2926,c_8068]) ).
tcf(c_11509,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,sK2)
| ~ 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),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11497,c_52]) ).
tcf(c_11749,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_3653]) ).
tcf(c_11752,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(X2),head_of(sK7(sK2,X0,X1)))) = head_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_3653]) ).
tcf(c_11753,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_2929,c_3653]) ).
tcf(c_11786,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_4081]) ).
tcf(c_11788,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_2059,c_4081]) ).
tcf(c_11789,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = head_of(X2) )
| ( tail_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(head_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4081]) ).
tcf(c_11790,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_2929,c_4081]) ).
tcf(c_11859,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_4082]) ).
tcf(c_11861,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_2059,c_4082]) ).
tcf(c_11862,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,X0,X1)) = tail_of(X2) )
| ( tail_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ( head_of(sK5(tail_of(X2),tail_of(sK7(sK2,X0,X1)))) = tail_of(sK7(sK2,X0,X1)) )
| ~ edge(X2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4082]) ).
tcf(c_11863,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_2929,c_4082]) ).
tcf(c_11904,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_4610]) ).
tcf(c_11907,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK7(sK2,X0,X1)))) = tail_of(sK3) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2196,c_4610]) ).
tcf(c_11908,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_2929,c_4610]) ).
tcf(c_11947,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_3905,c_3923]) ).
tcf(c_11948,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_4346,c_3923]) ).
tcf(c_11952,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_4854,c_3923]) ).
tcf(c_11956,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_5691,c_3923]) ).
tcf(c_12017,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_4346,c_3927]) ).
tcf(c_12021,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_4854,c_3927]) ).
tcf(c_12025,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_5691,c_3927]) ).
tcf(c_12093,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,sK2)
| ~ on_path(X3,sK2)
| ~ 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),sK2)
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2)
| ~ sequential(sK7(sK6(X6,X7,X8),X5,X9),X3)
| ~ sequential(sK7(sK6(X0,X1,X2),X3,X4),X5) ),
inference(superposition,[status(thm)],[c_2926,c_11495]) ).
tcf(c_12110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) )
| ~ sequential(sK4,X2)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_11357,c_2454,c_11357]) ).
tcf(c_12130,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK3)
| sequential(X1,sK7(sK2,X0,sK3))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,sK3)),sK7(sK2,X0,sK3))) = head_of(sK7(sK2,X1,sK7(sK2,X0,sK3))) )
| ~ sequential(sK4,X1)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_12110]) ).
tcf(c_12140,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ precedes(X0,X1,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X1,sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_11267,c_3260,c_11267]) ).
tcf(c_12141,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_12140]) ).
tcf(c_12157,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X1)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),sK4)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_12141]) ).
tcf(c_12158,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),sK4)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_12141]) ).
tcf(c_12160,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(X2,sK7(sK2,X0,X1))
| ( head_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,X2,sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8044,c_12141]) ).
tcf(c_12161,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(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK2,X5,sK7(sK6(X0,X1,X2),X3,X4))) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_12141]) ).
tcf(c_12251,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2)) )
| ~ sequential(X2,sK3)
| ~ on_path(X2,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK7(sK2,X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11355,c_2454]) ).
tcf(c_12282,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK4,sK7(sK2,X0,X1))
| sequential(sK7(sK2,sK4,sK7(sK2,X0,X1)),X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK4,sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,sK4,sK7(sK2,X0,X1))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK4,sK7(sK2,X0,X1)),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK4,sK7(sK2,X0,X1)),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK4,sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_12251]) ).
tcf(c_12299,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X2)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X2,sK2)
| ~ sequential(sK7(sK2,sK7(sK2,X0,X1),X2),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9166,c_2454]) ).
tcf(c_12318,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X0)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X0),X0)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X0)) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X0,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_12299]) ).
tcf(c_12377,plain,
( ~ precedes(sK3,sK4,sK2)
| ~ shortest_path(sK0,sK1,sK2)
| ( tail_of(sK3) != tail_of(sK3) )
| ( head_of(sK4) != head_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_4467]) ).
tcf(c_12378,plain,
tail_of(sK3) = tail_of(sK3),
inference(instantiation,[status(thm)],[c_1439]) ).
tcf(c_12423,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_7357,c_2042,c_2059,c_2912,c_2971,c_7154,c_7357]) ).
tcf(c_12444,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_2292,c_2928]) ).
tcf(c_12463,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_4346,c_4530]) ).
tcf(c_12466,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_5868,c_4530]) ).
tcf(c_12467,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_4854,c_4530]) ).
tcf(c_12468,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_4473,c_4530]) ).
tcf(c_12469,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_6113,c_4530]) ).
tcf(c_12470,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_5608,c_4530]) ).
tcf(c_12471,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_5014,c_4530]) ).
tcf(c_12472,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_6695,c_4530]) ).
tcf(c_12473,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_6037,c_4530]) ).
tcf(c_12474,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_5124,c_4530]) ).
tcf(c_12475,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_4530]) ).
tcf(c_12567,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_6118,c_4238]) ).
tcf(c_12568,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_5613,c_4238]) ).
tcf(c_12572,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_4129,c_4238]) ).
tcf(c_12573,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_5868,c_4238]) ).
tcf(c_12577,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_6212,c_4238]) ).
tcf(c_12579,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_6113,c_4238]) ).
tcf(c_12584,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_5124,c_4238]) ).
tcf(c_12660,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_6118,c_4242]) ).
tcf(c_12661,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_5613,c_4242]) ).
tcf(c_12664,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_4220,c_4242]) ).
tcf(c_12666,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_5868,c_4242]) ).
tcf(c_12670,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_6212,c_4242]) ).
tcf(c_12672,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_6113,c_4242]) ).
tcf(c_12677,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_5124,c_4242]) ).
tcf(c_12760,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_6118,c_4285]) ).
tcf(c_12761,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_5613,c_4285]) ).
tcf(c_12764,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_4220,c_4285]) ).
tcf(c_12766,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_5868,c_4285]) ).
tcf(c_12770,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_6212,c_4285]) ).
tcf(c_12772,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_6113,c_4285]) ).
tcf(c_12777,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_5124,c_4285]) ).
tcf(c_12809,plain,
( precedes(sK4,sK4,sK2)
| ~ precedes(sK3,sK4,sK2)
| ( sK4 != sK3 ) ),
inference(instantiation,[status(thm)],[c_4465]) ).
tcf(c_12829,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X2,X1)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8283,c_3801]) ).
tcf(c_12830,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK4)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3704]) ).
tcf(c_12831,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK2,X0,X1),sK4,sK2)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3194]) ).
tcf(c_12832,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3133]) ).
tcf(c_12833,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| precedes(X0,X2,sK2)
| ( head_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = tail_of(X2) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X1,X2),X2),X2)) = head_of(sK7(sK2,sK7(sK2,X1,X2),X2)) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X1,X2,sK2)
| ~ on_path(sK7(sK2,X1,X2),sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_8283,c_2859]) ).
tcf(c_12834,plain,
! [X0: $i,X1: $i] :
( sequential(X1,X0)
| ( head_of(sK7(sK2,sK7(sK2,X1,X0),X0)) = tail_of(X0) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X1,X0),X0),X0)) = head_of(sK7(sK2,sK7(sK2,X1,X0),X0)) )
| ~ on_path(X0,sK2)
| ~ precedes(X1,X0,sK2)
| ~ on_path(sK7(sK2,X1,X0),sK2)
| ~ sequential(X0,sK7(sK2,X1,X0)) ),
inference(superposition,[status(thm)],[c_8283,c_2424]) ).
tcf(c_12835,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,X0,X1)) = tail_of(X1) )
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_65]) ).
tcf(c_12836,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_63]) ).
tcf(c_12837,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_62]) ).
tcf(c_12838,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK3)) ),
inference(superposition,[status(thm)],[c_8283,c_557]) ).
tcf(c_12839,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK4))
| ~ on_path(sK7(sK2,X0,sK4),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3830]) ).
tcf(c_12840,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X1,X2),X2)) = head_of(sK7(sK2,X1,X2)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = tail_of(sK7(sK2,X1,X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) )
| ~ on_path(X2,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_10594]) ).
tcf(c_12841,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X2)
| sequential(X1,sK7(sK2,X0,X2))
| ( head_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,X2)),sK7(sK2,X0,X2))) = tail_of(sK7(sK2,X0,X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,X2)),sK7(sK2,X0,X2)),sK7(sK2,X0,X2))) = head_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,X2)),sK7(sK2,X0,X2))) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,X2,sK2)
| ~ precedes(X1,sK7(sK2,X0,X2),sK2)
| ~ on_path(sK7(sK2,X1,sK7(sK2,X0,X2)),sK2)
| ~ sequential(X0,sK7(sK2,X1,sK7(sK2,X0,X2))) ),
inference(superposition,[status(thm)],[c_8283,c_9095]) ).
tcf(c_12842,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = tail_of(sK7(sK2,X1,X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X2)
| ~ precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_2332]) ).
tcf(c_12843,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| precedes(sK7(sK2,X0,sK7(sK2,X1,X2)),X2,sK2)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = tail_of(sK7(sK2,X1,X2)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) )
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,X2)),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_2497]) ).
tcf(c_12844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ on_path(X2,sK2)
| ~ sequential(X2,X1)
| ~ path(X3,X4,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8283,c_3322]) ).
tcf(c_12846,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK3)
| sequential(X1,sK7(sK2,X0,sK3))
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X1,sK7(sK2,X0,sK3)),sK7(sK2,X0,sK3))) = head_of(sK7(sK2,X1,sK7(sK2,X0,sK3))) )
| ~ sequential(sK4,X1)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X1,X0)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_12110]) ).
tcf(c_12847,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK2,X0,sK3),sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK4)) = head_of(sK7(sK2,X0,sK3)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3108]) ).
tcf(c_12848,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_8229]) ).
tcf(c_12849,plain,
! [X0: $i] :
( sequential(X0,sK3)
| precedes(X0,sK4,sK2)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_6944]) ).
tcf(c_12850,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_3241]) ).
tcf(c_12855,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X0)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X0),X0)) = tail_of(X0) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X0),X0),X0)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X0),X0)) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X0,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_12299]) ).
tcf(c_12894,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK4))
| ~ on_path(sK7(sK2,X0,sK4),sK2) ),
inference(light_normalisation,[status(thm)],[c_12839,c_2077]) ).
tcf(c_13047,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = tail_of(sK3) )
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_13190,plain,
( ( head_of(sK3) = head_of(sK3) )
| ( sK3 != sK3 ) ),
inference(instantiation,[status(thm)],[c_8725]) ).
tcf(c_13204,plain,
! [X0: $i] :
( ~ precedes(X0,sK3,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(sK4,X0)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_12848,c_53,c_554,c_12848]) ).
tcf(c_13205,plain,
! [X0: $i] :
( ( head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(renaming,[status(thm)],[c_13204]) ).
tcf(c_13218,plain,
! [X0: $i] :
( sequential(X0,sK3)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK3))
| ~ on_path(sK7(sK2,X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_13205]) ).
tcf(c_13219,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK2,X1,sK3))
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK7(sK2,X1,sK3))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) )
| ~ precedes(X1,sK3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK3),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK7(sK2,X1,sK3)))
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_13205]) ).
tcf(c_13279,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12894,c_2454]) ).
tcf(c_13296,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ sequential(X1,sK3)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_12832,c_2454,c_12832]) ).
tcf(c_13316,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X2,sK2)
| ~ on_path(X1,sK2)
| ~ sequential(X2,X1)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_3829,c_2454,c_3829]) ).
tcf(c_13332,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X2,sK2)
| ~ on_path(sK7(sK2,sK7(sK2,X0,X1),X2),sK2)
| ~ sequential(sK7(sK2,sK7(sK2,X0,X1),X2),X1) ),
inference(superposition,[status(thm)],[c_2140,c_13316]) ).
tcf(c_13333,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK2,X3,X4),X5)
| ( X0 = X1 )
| ( tail_of(sK7(sK2,sK7(sK2,X3,X4),X4)) = head_of(sK7(sK2,X3,X4)) )
| ~ on_path(X4,sK2)
| ~ precedes(X3,X4,sK2)
| ~ path(X0,X1,X2)
| ~ precedes(sK7(sK2,X3,X4),X5,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),sK2)
| ~ sequential(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),X4) ),
inference(superposition,[status(thm)],[c_2169,c_13316]) ).
tcf(c_13334,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = tail_of(X1) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,X0,X1),X1)) )
| ~ on_path(X1,sK2)
| ~ sequential(X1,X1)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_13316]) ).
tcf(c_13335,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ on_path(X1,sK2)
| ~ sequential(X1,X1)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_13316]) ).
tcf(c_13368,plain,
! [X0: $i,X1: $i] :
( sequential(X0,sK4)
| sequential(sK7(sK2,X0,sK4),X1)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK4)
| ~ precedes(sK7(sK2,X0,sK4),X1,sK2)
| ~ sequential(sK7(sK2,sK7(sK2,X0,sK4),X1),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6923,c_2454]) ).
tcf(c_13387,plain,
! [X0: $i] :
( sequential(X0,sK4)
| sequential(sK7(sK2,X0,sK4),sK3)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK3),sK3)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK4)
| ~ precedes(sK7(sK2,X0,sK4),sK3,sK2) ),
inference(superposition,[status(thm)],[c_8283,c_13368]) ).
tcf(c_13388,plain,
! [X0: $i] :
( sequential(X0,sK4)
| sequential(sK7(sK2,X0,sK4),sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK3)) )
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK4)
| ~ precedes(sK7(sK2,X0,sK4),sK3,sK2) ),
inference(superposition,[status(thm)],[c_2335,c_13368]) ).
tcf(c_13434,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_5613,c_4534]) ).
tcf(c_13435,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_3905,c_4534]) ).
tcf(c_13439,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_5868,c_4534]) ).
tcf(c_13441,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_4473,c_4534]) ).
tcf(c_13442,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_6866,c_4534]) ).
tcf(c_13443,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_6212,c_4534]) ).
tcf(c_13444,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_5691,c_4534]) ).
tcf(c_13446,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_5608,c_4534]) ).
tcf(c_13447,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_5014,c_4534]) ).
tcf(c_13448,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_6695,c_4534]) ).
tcf(c_13449,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_6037,c_4534]) ).
tcf(c_13451,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_2077,c_4534]) ).
tcf(c_13452,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_6118,c_4534]) ).
tcf(c_13453,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_5613,c_4534]) ).
tcf(c_13454,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_3905,c_4534]) ).
tcf(c_13455,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_4346,c_4534]) ).
tcf(c_13458,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_5868,c_4534]) ).
tcf(c_13459,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_4854,c_4534]) ).
tcf(c_13460,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_4473,c_4534]) ).
tcf(c_13461,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_6866,c_4534]) ).
tcf(c_13462,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_6212,c_4534]) ).
tcf(c_13463,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_5691,c_4534]) ).
tcf(c_13464,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_6113,c_4534]) ).
tcf(c_13465,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_5608,c_4534]) ).
tcf(c_13466,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_5014,c_4534]) ).
tcf(c_13467,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_6695,c_4534]) ).
tcf(c_13468,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_6037,c_4534]) ).
tcf(c_13469,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_5124,c_4534]) ).
tcf(c_13470,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_4534]) ).
tcf(c_13827,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_4854,c_5307]) ).
tcf(c_13829,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_6113,c_5307]) ).
tcf(c_13830,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_5608,c_5307]) ).
tcf(c_13831,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_5014,c_5307]) ).
tcf(c_13832,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_5307]) ).
tcf(c_13873,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_2077,c_5311]) ).
tcf(c_13874,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_6118,c_5311]) ).
tcf(c_13875,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_5613,c_5311]) ).
tcf(c_13876,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_3905,c_5311]) ).
tcf(c_13877,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_4346,c_5311]) ).
tcf(c_13878,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_4220,c_5311]) ).
tcf(c_13879,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_4129,c_5311]) ).
tcf(c_13884,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_6212,c_5311]) ).
tcf(c_13885,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_5691,c_5311]) ).
tcf(c_13886,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_6113,c_5311]) ).
tcf(c_13887,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_5608,c_5311]) ).
tcf(c_13890,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_6037,c_5311]) ).
tcf(c_13891,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_5124,c_5311]) ).
tcf(c_13892,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_2077,c_5311]) ).
tcf(c_13893,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_6118,c_5311]) ).
tcf(c_13894,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_5613,c_5311]) ).
tcf(c_13895,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_3905,c_5311]) ).
tcf(c_13896,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_4346,c_5311]) ).
tcf(c_13897,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_4220,c_5311]) ).
tcf(c_13898,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_4129,c_5311]) ).
tcf(c_13900,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_4854,c_5311]) ).
tcf(c_13902,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_6866,c_5311]) ).
tcf(c_13903,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_6212,c_5311]) ).
tcf(c_13904,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_5691,c_5311]) ).
tcf(c_13905,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_6113,c_5311]) ).
tcf(c_13906,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_5608,c_5311]) ).
tcf(c_13907,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_5014,c_5311]) ).
tcf(c_13908,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_6695,c_5311]) ).
tcf(c_13909,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_6037,c_5311]) ).
tcf(c_13910,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_5124,c_5311]) ).
tcf(c_13911,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_5311]) ).
tcf(c_14220,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_3905,c_5548]) ).
tcf(c_14221,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_4346,c_5548]) ).
tcf(c_14222,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_4220,c_5548]) ).
tcf(c_14223,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_4129,c_5548]) ).
tcf(c_14224,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_5868,c_5548]) ).
tcf(c_14225,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_4854,c_5548]) ).
tcf(c_14226,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_4473,c_5548]) ).
tcf(c_14227,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_6866,c_5548]) ).
tcf(c_14228,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_6212,c_5548]) ).
tcf(c_14229,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_5691,c_5548]) ).
tcf(c_14230,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_6113,c_5548]) ).
tcf(c_14231,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_5608,c_5548]) ).
tcf(c_14232,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_5014,c_5548]) ).
tcf(c_14233,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_6695,c_5548]) ).
tcf(c_14234,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_6037,c_5548]) ).
tcf(c_14235,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_5124,c_5548]) ).
tcf(c_14236,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_5548]) ).
tcf(c_14411,plain,
( ( head_of(sK4) = head_of(sK4) )
| ( sK4 != sK4 ) ),
inference(instantiation,[status(thm)],[c_9611]) ).
tcf(c_14449,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_6118,c_4289]) ).
tcf(c_14450,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_5613,c_4289]) ).
tcf(c_14455,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_5868,c_4289]) ).
tcf(c_14459,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_6212,c_4289]) ).
tcf(c_14461,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_6113,c_4289]) ).
tcf(c_14466,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_5124,c_4289]) ).
tcf(c_14507,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_4346,c_4571]) ).
tcf(c_14511,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_4854,c_4571]) ).
tcf(c_14515,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_5691,c_4571]) ).
tcf(c_14533,plain,
head_of(sK4) != tail_of(sK3),
inference(global_subsumption_just,[status(thm)],[c_13873,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_5335,c_7116,c_12809]) ).
tcf(c_14535,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_12423,c_14533]) ).
tcf(c_14536,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_6823,c_14533]) ).
tcf(c_14537,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_6695,c_14533]) ).
tcf(c_14538,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_6113,c_14533]) ).
tcf(c_14539,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_6037,c_14533]) ).
tcf(c_14540,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_6008,c_14533]) ).
tcf(c_14541,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_5608,c_14533]) ).
tcf(c_14542,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_5491,c_14533]) ).
tcf(c_14543,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_5124,c_14533]) ).
tcf(c_14544,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_5014,c_14533]) ).
tcf(c_14570,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_14537,c_5311]) ).
tcf(c_14571,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_14537,c_4534]) ).
tcf(c_14572,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_14537,c_2051]) ).
tcf(c_14573,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_14537,c_61]) ).
tcf(c_14576,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_14537,c_5548]) ).
tcf(c_14578,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_14537,c_4534]) ).
tcf(c_14582,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_14537,c_4530]) ).
tcf(c_14585,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_14537,c_6876]) ).
tcf(c_14586,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_14537,c_6872]) ).
tcf(c_14587,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_14537,c_4482]) ).
tcf(c_14588,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_14537,c_4478]) ).
tcf(c_14591,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_14537,c_2051]) ).
tcf(c_14659,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_14538,c_5311]) ).
tcf(c_14660,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_14538,c_4534]) ).
tcf(c_14661,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_14538,c_2051]) ).
tcf(c_14662,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_14538,c_61]) ).
tcf(c_14664,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_14538,c_4289]) ).
tcf(c_14665,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_14538,c_5548]) ).
tcf(c_14666,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_14538,c_5311]) ).
tcf(c_14667,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_14538,c_5307]) ).
tcf(c_14669,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_14538,c_4285]) ).
tcf(c_14670,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_14538,c_4242]) ).
tcf(c_14671,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_14538,c_4238]) ).
tcf(c_14672,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_14538,c_4530]) ).
tcf(c_14681,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_14538,c_2051]) ).
tcf(c_14755,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_14539,c_5311]) ).
tcf(c_14756,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_14539,c_4534]) ).
tcf(c_14757,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_14539,c_2051]) ).
tcf(c_14758,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_14539,c_61]) ).
tcf(c_14761,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_14539,c_5548]) ).
tcf(c_14762,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_14539,c_5311]) ).
tcf(c_14763,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_14539,c_4534]) ).
tcf(c_14767,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_14539,c_4530]) ).
tcf(c_14770,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_14539,c_6876]) ).
tcf(c_14771,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_14539,c_6872]) ).
tcf(c_14772,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_14539,c_4482]) ).
tcf(c_14773,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_14539,c_4478]) ).
tcf(c_14776,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_14539,c_2051]) ).
tcf(c_14777,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_14539,c_74]) ).
tcf(c_14853,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_14540,c_66]) ).
tcf(c_14854,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_14540,c_10511]) ).
tcf(c_14855,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_14540,c_4479]) ).
tcf(c_14857,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_14540,c_61]) ).
tcf(c_14859,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_14540,c_66]) ).
tcf(c_14893,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_14541,c_5311]) ).
tcf(c_14894,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_14541,c_4534]) ).
tcf(c_14895,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_14541,c_2051]) ).
tcf(c_14896,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_14541,c_61]) ).
tcf(c_14899,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_14541,c_5548]) ).
tcf(c_14900,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_14541,c_5311]) ).
tcf(c_14901,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_14541,c_5307]) ).
tcf(c_14902,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_14541,c_4534]) ).
tcf(c_14906,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_14541,c_4530]) ).
tcf(c_14909,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_14541,c_6876]) ).
tcf(c_14910,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_14541,c_6872]) ).
tcf(c_14911,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_14541,c_4482]) ).
tcf(c_14912,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_14541,c_4478]) ).
tcf(c_14915,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_14541,c_2051]) ).
tcf(c_15014,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_4220,c_5552]) ).
tcf(c_15016,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_5868,c_5552]) ).
tcf(c_15018,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_4473,c_5552]) ).
tcf(c_15019,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_6866,c_5552]) ).
tcf(c_15020,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_6212,c_5552]) ).
tcf(c_15022,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_14541,c_5552]) ).
tcf(c_15024,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_14539,c_5552]) ).
tcf(c_15025,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_14537,c_5552]) ).
tcf(c_15026,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_2077,c_5552]) ).
tcf(c_15029,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_3905,c_5552]) ).
tcf(c_15030,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_4346,c_5552]) ).
tcf(c_15031,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_4220,c_5552]) ).
tcf(c_15032,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_4129,c_5552]) ).
tcf(c_15033,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_5868,c_5552]) ).
tcf(c_15034,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_4854,c_5552]) ).
tcf(c_15035,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_4473,c_5552]) ).
tcf(c_15036,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_6866,c_5552]) ).
tcf(c_15037,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_6212,c_5552]) ).
tcf(c_15038,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_5691,c_5552]) ).
tcf(c_15039,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_14541,c_5552]) ).
tcf(c_15040,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_14538,c_5552]) ).
tcf(c_15041,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_14539,c_5552]) ).
tcf(c_15042,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_14537,c_5552]) ).
tcf(c_15043,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_5552]) ).
tcf(c_15197,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_5691,c_6165]) ).
tcf(c_15198,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_4346,c_6165]) ).
tcf(c_15199,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_4220,c_6165]) ).
tcf(c_15200,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_4129,c_6165]) ).
tcf(c_15201,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_5868,c_6165]) ).
tcf(c_15202,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_4854,c_6165]) ).
tcf(c_15203,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_4473,c_6165]) ).
tcf(c_15204,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_14541,c_6165]) ).
tcf(c_15205,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_14538,c_6165]) ).
tcf(c_15206,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_14539,c_6165]) ).
tcf(c_15207,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_14537,c_6165]) ).
tcf(c_15208,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_6165]) ).
tcf(c_15345,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_6118,c_6169]) ).
tcf(c_15346,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_5613,c_6169]) ).
tcf(c_15347,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_3905,c_6169]) ).
tcf(c_15349,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_4220,c_6169]) ).
tcf(c_15350,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_4129,c_6169]) ).
tcf(c_15351,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_5868,c_6169]) ).
tcf(c_15357,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_14541,c_6169]) ).
tcf(c_15358,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_14538,c_6169]) ).
tcf(c_15359,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_14539,c_6169]) ).
tcf(c_15361,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_2077,c_6169]) ).
tcf(c_15362,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_6118,c_6169]) ).
tcf(c_15363,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_5613,c_6169]) ).
tcf(c_15364,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_3905,c_6169]) ).
tcf(c_15365,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_4346,c_6169]) ).
tcf(c_15366,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_4220,c_6169]) ).
tcf(c_15367,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_4129,c_6169]) ).
tcf(c_15368,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_5868,c_6169]) ).
tcf(c_15369,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_4854,c_6169]) ).
tcf(c_15370,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_4473,c_6169]) ).
tcf(c_15373,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_5691,c_6169]) ).
tcf(c_15374,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_14541,c_6169]) ).
tcf(c_15375,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_14538,c_6169]) ).
tcf(c_15376,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_14539,c_6169]) ).
tcf(c_15377,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_14537,c_6169]) ).
tcf(c_15378,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_6169]) ).
tcf(c_15630,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_14542,c_66]) ).
tcf(c_15631,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_14542,c_10511]) ).
tcf(c_15632,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_14542,c_4479]) ).
tcf(c_15634,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_14542,c_61]) ).
tcf(c_15636,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_14542,c_66]) ).
tcf(c_15671,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_14543,c_6169]) ).
tcf(c_15672,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_14543,c_5552]) ).
tcf(c_15673,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_14543,c_5311]) ).
tcf(c_15674,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_14543,c_4534]) ).
tcf(c_15675,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_14543,c_2051]) ).
tcf(c_15676,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_14543,c_61]) ).
tcf(c_15677,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_14543,c_6169]) ).
tcf(c_15678,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_14543,c_6165]) ).
tcf(c_15681,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_14543,c_4289]) ).
tcf(c_15682,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_14543,c_5548]) ).
tcf(c_15683,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_14543,c_5311]) ).
tcf(c_15685,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_14543,c_4285]) ).
tcf(c_15686,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_14543,c_4242]) ).
tcf(c_15687,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_14543,c_4238]) ).
tcf(c_15688,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_14543,c_4530]) ).
tcf(c_15697,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_14543,c_2051]) ).
tcf(c_15818,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_14544,c_6169]) ).
tcf(c_15819,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_14544,c_5552]) ).
tcf(c_15820,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_14544,c_5311]) ).
tcf(c_15821,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_14544,c_4534]) ).
tcf(c_15822,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_14544,c_2051]) ).
tcf(c_15823,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_14544,c_61]) ).
tcf(c_15825,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_14544,c_6165]) ).
tcf(c_15826,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_14544,c_5552]) ).
tcf(c_15829,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_14544,c_5548]) ).
tcf(c_15831,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_14544,c_5307]) ).
tcf(c_15832,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_14544,c_4534]) ).
tcf(c_15836,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_14544,c_4530]) ).
tcf(c_15839,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_14544,c_6876]) ).
tcf(c_15840,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_14544,c_6872]) ).
tcf(c_15841,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_14544,c_4482]) ).
tcf(c_15842,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_14544,c_4478]) ).
tcf(c_15845,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_14544,c_2051]) ).
tcf(c_15953,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK2,X0,sK3),sK3)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK7(sK2,X0,sK3),sK4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7014,c_2454]) ).
tcf(c_15969,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ precedes(X0,X1,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_11089,c_63,c_11089]) ).
tcf(c_15970,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(renaming,[status(thm)],[c_15969]) ).
tcf(c_15977,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1)) )
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2314,c_15970]) ).
tcf(c_15978,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1),X1)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X1),X1),X1),X1),X1)) )
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_2293,c_15970]) ).
tcf(c_15979,plain,
! [X0: $i,X1: $i,X2: $i] :
( edge(X2)
| sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2))) = head_of(sK7(sK2,X0,sK7(sK2,X1,X2))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2),X2),X2),X2)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,X2)),X2),X2),X2),X2),X2)) )
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_15970]) ).
tcf(c_15981,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| edge(sK7(sK2,X0,X1))
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X2,sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1)),sK7(sK2,X0,X1))) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK2) ),
inference(superposition,[status(thm)],[c_8044,c_15970]) ).
tcf(c_15982,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(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,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)),sK7(sK6(X0,X1,X2),X3,X4))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,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))) )
| ~ on_path(X5,sK2)
| ~ on_path(X3,sK2)
| ~ sequential(X5,X3)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),X3,X4),sK2) ),
inference(superposition,[status(thm)],[c_2926,c_15970]) ).
tcf(c_16031,plain,
! [X0: $i] :
( sequential(X0,sK3)
| sequential(sK7(sK2,X0,sK3),sK3)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ sequential(sK7(sK2,X0,sK3),sK4)
| ~ on_path(sK7(sK2,X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_12850]) ).
tcf(c_16032,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK2,X1,sK3))
| sequential(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3)
| ( head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) = tail_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK7(sK2,X1,sK3))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) )
| ~ precedes(X1,sK3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK3),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK4)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_12850]) ).
tcf(c_16052,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X0,X1),X1)) = head_of(sK7(sK2,X0,X1)) )
| ~ sequential(X1,sK4)
| ~ on_path(X1,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ sequential(sK7(sK2,X0,X1),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_3738,c_2454,c_3738]) ).
tcf(c_16068,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = tail_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_8283,c_16052]) ).
tcf(c_16069,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK3) ),
inference(superposition,[status(thm)],[c_2335,c_16052]) ).
tcf(c_16070,plain,
! [X0: $i] :
( sequential(X0,sK4)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK7(sK2,X0,sK4)) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK4),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK4),sK4)) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2)
| ~ precedes(X0,sK4,sK2)
| ~ sequential(sK7(sK2,X0,sK4),sK3) ),
inference(light_normalisation,[status(thm)],[c_16068,c_2077]) ).
tcf(c_16071,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X2,X3)
| sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X2,X3),sK2)
| ~ sequential(sK7(sK2,X0,X1),X2)
| ~ sequential(sK7(sK2,X2,X3),X0) ),
inference(global_subsumption_just,[status(thm)],[c_8263,c_2454,c_8263]) ).
tcf(c_16072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X2,X3)
| sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X0,X1,sK2)
| ~ on_path(sK7(sK2,X2,X3),sK2)
| ~ sequential(sK7(sK2,X2,X3),X0)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(renaming,[status(thm)],[c_16071]) ).
tcf(c_16082,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X2,X3)
| sequential(X0,X1)
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X2,X3),X0)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16072,c_2454]) ).
tcf(c_16107,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| sequential(sK7(sK2,X0,X1),X2)
| sequential(sK7(sK2,sK7(sK2,X0,X1),X2),X3)
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ precedes(sK7(sK2,X0,X1),X2,sK2)
| ~ on_path(sK7(sK2,sK7(sK2,X0,X1),X2),sK2)
| ~ precedes(sK7(sK2,sK7(sK2,X0,X1),X2),X3,sK2)
| ~ sequential(sK7(sK2,sK7(sK2,sK7(sK2,X0,X1),X2),X3),X0) ),
inference(superposition,[status(thm)],[c_2140,c_16082]) ).
tcf(c_16108,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X3,X4)
| shortest_path(X0,X1,X2)
| sequential(sK7(sK2,X3,X4),X5)
| sequential(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),X6)
| ( X0 = X1 )
| ~ on_path(X3,sK2)
| ~ precedes(X3,X4,sK2)
| ~ path(X0,X1,X2)
| ~ precedes(sK7(sK2,X3,X4),X5,sK6(X0,X1,X2))
| ~ on_path(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),sK2)
| ~ precedes(sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),X6,sK2)
| ~ sequential(sK7(sK2,sK7(sK6(X0,X1,X2),sK7(sK2,X3,X4),X5),X6),X3) ),
inference(superposition,[status(thm)],[c_2169,c_16082]) ).
tcf(c_16109,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X0,X1)
| ( head_of(sK7(sK2,sK7(sK2,X2,X0),X0)) = tail_of(X0) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X2,X0),X0),X0)) = head_of(sK7(sK2,sK7(sK2,X2,X0),X0)) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_8283,c_16082]) ).
tcf(c_16110,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X2,X0)
| sequential(X0,X1)
| ( tail_of(sK7(sK2,sK7(sK2,X2,X0),X0)) = head_of(sK7(sK2,X2,X0)) )
| ~ on_path(X2,sK2)
| ~ on_path(X0,sK2)
| ~ precedes(X2,X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),X2) ),
inference(superposition,[status(thm)],[c_2335,c_16082]) ).
tcf(c_16183,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)
| sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| precedes(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5,sK6(X1,X2,X3))
| ( X1 = X2 )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = tail_of(sK7(sK6(X1,X2,X3),X4,X5)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) )
| ~ path(X1,X2,X3)
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_8283,c_3357]) ).
tcf(c_16184,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)
| sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| precedes(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5,sK6(X1,X2,X3))
| ( X1 = X2 )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = head_of(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5))) )
| ~ path(X1,X2,X3)
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_2335,c_3357]) ).
tcf(c_16223,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_14543,c_14853]) ).
tcf(c_16226,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_5868,c_14853]) ).
tcf(c_16227,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_4854,c_14853]) ).
tcf(c_16228,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_4473,c_14853]) ).
tcf(c_16229,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_14544,c_14853]) ).
tcf(c_16230,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_14541,c_14853]) ).
tcf(c_16231,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_14538,c_14853]) ).
tcf(c_16232,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_14853]) ).
tcf(c_16305,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_6118,c_14859]) ).
tcf(c_16307,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_3905,c_14859]) ).
tcf(c_16308,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_4346,c_14859]) ).
tcf(c_16310,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_4129,c_14859]) ).
tcf(c_16311,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_5868,c_14859]) ).
tcf(c_16312,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_4854,c_14859]) ).
tcf(c_16315,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_6212,c_14859]) ).
tcf(c_16316,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_5691,c_14859]) ).
tcf(c_16318,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_14541,c_14859]) ).
tcf(c_16323,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_2077,c_14859]) ).
tcf(c_16324,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_6118,c_14859]) ).
tcf(c_16325,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_5613,c_14859]) ).
tcf(c_16326,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_3905,c_14859]) ).
tcf(c_16327,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_4346,c_14859]) ).
tcf(c_16328,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_4220,c_14859]) ).
tcf(c_16329,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_4129,c_14859]) ).
tcf(c_16330,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_5868,c_14859]) ).
tcf(c_16331,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_4854,c_14859]) ).
tcf(c_16332,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_4473,c_14859]) ).
tcf(c_16333,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_6866,c_14859]) ).
tcf(c_16334,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_6212,c_14859]) ).
tcf(c_16335,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_5691,c_14859]) ).
tcf(c_16336,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_14544,c_14859]) ).
tcf(c_16337,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_14541,c_14859]) ).
tcf(c_16338,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_14538,c_14859]) ).
tcf(c_16339,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_14543,c_14859]) ).
tcf(c_16342,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_14859]) ).
tcf(c_16569,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_14538,c_15630]) ).
tcf(c_16570,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_15630]) ).
tcf(c_16626,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_6118,c_15636]) ).
tcf(c_16628,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_3905,c_15636]) ).
tcf(c_16629,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_4346,c_15636]) ).
tcf(c_16631,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_4129,c_15636]) ).
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(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_5868,c_15636]) ).
tcf(c_16633,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_4854,c_15636]) ).
tcf(c_16636,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_6212,c_15636]) ).
tcf(c_16637,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_5691,c_15636]) ).
tcf(c_16641,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_14543,c_15636]) ).
tcf(c_16642,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_14539,c_15636]) ).
tcf(c_16644,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_2077,c_15636]) ).
tcf(c_16645,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_6118,c_15636]) ).
tcf(c_16646,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_5613,c_15636]) ).
tcf(c_16647,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_3905,c_15636]) ).
tcf(c_16648,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_4346,c_15636]) ).
tcf(c_16649,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_4220,c_15636]) ).
tcf(c_16650,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_4129,c_15636]) ).
tcf(c_16651,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_5868,c_15636]) ).
tcf(c_16652,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_4854,c_15636]) ).
tcf(c_16653,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_4473,c_15636]) ).
tcf(c_16654,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_6866,c_15636]) ).
tcf(c_16655,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_6212,c_15636]) ).
tcf(c_16656,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_5691,c_15636]) ).
tcf(c_16659,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_14538,c_15636]) ).
tcf(c_16660,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_14543,c_15636]) ).
tcf(c_16661,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_14539,c_15636]) ).
tcf(c_16662,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_14537,c_15636]) ).
tcf(c_16663,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_15636]) ).
tcf(c_16899,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_4854,c_4575]) ).
tcf(c_16903,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_5691,c_4575]) ).
tcf(c_16957,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_4854,c_4860]) ).
tcf(c_16961,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_5691,c_4860]) ).
tcf(c_17018,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_5691,c_4864]) ).
tcf(c_17042,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_3905,c_16323]) ).
tcf(c_17043,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_4346,c_16323]) ).
tcf(c_17047,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_4854,c_16323]) ).
tcf(c_17051,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_5691,c_16323]) ).
tcf(c_17114,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_3905,c_16644]) ).
tcf(c_17115,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_4346,c_16644]) ).
tcf(c_17119,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_4854,c_16644]) ).
tcf(c_17123,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_5691,c_16644]) ).
tcf(c_17193,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) ),
inference(global_subsumption_just,[status(thm)],[c_17047,c_5302,c_17047]) ).
tcf(c_17203,plain,
! [X0: $i,X1: $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) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_17193]) ).
tcf(c_17204,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) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2313,c_17193]) ).
tcf(c_17205,plain,
! [X0: $i,X1: $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(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17203,c_52]) ).
tcf(c_17230,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) ),
inference(global_subsumption_just,[status(thm)],[c_17051,c_2042,c_2911,c_6006,c_17051]) ).
tcf(c_17240,plain,
! [X0: $i,X1: $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) )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_17230]) ).
tcf(c_17241,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( 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(sK4),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2313,c_17230]) ).
tcf(c_17242,plain,
! [X0: $i,X1: $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(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17240,c_52]) ).
tcf(c_17286,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)
| sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| ( X1 = X2 )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = tail_of(sK7(sK6(X1,X2,X3),X4,X5)) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) )
| ~ path(X1,X2,X3)
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5)
| ~ precedes(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5,sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_8283,c_3358]) ).
tcf(c_17287,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)
| sequential(X0,sK7(sK6(X1,X2,X3),X4,X5))
| ( X1 = X2 )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),sK7(sK6(X1,X2,X3),X4,X5))) = head_of(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5))) )
| ~ path(X1,X2,X3)
| ~ path(X6,X7,sK6(X1,X2,X3))
| ~ precedes(X4,X5,sK6(X1,X2,X3))
| ~ precedes(X0,sK7(sK6(X1,X2,X3),X4,X5),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5)
| ~ precedes(sK7(sK2,X0,sK7(sK6(X1,X2,X3),X4,X5)),X5,sK6(X1,X2,X3)) ),
inference(superposition,[status(thm)],[c_2335,c_3358]) ).
tcf(c_17373,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_3924]) ).
tcf(c_17374,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_17373,c_2042]) ).
tcf(c_17391,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_5496,c_4239]) ).
tcf(c_17397,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_4239]) ).
tcf(c_17398,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_17397,c_2059]) ).
tcf(c_17421,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(sK4),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5496,c_4286]) ).
tcf(c_17427,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)
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_4286]) ).
tcf(c_17428,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(sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17427,c_2059]) ).
tcf(c_17448,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_6118,c_5656]) ).
tcf(c_17449,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_5613,c_5656]) ).
tcf(c_17462,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_14538,c_5656]) ).
tcf(c_17463,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_14543,c_5656]) ).
tcf(c_17515,plain,
( ( head_of(sK3) = tail_of(sK3) )
| ( tail_of(sK3) != head_of(sK3) )
| ( head_of(sK3) != head_of(sK3) ) ),
inference(instantiation,[status(thm)],[c_8724]) ).
tcf(c_17541,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_14538,c_5660]) ).
tcf(c_17542,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_14543,c_5660]) ).
tcf(c_17573,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_5691,c_5696]) ).
tcf(c_17616,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,sK2)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_17374,c_3801]) ).
tcf(c_17617,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_3704]) ).
tcf(c_17618,plain,
( precedes(sK3,sK4,sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_3194]) ).
tcf(c_17619,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_3133]) ).
tcf(c_17620,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_2859]) ).
tcf(c_17621,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_2424]) ).
tcf(c_17625,plain,
( ( 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)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17621,c_51]) ).
tcf(c_17633,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17620,c_51]) ).
tcf(c_17641,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17616,c_51]) ).
tcf(c_17669,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17625,c_62]) ).
tcf(c_17696,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_105]) ).
tcf(c_17697,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_79]) ).
tcf(c_17701,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_12141]) ).
tcf(c_17705,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_2776]) ).
tcf(c_17707,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_17633,c_3302]) ).
tcf(c_17709,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_17633,c_2372]) ).
tcf(c_17710,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_2195]) ).
tcf(c_17711,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_2207]) ).
tcf(c_17712,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK2) ),
inference(superposition,[status(thm)],[c_17633,c_2112]) ).
tcf(c_17716,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_17633,c_8068]) ).
tcf(c_17717,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,sK2)
| ~ path(X0,X1,X2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_11495]) ).
tcf(c_17869,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_8713]) ).
tcf(c_17886,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,sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_17641,c_2059,c_2079,c_2085,c_2971,c_17641,c_17869]) ).
tcf(c_17887,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(renaming,[status(thm)],[c_17886]) ).
tcf(c_17901,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_17887]) ).
tcf(c_17902,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_17887]) ).
tcf(c_17903,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,sK2)
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17374,c_17887]) ).
tcf(c_17948,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_17398,c_3801]) ).
tcf(c_17950,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17398,c_3194]) ).
tcf(c_17951,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,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17398,c_3133]) ).
tcf(c_17952,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17398,c_2859]) ).
tcf(c_17953,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17398,c_2424]) ).
tcf(c_17957,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17953,c_52]) ).
tcf(c_17963,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17950,c_2393,c_52]) ).
tcf(c_17969,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17952,c_52]) ).
tcf(c_17977,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17948,c_52]) ).
tcf(c_18019,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17957,c_62]) ).
tcf(c_18037,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17963,c_62]) ).
tcf(c_18064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_105]) ).
tcf(c_18065,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_79]) ).
tcf(c_18069,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_12141]) ).
tcf(c_18070,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_11207]) ).
tcf(c_18073,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_2776]) ).
tcf(c_18075,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_17969,c_3302]) ).
tcf(c_18077,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_17969,c_2372]) ).
tcf(c_18078,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_2195]) ).
tcf(c_18079,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_2207]) ).
tcf(c_18080,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_17969,c_2112]) ).
tcf(c_18084,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_17969,c_8068]) ).
tcf(c_18085,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,sK2)
| ~ path(X0,X1,X2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_17969,c_11495]) ).
tcf(c_18286,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_3360]) ).
tcf(c_18324,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(sK4),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_6118,c_4532]) ).
tcf(c_18325,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(sK4),head_of(sK3)))
| ~ edge(sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_5613,c_4532]) ).
tcf(c_18338,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)))
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_14538,c_4532]) ).
tcf(c_18339,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)))
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_14543,c_4532]) ).
tcf(c_18414,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)
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_4572]) ).
tcf(c_18415,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(sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18414,c_2042]) ).
tcf(c_18438,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)
| ~ edge(sK5(tail_of(sK3),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_4861]) ).
tcf(c_18439,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(sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18438,c_2042]) ).
tcf(c_18486,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_5868,c_5874]) ).
tcf(c_18490,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_6212,c_5874]) ).
tcf(c_18492,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_14544,c_5874]) ).
tcf(c_18493,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_14541,c_5874]) ).
tcf(c_18496,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_14539,c_5874]) ).
tcf(c_18497,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_14537,c_5874]) ).
tcf(c_18498,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_5874]) ).
tcf(c_18531,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_18498]) ).
tcf(c_18532,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_2313,c_18498]) ).
tcf(c_18533,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18531,c_51]) ).
tcf(c_18583,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17977,c_63]) ).
tcf(c_18602,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_18583]) ).
tcf(c_18603,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_18583]) ).
tcf(c_18604,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17398,c_18583]) ).
tcf(c_18658,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_17428,c_3801]) ).
tcf(c_18660,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_3194]) ).
tcf(c_18661,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,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_3133]) ).
tcf(c_18662,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_2859]) ).
tcf(c_18663,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_2424]) ).
tcf(c_18667,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_18583]) ).
tcf(c_18668,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ 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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18663,c_52]) ).
tcf(c_18674,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18660,c_2393,c_52]) ).
tcf(c_18680,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18662,c_52]) ).
tcf(c_18688,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18658,c_52]) ).
tcf(c_18699,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_9335]) ).
tcf(c_18701,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_9335]) ).
tcf(c_18706,plain,
( ( 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)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4) ),
inference(global_subsumption_just,[status(thm)],[c_18668,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18668,c_18701]) ).
tcf(c_18707,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)),sK2) ),
inference(renaming,[status(thm)],[c_18706]) ).
tcf(c_18716,plain,
( ( 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)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_18674,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18674,c_18701]) ).
tcf(c_18717,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)),sK2) ),
inference(renaming,[status(thm)],[c_18716]) ).
tcf(c_18726,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_18680,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_4290,c_7116,c_12377,c_12378,c_17969,c_18701]) ).
tcf(c_18741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_105]) ).
tcf(c_18742,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_79]) ).
tcf(c_18745,plain,
! [X0: $i] :
( 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) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_15970]) ).
tcf(c_18746,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_12141]) ).
tcf(c_18747,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_11207]) ).
tcf(c_18748,plain,
! [X0: $i] :
( 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) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_11081]) ).
tcf(c_18749,plain,
! [X0: $i] :
( 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) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_9702]) ).
tcf(c_18750,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_2776]) ).
tcf(c_18751,plain,
! [X0: $i] :
( 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) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_6972]) ).
tcf(c_18752,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_18726,c_3302]) ).
tcf(c_18753,plain,
! [X0: $i] :
( 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) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_3013]) ).
tcf(c_18754,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_18726,c_2372]) ).
tcf(c_18755,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_2195]) ).
tcf(c_18756,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_2207]) ).
tcf(c_18757,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_18726,c_2112]) ).
tcf(c_18759,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,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_2985]) ).
tcf(c_18761,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_18726,c_8068]) ).
tcf(c_18762,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_18726,c_11495]) ).
tcf(c_18959,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,sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_18688,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18688,c_18701]) ).
tcf(c_18960,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(renaming,[status(thm)],[c_18959]) ).
tcf(c_18974,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_18960]) ).
tcf(c_18975,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_18960]) ).
tcf(c_18976,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,sK2)
| ~ edge(sK5(head_of(sK4),head_of(sK3)))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_17428,c_18960]) ).
tcf(c_19003,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(global_subsumption_just,[status(thm)],[c_18415,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18415,c_18701]) ).
tcf(c_19011,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,sK2)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_19003,c_3801]) ).
tcf(c_19012,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,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_3704]) ).
tcf(c_19013,plain,
( precedes(sK3,sK4,sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_3194]) ).
tcf(c_19014,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,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_3133]) ).
tcf(c_19015,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_2859]) ).
tcf(c_19016,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_2424]) ).
tcf(c_19018,plain,
( edge(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(superposition,[status(thm)],[c_19003,c_63]) ).
tcf(c_19025,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19016,c_51]) ).
tcf(c_19032,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19015,c_51]) ).
tcf(c_19039,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19011,c_51]) ).
tcf(c_19049,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_10339]) ).
tcf(c_19076,plain,
edge(sK5(head_of(sK4),head_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_19018,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18701]) ).
tcf(c_19078,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17969,c_19076]) ).
tcf(c_19079,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(backward_subsumption_resolution,[status(thm)],[c_17428,c_19076]) ).
tcf(c_19080,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_17398,c_19076]) ).
tcf(c_19081,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(backward_subsumption_resolution,[status(thm)],[c_4572,c_19076]) ).
tcf(c_19082,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(backward_subsumption_resolution,[status(thm)],[c_4532,c_19076]) ).
tcf(c_19083,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_4290,c_19076]) ).
tcf(c_19084,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(backward_subsumption_resolution,[status(thm)],[c_4286,c_19076]) ).
tcf(c_19085,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_4239,c_19076]) ).
tcf(c_19125,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_19076,c_4082]) ).
tcf(c_19126,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_19076,c_4081]) ).
tcf(c_19127,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_19076,c_3653]) ).
tcf(c_19128,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_19076,c_3652]) ).
tcf(c_19129,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_19076,c_3614]) ).
tcf(c_19130,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_19076,c_3613]) ).
tcf(c_19131,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_19076,c_3575]) ).
tcf(c_19132,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_19076,c_3574]) ).
tcf(c_19133,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_19076,c_3536]) ).
tcf(c_19134,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_19076,c_3535]) ).
tcf(c_19135,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_19076,c_3487]) ).
tcf(c_19136,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_19076,c_3486]) ).
tcf(c_19137,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_19076,c_3457]) ).
tcf(c_19138,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_19076,c_3456]) ).
tcf(c_19139,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_19076,c_3427]) ).
tcf(c_19140,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_19076,c_3426]) ).
tcf(c_19141,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_19076,c_4610]) ).
tcf(c_19142,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_19076,c_4609]) ).
tcf(c_19143,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_19076,c_4608]) ).
tcf(c_19144,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_19076,c_4607]) ).
tcf(c_19145,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_19076,c_4606]) ).
tcf(c_19146,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_19076,c_4605]) ).
tcf(c_19147,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_19076,c_4604]) ).
tcf(c_19148,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_19076,c_4603]) ).
tcf(c_19149,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_19076,c_4322]) ).
tcf(c_19150,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_19076,c_4321]) ).
tcf(c_19151,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_19076,c_4320]) ).
tcf(c_19152,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_19076,c_4319]) ).
tcf(c_19153,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_19076,c_4318]) ).
tcf(c_19154,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_19076,c_4317]) ).
tcf(c_19155,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_19076,c_4316]) ).
tcf(c_19156,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_19076,c_6692]) ).
tcf(c_19157,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_19076,c_4315]) ).
tcf(c_19158,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_19076,c_6691]) ).
tcf(c_19159,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_19076,c_6111]) ).
tcf(c_19160,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_19076,c_6110]) ).
tcf(c_19161,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_19076,c_6034]) ).
tcf(c_19162,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_19076,c_6033]) ).
tcf(c_19163,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_19076,c_6005]) ).
tcf(c_19164,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_19076,c_6004]) ).
tcf(c_19165,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_19076,c_5606]) ).
tcf(c_19166,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_19076,c_5605]) ).
tcf(c_19167,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_19076,c_5489]) ).
tcf(c_19168,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_19076,c_5488]) ).
tcf(c_19169,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_19076,c_4083]) ).
tcf(c_19170,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_19076,c_3654]) ).
tcf(c_19171,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_19076,c_3615]) ).
tcf(c_19172,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_19076,c_3576]) ).
tcf(c_19173,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_19076,c_3537]) ).
tcf(c_19174,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_19076,c_3488]) ).
tcf(c_19175,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_19076,c_5121]) ).
tcf(c_19176,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_19076,c_5120]) ).
tcf(c_19177,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_19076,c_3458]) ).
tcf(c_19178,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_19076,c_5012]) ).
tcf(c_19179,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_19076,c_5011]) ).
tcf(c_19180,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_19076,c_2725]) ).
tcf(c_19181,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_19076,c_2724]) ).
tcf(c_19182,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_19076,c_2692]) ).
tcf(c_19183,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_19076,c_2691]) ).
tcf(c_19184,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_19076,c_2669]) ).
tcf(c_19185,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_19076,c_2668]) ).
tcf(c_19186,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_19076,c_2644]) ).
tcf(c_19187,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_19076,c_2643]) ).
tcf(c_19188,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_19076,c_3428]) ).
tcf(c_19722,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_6118,c_19082]) ).
tcf(c_19723,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_5613,c_19082]) ).
tcf(c_19736,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_14538,c_19082]) ).
tcf(c_19737,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_14543,c_19082]) ).
tcf(c_19774,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_19079,c_3801]) ).
tcf(c_19776,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19079,c_3194]) ).
tcf(c_19778,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19079,c_2859]) ).
tcf(c_19779,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19079,c_2424]) ).
tcf(c_19783,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19079,c_18960]) ).
tcf(c_19784,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19079,c_18583]) ).
tcf(c_19795,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_19080,c_3801]) ).
tcf(c_19797,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19080,c_3194]) ).
tcf(c_19798,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,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19080,c_3133]) ).
tcf(c_19799,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19080,c_2859]) ).
tcf(c_19800,plain,
( ( sK5(head_of(sK4),head_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19080,c_2424]) ).
tcf(c_19805,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19080,c_18583]) ).
tcf(c_19829,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_6212,c_5878]) ).
tcf(c_19831,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_14544,c_5878]) ).
tcf(c_19832,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_14541,c_5878]) ).
tcf(c_19835,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_14539,c_5878]) ).
tcf(c_19836,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_14537,c_5878]) ).
tcf(c_19837,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_5878]) ).
tcf(c_19881,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_105]) ).
tcf(c_19882,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_79]) ).
tcf(c_19886,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_12141]) ).
tcf(c_19890,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_2776]) ).
tcf(c_19892,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_19032,c_3302]) ).
tcf(c_19894,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19032,c_2372]) ).
tcf(c_19895,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_2195]) ).
tcf(c_19896,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_2207]) ).
tcf(c_19897,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_19032,c_2112]) ).
tcf(c_19901,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19032,c_8068]) ).
tcf(c_19902,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_11495]) ).
tcf(c_20073,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_19039]) ).
tcf(c_20074,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_19039]) ).
tcf(c_20077,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19003,c_19039]) ).
tcf(c_20097,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(global_subsumption_just,[status(thm)],[c_18439,c_2042,c_2079,c_2912,c_2911,c_3052,c_13190,c_17515,c_18439,c_18699]) ).
tcf(c_20105,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,sK2)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_20097,c_3801]) ).
tcf(c_20106,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,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_3704]) ).
tcf(c_20107,plain,
( precedes(sK3,sK4,sK2)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_3194]) ).
tcf(c_20108,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,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_3133]) ).
tcf(c_20109,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK2)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_2859]) ).
tcf(c_20110,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_2424]) ).
tcf(c_20112,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_20097,c_63]) ).
tcf(c_20117,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20110,c_51]) ).
tcf(c_20124,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20109,c_51]) ).
tcf(c_20131,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20105,c_51]) ).
tcf(c_20190,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(tail_of(sK3),head_of(sK3)),sK2)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_105]) ).
tcf(c_20191,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ sequential(X3,sK3)
| ~ on_path(X3,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3)))
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_79]) ).
tcf(c_20195,plain,
! [X0: $i] :
( sequential(X0,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) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_12141]) ).
tcf(c_20199,plain,
! [X0: $i] :
( sequential(X0,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) )
| ( head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3)))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_2776]) ).
tcf(c_20201,plain,
! [X0: $i,X1: $i,X2: $i,X3: $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(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X1,sK5(tail_of(sK3),head_of(sK3)))
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_20124,c_3302]) ).
tcf(c_20203,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_20124,c_2372]) ).
tcf(c_20204,plain,
! [X0: $i] :
( sequential(X0,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) )
| ( tail_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_2195]) ).
tcf(c_20205,plain,
! [X0: $i] :
( edge(X0)
| ( 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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_2207]) ).
tcf(c_20206,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_20124,c_2112]) ).
tcf(c_20212,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_20124,c_8068]) ).
tcf(c_20213,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(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X3,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK5(tail_of(sK3),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),sK2) ),
inference(superposition,[status(thm)],[c_20124,c_11495]) ).
tcf(c_20332,plain,
! [X0: $i] :
( sequential(X0,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) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) = tail_of(sK5(tail_of(sK3),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_20131]) ).
tcf(c_20333,plain,
! [X0: $i] :
( sequential(X0,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) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK5(tail_of(sK3),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK3,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_20131]) ).
tcf(c_20334,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_20097,c_20131]) ).
tcf(c_20360,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_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_4343,c_19141]) ).
tcf(c_20361,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_15636]) ).
tcf(c_20362,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_14859]) ).
tcf(c_20363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_6169]) ).
tcf(c_20364,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_5552]) ).
tcf(c_20365,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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_19141,c_5311]) ).
tcf(c_20366,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_4534]) ).
tcf(c_20367,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19141,c_2051]) ).
tcf(c_20368,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19141,c_61]) ).
tcf(c_20369,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19141,c_5878]) ).
tcf(c_20371,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19141,c_5874]) ).
tcf(c_20382,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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_19141,c_15630]) ).
tcf(c_20384,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_14853]) ).
tcf(c_20386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_6165]) ).
tcf(c_20387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19141,c_5552]) ).
tcf(c_20390,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_5548]) ).
tcf(c_20392,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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_19141,c_5307]) ).
tcf(c_20393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19141,c_4534]) ).
tcf(c_20397,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_4530]) ).
tcf(c_20400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19141,c_6876]) ).
tcf(c_20401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),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(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19141,c_6872]) ).
tcf(c_20402,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19141,c_4482]) ).
tcf(c_20403,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19141,c_4478]) ).
tcf(c_20406,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19141,c_2051]) ).
tcf(c_20639,plain,
edge(sK5(tail_of(sK3),head_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_20112,c_2042,c_2079,c_2912,c_2911,c_3052,c_13190,c_17515,c_18699]) ).
tcf(c_20641,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_5879,c_20639]) ).
tcf(c_20642,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(backward_subsumption_resolution,[status(thm)],[c_4861,c_20639]) ).
tcf(c_20643,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_4479,c_20639]) ).
tcf(c_20658,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_20639,c_4082]) ).
tcf(c_20659,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_20639,c_4081]) ).
tcf(c_20660,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_20639,c_3653]) ).
tcf(c_20661,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_20639,c_3652]) ).
tcf(c_20662,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_20639,c_3614]) ).
tcf(c_20663,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_20639,c_3613]) ).
tcf(c_20664,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_20639,c_3575]) ).
tcf(c_20665,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_20639,c_3574]) ).
tcf(c_20666,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_20639,c_3536]) ).
tcf(c_20667,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_20639,c_3535]) ).
tcf(c_20668,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_20639,c_3487]) ).
tcf(c_20669,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_20639,c_3486]) ).
tcf(c_20670,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_20639,c_3457]) ).
tcf(c_20671,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_20639,c_3456]) ).
tcf(c_20672,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_20639,c_3427]) ).
tcf(c_20673,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_20639,c_3426]) ).
tcf(c_20674,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_20639,c_4610]) ).
tcf(c_20675,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_20639,c_4609]) ).
tcf(c_20676,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_20639,c_4608]) ).
tcf(c_20677,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_20639,c_4607]) ).
tcf(c_20678,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_20639,c_4606]) ).
tcf(c_20679,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_20639,c_4605]) ).
tcf(c_20680,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_20639,c_4604]) ).
tcf(c_20681,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_20639,c_4603]) ).
tcf(c_20682,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_20639,c_4322]) ).
tcf(c_20683,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_20639,c_4321]) ).
tcf(c_20684,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_20639,c_4320]) ).
tcf(c_20685,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_20639,c_4319]) ).
tcf(c_20686,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_20639,c_4318]) ).
tcf(c_20687,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_20639,c_4317]) ).
tcf(c_20688,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_20639,c_4316]) ).
tcf(c_20689,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_20639,c_6692]) ).
tcf(c_20690,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_20639,c_4315]) ).
tcf(c_20691,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_20639,c_6691]) ).
tcf(c_20692,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_20639,c_6111]) ).
tcf(c_20693,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_20639,c_6110]) ).
tcf(c_20694,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_20639,c_6034]) ).
tcf(c_20695,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_20639,c_6033]) ).
tcf(c_20696,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_20639,c_6005]) ).
tcf(c_20697,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_20639,c_6004]) ).
tcf(c_20698,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_20639,c_5606]) ).
tcf(c_20699,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_20639,c_5605]) ).
tcf(c_20700,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_20639,c_5489]) ).
tcf(c_20701,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_20639,c_5488]) ).
tcf(c_20702,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_20639,c_4083]) ).
tcf(c_20703,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_20639,c_3654]) ).
tcf(c_20704,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_20639,c_3615]) ).
tcf(c_20705,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_20639,c_3576]) ).
tcf(c_20706,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_20639,c_3537]) ).
tcf(c_20707,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_20639,c_3488]) ).
tcf(c_20708,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_20639,c_5121]) ).
tcf(c_20709,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_20639,c_5120]) ).
tcf(c_20710,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_20639,c_3458]) ).
tcf(c_20711,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_20639,c_5012]) ).
tcf(c_20712,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_20639,c_5011]) ).
tcf(c_20713,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_20639,c_2725]) ).
tcf(c_20714,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_20639,c_2724]) ).
tcf(c_20715,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_20639,c_2692]) ).
tcf(c_20716,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_20639,c_2691]) ).
tcf(c_20717,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_20639,c_2669]) ).
tcf(c_20718,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_20639,c_2668]) ).
tcf(c_20719,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_20639,c_2644]) ).
tcf(c_20720,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_20639,c_2643]) ).
tcf(c_20721,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_20639,c_3428]) ).
tcf(c_21175,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_5496,c_19084]) ).
tcf(c_21197,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_5496,c_19085]) ).
tcf(c_21215,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_19837]) ).
tcf(c_21216,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_2313,c_19837]) ).
tcf(c_21218,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21215,c_51]) ).
tcf(c_21240,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_6118,c_6136]) ).
tcf(c_21254,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_14538,c_6136]) ).
tcf(c_21255,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_14543,c_6136]) ).
tcf(c_21300,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_14538,c_6140]) ).
tcf(c_21301,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_14543,c_6140]) ).
tcf(c_21337,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)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(head_of(sK4),head_of(sK3)),X0),sK4)
| ~ on_path(sK7(sK2,sK5(head_of(sK4),head_of(sK3)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_18754]) ).
tcf(c_21338,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_18754]) ).
tcf(c_21377,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),head_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_105]) ).
tcf(c_21378,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_79]) ).
tcf(c_21382,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_12141]) ).
tcf(c_21383,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_11207]) ).
tcf(c_21386,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3))),sK5(head_of(sK4),head_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_2776]) ).
tcf(c_21388,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(X1,sK5(head_of(sK4),head_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_19078,c_3302]) ).
tcf(c_21390,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19078,c_2372]) ).
tcf(c_21391,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(sK2,X0,sK5(head_of(sK4),head_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_2195]) ).
tcf(c_21392,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_2207]) ).
tcf(c_21393,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,sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_19078,c_2112]) ).
tcf(c_21397,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19078,c_8068]) ).
tcf(c_21398,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_11495]) ).
tcf(c_21575,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)),sK2)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(head_of(sK4),head_of(sK3)),X0),sK3)
| ~ on_path(sK7(sK2,sK5(head_of(sK4),head_of(sK3)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_19894]) ).
tcf(c_21576,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_19894]) ).
tcf(c_21615,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4346,c_19142]) ).
tcf(c_21616,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_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_4220,c_19142]) ).
tcf(c_21617,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4129,c_19142]) ).
tcf(c_21618,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_15636]) ).
tcf(c_21619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_14859]) ).
tcf(c_21620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_6169]) ).
tcf(c_21621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_5552]) ).
tcf(c_21622,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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_19142,c_5311]) ).
tcf(c_21623,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_4534]) ).
tcf(c_21624,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19142,c_2051]) ).
tcf(c_21625,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19142,c_61]) ).
tcf(c_21628,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19142,c_5878]) ).
tcf(c_21630,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19142,c_5874]) ).
tcf(c_21641,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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_19142,c_15630]) ).
tcf(c_21643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_14853]) ).
tcf(c_21645,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_6165]) ).
tcf(c_21646,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19142,c_5552]) ).
tcf(c_21649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_5548]) ).
tcf(c_21651,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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_19142,c_5307]) ).
tcf(c_21652,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19142,c_4534]) ).
tcf(c_21659,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19142,c_6876]) ).
tcf(c_21660,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19142,c_6872]) ).
tcf(c_21661,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19142,c_4482]) ).
tcf(c_21662,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19142,c_4478]) ).
tcf(c_21665,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(X0) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19142,c_2051]) ).
tcf(c_21944,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_6160,c_20643]) ).
tcf(c_21945,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_14542,c_20643]) ).
tcf(c_21946,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_14540,c_20643]) ).
tcf(c_21970,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_5309,c_2042,c_2079,c_2912,c_2911,c_3052,c_5309,c_13190,c_17515,c_18699]) ).
tcf(c_21993,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_6866,c_21970]) ).
tcf(c_21994,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_6212,c_21970]) ).
tcf(c_21996,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_14544,c_21970]) ).
tcf(c_21997,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_14541,c_21970]) ).
tcf(c_22000,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_14539,c_21970]) ).
tcf(c_22001,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_14537,c_21970]) ).
tcf(c_22002,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19141,c_21970]) ).
tcf(c_22003,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19142,c_21970]) ).
tcf(c_22004,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_21970]) ).
tcf(c_22005,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_22004,c_2042]) ).
tcf(c_22083,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_5550,c_2059,c_2079,c_2085,c_2971,c_5550,c_17869]) ).
tcf(c_22101,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(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4220,c_22083]) ).
tcf(c_22102,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))) ),
inference(superposition,[status(thm)],[c_4129,c_22083]) ).
tcf(c_22111,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_14538,c_22083]) ).
tcf(c_22112,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_14543,c_22083]) ).
tcf(c_22127,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_22102,c_19076]) ).
tcf(c_22132,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_22101,c_19076]) ).
tcf(c_22151,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)),sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_20117,c_22005]) ).
tcf(c_22155,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,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_22005,c_3801]) ).
tcf(c_22156,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,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_22005,c_3704]) ).
tcf(c_22157,plain,
( precedes(sK5(tail_of(sK3),head_of(sK3)),sK4,sK2)
| ( 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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22005,c_3194]) ).
tcf(c_22158,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,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK3)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22005,c_3133]) ).
tcf(c_22159,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_22005,c_2859]) ).
tcf(c_22160,plain,
( ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22005,c_2424]) ).
tcf(c_22164,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_22005,c_557]) ).
tcf(c_22168,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22160,c_51]) ).
tcf(c_22173,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK3)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22159,c_51]) ).
tcf(c_22181,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22156,c_53,c_51]) ).
tcf(c_22253,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_6212,c_6218]) ).
tcf(c_22255,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_14544,c_6218]) ).
tcf(c_22256,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_14541,c_6218]) ).
tcf(c_22259,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_14539,c_6218]) ).
tcf(c_22260,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_14537,c_6218]) ).
tcf(c_22261,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19141,c_6218]) ).
tcf(c_22262,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19142,c_6218]) ).
tcf(c_22263,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_6218]) ).
tcf(c_22333,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) )
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ 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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_18757]) ).
tcf(c_22334,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)),sK2) ),
inference(superposition,[status(thm)],[c_19078,c_18757]) ).
tcf(c_22375,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) )
| ~ edge(sK5(head_of(sK3),head_of(sK4)))
| ~ 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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_19897]) ).
tcf(c_22406,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(sK3),head_of(sK4)))
| ~ 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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_17633,c_21393]) ).
tcf(c_22426,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4343,c_19143]) ).
tcf(c_22427,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_15636]) ).
tcf(c_22428,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_14859]) ).
tcf(c_22429,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_6169]) ).
tcf(c_22430,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_5552]) ).
tcf(c_22431,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_5311]) ).
tcf(c_22432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_4534]) ).
tcf(c_22433,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_2051]) ).
tcf(c_22434,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_61]) ).
tcf(c_22436,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_22083]) ).
tcf(c_22438,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_6140]) ).
tcf(c_22439,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_6136]) ).
tcf(c_22441,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_19082]) ).
tcf(c_22443,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_5700]) ).
tcf(c_22444,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_5696]) ).
tcf(c_22445,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_5660]) ).
tcf(c_22446,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_5656]) ).
tcf(c_22447,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != head_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_19143,c_16644]) ).
tcf(c_22448,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != head_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_19143,c_16323]) ).
tcf(c_22449,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_4864]) ).
tcf(c_22450,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_4860]) ).
tcf(c_22452,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_15636]) ).
tcf(c_22453,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19143,c_15630]) ).
tcf(c_22454,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_14859]) ).
tcf(c_22455,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19143,c_14853]) ).
tcf(c_22456,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_6169]) ).
tcf(c_22457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19143,c_6165]) ).
tcf(c_22458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_5552]) ).
tcf(c_22460,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(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) ) ),
inference(superposition,[status(thm)],[c_19143,c_4289]) ).
tcf(c_22461,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19143,c_5548]) ).
tcf(c_22462,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_5311]) ).
tcf(c_22463,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19143,c_5307]) ).
tcf(c_22464,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_4534]) ).
tcf(c_22465,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_4285]) ).
tcf(c_22468,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19143,c_4530]) ).
tcf(c_22469,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_3927]) ).
tcf(c_22470,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_3923]) ).
tcf(c_22475,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_2250]) ).
tcf(c_22476,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19143,c_2249]) ).
tcf(c_22477,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_2051]) ).
tcf(c_22478,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) )
| ~ edge(sK5(tail_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_19143,c_74]) ).
tcf(c_22479,plain,
( vertex(head_of(sK5(head_of(sK4),head_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))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19143,c_76]) ).
tcf(c_22874,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_5657,c_2059,c_2079,c_2085,c_2971,c_5657,c_17869]) ).
tcf(c_22888,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(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4343,c_22874]) ).
tcf(c_22893,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_22874]) ).
tcf(c_22894,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_22893,c_2059]) ).
tcf(c_22898,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_22888,c_19076]) ).
tcf(c_22930,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_5697,c_2042,c_2079,c_2912,c_2911,c_4559,c_5697]) ).
tcf(c_22949,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_22930]) ).
tcf(c_22950,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_22949,c_2042]) ).
tcf(c_22997,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_5875,c_2042,c_2079,c_2912,c_2911,c_3052,c_4479,c_13190,c_17515,c_18699,c_20641]) ).
tcf(c_23013,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(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_6160,c_22997]) ).
tcf(c_23014,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_14542,c_22997]) ).
tcf(c_23015,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_14540,c_22997]) ).
tcf(c_23105,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_6137,c_2059,c_2079,c_2085,c_2971,c_6137,c_17869]) ).
tcf(c_23119,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(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4343,c_23105]) ).
tcf(c_23124,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_23105]) ).
tcf(c_23125,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_23124,c_2059]) ).
tcf(c_23129,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_23119,c_19076]) ).
tcf(c_23157,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_22263]) ).
tcf(c_23158,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_2313,c_22263]) ).
tcf(c_23159,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23157,c_51]) ).
tcf(c_23205,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_22894,c_3801]) ).
tcf(c_23207,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_22894,c_3194]) ).
tcf(c_23208,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,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_22894,c_3133]) ).
tcf(c_23209,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_22894,c_2859]) ).
tcf(c_23210,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_22894,c_2424]) ).
tcf(c_23212,plain,
( edge(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(superposition,[status(thm)],[c_22894,c_63]) ).
tcf(c_23218,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23210,c_52]) ).
tcf(c_23223,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23207,c_2393,c_52]) ).
tcf(c_23228,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23209,c_52]) ).
tcf(c_23235,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23205,c_52]) ).
tcf(c_23315,plain,
edge(sK5(head_of(sK3),head_of(sK4))),
inference(global_subsumption_just,[status(thm)],[c_23212,c_2059,c_2079,c_2085,c_2971,c_17869]) ).
tcf(c_23317,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_17633,c_23315]) ).
tcf(c_23318,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(backward_subsumption_resolution,[status(thm)],[c_17374,c_23315]) ).
tcf(c_23319,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_5661,c_23315]) ).
tcf(c_23320,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_3924,c_23315]) ).
tcf(c_23339,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_23315,c_4082]) ).
tcf(c_23340,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_23315,c_4081]) ).
tcf(c_23341,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_23315,c_3653]) ).
tcf(c_23342,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_23315,c_3652]) ).
tcf(c_23343,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_23315,c_3614]) ).
tcf(c_23344,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_23315,c_3613]) ).
tcf(c_23345,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_23315,c_3575]) ).
tcf(c_23346,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_23315,c_3574]) ).
tcf(c_23347,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_23315,c_3536]) ).
tcf(c_23348,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_23315,c_3535]) ).
tcf(c_23349,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_23315,c_3487]) ).
tcf(c_23350,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_23315,c_3486]) ).
tcf(c_23351,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_23315,c_3457]) ).
tcf(c_23352,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_23315,c_3456]) ).
tcf(c_23353,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_23315,c_3427]) ).
tcf(c_23354,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_23315,c_3426]) ).
tcf(c_23355,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_23315,c_4610]) ).
tcf(c_23356,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_23315,c_4609]) ).
tcf(c_23357,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_23315,c_4608]) ).
tcf(c_23358,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_23315,c_4607]) ).
tcf(c_23359,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_23315,c_4606]) ).
tcf(c_23360,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_23315,c_4605]) ).
tcf(c_23361,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_23315,c_4604]) ).
tcf(c_23362,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_23315,c_4603]) ).
tcf(c_23363,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_23315,c_4322]) ).
tcf(c_23364,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_23315,c_4321]) ).
tcf(c_23365,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_23315,c_4320]) ).
tcf(c_23366,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_23315,c_4319]) ).
tcf(c_23367,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_23315,c_4318]) ).
tcf(c_23368,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_23315,c_4317]) ).
tcf(c_23369,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_23315,c_4316]) ).
tcf(c_23370,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_23315,c_6692]) ).
tcf(c_23371,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_23315,c_4315]) ).
tcf(c_23372,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_23315,c_6691]) ).
tcf(c_23373,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_23315,c_6111]) ).
tcf(c_23374,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_23315,c_6110]) ).
tcf(c_23375,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_23315,c_6034]) ).
tcf(c_23376,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_23315,c_6033]) ).
tcf(c_23377,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_23315,c_6005]) ).
tcf(c_23378,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_23315,c_6004]) ).
tcf(c_23379,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_23315,c_5606]) ).
tcf(c_23380,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_23315,c_5605]) ).
tcf(c_23381,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_23315,c_5489]) ).
tcf(c_23382,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_23315,c_5488]) ).
tcf(c_23383,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_23315,c_4083]) ).
tcf(c_23384,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_23315,c_3654]) ).
tcf(c_23385,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_23315,c_3615]) ).
tcf(c_23386,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_23315,c_3576]) ).
tcf(c_23387,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_23315,c_3537]) ).
tcf(c_23388,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_23315,c_3488]) ).
tcf(c_23389,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_23315,c_5121]) ).
tcf(c_23390,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_23315,c_5120]) ).
tcf(c_23391,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_23315,c_3458]) ).
tcf(c_23392,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_23315,c_5012]) ).
tcf(c_23393,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_23315,c_5011]) ).
tcf(c_23394,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_23315,c_2725]) ).
tcf(c_23395,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_23315,c_2724]) ).
tcf(c_23396,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_23315,c_2692]) ).
tcf(c_23397,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_23315,c_2691]) ).
tcf(c_23398,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_23315,c_2669]) ).
tcf(c_23399,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_23315,c_2668]) ).
tcf(c_23400,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_23315,c_2644]) ).
tcf(c_23401,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_23315,c_2643]) ).
tcf(c_23402,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_23315,c_3428]) ).
tcf(c_24016,plain,
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_23159,c_6521,c_13047]) ).
tcf(c_24050,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_105]) ).
tcf(c_24051,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_79]) ).
tcf(c_24055,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_12141]) ).
tcf(c_24056,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_11207]) ).
tcf(c_24059,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_2776]) ).
tcf(c_24061,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_23228,c_3302]) ).
tcf(c_24063,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_23228,c_2372]) ).
tcf(c_24064,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_2195]) ).
tcf(c_24065,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_2207]) ).
tcf(c_24066,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK2) ),
inference(superposition,[status(thm)],[c_23228,c_2112]) ).
tcf(c_24070,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_23228,c_8068]) ).
tcf(c_24071,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_11495]) ).
tcf(c_24072,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_21393]) ).
tcf(c_24073,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_19897]) ).
tcf(c_24074,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23228,c_18757]) ).
tcf(c_24221,plain,
( vertex(tail_of(sK5(head_of(sK4),head_of(sK3))))
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_24222,plain,
( vertex(head_of(sK5(head_of(sK4),head_of(sK3))))
| ~ edge(sK5(head_of(sK4),head_of(sK3))) ),
inference(instantiation,[status(thm)],[c_75]) ).
tcf(c_24274,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_23235]) ).
tcf(c_24275,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_23235]) ).
tcf(c_24276,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_22894,c_23235]) ).
tcf(c_24302,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,sK2)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_22950,c_3801]) ).
tcf(c_24303,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,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22950,c_3704]) ).
tcf(c_24304,plain,
( precedes(sK3,sK4,sK2)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22950,c_3194]) ).
tcf(c_24305,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,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22950,c_3133]) ).
tcf(c_24306,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),tail_of(sK3)),sK2)
| ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22950,c_2859]) ).
tcf(c_24307,plain,
( ( sK5(head_of(sK3),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_22950,c_2424]) ).
tcf(c_24309,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_22950,c_63]) ).
tcf(c_24314,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24307,c_51]) ).
tcf(c_24321,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),tail_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24306,c_51]) ).
tcf(c_24328,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,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24302,c_51]) ).
tcf(c_24337,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)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_24314,c_2042,c_2079,c_2912,c_2911,c_4559,c_6006,c_8039,c_24314]) ).
tcf(c_24354,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4346,c_19144]) ).
tcf(c_24355,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4220,c_19144]) ).
tcf(c_24356,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4129,c_19144]) ).
tcf(c_24357,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_15636]) ).
tcf(c_24358,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_14859]) ).
tcf(c_24359,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_6169]) ).
tcf(c_24360,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_5552]) ).
tcf(c_24361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_5311]) ).
tcf(c_24362,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_4534]) ).
tcf(c_24363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_2051]) ).
tcf(c_24364,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_61]) ).
tcf(c_24366,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_22083]) ).
tcf(c_24368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_6140]) ).
tcf(c_24369,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_6136]) ).
tcf(c_24371,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_19082]) ).
tcf(c_24373,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_5700]) ).
tcf(c_24374,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_5696]) ).
tcf(c_24375,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_5660]) ).
tcf(c_24376,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_5656]) ).
tcf(c_24377,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != head_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_19144,c_16644]) ).
tcf(c_24378,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != head_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_19144,c_16323]) ).
tcf(c_24379,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_4864]) ).
tcf(c_24380,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_4860]) ).
tcf(c_24381,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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) ) ),
inference(superposition,[status(thm)],[c_19144,c_4575]) ).
tcf(c_24382,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_15636]) ).
tcf(c_24383,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19144,c_15630]) ).
tcf(c_24384,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_14859]) ).
tcf(c_24385,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19144,c_14853]) ).
tcf(c_24386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_6169]) ).
tcf(c_24387,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19144,c_6165]) ).
tcf(c_24388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_5552]) ).
tcf(c_24389,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_4571]) ).
tcf(c_24390,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4289]) ).
tcf(c_24391,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19144,c_5548]) ).
tcf(c_24392,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_5311]) ).
tcf(c_24393,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19144,c_5307]) ).
tcf(c_24394,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4534]) ).
tcf(c_24395,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4285]) ).
tcf(c_24396,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4242]) ).
tcf(c_24397,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4238]) ).
tcf(c_24398,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_4530]) ).
tcf(c_24399,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_3927]) ).
tcf(c_24400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_3923]) ).
tcf(c_24405,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_2250]) ).
tcf(c_24406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK4,X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19144,c_2249]) ).
tcf(c_24407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_2051]) ).
tcf(c_24408,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) )
| ~ edge(sK5(tail_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_19144,c_74]) ).
tcf(c_24409,plain,
( vertex(tail_of(sK5(head_of(sK4),head_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(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19144,c_76]) ).
tcf(c_24825,plain,
edge(sK5(head_of(sK3),tail_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_24309,c_2042,c_2079,c_2912,c_2911,c_4559]) ).
tcf(c_24827,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_24825,c_4082]) ).
tcf(c_24828,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_24825,c_4081]) ).
tcf(c_24829,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_24825,c_3653]) ).
tcf(c_24830,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_24825,c_3652]) ).
tcf(c_24831,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_24825,c_3614]) ).
tcf(c_24832,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_24825,c_3613]) ).
tcf(c_24833,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_24825,c_3575]) ).
tcf(c_24834,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_24825,c_3574]) ).
tcf(c_24835,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_24825,c_3536]) ).
tcf(c_24836,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_24825,c_3535]) ).
tcf(c_24837,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_24825,c_3487]) ).
tcf(c_24838,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_24825,c_3486]) ).
tcf(c_24839,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_24825,c_3457]) ).
tcf(c_24840,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_24825,c_3456]) ).
tcf(c_24841,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_24825,c_3427]) ).
tcf(c_24842,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_24825,c_3426]) ).
tcf(c_24843,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_24825,c_4610]) ).
tcf(c_24844,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_24825,c_4609]) ).
tcf(c_24845,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_24825,c_4608]) ).
tcf(c_24846,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_24825,c_4607]) ).
tcf(c_24847,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_24825,c_4606]) ).
tcf(c_24848,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_24825,c_4605]) ).
tcf(c_24849,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_24825,c_4604]) ).
tcf(c_24850,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_24825,c_4603]) ).
tcf(c_24851,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_24825,c_4322]) ).
tcf(c_24852,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_24825,c_4321]) ).
tcf(c_24853,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_24825,c_4320]) ).
tcf(c_24854,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_24825,c_4319]) ).
tcf(c_24855,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_24825,c_4318]) ).
tcf(c_24856,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_24825,c_4317]) ).
tcf(c_24857,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_24825,c_4316]) ).
tcf(c_24858,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_24825,c_6692]) ).
tcf(c_24859,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_24825,c_4315]) ).
tcf(c_24860,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_24825,c_6691]) ).
tcf(c_24861,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_24825,c_6111]) ).
tcf(c_24862,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_24825,c_6110]) ).
tcf(c_24863,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_24825,c_6034]) ).
tcf(c_24864,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_24825,c_6033]) ).
tcf(c_24865,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_24825,c_6005]) ).
tcf(c_24866,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_24825,c_6004]) ).
tcf(c_24867,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_24825,c_5606]) ).
tcf(c_24868,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_24825,c_5605]) ).
tcf(c_24869,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_24825,c_5489]) ).
tcf(c_24870,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_24825,c_5488]) ).
tcf(c_24871,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_24825,c_4083]) ).
tcf(c_24872,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_24825,c_3654]) ).
tcf(c_24873,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_24825,c_3615]) ).
tcf(c_24874,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_24825,c_3576]) ).
tcf(c_24875,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_24825,c_3537]) ).
tcf(c_24876,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_24825,c_3488]) ).
tcf(c_24877,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_24825,c_5121]) ).
tcf(c_24878,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_24825,c_5120]) ).
tcf(c_24879,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_24825,c_3458]) ).
tcf(c_24880,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_24825,c_5012]) ).
tcf(c_24881,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_24825,c_5011]) ).
tcf(c_24882,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_24825,c_2725]) ).
tcf(c_24883,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_24825,c_2724]) ).
tcf(c_24884,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_24825,c_2692]) ).
tcf(c_24885,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_24825,c_2691]) ).
tcf(c_24886,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_24825,c_2669]) ).
tcf(c_24887,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_24825,c_2668]) ).
tcf(c_24888,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_24825,c_2644]) ).
tcf(c_24889,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_24825,c_2643]) ).
tcf(c_24890,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_24825,c_3428]) ).
tcf(c_25269,plain,
( ( head_of(sK4) = tail_of(sK3) )
| ( tail_of(sK3) != head_of(sK4) )
| ( head_of(sK4) != head_of(sK4) ) ),
inference(instantiation,[status(thm)],[c_7158]) ).
tcf(c_29333,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_9347]) ).
tcf(c_29407,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_6167,c_2042,c_2079,c_2912,c_2911,c_4559,c_6167]) ).
tcf(c_29427,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_5868,c_29407]) ).
tcf(c_29429,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(superposition,[status(thm)],[c_4473,c_29407]) ).
tcf(c_29433,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_14544,c_29407]) ).
tcf(c_29434,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_14541,c_29407]) ).
tcf(c_29437,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_14539,c_29407]) ).
tcf(c_29438,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_14537,c_29407]) ).
tcf(c_29440,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19141,c_29407]) ).
tcf(c_29442,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19142,c_29407]) ).
tcf(c_29443,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_29407]) ).
tcf(c_29444,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_29443,c_2042]) ).
tcf(c_29468,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_29429,c_20639]) ).
tcf(c_29473,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_29427,c_20639]) ).
tcf(c_29535,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_6219,c_2042,c_2079,c_2912,c_2911,c_4559,c_6219]) ).
tcf(c_29550,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_5302,c_29535]) ).
tcf(c_29552,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_14542,c_29535]) ).
tcf(c_29553,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_14540,c_29535]) ).
tcf(c_29564,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_29550,c_20639]) ).
tcf(c_29575,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_23125,c_3801]) ).
tcf(c_29577,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_3194]) ).
tcf(c_29578,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,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_3133]) ).
tcf(c_29579,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_2859]) ).
tcf(c_29580,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_2424]) ).
tcf(c_29584,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_23235]) ).
tcf(c_29586,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29580,c_52]) ).
tcf(c_29591,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29577,c_2393,c_52]) ).
tcf(c_29596,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29579,c_52]) ).
tcf(c_29603,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29575,c_52]) ).
tcf(c_29643,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,sK2)
| ~ sequential(sK3,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_23318,c_3801]) ).
tcf(c_29644,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,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_3704]) ).
tcf(c_29645,plain,
( precedes(sK3,sK4,sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_3194]) ).
tcf(c_29646,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,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_3133]) ).
tcf(c_29647,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_2859]) ).
tcf(c_29648,plain,
( ( sK5(head_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(head_of(sK3),head_of(sK4))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_2424]) ).
tcf(c_29653,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23318,c_17887]) ).
tcf(c_29659,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_29444,c_2042,c_2079,c_2912,c_2911,c_4559,c_6006,c_8039,c_29333]) ).
tcf(c_29665,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_5788,c_29659]) ).
tcf(c_29669,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_29659,c_3801]) ).
tcf(c_29670,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK4)
| ~ on_path(sK3,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_29659,c_3704]) ).
tcf(c_29671,plain,
( precedes(sK5(head_of(sK3),tail_of(sK3)),sK4,sK2)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_29659,c_3194]) ).
tcf(c_29672,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK3)
| ~ on_path(sK3,sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_29659,c_3133]) ).
tcf(c_29673,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_29659,c_2859]) ).
tcf(c_29674,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_29659,c_2424]) ).
tcf(c_29678,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_29659,c_557]) ).
tcf(c_29682,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29674,c_51]) ).
tcf(c_29686,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29673,c_51]) ).
tcf(c_29692,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29669,c_51]) ).
tcf(c_29698,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29670,c_53,c_51]) ).
tcf(c_29741,plain,
( ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_29682,c_24314,c_29333,c_29659]) ).
tcf(c_29783,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_105]) ).
tcf(c_29784,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_79]) ).
tcf(c_29788,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_12141]) ).
tcf(c_29789,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_11207]) ).
tcf(c_29792,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_2776]) ).
tcf(c_29794,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_29596,c_3302]) ).
tcf(c_29796,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_29596,c_2372]) ).
tcf(c_29797,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_2195]) ).
tcf(c_29798,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_2207]) ).
tcf(c_29799,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK2) ),
inference(superposition,[status(thm)],[c_29596,c_2112]) ).
tcf(c_29803,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_29596,c_8068]) ).
tcf(c_29804,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_11495]) ).
tcf(c_29805,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_21393]) ).
tcf(c_29806,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_19897]) ).
tcf(c_29807,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_18757]) ).
tcf(c_29997,plain,
( ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_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_4343,c_19145]) ).
tcf(c_29999,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( 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) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19145,c_66]) ).
tcf(c_30001,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19145,c_23320]) ).
tcf(c_30002,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_23105]) ).
tcf(c_30004,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19145,c_22930]) ).
tcf(c_30005,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_22874]) ).
tcf(c_30007,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19145,c_20642]) ).
tcf(c_30009,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_19084]) ).
tcf(c_30012,plain,
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK4)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19145,c_2155]) ).
tcf(c_30013,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19145,c_61]) ).
tcf(c_30014,plain,
( vertex(head_of(sK5(head_of(sK4),head_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) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19145,c_75]) ).
tcf(c_30015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( 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) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19145,c_66]) ).
tcf(c_30124,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_14573,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_5335,c_7116,c_7154,c_7431,c_12809]) ).
tcf(c_30139,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_5302,c_30124]) ).
tcf(c_30140,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_6160,c_30124]) ).
tcf(c_30141,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_14542,c_30124]) ).
tcf(c_30149,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_30140,c_24825]) ).
tcf(c_30154,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_30139,c_20639]) ).
tcf(c_30531,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_14662,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_3413,c_5335,c_7116,c_7396,c_12809,c_14411,c_19049,c_25269]) ).
tcf(c_30544,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_5496,c_30531]) ).
tcf(c_30545,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_4343,c_30531]) ).
tcf(c_30550,plain,
( sequential(sK5(tail_of(sK3),head_of(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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_30531]) ).
tcf(c_30551,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_30531]) ).
tcf(c_30552,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_30551,c_2059]) ).
tcf(c_30556,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_30545,c_19076]) ).
tcf(c_30561,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_30544,c_23315]) ).
tcf(c_30598,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_14758,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_5335,c_7116,c_7154,c_7352,c_12809]) ).
tcf(c_30613,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_5302,c_30598]) ).
tcf(c_30614,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_6160,c_30598]) ).
tcf(c_30615,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_14542,c_30598]) ).
tcf(c_30623,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_30614,c_24825]) ).
tcf(c_30628,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_30613,c_20639]) ).
tcf(c_30669,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_30552,c_3801]) ).
tcf(c_30671,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30552,c_3194]) ).
tcf(c_30672,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,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30552,c_3133]) ).
tcf(c_30673,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30552,c_2859]) ).
tcf(c_30674,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30552,c_2424]) ).
tcf(c_30676,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_30552,c_63]) ).
tcf(c_30681,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30674,c_52]) ).
tcf(c_30686,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30671,c_2393,c_52]) ).
tcf(c_30691,plain,
! [X0: $i] :
( precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30673,c_52]) ).
tcf(c_30698,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30669,c_52]) ).
tcf(c_30733,plain,
edge(sK5(tail_of(sK3),head_of(sK4))),
inference(global_subsumption_just,[status(thm)],[c_30676,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_3413,c_5335,c_7116,c_12809,c_14411,c_19049,c_25269]) ).
tcf(c_30735,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_14536,c_30733]) ).
tcf(c_30738,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_30733,c_4082]) ).
tcf(c_30739,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_30733,c_4081]) ).
tcf(c_30740,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_30733,c_3653]) ).
tcf(c_30741,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_30733,c_3652]) ).
tcf(c_30742,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_30733,c_3614]) ).
tcf(c_30743,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_30733,c_3613]) ).
tcf(c_30744,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_30733,c_3575]) ).
tcf(c_30745,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_30733,c_3574]) ).
tcf(c_30746,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_30733,c_3536]) ).
tcf(c_30747,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_30733,c_3535]) ).
tcf(c_30748,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_30733,c_3487]) ).
tcf(c_30749,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_30733,c_3486]) ).
tcf(c_30750,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_30733,c_3457]) ).
tcf(c_30751,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_30733,c_3456]) ).
tcf(c_30752,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_30733,c_3427]) ).
tcf(c_30753,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_30733,c_3426]) ).
tcf(c_30754,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_30733,c_4610]) ).
tcf(c_30755,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_30733,c_4609]) ).
tcf(c_30756,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_30733,c_4608]) ).
tcf(c_30757,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_30733,c_4607]) ).
tcf(c_30758,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_30733,c_4606]) ).
tcf(c_30759,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_30733,c_4605]) ).
tcf(c_30760,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_30733,c_4604]) ).
tcf(c_30761,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_30733,c_4603]) ).
tcf(c_30762,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_30733,c_4322]) ).
tcf(c_30763,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_30733,c_4321]) ).
tcf(c_30764,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_30733,c_4320]) ).
tcf(c_30765,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_30733,c_4319]) ).
tcf(c_30766,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_30733,c_4318]) ).
tcf(c_30767,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_30733,c_4317]) ).
tcf(c_30768,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_30733,c_4316]) ).
tcf(c_30769,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_30733,c_6692]) ).
tcf(c_30770,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_30733,c_4315]) ).
tcf(c_30771,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_30733,c_6691]) ).
tcf(c_30772,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_30733,c_6111]) ).
tcf(c_30773,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_30733,c_6110]) ).
tcf(c_30774,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_30733,c_6034]) ).
tcf(c_30775,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_30733,c_6033]) ).
tcf(c_30776,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_30733,c_6005]) ).
tcf(c_30777,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_30733,c_6004]) ).
tcf(c_30778,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_30733,c_5606]) ).
tcf(c_30779,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_30733,c_5605]) ).
tcf(c_30780,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_30733,c_5489]) ).
tcf(c_30781,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_30733,c_5488]) ).
tcf(c_30782,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_30733,c_4083]) ).
tcf(c_30783,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_30733,c_3654]) ).
tcf(c_30784,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_30733,c_3615]) ).
tcf(c_30785,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_30733,c_3576]) ).
tcf(c_30786,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_30733,c_3537]) ).
tcf(c_30787,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_30733,c_3488]) ).
tcf(c_30788,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_30733,c_5121]) ).
tcf(c_30789,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_30733,c_5120]) ).
tcf(c_30790,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_30733,c_3458]) ).
tcf(c_30791,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_30733,c_5012]) ).
tcf(c_30792,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_30733,c_5011]) ).
tcf(c_30793,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_30733,c_2725]) ).
tcf(c_30794,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_30733,c_2724]) ).
tcf(c_30795,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_30733,c_2692]) ).
tcf(c_30796,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_30733,c_2691]) ).
tcf(c_30797,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_30733,c_2669]) ).
tcf(c_30798,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_30733,c_2668]) ).
tcf(c_30799,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_30733,c_2644]) ).
tcf(c_30800,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_30733,c_2643]) ).
tcf(c_30801,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_30733,c_3428]) ).
tcf(c_31457,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_29603]) ).
tcf(c_31458,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_29603]) ).
tcf(c_31459,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23125,c_29603]) ).
tcf(c_31493,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_105]) ).
tcf(c_31494,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_79]) ).
tcf(c_31498,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(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_12141]) ).
tcf(c_31499,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(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_11207]) ).
tcf(c_31502,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(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_2776]) ).
tcf(c_31504,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X1,sK5(tail_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_30691,c_3302]) ).
tcf(c_31506,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30691,c_2372]) ).
tcf(c_31507,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(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_2195]) ).
tcf(c_31508,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_2207]) ).
tcf(c_31509,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK2) ),
inference(superposition,[status(thm)],[c_30691,c_2112]) ).
tcf(c_31512,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_30691,c_8068]) ).
tcf(c_31513,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_11495]) ).
tcf(c_31514,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_21393]) ).
tcf(c_31515,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_19897]) ).
tcf(c_31516,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_18757]) ).
tcf(c_31673,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(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_30698]) ).
tcf(c_31674,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(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))))
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_30698]) ).
tcf(c_31675,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30552,c_30698]) ).
tcf(c_31701,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_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(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4346,c_19146]) ).
tcf(c_31702,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4220,c_19146]) ).
tcf(c_31703,plain,
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_4129,c_19146]) ).
tcf(c_31705,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( 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) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X1) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19146,c_66]) ).
tcf(c_31707,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_30531]) ).
tcf(c_31710,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19146,c_23320]) ).
tcf(c_31711,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_23105]) ).
tcf(c_31713,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19146,c_22930]) ).
tcf(c_31714,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_22874]) ).
tcf(c_31716,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19146,c_20642]) ).
tcf(c_31717,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_19085]) ).
tcf(c_31718,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_19084]) ).
tcf(c_31719,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19146,c_19081]) ).
tcf(c_31721,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK4)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK4 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19146,c_2155]) ).
tcf(c_31722,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19146,c_61]) ).
tcf(c_31723,plain,
( vertex(tail_of(sK5(head_of(sK4),head_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) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19146,c_75]) ).
tcf(c_31724,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( 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) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19146,c_66]) ).
tcf(c_31897,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_14857,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_5335,c_7116,c_7154,c_7204,c_12809]) ).
tcf(c_31917,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_5868,c_31897]) ).
tcf(c_31919,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_4473,c_31897]) ).
tcf(c_31920,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_6866,c_31897]) ).
tcf(c_31921,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_6212,c_31897]) ).
tcf(c_31923,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_14544,c_31897]) ).
tcf(c_31924,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_14541,c_31897]) ).
tcf(c_31930,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19141,c_31897]) ).
tcf(c_31932,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19142,c_31897]) ).
tcf(c_31933,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_31897]) ).
tcf(c_31934,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_31933,c_2042]) ).
tcf(c_31938,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_31924,c_30733]) ).
tcf(c_31943,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_31923,c_30733]) ).
tcf(c_31948,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_31921,c_24825]) ).
tcf(c_31953,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_31920,c_24825]) ).
tcf(c_31958,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_31919,c_20639]) ).
tcf(c_31963,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_31917,c_20639]) ).
tcf(c_32054,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_14896,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_3413,c_5335,c_6460,c_7116,c_12809,c_14411,c_14536,c_19049,c_25269]) ).
tcf(c_32069,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_5302,c_32054]) ).
tcf(c_32070,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_6160,c_32054]) ).
tcf(c_32075,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_32070,c_24825]) ).
tcf(c_32080,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_32069,c_20639]) ).
tcf(c_32085,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_15634,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_3413,c_5335,c_6783,c_7116,c_12809,c_14411,c_19049,c_25269]) ).
tcf(c_32105,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_5868,c_32085]) ).
tcf(c_32107,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_4473,c_32085]) ).
tcf(c_32108,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_6866,c_32085]) ).
tcf(c_32109,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_6212,c_32085]) ).
tcf(c_32115,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(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_14539,c_32085]) ).
tcf(c_32116,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_14537,c_32085]) ).
tcf(c_32118,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19141,c_32085]) ).
tcf(c_32120,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19142,c_32085]) ).
tcf(c_32121,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_32085]) ).
tcf(c_32122,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_32121,c_2042]) ).
tcf(c_32136,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_32109,c_24825]) ).
tcf(c_32141,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_32108,c_24825]) ).
tcf(c_32146,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_32107,c_20639]) ).
tcf(c_32151,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_32105,c_20639]) ).
tcf(c_32209,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_15676,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_5335,c_6729,c_7116,c_7154,c_12809]) ).
tcf(c_32222,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_5496,c_32209]) ).
tcf(c_32223,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_4343,c_32209]) ).
tcf(c_32228,plain,
( sequential(sK5(tail_of(sK3),head_of(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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_32209]) ).
tcf(c_32229,plain,
( sequential(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_32209]) ).
tcf(c_32230,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_32209]) ).
tcf(c_32231,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_32230,c_2059]) ).
tcf(c_32235,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_32223,c_19076]) ).
tcf(c_32240,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_32222,c_23315]) ).
tcf(c_32265,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,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_31934,c_3801]) ).
tcf(c_32266,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,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_31934,c_3704]) ).
tcf(c_32267,plain,
( precedes(sK5(head_of(sK4),tail_of(sK3)),sK4,sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_31934,c_3194]) ).
tcf(c_32268,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,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_31934,c_3133]) ).
tcf(c_32269,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK3,sK2)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_31934,c_2859]) ).
tcf(c_32270,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_31934,c_2424]) ).
tcf(c_32273,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_31934,c_62]) ).
tcf(c_32274,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_31934,c_557]) ).
tcf(c_32281,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32270,c_51]) ).
tcf(c_32286,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32269,c_51]) ).
tcf(c_32293,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32265,c_51]) ).
tcf(c_32300,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32266,c_53,c_51]) ).
tcf(c_32345,plain,
edge(sK5(head_of(sK4),tail_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_32273,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_5335,c_7116,c_7154,c_12809]) ).
tcf(c_32347,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_32345,c_4082]) ).
tcf(c_32348,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_32345,c_4081]) ).
tcf(c_32349,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_32345,c_3653]) ).
tcf(c_32350,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_32345,c_3652]) ).
tcf(c_32351,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_32345,c_3614]) ).
tcf(c_32352,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_32345,c_3613]) ).
tcf(c_32353,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_32345,c_3575]) ).
tcf(c_32354,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_32345,c_3574]) ).
tcf(c_32355,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_32345,c_3536]) ).
tcf(c_32356,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_32345,c_3535]) ).
tcf(c_32357,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_32345,c_3487]) ).
tcf(c_32358,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_32345,c_3486]) ).
tcf(c_32359,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_32345,c_3457]) ).
tcf(c_32360,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_32345,c_3456]) ).
tcf(c_32361,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_32345,c_3427]) ).
tcf(c_32362,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_32345,c_3426]) ).
tcf(c_32363,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_32345,c_4610]) ).
tcf(c_32364,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_32345,c_4609]) ).
tcf(c_32365,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_32345,c_4608]) ).
tcf(c_32366,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_32345,c_4607]) ).
tcf(c_32367,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_32345,c_4606]) ).
tcf(c_32368,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_32345,c_4605]) ).
tcf(c_32369,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_32345,c_4604]) ).
tcf(c_32370,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_32345,c_4603]) ).
tcf(c_32371,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_32345,c_4322]) ).
tcf(c_32372,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_32345,c_4321]) ).
tcf(c_32373,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_32345,c_4320]) ).
tcf(c_32374,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_32345,c_4319]) ).
tcf(c_32375,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_32345,c_4318]) ).
tcf(c_32376,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_32345,c_4317]) ).
tcf(c_32377,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_32345,c_4316]) ).
tcf(c_32378,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_32345,c_6692]) ).
tcf(c_32379,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_32345,c_4315]) ).
tcf(c_32380,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_32345,c_6691]) ).
tcf(c_32381,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_32345,c_6111]) ).
tcf(c_32382,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_32345,c_6110]) ).
tcf(c_32383,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_32345,c_6034]) ).
tcf(c_32384,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_32345,c_6033]) ).
tcf(c_32385,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_32345,c_6005]) ).
tcf(c_32386,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_32345,c_6004]) ).
tcf(c_32387,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_32345,c_5606]) ).
tcf(c_32388,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_32345,c_5605]) ).
tcf(c_32389,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_32345,c_5489]) ).
tcf(c_32390,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_32345,c_5488]) ).
tcf(c_32391,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_32345,c_4083]) ).
tcf(c_32392,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_32345,c_3654]) ).
tcf(c_32393,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_32345,c_3615]) ).
tcf(c_32394,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_32345,c_3576]) ).
tcf(c_32395,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_32345,c_3537]) ).
tcf(c_32396,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_32345,c_3488]) ).
tcf(c_32397,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_32345,c_5121]) ).
tcf(c_32398,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_32345,c_5120]) ).
tcf(c_32399,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_32345,c_3458]) ).
tcf(c_32400,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_32345,c_5012]) ).
tcf(c_32401,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_32345,c_5011]) ).
tcf(c_32402,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_32345,c_2725]) ).
tcf(c_32403,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_32345,c_2724]) ).
tcf(c_32404,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_32345,c_2692]) ).
tcf(c_32405,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_32345,c_2691]) ).
tcf(c_32406,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_32345,c_2669]) ).
tcf(c_32407,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_32345,c_2668]) ).
tcf(c_32408,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_32345,c_2644]) ).
tcf(c_32409,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_32345,c_2643]) ).
tcf(c_32410,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_32345,c_3428]) ).
tcf(c_32813,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,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_32122,c_3801]) ).
tcf(c_32814,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,sK2)
| ~ 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)),sK2) ),
inference(superposition,[status(thm)],[c_32122,c_3704]) ).
tcf(c_32815,plain,
( precedes(sK5(tail_of(sK3),head_of(sK4)),sK4,sK2)
| ( 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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32122,c_3194]) ).
tcf(c_32816,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,sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),sK4)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32122,c_3133]) ).
tcf(c_32817,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK3,sK2)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_32122,c_2859]) ).
tcf(c_32818,plain,
( ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(sK3,sK2)
| ~ sequential(sK3,sK5(tail_of(sK3),head_of(sK4)))
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32122,c_2424]) ).
tcf(c_32822,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_32122,c_557]) ).
tcf(c_32826,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32818,c_51]) ).
tcf(c_32831,plain,
! [X0: $i] :
( precedes(X0,sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ~ on_path(X0,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(tail_of(sK3),head_of(sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32817,c_51]) ).
tcf(c_32838,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32813,c_51]) ).
tcf(c_32845,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32814,c_53,c_51]) ).
tcf(c_32859,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,sK2)
| ~ sequential(sK4,X0)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_32231,c_3801]) ).
tcf(c_32861,plain,
( precedes(sK4,sK4,sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_3194]) ).
tcf(c_32862,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,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_3133]) ).
tcf(c_32863,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_2859]) ).
tcf(c_32864,plain,
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ on_path(sK4,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK4)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_2424]) ).
tcf(c_32868,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32864,c_52]) ).
tcf(c_32873,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32861,c_2393,c_52]) ).
tcf(c_32878,plain,
! [X0: $i] :
( precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32863,c_52]) ).
tcf(c_32885,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32859,c_52]) ).
tcf(c_32975,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| precedes(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK3,sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_32286]) ).
tcf(c_32976,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| precedes(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK3,sK2)
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_32286]) ).
tcf(c_32977,plain,
( precedes(sK4,sK3,sK2)
| ( 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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_32286]) ).
tcf(c_32978,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)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32977,c_11077,c_52]) ).
tcf(c_33002,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(global_subsumption_just,[status(thm)],[c_32978,c_32231,c_32274]) ).
tcf(c_33011,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_33002,c_117]) ).
tcf(c_33012,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_33002,c_66]) ).
tcf(c_33016,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_33002,c_30531]) ).
tcf(c_33020,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_33002,c_23105]) ).
tcf(c_33023,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_33002,c_22874]) ).
tcf(c_33026,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_33002,c_19085]) ).
tcf(c_33027,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_33002,c_19084]) ).
tcf(c_33031,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_33002,c_61]) ).
tcf(c_33033,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_33002,c_66]) ).
tcf(c_33048,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_33031,c_32345]) ).
tcf(c_33055,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_33027,c_32345]) ).
tcf(c_33061,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_33026,c_32345]) ).
tcf(c_33067,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_33023,c_32345]) ).
tcf(c_33073,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_33020,c_32345]) ).
tcf(c_33079,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_33016,c_32345]) ).
tcf(c_33085,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_33011,c_14533,c_4601,c_4313]) ).
tcf(c_33150,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)),sK2)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(head_of(sK4),tail_of(sK3)),X0),sK3)
| ~ on_path(sK7(sK2,sK5(head_of(sK4),tail_of(sK3)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_32293]) ).
tcf(c_33151,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_32293]) ).
tcf(c_33152,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_31934,c_32293]) ).
tcf(c_33189,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)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_32300,c_31934,c_32300]) ).
tcf(c_33233,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = 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_4343,c_19147]) ).
tcf(c_33234,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_15636]) ).
tcf(c_33235,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_14859]) ).
tcf(c_33236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_6169]) ).
tcf(c_33237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_5552]) ).
tcf(c_33238,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_5311]) ).
tcf(c_33239,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_4534]) ).
tcf(c_33240,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_2051]) ).
tcf(c_33241,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_61]) ).
tcf(c_33246,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_22083]) ).
tcf(c_33248,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_6140]) ).
tcf(c_33249,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_6136]) ).
tcf(c_33251,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = 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))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_19082]) ).
tcf(c_33253,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_5700]) ).
tcf(c_33254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_5696]) ).
tcf(c_33255,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_5660]) ).
tcf(c_33256,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_5656]) ).
tcf(c_33257,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_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_19147,c_16644]) ).
tcf(c_33258,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_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_19147,c_16323]) ).
tcf(c_33259,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_4864]) ).
tcf(c_33260,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_4860]) ).
tcf(c_33262,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_15636]) ).
tcf(c_33263,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19147,c_15630]) ).
tcf(c_33264,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_14859]) ).
tcf(c_33265,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19147,c_14853]) ).
tcf(c_33266,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_6169]) ).
tcf(c_33267,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19147,c_6165]) ).
tcf(c_33268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_5552]) ).
tcf(c_33270,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(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) ) ),
inference(superposition,[status(thm)],[c_19147,c_4289]) ).
tcf(c_33271,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19147,c_5548]) ).
tcf(c_33272,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_5311]) ).
tcf(c_33273,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19147,c_5307]) ).
tcf(c_33274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_4534]) ).
tcf(c_33275,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))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_4285]) ).
tcf(c_33278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19147,c_4530]) ).
tcf(c_33279,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_3927]) ).
tcf(c_33280,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_3923]) ).
tcf(c_33285,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_2250]) ).
tcf(c_33286,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19147,c_2249]) ).
tcf(c_33287,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_2051]) ).
tcf(c_33289,plain,
( vertex(head_of(sK5(head_of(sK4),head_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))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19147,c_76]) ).
tcf(c_33692,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),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))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_33048]) ).
tcf(c_33693,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_33048]) ).
tcf(c_33695,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_33048]) ).
tcf(c_33721,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_15823,c_53,c_52,c_51,c_656,c_2042,c_2059,c_2273,c_2440,c_2912,c_2971,c_3413,c_5335,c_6460,c_7116,c_12809,c_14411,c_19049,c_25269]) ).
tcf(c_33735,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_5302,c_33721]) ).
tcf(c_33736,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_6160,c_33721]) ).
tcf(c_33742,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_33736,c_24825]) ).
tcf(c_33747,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_33735,c_20639]) ).
tcf(c_33752,plain,
vertex(head_of(sK5(head_of(sK4),head_of(sK3)))),
inference(global_subsumption_just,[status(thm)],[c_22479,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18701,c_24222]) ).
tcf(c_33755,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2582]) ).
tcf(c_33756,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2581]) ).
tcf(c_33757,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2614]) ).
tcf(c_33758,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2613]) ).
tcf(c_33759,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2522]) ).
tcf(c_33760,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2521]) ).
tcf(c_33761,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2552]) ).
tcf(c_33762,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(head_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_33752,c_2551]) ).
tcf(c_33763,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33752,c_114]) ).
tcf(c_33764,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33752,c_112]) ).
tcf(c_33765,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( head_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33752,c_110]) ).
tcf(c_33766,plain,
! [X0: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( tail_of(sK5(X0,head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_33752,c_107]) ).
tcf(c_34371,plain,
vertex(tail_of(sK5(head_of(sK4),head_of(sK3)))),
inference(global_subsumption_just,[status(thm)],[c_24409,c_53,c_52,c_51,c_50,c_656,c_2059,c_2079,c_2971,c_7116,c_12377,c_12378,c_18701,c_24221]) ).
tcf(c_34376,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2582]) ).
tcf(c_34377,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2581]) ).
tcf(c_34378,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2614]) ).
tcf(c_34379,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2613]) ).
tcf(c_34380,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2522]) ).
tcf(c_34381,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2521]) ).
tcf(c_34382,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),tail_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2552]) ).
tcf(c_34383,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(X0) )
| ( tail_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(tail_of(sK5(head_of(sK4),head_of(sK3))),head_of(X0))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_34371,c_2551]) ).
tcf(c_34384,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_34371,c_114]) ).
tcf(c_34385,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_34371,c_112]) ).
tcf(c_34386,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( head_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_34371,c_110]) ).
tcf(c_34387,plain,
! [X0: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = X0 )
| ( tail_of(sK5(X0,tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_34371,c_107]) ).
tcf(c_34473,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_30552,c_32822]) ).
tcf(c_34485,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_34473,c_66]) ).
tcf(c_34487,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_34473,c_32209]) ).
tcf(c_34494,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_34473,c_23105]) ).
tcf(c_34497,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_34473,c_22874]) ).
tcf(c_34500,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_34473,c_19085]) ).
tcf(c_34501,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_34473,c_19084]) ).
tcf(c_34505,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_34473,c_61]) ).
tcf(c_34507,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_34473,c_66]) ).
tcf(c_34522,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_34505,c_30733]) ).
tcf(c_34529,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_34501,c_30733]) ).
tcf(c_34535,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_34500,c_30733]) ).
tcf(c_34541,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_34497,c_30733]) ).
tcf(c_34547,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_34494,c_30733]) ).
tcf(c_34553,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_34487,c_30733]) ).
tcf(c_34572,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| precedes(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = tail_of(sK5(tail_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_32831]) ).
tcf(c_34573,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),head_of(sK4)))
| precedes(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK3,sK2)
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ( head_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK5(tail_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4)))) )
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),sK2)
| ~ on_path(sK7(sK2,X0,sK5(tail_of(sK3),head_of(sK4))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_32831]) ).
tcf(c_34606,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)),sK2)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(tail_of(sK3),head_of(sK4)),X0),sK3)
| ~ on_path(sK7(sK2,sK5(tail_of(sK3),head_of(sK4)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_32838]) ).
tcf(c_34607,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_32838]) ).
tcf(c_34608,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,sK2)
| ~ on_path(sK5(tail_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32122,c_32838]) ).
tcf(c_34627,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)),sK2) ),
inference(global_subsumption_just,[status(thm)],[c_32845,c_32122,c_32845]) ).
tcf(c_34649,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_105]) ).
tcf(c_34650,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3)))
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_79]) ).
tcf(c_34654,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_12141]) ).
tcf(c_34655,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(sK4,X0)
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_11207]) ).
tcf(c_34658,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(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_2776]) ).
tcf(c_34660,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(X1,sK5(head_of(sK4),tail_of(sK3)))
| ~ sequential(X0,sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_32878,c_3302]) ).
tcf(c_34662,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_32878,c_2372]) ).
tcf(c_34663,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(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) = head_of(X0) )
| ~ sequential(X0,sK4)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_2195]) ).
tcf(c_34664,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_2207]) ).
tcf(c_34665,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK2) ),
inference(superposition,[status(thm)],[c_32878,c_2112]) ).
tcf(c_34668,plain,
! [X0: $i,X1: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ( head_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_17230]) ).
tcf(c_34669,plain,
! [X0: $i,X1: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = head_of(sK4) )
| ~ sequential(sK4,sK4)
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_17193]) ).
tcf(c_34670,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK4)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_32878,c_8068]) ).
tcf(c_34671,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_11495]) ).
tcf(c_34672,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_21393]) ).
tcf(c_34673,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_19897]) ).
tcf(c_34674,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)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_18757]) ).
tcf(c_34819,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = tail_of(sK5(head_of(sK4),tail_of(sK3))) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_8283,c_32885]) ).
tcf(c_34820,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(sK2,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK5(head_of(sK4),tail_of(sK3)))) = head_of(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3)))) )
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ sequential(sK4,sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))))
| ~ on_path(sK7(sK2,X0,sK5(head_of(sK4),tail_of(sK3))),sK2) ),
inference(superposition,[status(thm)],[c_2335,c_32885]) ).
tcf(c_34821,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,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32231,c_32885]) ).
tcf(c_34853,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X2,sK5(head_of(sK3),head_of(sK4)),sK2)
| ( 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,sK2)
| ~ on_path(X2,sK2)
| ~ sequential(X2,X3)
| ~ path(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_105]) ).
tcf(c_34854,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,sK2)
| ~ sequential(X0,X3)
| ~ path(X1,X2,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4)))
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_79]) ).
tcf(c_34858,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(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) = head_of(sK3) )
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4),sK4)) = head_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK4)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK3)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_12141]) ).
tcf(c_34862,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = tail_of(sK5(head_of(sK3),head_of(sK4))) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4))),sK5(head_of(sK3),head_of(sK4)))) = head_of(sK7(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_2776]) ).
tcf(c_34864,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,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(X1,sK5(head_of(sK3),head_of(sK4)))
| ~ sequential(X0,sK5(head_of(sK3),head_of(sK4))) ),
inference(superposition,[status(thm)],[c_23317,c_3302]) ).
tcf(c_34866,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_23317,c_2372]) ).
tcf(c_34867,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(sK2,X0,sK5(head_of(sK3),head_of(sK4)))) = head_of(X0) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_2195]) ).
tcf(c_34868,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_2207]) ).
tcf(c_34869,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,sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),X0,sK2) ),
inference(superposition,[status(thm)],[c_23317,c_2112]) ).
tcf(c_34873,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,sK2)
| ~ precedes(X0,X1,sK2)
| ~ sequential(sK7(sK2,X0,X1),sK3)
| ~ on_path(sK7(sK2,X0,X1),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_23317,c_8068]) ).
tcf(c_34874,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,sK2)
| ~ path(X0,X1,X2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_11495]) ).
tcf(c_34875,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_21393]) ).
tcf(c_34876,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_19897]) ).
tcf(c_34877,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_18757]) ).
tcf(c_35031,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_4346,c_19148]) ).
tcf(c_35032,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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_4220,c_19148]) ).
tcf(c_35033,plain,
( ( tail_of(sK5(tail_of(sK3),head_of(sK4))) = head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_4129,c_19148]) ).
tcf(c_35034,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_15636]) ).
tcf(c_35035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_14859]) ).
tcf(c_35036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_6169]) ).
tcf(c_35037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_5552]) ).
tcf(c_35038,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_5311]) ).
tcf(c_35039,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_4534]) ).
tcf(c_35040,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_2051]) ).
tcf(c_35041,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_61]) ).
tcf(c_35042,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),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))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_33048]) ).
tcf(c_35047,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_22083]) ).
tcf(c_35049,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_6140]) ).
tcf(c_35050,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_6136]) ).
tcf(c_35052,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = 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))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_19082]) ).
tcf(c_35054,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_5700]) ).
tcf(c_35055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_5696]) ).
tcf(c_35056,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_5660]) ).
tcf(c_35057,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_5656]) ).
tcf(c_35058,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_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_19148,c_16644]) ).
tcf(c_35059,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_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_19148,c_16323]) ).
tcf(c_35060,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_4864]) ).
tcf(c_35061,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_4860]) ).
tcf(c_35062,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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) ) ),
inference(superposition,[status(thm)],[c_19148,c_4575]) ).
tcf(c_35063,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_15636]) ).
tcf(c_35064,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19148,c_15630]) ).
tcf(c_35065,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_14859]) ).
tcf(c_35066,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19148,c_14853]) ).
tcf(c_35067,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_6169]) ).
tcf(c_35068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19148,c_6165]) ).
tcf(c_35069,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_5552]) ).
tcf(c_35070,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_4571]) ).
tcf(c_35071,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4289]) ).
tcf(c_35072,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK3),head_of(sK4))) != tail_of(sK5(head_of(sK4),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19148,c_5548]) ).
tcf(c_35073,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_5311]) ).
tcf(c_35074,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19148,c_5307]) ).
tcf(c_35075,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4534]) ).
tcf(c_35076,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4285]) ).
tcf(c_35077,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4242]) ).
tcf(c_35078,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4238]) ).
tcf(c_35079,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_4530]) ).
tcf(c_35080,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_3927]) ).
tcf(c_35081,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_3923]) ).
tcf(c_35086,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_2250]) ).
tcf(c_35087,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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))) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK4,X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19148,c_2249]) ).
tcf(c_35088,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_2051]) ).
tcf(c_35594,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_34522]) ).
tcf(c_35595,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_34522]) ).
tcf(c_35597,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK5(head_of(sK4),head_of(sK3))) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_34522]) ).
tcf(c_35598,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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))) = tail_of(sK3) )
| ( sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ edge(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_34522]) ).
tcf(c_35673,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_14544,c_6222]) ).
tcf(c_35674,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_14541,c_6222]) ).
tcf(c_35677,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_14539,c_6222]) ).
tcf(c_35678,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_14537,c_6222]) ).
tcf(c_35681,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19141,c_6222]) ).
tcf(c_35684,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19142,c_6222]) ).
tcf(c_35685,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_6222]) ).
tcf(c_35736,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_35685]) ).
tcf(c_35737,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_2313,c_35685]) ).
tcf(c_35738,plain,
! [X0: $i,X1: $i] :
( ( tail_of(sK5(head_of(sK3),tail_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK3,sK5(head_of(sK3),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK3),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35736,c_51]) ).
tcf(c_35751,plain,
! [X0: $i] :
( ~ precedes(X0,sK3,sK2)
| ~ on_path(X0,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| precedes(X0,sK4,sK2) ),
inference(global_subsumption_just,[status(thm)],[c_6956,c_2887,c_6956]) ).
tcf(c_35752,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ on_path(X0,sK2)
| ~ precedes(X0,sK3,sK2) ),
inference(renaming,[status(thm)],[c_35751]) ).
tcf(c_35762,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ on_path(sK3,sK2)
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(superposition,[status(thm)],[c_2314,c_35752]) ).
tcf(c_35763,plain,
! [X0: $i] :
( sequential(X0,sK3)
| precedes(sK7(sK2,X0,sK3),sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK3),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) )
| ~ precedes(X0,sK3,sK2)
| ~ on_path(sK7(sK2,X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_2293,c_35752]) ).
tcf(c_35764,plain,
! [X0: $i,X1: $i] :
( sequential(X1,sK3)
| sequential(X0,sK7(sK2,X1,sK3))
| precedes(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3),sK3)) = head_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK3)) )
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK3)),sK7(sK2,X1,sK3))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK3))) )
| ~ precedes(X1,sK3,sK2)
| ~ precedes(X0,sK7(sK2,X1,sK3),sK2)
| ~ on_path(sK7(sK2,X0,sK7(sK2,X1,sK3)),sK2) ),
inference(superposition,[status(thm)],[c_9792,c_35752]) ).
tcf(c_35765,plain,
! [X0: $i] :
( precedes(X0,sK4,sK2)
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK3),sK3)) = head_of(sK7(sK2,X0,sK3)) )
| ~ sequential(X0,sK3)
| ~ on_path(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35762,c_51]) ).
tcf(c_35819,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)),sK2)
| ~ precedes(sK5(tail_of(sK3),head_of(sK4)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(tail_of(sK3),head_of(sK4)),X0),sK4)
| ~ on_path(sK7(sK2,sK5(tail_of(sK3),head_of(sK4)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_31506]) ).
tcf(c_35820,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_31506]) ).
tcf(c_35852,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)),sK2)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),X0,sK2)
| ~ sequential(sK7(sK2,sK5(head_of(sK4),tail_of(sK3)),X0),sK4)
| ~ on_path(sK7(sK2,sK5(head_of(sK4),tail_of(sK3)),X0),sK2) ),
inference(superposition,[status(thm)],[c_2140,c_34662]) ).
tcf(c_35853,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)),sK2)
| ~ 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),sK2) ),
inference(superposition,[status(thm)],[c_2169,c_34662]) ).
tcf(c_35890,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)),sK2) ),
inference(superposition,[status(thm)],[c_29596,c_24066]) ).
tcf(c_35895,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_24066]) ).
tcf(c_35896,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_24066]) ).
tcf(c_35948,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_30691,c_29799]) ).
tcf(c_35949,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_29799]) ).
tcf(c_35982,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_31509]) ).
tcf(c_35989,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)),sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_32878,c_31509]) ).
tcf(c_36022,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)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2) ),
inference(superposition,[status(thm)],[c_23317,c_34665]) ).
tcf(c_36045,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) )
| ( head_of(sK5(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(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_19149,c_15636]) ).
tcf(c_36046,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) )
| ( head_of(sK5(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(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_19149,c_14859]) ).
tcf(c_36047,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) )
| ( head_of(sK5(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(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_19149,c_6169]) ).
tcf(c_36048,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) )
| ( head_of(sK5(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(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_19149,c_5552]) ).
tcf(c_36049,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) )
| ( head_of(sK5(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(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_19149,c_5311]) ).
tcf(c_36051,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(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19149,c_2051]) ).
tcf(c_36052,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19149,c_61]) ).
tcf(c_36054,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19149,c_34522]) ).
tcf(c_36055,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19149,c_33048]) ).
tcf(c_36060,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(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) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19149,c_22083]) ).
tcf(c_36062,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_19149,c_6140]) ).
tcf(c_36063,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) )
| ( head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19149,c_6136]) ).
tcf(c_36069,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_19149,c_5660]) ).
tcf(c_36070,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) )
| ( head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19149,c_5656]) ).
tcf(c_36076,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19149,c_15636]) ).
tcf(c_36077,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_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_19149,c_15630]) ).
tcf(c_36078,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19149,c_14859]) ).
tcf(c_36079,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_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_19149,c_14853]) ).
tcf(c_36080,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) )
| ( head_of(sK5(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(sK3),tail_of(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19149,c_6169]) ).
tcf(c_36081,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) )
| ( head_of(sK5(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(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_19149,c_6165]) ).
tcf(c_36085,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) )
| ( head_of(sK5(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(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_19149,c_5548]) ).
tcf(c_36086,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) )
| ( head_of(sK5(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(sK3)),X1)
| ( tail_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19149,c_5311]) ).
tcf(c_36087,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_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_19149,c_5307]) ).
tcf(c_36090,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),head_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_19149,c_4242]) ).
tcf(c_36091,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19149,c_4238]) ).
tcf(c_36101,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(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19149,c_2051]) ).
tcf(c_36309,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_34473,c_12475]) ).
tcf(c_36311,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_33002,c_12475]) ).
tcf(c_36313,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_12475]) ).
tcf(c_36314,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_12475]) ).
tcf(c_36350,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_34473,c_13470]) ).
tcf(c_36352,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_33002,c_13470]) ).
tcf(c_36354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),head_of(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) ) ),
inference(superposition,[status(thm)],[c_19145,c_13470]) ).
tcf(c_36355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(tail_of(sK3),tail_of(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(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_13470]) ).
tcf(c_36397,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_14542,c_13832]) ).
tcf(c_36399,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_14540,c_13832]) ).
tcf(c_36436,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_14542,c_13911]) ).
tcf(c_36438,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_14540,c_13911]) ).
tcf(c_36486,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_14539,c_33012]) ).
tcf(c_36487,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_14537,c_33012]) ).
tcf(c_36488,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_5868,c_33012]) ).
tcf(c_36489,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_4854,c_33012]) ).
tcf(c_36490,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_4473,c_33012]) ).
tcf(c_36491,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_14544,c_33012]) ).
tcf(c_36492,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_14541,c_33012]) ).
tcf(c_36493,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_14538,c_33012]) ).
tcf(c_36494,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19147,c_33012]) ).
tcf(c_36495,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19143,c_33012]) ).
tcf(c_36496,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_33012]) ).
tcf(c_36497,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19148,c_33012]) ).
tcf(c_36498,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19144,c_33012]) ).
tcf(c_36499,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_33012]) ).
tcf(c_36500,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_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_19149,c_33012]) ).
tcf(c_36501,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_33012]) ).
tcf(c_36650,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_2077,c_33033]) ).
tcf(c_36652,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_5613,c_33033]) ).
tcf(c_36653,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_3905,c_33033]) ).
tcf(c_36654,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_4346,c_33033]) ).
tcf(c_36655,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_4220,c_33033]) ).
tcf(c_36657,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_5868,c_33033]) ).
tcf(c_36658,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_4854,c_33033]) ).
tcf(c_36659,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_4473,c_33033]) ).
tcf(c_36660,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_6866,c_33033]) ).
tcf(c_36661,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_6212,c_33033]) ).
tcf(c_36662,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_5691,c_33033]) ).
tcf(c_36663,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_14544,c_33033]) ).
tcf(c_36664,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_14541,c_33033]) ).
tcf(c_36669,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_33033]) ).
tcf(c_36670,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_33033]) ).
tcf(c_36671,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19141,c_33033]) ).
tcf(c_36672,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK3)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_33033]) ).
tcf(c_36673,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_33033]) ).
tcf(c_36674,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19142,c_33033]) ).
tcf(c_36676,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_2077,c_33033]) ).
tcf(c_36677,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_6118,c_33033]) ).
tcf(c_36678,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_5613,c_33033]) ).
tcf(c_36679,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_3905,c_33033]) ).
tcf(c_36680,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_4346,c_33033]) ).
tcf(c_36681,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_4220,c_33033]) ).
tcf(c_36682,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_4129,c_33033]) ).
tcf(c_36683,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_5868,c_33033]) ).
tcf(c_36684,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_4854,c_33033]) ).
tcf(c_36685,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_4473,c_33033]) ).
tcf(c_36686,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_6866,c_33033]) ).
tcf(c_36687,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_6212,c_33033]) ).
tcf(c_36688,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_5691,c_33033]) ).
tcf(c_36689,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_14544,c_33033]) ).
tcf(c_36690,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_14541,c_33033]) ).
tcf(c_36691,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_14538,c_33033]) ).
tcf(c_36693,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_14539,c_33033]) ).
tcf(c_36694,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_14537,c_33033]) ).
tcf(c_36695,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_33033]) ).
tcf(c_36696,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_33033]) ).
tcf(c_36697,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_33033]) ).
tcf(c_36698,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_33033]) ).
tcf(c_36699,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_33033]) ).
tcf(c_36700,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_33033]) ).
tcf(c_36701,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) )
| ( head_of(sK5(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(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_19149,c_33033]) ).
tcf(c_36702,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_33033]) ).
tcf(c_36714,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_36650]) ).
tcf(c_37287,plain,
! [X0: $i,X1: $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(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2314,c_36311]) ).
tcf(c_37288,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( 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) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2313,c_36311]) ).
tcf(c_37326,plain,
! [X0: $i,X1: $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(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2314,c_36352]) ).
tcf(c_37327,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( 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) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_2313,c_36352]) ).
tcf(c_37329,plain,
! [X0: $i,X1: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ( sK5(head_of(sK4),head_of(sK3)) = sK3 )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK4),head_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_19032,c_36352]) ).
tcf(c_37368,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0)
| ( head_of(sK4) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2077,c_36676]) ).
tcf(c_37394,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),tail_of(sK3)),X0) ),
inference(equality_resolution_simp,[status(thm)],[c_37368]) ).
tcf(c_37411,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(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_4346,c_19150]) ).
tcf(c_37414,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(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_33033]) ).
tcf(c_37415,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_15636]) ).
tcf(c_37416,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_14859]) ).
tcf(c_37417,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_6169]) ).
tcf(c_37418,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_5552]) ).
tcf(c_37419,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_5311]) ).
tcf(c_37421,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19150,c_2051]) ).
tcf(c_37422,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19150,c_61]) ).
tcf(c_37424,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(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_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_19150,c_33012]) ).
tcf(c_37426,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19150,c_34522]) ).
tcf(c_37427,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( 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(sK4) )
| ( sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19150,c_33048]) ).
tcf(c_37432,plain,
( sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK3),head_of(sK4)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19150,c_22083]) ).
tcf(c_37434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_19150,c_6140]) ).
tcf(c_37435,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19150,c_6136]) ).
tcf(c_37437,plain,
( sequential(sK5(head_of(sK4),head_of(sK3)),sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))))
| ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3)))) = sK5(head_of(sK4),head_of(sK3)) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) ),
inference(superposition,[status(thm)],[c_19150,c_19082]) ).
tcf(c_37441,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_19150,c_5660]) ).
tcf(c_37442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19150,c_5656]) ).
tcf(c_37448,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(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),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19150,c_15636]) ).
tcf(c_37449,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_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_19150,c_15630]) ).
tcf(c_37450,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(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),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19150,c_14859]) ).
tcf(c_37451,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_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_19150,c_14853]) ).
tcf(c_37452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_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(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19150,c_6169]) ).
tcf(c_37453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_6165]) ).
tcf(c_37457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_5548]) ).
tcf(c_37458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(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),tail_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19150,c_5311]) ).
tcf(c_37459,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_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_19150,c_5307]) ).
tcf(c_37473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( tail_of(X0) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19150,c_2051]) ).
tcf(c_37476,plain,
( ( tail_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))))) = head_of(sK4) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37411,c_2085]) ).
tcf(c_38210,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK2)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2))
| ~ precedes(X0,sK7(sK2,X1,X2),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8059,c_77]) ).
tcf(c_38235,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ on_path(sK7(sK2,X1,X2),sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2314,c_38210]) ).
tcf(c_38236,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| sequential(X0,sK7(sK2,X1,X2))
| ~ on_path(X3,sK2)
| ~ sequential(X3,X1)
| ~ path(X4,X5,sK2)
| ~ precedes(X1,X2,sK2)
| ~ precedes(X0,sK7(sK2,X1,X2),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),X3)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,X2)),sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_2293,c_38210]) ).
tcf(c_38237,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( sequential(X2,X3)
| sequential(X1,sK7(sK2,X2,X3))
| sequential(X0,sK7(sK2,X1,sK7(sK2,X2,X3)))
| ( tail_of(sK7(sK2,sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),sK7(sK2,X1,sK7(sK2,X2,X3)))) = head_of(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3)))) )
| ~ on_path(X4,sK2)
| ~ sequential(X4,X2)
| ~ path(X5,X6,sK2)
| ~ precedes(X2,X3,sK2)
| ~ precedes(X1,sK7(sK2,X2,X3),sK2)
| ~ precedes(X0,sK7(sK2,X1,sK7(sK2,X2,X3)),sK2)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),X4)
| ~ sequential(sK7(sK2,X0,sK7(sK2,X1,sK7(sK2,X2,X3))),sK7(sK2,X2,X3)) ),
inference(superposition,[status(thm)],[c_9792,c_38210]) ).
tcf(c_38238,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sequential(X1,X2)
| ~ on_path(X5,sK2)
| ~ on_path(X1,sK2)
| ~ on_path(X0,sK2)
| ~ sequential(X5,X1)
| ~ sequential(X0,X5)
| ~ sequential(X0,X1)
| ~ path(X3,X4,sK2)
| ~ precedes(X1,X2,sK2)
| ~ sequential(X0,sK7(sK2,X1,X2)) ),
inference(superposition,[status(thm)],[c_8044,c_38210]) ).
tcf(c_38291,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_14544,c_34485]) ).
tcf(c_38292,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_14541,c_34485]) ).
tcf(c_38294,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19147,c_34485]) ).
tcf(c_38295,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19143,c_34485]) ).
tcf(c_38296,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_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_19141,c_34485]) ).
tcf(c_38297,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19148,c_34485]) ).
tcf(c_38298,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19144,c_34485]) ).
tcf(c_38299,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_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_19142,c_34485]) ).
tcf(c_38300,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) )
| ( head_of(sK5(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(sK5(head_of(sK4),head_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_19149,c_34485]) ).
tcf(c_38301,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(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_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_19150,c_34485]) ).
tcf(c_38302,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_34485]) ).
tcf(c_38426,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_2077,c_34507]) ).
tcf(c_38428,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_5613,c_34507]) ).
tcf(c_38429,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_3905,c_34507]) ).
tcf(c_38430,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_4346,c_34507]) ).
tcf(c_38431,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_4220,c_34507]) ).
tcf(c_38433,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_5868,c_34507]) ).
tcf(c_38434,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_4854,c_34507]) ).
tcf(c_38435,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_4473,c_34507]) ).
tcf(c_38436,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_6866,c_34507]) ).
tcf(c_38437,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_6212,c_34507]) ).
tcf(c_38438,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_5691,c_34507]) ).
tcf(c_38443,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_14539,c_34507]) ).
tcf(c_38444,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_14537,c_34507]) ).
tcf(c_38445,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19147,c_34507]) ).
tcf(c_38446,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19143,c_34507]) ).
tcf(c_38447,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19141,c_34507]) ).
tcf(c_38448,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(tail_of(sK3),head_of(sK4)),X1)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19148,c_34507]) ).
tcf(c_38449,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19144,c_34507]) ).
tcf(c_38450,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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),tail_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19142,c_34507]) ).
tcf(c_38453,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_2077,c_34507]) ).
tcf(c_38454,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_6118,c_34507]) ).
tcf(c_38455,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_5613,c_34507]) ).
tcf(c_38456,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_3905,c_34507]) ).
tcf(c_38457,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_4346,c_34507]) ).
tcf(c_38458,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_4220,c_34507]) ).
tcf(c_38459,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_4129,c_34507]) ).
tcf(c_38460,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_5868,c_34507]) ).
tcf(c_38461,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_4854,c_34507]) ).
tcf(c_38462,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_4473,c_34507]) ).
tcf(c_38463,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_6866,c_34507]) ).
tcf(c_38464,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_6212,c_34507]) ).
tcf(c_38465,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_5691,c_34507]) ).
tcf(c_38466,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_14544,c_34507]) ).
tcf(c_38467,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_14541,c_34507]) ).
tcf(c_38469,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_14543,c_34507]) ).
tcf(c_38470,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_14539,c_34507]) ).
tcf(c_38471,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_14537,c_34507]) ).
tcf(c_38472,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19147,c_34507]) ).
tcf(c_38473,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19143,c_34507]) ).
tcf(c_38474,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),head_of(sK5(head_of(sK4),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_19141,c_34507]) ).
tcf(c_38475,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))) = 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))) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19148,c_34507]) ).
tcf(c_38476,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))) = tail_of(sK3) )
| ( tail_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19144,c_34507]) ).
tcf(c_38477,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))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),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_19142,c_34507]) ).
tcf(c_38478,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) )
| ( head_of(sK5(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(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_19149,c_34507]) ).
tcf(c_38479,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(sK4) )
| ( head_of(sK5(head_of(sK4),tail_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),tail_of(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_19150,c_34507]) ).
tcf(c_38480,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_34507]) ).
tcf(c_38492,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_38426]) ).
tcf(c_39321,plain,
! [X0: $i,X1: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ on_path(sK4,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_37394]) ).
tcf(c_39322,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ path(X0,X1,X2)
| ~ on_path(sK4,sK6(X0,X1,X2))
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2313,c_37394]) ).
tcf(c_39324,plain,
! [X0: $i,X1: $i] :
( ( sK5(head_of(sK4),tail_of(sK3)) = sK4 )
| ( sK5(head_of(sK4),tail_of(sK3)) = sK3 )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK4,sK5(head_of(sK4),tail_of(sK3)))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39321,c_52]) ).
tcf(c_39351,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_34473,c_14236]) ).
tcf(c_39353,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_33002,c_14236]) ).
tcf(c_39355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19145,c_14236]) ).
tcf(c_39356,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_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(sK4),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(sK4),head_of(sK3)))),X0)
| ( tail_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19146,c_14236]) ).
tcf(c_39401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(tail_of(sK3),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)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_14544,c_14572]) ).
tcf(c_39402,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_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(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(superposition,[status(thm)],[c_14541,c_14572]) ).
tcf(c_39406,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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(sK4),tail_of(sK3)),X0) ),
inference(superposition,[status(thm)],[c_14537,c_14572]) ).
tcf(c_39409,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),head_of(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19141,c_14572]) ).
tcf(c_39412,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(head_of(sK4),head_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( head_of(sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3))))) = tail_of(sK3) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(tail_of(sK3),tail_of(sK5(head_of(sK4),head_of(sK3)))),X0) ),
inference(superposition,[status(thm)],[c_19142,c_14572]) ).
tcf(c_39415,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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)),sK3,X0) ),
inference(equality_resolution,[status(thm)],[c_14572]) ).
tcf(c_39446,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ on_path(sK3,sK2)
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(superposition,[status(thm)],[c_2314,c_39415]) ).
tcf(c_39447,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ path(X0,X1,X2)
| ~ on_path(sK3,sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2)) ),
inference(superposition,[status(thm)],[c_2313,c_39415]) ).
tcf(c_39448,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ~ shortest_path(X0,X1,sK2)
| ~ sequential(sK5(head_of(sK4),tail_of(sK3)),sK3)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_39446,c_51]) ).
tcf(c_39509,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0)
| ( head_of(sK4) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_2077,c_38453]) ).
tcf(c_39536,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK5(tail_of(sK3),head_of(sK4)) = sK4 )
| ( sK5(tail_of(sK3),head_of(sK4)) = sK3 )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(tail_of(sK3),head_of(sK4)),X0) ),
inference(equality_resolution_simp,[status(thm)],[c_39509]) ).
tcf(c_39555,plain,
! [X0: $i,X1: $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(X0,X1,sK2)
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK2)
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK2)
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2314,c_39353]) ).
tcf(c_39556,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( shortest_path(X0,X1,X2)
| ( X0 = X1 )
| ( 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) )
| ~ path(X0,X1,X2)
| ~ shortest_path(X3,X4,sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK4),tail_of(sK3)),sK6(X0,X1,X2))
| ~ on_path(sK5(head_of(sK3),head_of(sK4)),sK6(X0,X1,X2))
| ~ sequential(sK5(head_of(sK3),head_of(sK4)),sK5(head_of(sK4),tail_of(sK3))) ),
inference(superposition,[status(thm)],[c_2313,c_39353]) ).
tcf(c_39603,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_34507]) ).
tcf(c_39604,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_33033]) ).
tcf(c_39605,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_15636]) ).
tcf(c_39606,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK4),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_14859]) ).
tcf(c_39607,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_6169]) ).
tcf(c_39608,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_5552]) ).
tcf(c_39609,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_5311]) ).
tcf(c_39611,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_2051]) ).
tcf(c_39612,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = X0 )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_61]) ).
tcf(c_39613,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( head_of(sK5(head_of(sK4),tail_of(sK3))) = tail_of(sK3) )
| ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_14572]) ).
tcf(c_39614,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) )
| ( tail_of(sK5(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)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19151,c_34507]) ).
tcf(c_39615,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19151,c_34485]) ).
tcf(c_39616,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) )
| ( tail_of(sK5(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)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19151,c_33033]) ).
tcf(c_39617,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19151,c_33012]) ).
tcf(c_39618,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_6222]) ).
tcf(c_39621,plain,
( sequential(sK5(tail_of(sK3),head_of(sK4)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_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) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK4)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_32085]) ).
tcf(c_39622,plain,
( sequential(sK5(head_of(sK4),tail_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_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) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK4),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_31897]) ).
tcf(c_39623,plain,
( sequential(sK5(head_of(sK3),tail_of(sK3)),sK5(head_of(sK4),head_of(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))) = head_of(sK3) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(head_of(sK3),tail_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_29407]) ).
tcf(c_39624,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) )
| ( tail_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_6218]) ).
tcf(c_39626,plain,
( sequential(sK5(tail_of(sK3),head_of(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(tail_of(sK3),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) = head_of(sK4) )
| ( sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))) = sK5(tail_of(sK3),head_of(sK3)) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) = head_of(sK4) )
| ~ edge(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))))
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_21970]) ).
tcf(c_39629,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_5878]) ).
tcf(c_39631,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) )
| ( tail_of(sK5(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(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_5874]) ).
tcf(c_39632,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(sK3) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_5700]) ).
tcf(c_39633,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(sK3) )
| ( tail_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_5696]) ).
tcf(c_39636,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) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_16644]) ).
tcf(c_39637,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) )
| ( tail_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_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(sK4),head_of(sK3))) != head_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_16323]) ).
tcf(c_39638,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(sK4) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_4864]) ).
tcf(c_39639,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(sK4) )
| ( tail_of(sK5(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(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_4860]) ).
tcf(c_39641,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) )
| ( tail_of(sK5(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)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_15636]) ).
tcf(c_39642,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19151,c_15630]) ).
tcf(c_39643,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) )
| ( tail_of(sK5(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)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_14859]) ).
tcf(c_39644,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK4),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19151,c_14853]) ).
tcf(c_39645,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) )
| ( tail_of(sK5(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(sK3),tail_of(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_6169]) ).
tcf(c_39646,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),tail_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19151,c_6165]) ).
tcf(c_39647,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) )
| ( tail_of(sK5(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(sK3),head_of(sK4)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != head_of(sK4) ) ),
inference(superposition,[status(thm)],[c_19151,c_5552]) ).
tcf(c_39650,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != head_of(sK4) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(head_of(sK3),head_of(sK4))) ) ),
inference(superposition,[status(thm)],[c_19151,c_5548]) ).
tcf(c_39651,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) )
| ( tail_of(sK5(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(sK3)),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) )
| ( head_of(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3))))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_5311]) ).
tcf(c_39652,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),X0,X1)
| ( head_of(X0) != tail_of(sK3) )
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK5(tail_of(sK3),head_of(sK3))) ) ),
inference(superposition,[status(thm)],[c_19151,c_5307]) ).
tcf(c_39658,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(sK3) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),head_of(sK4)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_3927]) ).
tcf(c_39659,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(sK3) )
| ( tail_of(sK5(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_3923]) ).
tcf(c_39660,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(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(sK5(head_of(sK4),head_of(sK3)))),sK5(head_of(sK3),tail_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_6876]) ).
tcf(c_39661,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(head_of(sK4),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(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_6872]) ).
tcf(c_39662,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) )
| ( tail_of(sK5(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(sK5(head_of(sK4),head_of(sK3)))),sK5(tail_of(sK3),head_of(sK3)),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_4482]) ).
tcf(c_39663,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) )
| ( tail_of(sK5(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(sK3)),sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_4478]) ).
tcf(c_39664,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4,sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_2250]) ).
tcf(c_39665,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( 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) )
| ~ shortest_path(X1,X2,X0)
| ~ precedes(sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),sK4,X0)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_19151,c_2249]) ).
tcf(c_39666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( 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) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK4),head_of(sK5(head_of(sK4),head_of(sK3)))),X1)
| ( head_of(sK5(head_of(sK4),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_19151,c_2051]) ).
tcf(c_39667,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) )
| ~ edge(sK5(head_of(sK4),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_19151,c_74]) ).
tcf(c_40058,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_39667,c_39666,c_39665,c_39664,c_39663,c_39662,c_39661,c_39660,c_39659,c_39658,c_39652,c_39651,c_39650,c_39647,c_39646,c_39645,c_39644,c_39643,c_39642,c_39641,c_39639,c_39638,c_39637,c_39636,c_39633,c_39632,c_39631,c_39629,c_39626,c_39624,c_39623,c_39622,c_39621,c_39618,c_39617,c_39616,c_39615,c_39614,c_39613,c_39612,c_39611,c_39609,c_39608,c_39607,c_39606,c_39605,c_39604,c_39603,c_39556,c_39555,c_39536,c_39448,c_39447,c_39446,c_39415,c_39412,c_39409,c_39406,c_39402,c_39401,c_39356,c_39355,c_39353,c_39351,c_39324,c_39322,c_39321,c_38492,c_38480,c_38479,c_38478,c_38477,c_38476,c_38475,c_38474,c_38473,c_38472,c_38471,c_38470,c_38469,c_38467,c_38466,c_38465,c_38464,c_38463,c_38462,c_38461,c_38460,c_38459,c_38458,c_38457,c_38456,c_38455,c_38454,c_38453,c_38450,c_38449,c_38448,c_38447,c_38446,c_38445,c_38444,c_38443,c_38438,c_38437,c_38436,c_38435,c_38434,c_38433,c_38431,c_38430,c_38429,c_38428,c_38302,c_38301,c_38300,c_38299,c_38298,c_38297,c_38296,c_38295,c_38294,c_38292,c_38291,c_38238,c_38237,c_38236,c_38235,c_38210,c_37476,c_37473,c_37459,c_37458,c_37457,c_37453,c_37452,c_37451,c_37450,c_37449,c_37448,c_37442,c_37441,c_37437,c_37435,c_37434,c_37432,c_37427,c_37426,c_37424,c_37422,c_37421,c_37419,c_37418,c_37417,c_37416,c_37415,c_37414,c_37411,c_37394,c_37329,c_37327,c_37326,c_37288,c_37287,c_36714,c_36702,c_36701,c_36700,c_36699,c_36698,c_36697,c_36696,c_36695,c_36694,c_36693,c_36691,c_36690,c_36689,c_36688,c_36687,c_36686,c_36685,c_36684,c_36683,c_36682,c_36681,c_36680,c_36679,c_36678,c_36677,c_36676,c_36674,c_36673,c_36672,c_36671,c_36670,c_36669,c_36664,c_36663,c_36662,c_36661,c_36660,c_36659,c_36658,c_36657,c_36655,c_36654,c_36653,c_36652,c_36501,c_36500,c_36499,c_36498,c_36497,c_36496,c_36495,c_36494,c_36493,c_36492,c_36491,c_36490,c_36489,c_36488,c_36487,c_36486,c_36438,c_36436,c_36399,c_36397,c_36355,c_36354,c_36352,c_36350,c_36314,c_36313,c_36311,c_36309,c_36101,c_36091,c_36090,c_36087,c_36086,c_36085,c_36081,c_36080,c_36079,c_36078,c_36077,c_36076,c_36070,c_36069,c_36063,c_36062,c_36060,c_36055,c_36054,c_36052,c_36051,c_36049,c_36048,c_36047,c_36046,c_36045,c_36022,c_35989,c_35982,c_35949,c_35948,c_35896,c_35895,c_35890,c_35853,c_35852,c_35820,c_35819,c_35765,c_35764,c_35763,c_35762,c_35752,c_35738,c_35737,c_35736,c_35685,c_35684,c_35681,c_35678,c_35677,c_35674,c_35673,c_35598,c_35597,c_35595,c_35594,c_35088,c_35087,c_35086,c_35081,c_35080,c_35079,c_35078,c_35077,c_35076,c_35075,c_35074,c_35073,c_35072,c_35071,c_35070,c_35069,c_35068,c_35067,c_35066,c_35065,c_35064,c_35063,c_35062,c_35061,c_35060,c_35059,c_35058,c_35057,c_35056,c_35055,c_35054,c_35052,c_35050,c_35049,c_35047,c_35042,c_35041,c_35040,c_35039,c_35038,c_35037,c_35036,c_35035,c_35034,c_35033,c_35032,c_35031,c_34877,c_34876,c_34875,c_34874,c_34873,c_34869,c_34868,c_34867,c_34866,c_34864,c_34862,c_34858,c_34854,c_34853,c_34821,c_34820,c_34819,c_34674,c_34673,c_34672,c_34671,c_34670,c_34669,c_34668,c_34665,c_34664,c_34663,c_34662,c_34660,c_34658,c_34655,c_34654,c_34650,c_34649,c_34627,c_34608,c_34607,c_34606,c_34573,c_34572,c_34553,c_34547,c_34541,c_34535,c_34529,c_34522,c_34507,c_34505,c_34501,c_34500,c_34497,c_34494,c_34487,c_34485,c_34473,c_34387,c_34386,c_34385,c_34384,c_34383,c_34382,c_34381,c_34380,c_34379,c_34378,c_34377,c_34376,c_34371,c_33766,c_33765,c_33764,c_33763,c_33762,c_33761,c_33760,c_33759,c_33758,c_33757,c_33756,c_33755,c_33752,c_33747,c_33742,c_33695,c_33693,c_33692,c_33736,c_33735,c_33721,c_33289,c_33287,c_33286,c_33285,c_33280,c_33279,c_33278,c_33275,c_33274,c_33273,c_33272,c_33271,c_33270,c_33268,c_33267,c_33266,c_33265,c_33264,c_33263,c_33262,c_33260,c_33259,c_33258,c_33257,c_33256,c_33255,c_33254,c_33253,c_33251,c_33249,c_33248,c_33246,c_33241,c_33240,c_33239,c_33238,c_33237,c_33236,c_33235,c_33234,c_33233,c_33189,c_33152,c_33151,c_33150,c_33085,c_33079,c_33073,c_33067,c_33061,c_33055,c_33048,c_33033,c_33031,c_33027,c_33026,c_33023,c_33020,c_33016,c_33012,c_33011,c_33002,c_32978,c_32977,c_32976,c_32975,c_32885,c_32878,c_32873,c_32868,c_32864,c_32863,c_32862,c_32861,c_32859,c_32845,c_32838,c_32831,c_32826,c_32822,c_32818,c_32817,c_32816,c_32815,c_32814,c_32813,c_32410,c_32409,c_32408,c_32407,c_32406,c_32405,c_32404,c_32403,c_32402,c_32401,c_32400,c_32399,c_32398,c_32397,c_32396,c_32395,c_32394,c_32393,c_32392,c_32391,c_32390,c_32389,c_32388,c_32387,c_32386,c_32385,c_32384,c_32383,c_32382,c_32381,c_32380,c_32379,c_32378,c_32377,c_32376,c_32375,c_32374,c_32373,c_32372,c_32371,c_32370,c_32369,c_32368,c_32367,c_32366,c_32365,c_32364,c_32363,c_32362,c_32361,c_32360,c_32359,c_32358,c_32357,c_32356,c_32355,c_32354,c_32353,c_32352,c_32351,c_32350,c_32349,c_32348,c_32347,c_32345,c_32300,c_32293,c_32286,c_32281,c_32274,c_32273,c_32270,c_32269,c_32268,c_32267,c_32266,c_32265,c_32240,c_32235,c_32231,c_32230,c_32229,c_32228,c_32223,c_32222,c_32209,c_32151,c_32146,c_32141,c_32136,c_32122,c_32121,c_32120,c_32118,c_32116,c_32115,c_32109,c_32108,c_32107,c_32105,c_32085,c_32080,c_32075,c_32070,c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).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA009+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 12:42:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 22.09/3.81 % SZS status Started for theBenchmark.p
% 22.09/3.81 % SZS status Theorem for theBenchmark.p
% 22.09/3.81
% 22.09/3.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.09/3.81
% 22.09/3.81 % ------ iProver source info
% 22.09/3.81
% 22.09/3.81 % git: date: 2026-07-19 20:42:38 +0200
% 22.09/3.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.09/3.81 % git: non_committed_changes: false
% 22.09/3.81
% 22.09/3.81 % ------ Parsing...
% 22.09/3.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.09/3.81
% 22.09/3.81 % ------ 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 %
% 22.09/3.81
% 22.09/3.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.09/3.81
% 22.09/3.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.09/3.81 % ------ Proving...
% 22.09/3.81 % ------ Problem Properties
% 22.09/3.81
% 22.09/3.81 %
% 22.09/3.81 % clauses 33
% 22.09/3.81 % conjectures 4
% 22.09/3.81 % EPR 16
% 22.09/3.81 % Horn 23
% 22.09/3.81 % unary 6
% 22.09/3.81 % binary 8
% 22.09/3.81 % lits 105
% 22.09/3.81 % lits eq 26
% 22.09/3.81 % fd_pure 0
% 22.09/3.81 % fd_pseudo 0
% 22.09/3.81 % fd_cond 0
% 22.09/3.81 % fd_pseudo_cond 5
% 22.09/3.81 % AC symbols 0
% 22.09/3.81
% 22.09/3.81 % ------ Schedule dynamic 5 is on
% 22.09/3.81
% 22.09/3.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.09/3.81
% 22.09/3.81
% 22.09/3.81 % ------
% 22.09/3.81 % Current options:
% 22.09/3.81 % ------
% 22.09/3.81
% 22.09/3.81
% 22.09/3.81 %
% 22.09/3.81
% 22.09/3.81 % ------ Proving...
% 22.09/3.81 %
% 22.09/3.81
% 22.09/3.81 % SZS status Theorem for theBenchmark.p
% 22.09/3.81
% 22.09/3.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.10/3.91
% 22.10/3.91
%------------------------------------------------------------------------------