%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA011+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 : n014.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 01:23:38 PM UTC 2026
% Result : Theorem 50.07s 7.86s
% Output : CNFRefutation 50.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 16
% Syntax : Number of formulae : 228 ( 26 unt; 0 def)
% Number of atoms : 905 ( 354 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1137 ( 460 ~; 537 |; 114 &)
% ( 4 <=>; 17 =>; 0 <=; 5 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 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 : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 455 ( 0 sgn 432 !; 23 ?; 219 :)
% 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(f16,axiom,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f21,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
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] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0)
& ! [X5] : ~ triangle(X3,X4,X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(flattening,[],[f25]) ).
fof(f27,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(f28,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,[],[f27]) ).
fof(f29,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(f30,plain,
! [X0] :
( ~ edge(X0)
| ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f31,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(f32,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,[],[f31]) ).
fof(f33,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(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(ennf_transformation,[],[f9]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
( complete
& shortest_path(sK1,sK2,sK0)
& number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21]) ).
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(nnf_transformation,[],[f24]) ).
fof(f38,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,[],[f37]) ).
fof(f39,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ( ( ( tail_of(sK3(X0,X1)) = X1
& head_of(sK3(X0,X1)) = X0 )
| ( tail_of(sK3(X0,X1)) = X0
& head_of(sK3(X0,X1)) = X1 ) )
& ( tail_of(sK3(X0,X1)) != X1
| head_of(sK3(X0,X1)) != X0
| tail_of(sK3(X0,X1)) != X0
| head_of(sK3(X0,X1)) != X1 )
& edge(sK3(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ( sequential(sK4(X0),sK5(X0))
& on_path(sK5(X0),X0)
& on_path(sK4(X0),X0)
& ! [X5] : ~ triangle(sK4(X0),sK5(X0),X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X3,sK4(X0)),skolemize(X4,sK5(X0))],[f26]) ).
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,[],[f29]) ).
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] :
( ( ~ 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(f46,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,[],[f45]) ).
fof(f47,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,[],[f33]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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))],[f49]) ).
fof(f51,plain,
complete,
inference(cnf_transformation,[],[f36]) ).
fof(f52,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f36]) ).
fof(f54,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK3(X0,X1)) = X0
| tail_of(sK3(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f39]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK3(X0,X1)) = X1
| head_of(sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK3(X0,X1)) = X0
| head_of(sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f39]) ).
fof(f60,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f61,plain,
! [X2,X0,X1] :
( sequential(sK4(X0),sK5(X0))
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X2,X0,X1] :
( on_path(sK5(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X2,X0,X1] :
( on_path(sK4(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f64,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK4(X0),sK5(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f65,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f66,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,[],[f28]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f72,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f73,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f76,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f78,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f79,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,[],[f32]) ).
fof(f83,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f84,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f86,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,[],[f35]) ).
tcf(c_49,negated_conjecture,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
complete,
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,plain,
! [X0: $i] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ path(X2,X3,X0)
| ~ triangle(sK4(X0),sK5(X0),X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK4(X2),X2)
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK5(X2),X2)
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(sK4(X2),sK5(X2))
| ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_63,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,[],[f66]) ).
tcf(c_64,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,[],[f65]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_70,plain,
! [X0: $i] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_71,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_77,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,[],[f79]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_83,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,[],[f86]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_51,c_53]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_103]) ).
tcf(c_106,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_77,c_74,c_73,c_77]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_51,c_57]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_113]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_51,c_56]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_51,c_55]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_117]) ).
tcf(c_145,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_106,c_73]) ).
tcf(c_600,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ sequential(X4,X1)
| ~ sequential(X2,X4)
| ~ sequential(X1,X2)
| ~ path(X5,X6,X0)
| ( X3 != X4 )
| ( sK5(X0) != X2 )
| ( sK4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_145]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ sequential(X3,sK4(X0))
| ~ sequential(sK5(X0),X3)
| ~ path(X1,X2,X0)
| ~ sequential(sK4(X0),sK5(X0)) ),
inference(unflattening,[status(thm)],[c_600]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) )
| ~ sequential(X3,sK4(X2))
| ~ sequential(sK5(X2),X3)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_601,c_62]) ).
tcf(c_711,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X1,X2,X0)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_67]) ).
tcf(c_712,plain,
path(sK1,sK2,sK0),
inference(unflattening,[status(thm)],[c_711]) ).
tcf(c_1538,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1540,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1543,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1544,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1548,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(X0,X2)
| ~ on_path(X1,X2)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2211,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_50,c_67]) ).
tcf(c_2226,plain,
! [X0: $i,X1: $i] :
( on_path(X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2211,c_78]) ).
tcf(c_2239,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2211,c_79]) ).
tcf(c_2260,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_50,c_64]) ).
tcf(c_2286,plain,
( on_path(sK4(sK0),sK0)
| ( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0) ) ),
inference(superposition,[status(thm)],[c_2211,c_60]) ).
tcf(c_2287,plain,
on_path(sK4(sK0),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2286,c_49]) ).
tcf(c_2294,plain,
( on_path(sK5(sK0),sK0)
| ( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0) ) ),
inference(superposition,[status(thm)],[c_2211,c_61]) ).
tcf(c_2295,plain,
on_path(sK5(sK0),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2294,c_49]) ).
tcf(c_2312,plain,
( sequential(sK4(sK0),sK5(sK0))
| ( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0) ) ),
inference(superposition,[status(thm)],[c_2211,c_62]) ).
tcf(c_2313,plain,
sequential(sK4(sK0),sK5(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2312,c_49]) ).
tcf(c_2390,plain,
head_of(sK4(sK0)) = tail_of(sK5(sK0)),
inference(superposition,[status(thm)],[c_2313,c_76]) ).
tcf(c_2391,plain,
edge(sK5(sK0)),
inference(superposition,[status(thm)],[c_2313,c_74]) ).
tcf(c_2392,plain,
edge(sK4(sK0)),
inference(superposition,[status(thm)],[c_2313,c_73]) ).
tcf(c_2393,plain,
( ~ edge(sK5(sK0))
| ( head_of(sK4(sK0)) != head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2390,c_52]) ).
tcf(c_2394,plain,
( vertex(head_of(sK4(sK0)))
| ~ edge(sK5(sK0)) ),
inference(superposition,[status(thm)],[c_2390,c_71]) ).
tcf(c_2396,plain,
vertex(head_of(sK4(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_2394,c_2391]) ).
tcf(c_2397,plain,
head_of(sK4(sK0)) != head_of(sK5(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2393,c_2391]) ).
tcf(c_2496,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2211,c_83]) ).
tcf(c_2565,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2496,c_2260]) ).
tcf(c_2601,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2565,c_2226,c_2239,c_2565]) ).
tcf(c_2607,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2496,c_2601]) ).
tcf(c_2666,plain,
( ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK4(sK0),sK0)
| ~ sequential(sK5(sK0),sK4(sK0)) ),
inference(superposition,[status(thm)],[c_2313,c_2607]) ).
tcf(c_2668,plain,
~ sequential(sK5(sK0),sK4(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2666,c_2295,c_2287]) ).
tcf(c_2752,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(X2,X0,sK0)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_2762,plain,
! [X0: $i] :
( ( number_of_in(sequential_pairs,sK0) = number_of_in(triangles,sK0) )
| ~ sequential(X0,sK4(sK0))
| ~ sequential(sK5(sK0),X0) ),
inference(superposition,[status(thm)],[c_2211,c_613]) ).
tcf(c_2763,plain,
! [X0: $i] :
( ~ sequential(X0,sK4(sK0))
| ~ sequential(sK5(sK0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2762,c_49]) ).
tcf(c_2785,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ( head_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_71,c_114]) ).
tcf(c_3007,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_71,c_116]) ).
tcf(c_3037,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_71,c_118]) ).
tcf(c_3038,plain,
! [X0: $i] :
( ( head_of(sK4(sK0)) = X0 )
| ( head_of(sK3(head_of(sK4(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK4(sK0)),X0)) = head_of(sK4(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2396,c_118]) ).
tcf(c_3345,plain,
! [X0: $i] :
( ( tail_of(sK4(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK4(sK0)),X0)) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),X0)) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2392,c_3007]) ).
tcf(c_3557,plain,
! [X0: $i] :
( ( tail_of(sK4(sK0)) = head_of(X0) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(X0))) = head_of(X0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_70,c_3345]) ).
tcf(c_4215,plain,
! [X0: $i] :
( ( tail_of(sK4(sK0)) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),X0)) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),X0)) = tail_of(sK4(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2392,c_3037]) ).
tcf(c_4236,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(sK4(sK0),X2,sK0)
| ~ on_path(X2,sK0)
| ~ on_path(sK4(sK0),sK0)
| ~ sequential(sK4(sK0),X2)
| ~ path(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_4239,plain,
! [X0: $i] :
( on_path(X0,sK0)
| ~ on_path(sK4(sK0),sK0)
| ( X0 != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_1548]) ).
tcf(c_4373,plain,
! [X0: $i] :
( ( tail_of(sK4(sK0)) = head_of(X0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(X0))) = head_of(X0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(X0))) = tail_of(sK4(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_70,c_4215]) ).
tcf(c_4673,plain,
! [X0: $i] :
( ( tail_of(sK4(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK4(sK0)),X0)) = tail_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),X0)) = tail_of(sK4(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2392,c_2785]) ).
tcf(c_5681,plain,
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2391,c_3557]) ).
tcf(c_5944,plain,
! [X0: $i] :
( ( head_of(sK4(sK0)) = head_of(X0) )
| ( head_of(sK3(head_of(sK4(sK0)),head_of(X0))) = head_of(X0) )
| ( head_of(sK3(head_of(sK4(sK0)),head_of(X0))) = head_of(sK4(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_70,c_3038]) ).
tcf(c_6050,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(X0)
| ~ edge(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( head_of(sK5(sK0)) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_5681,c_72]) ).
tcf(c_6220,plain,
( vertex(head_of(sK5(sK0)))
| ~ edge(sK5(sK0)) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_6437,plain,
( vertex(tail_of(sK4(sK0)))
| ~ edge(sK4(sK0)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_6491,plain,
! [X0: $i] :
( sequential(X0,sK5(sK0))
| ( X0 = sK5(sK0) )
| ~ edge(X0)
| ~ edge(sK5(sK0))
| ( head_of(X0) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_6667,plain,
! [X0: $i] :
( sequential(X0,sK4(sK0))
| ( X0 = sK4(sK0) )
| ~ edge(X0)
| ~ edge(sK4(sK0))
| ( head_of(X0) != tail_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_7211,plain,
sK4(sK0) = sK4(sK0),
inference(instantiation,[status(thm)],[c_1538]) ).
tcf(c_7568,plain,
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2391,c_4373]) ).
tcf(c_7690,plain,
( ( head_of(sK4(sK0)) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK4(sK0)) ) ),
inference(superposition,[status(thm)],[c_2391,c_5944]) ).
tcf(c_7694,plain,
( ( head_of(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK4(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7690,c_2397]) ).
tcf(c_7748,plain,
! [X0: $i,X1: $i] :
( precedes(sK4(sK0),sK5(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK4(sK0),sK0)
| ~ path(X0,X1,sK0)
| ~ sequential(sK4(sK0),sK5(sK0)) ),
inference(instantiation,[status(thm)],[c_4236]) ).
tcf(c_7757,plain,
( vertex(head_of(sK5(sK0)))
| ( head_of(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK4(sK0)) )
| ~ edge(sK3(head_of(sK4(sK0)),head_of(sK5(sK0)))) ),
inference(superposition,[status(thm)],[c_7694,c_70]) ).
tcf(c_7789,plain,
vertex(head_of(sK5(sK0))),
inference(global_subsumption_just,[status(thm)],[c_7757,c_2391,c_6220]) ).
tcf(c_7793,plain,
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK4(sK0)) ) ),
inference(superposition,[status(thm)],[c_7789,c_4673]) ).
tcf(c_7908,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),X0)
| ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(X0)
| ~ edge(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( tail_of(sK4(sK0)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_7568,c_72]) ).
tcf(c_7911,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK4(sK0)) != head_of(X1) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_7568,c_63]) ).
tcf(c_8660,plain,
! [X0: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK4(sK0),sK5(sK0),sK0)
| ( tail_of(X0) != tail_of(sK4(sK0)) )
| ( head_of(sK5(sK0)) != head_of(X0) ) ),
inference(instantiation,[status(thm)],[c_2752]) ).
tcf(c_10588,plain,
( sequential(sK5(sK0),sK4(sK0))
| ( sK5(sK0) = sK4(sK0) )
| ~ edge(sK5(sK0))
| ~ edge(sK4(sK0))
| ( head_of(sK5(sK0)) != tail_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_6667]) ).
tcf(c_11516,plain,
( precedes(sK4(sK0),sK5(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK4(sK0),sK0)
| ~ path(sK1,sK2,sK0)
| ~ sequential(sK4(sK0),sK5(sK0)) ),
inference(instantiation,[status(thm)],[c_7748]) ).
tcf(c_12679,plain,
! [X0: $i,X1: $i] :
( ( X1 = tail_of(sK5(sK0)) )
| ( X1 != X0 )
| ( tail_of(sK5(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1540]) ).
tcf(c_12682,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK5(sK0)) )
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1544]) ).
tcf(c_12817,plain,
! [X0: $i] :
( ( X0 = head_of(sK5(sK0)) )
| ( tail_of(sK3(X0,head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(X0,head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ vertex(X0)
| ~ vertex(head_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_12821,plain,
! [X0: $i] :
( edge(sK3(X0,head_of(sK5(sK0))))
| ( X0 = head_of(sK5(sK0)) )
| ~ vertex(X0)
| ~ vertex(head_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_104]) ).
tcf(c_12831,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK5(sK0)) )
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1543]) ).
tcf(c_14260,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = head_of(X0) )
| ( sK5(sK0) != X0 ) ),
inference(instantiation,[status(thm)],[c_1543]) ).
tcf(c_14266,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(sK0)) = X1 )
| ( X1 != X0 )
| ( head_of(sK5(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1540]) ).
tcf(c_14470,plain,
! [X0: $i] :
( ( tail_of(X0) = tail_of(sK4(sK0)) )
| ( X0 != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_1544]) ).
tcf(c_14945,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK4(sK0)) )
| ( X0 != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_1543]) ).
tcf(c_14951,plain,
! [X0: $i,X1: $i] :
( ( X1 = head_of(sK4(sK0)) )
| ( X1 != X0 )
| ( head_of(sK4(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1540]) ).
tcf(c_15604,plain,
sK5(sK0) = sK5(sK0),
inference(instantiation,[status(thm)],[c_1538]) ).
tcf(c_15850,plain,
head_of(sK5(sK0)) = head_of(sK5(sK0)),
inference(instantiation,[status(thm)],[c_1538]) ).
tcf(c_16251,plain,
( ( tail_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( sK5(sK0) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_12682]) ).
tcf(c_16432,plain,
( ( tail_of(sK4(sK0)) = tail_of(sK4(sK0)) )
| ( sK4(sK0) != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_14470]) ).
tcf(c_20515,plain,
( edge(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( tail_of(sK4(sK0)) = head_of(sK5(sK0)) )
| ~ vertex(tail_of(sK4(sK0)))
| ~ vertex(head_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_12821]) ).
tcf(c_21440,plain,
( ( tail_of(sK4(sK0)) = head_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ vertex(tail_of(sK4(sK0)))
| ~ vertex(head_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_12817]) ).
tcf(c_22103,plain,
! [X0: $i] :
( ( X0 = head_of(sK4(sK0)) )
| ( X0 != tail_of(sK5(sK0)) )
| ( head_of(sK4(sK0)) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_14951]) ).
tcf(c_26174,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( X0 != head_of(sK5(sK0)) )
| ( head_of(sK5(sK0)) != head_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_14266]) ).
tcf(c_26188,plain,
( ( tail_of(sK5(sK0)) = head_of(sK4(sK0)) )
| ( tail_of(sK5(sK0)) != tail_of(sK5(sK0)) )
| ( head_of(sK4(sK0)) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_22103]) ).
tcf(c_26526,plain,
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK4(sK0))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK4(sK0) )
| ~ edge(sK4(sK0))
| ~ edge(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_6667]) ).
tcf(c_26527,plain,
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK5(sK0))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ~ edge(sK5(sK0))
| ~ edge(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_6491]) ).
tcf(c_32194,plain,
! [X0: $i] :
( ( X0 = tail_of(sK5(sK0)) )
| ( X0 != head_of(sK4(sK0)) )
| ( tail_of(sK5(sK0)) != head_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_12679]) ).
tcf(c_32698,plain,
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK4(sK0),sK5(sK0),sK0)
| ( tail_of(sK4(sK0)) != tail_of(sK4(sK0)) )
| ( head_of(sK5(sK0)) != head_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_8660]) ).
tcf(c_32898,plain,
( ( head_of(sK5(sK0)) = head_of(sK4(sK0)) )
| ( sK5(sK0) != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_14260]) ).
tcf(c_41845,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(X0) )
| ( tail_of(sK4(sK0)) != head_of(X1) )
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4)
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_7911,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_7211,c_7911,c_10588,c_11516,c_16432,c_32698,c_32898]) ).
tcf(c_41846,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK4(sK0)) != head_of(X1) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(X0) ) ),
inference(renaming,[status(thm)],[c_41845]) ).
tcf(c_43782,plain,
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( tail_of(sK4(sK0)) != head_of(sK5(sK0)) )
| ( head_of(sK5(sK0)) != head_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_26174]) ).
tcf(c_55009,plain,
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK4(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_14945]) ).
tcf(c_55015,plain,
( on_path(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK0)
| ~ on_path(sK4(sK0),sK0)
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) != sK4(sK0) ) ),
inference(instantiation,[status(thm)],[c_4239]) ).
tcf(c_60579,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( head_of(sK5(sK0)) != head_of(X0) )
| ~ edge(X0)
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_6050,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_6050,c_6220,c_6437,c_7211,c_10588,c_11516,c_15850,c_16432,c_20515,c_32698,c_32898,c_43782]) ).
tcf(c_60580,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(X0)
| ( head_of(sK5(sK0)) != head_of(X0) ) ),
inference(renaming,[status(thm)],[c_60579]) ).
tcf(c_60604,plain,
( sequential(sK5(sK0),sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK5(sK0)) ),
inference(equality_resolution,[status(thm)],[c_60580]) ).
tcf(c_60605,plain,
( sequential(sK5(sK0),sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_60604,c_2391]) ).
tcf(c_61081,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK0)
| ~ sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_60605,c_2607]) ).
tcf(c_61082,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_60605,c_76]) ).
tcf(c_61087,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK4(sK0)) ),
inference(superposition,[status(thm)],[c_60605,c_2763]) ).
tcf(c_61097,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ on_path(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK0)
| ~ sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK5(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_61081,c_2295]) ).
tcf(c_62352,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK5(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_61097,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_6220,c_6437,c_7211,c_7568,c_10588,c_11516,c_15850,c_16432,c_20515,c_26526,c_32698,c_32898,c_43782,c_55015,c_61087,c_61097]) ).
tcf(c_64924,plain,
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_61082,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_6220,c_6437,c_7211,c_10588,c_11516,c_15850,c_16432,c_21440,c_32698,c_32898,c_43782]) ).
tcf(c_64925,plain,
( ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_64924]) ).
tcf(c_64970,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK4(sK0)) != head_of(X1) )
| ( head_of(sK5(sK0)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_64925,c_41846]) ).
tcf(c_67585,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),X0)
| ( tail_of(sK4(sK0)) != tail_of(X0) )
| ~ edge(X0)
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_7908,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_6220,c_6437,c_7211,c_7908,c_10588,c_11516,c_15850,c_16432,c_20515,c_32698,c_32898,c_43782]) ).
tcf(c_67586,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),X0)
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(X0)
| ( tail_of(sK4(sK0)) != tail_of(X0) ) ),
inference(renaming,[status(thm)],[c_67585]) ).
tcf(c_67627,plain,
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK4(sK0))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK4(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK4(sK0)) ),
inference(equality_resolution,[status(thm)],[c_67586]) ).
tcf(c_67628,plain,
( sequential(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))),sK4(sK0))
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK4(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_67627,c_2392]) ).
tcf(c_68011,plain,
( ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK5(sK0) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) = sK4(sK0) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_67628,c_61087]) ).
tcf(c_88404,plain,
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( sK3(tail_of(sK4(sK0)),head_of(sK5(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_12831]) ).
tcf(c_89277,plain,
( ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK5(sK0)) != head_of(sK4(sK0)) )
| ( head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != head_of(sK4(sK0)) ) ),
inference(instantiation,[status(thm)],[c_32194]) ).
tcf(c_90938,plain,
head_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)),
inference(global_subsumption_just,[status(thm)],[c_64970,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2390,c_2668,c_6220,c_6437,c_7211,c_10588,c_11516,c_15604,c_15850,c_16251,c_16432,c_20515,c_26188,c_26527,c_32698,c_32898,c_43782,c_55009,c_62352,c_68011,c_88404,c_89277]) ).
tcf(c_90969,plain,
( ( head_of(sK5(sK0)) = tail_of(sK4(sK0)) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK4(sK0)) ) ),
inference(demodulation,[status(thm)],[c_7793,c_90938]) ).
tcf(c_91025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(sK5(sK0)) != head_of(X1) )
| ( tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_90938,c_63]) ).
tcf(c_91176,plain,
tail_of(sK3(tail_of(sK4(sK0)),head_of(sK5(sK0)))) = tail_of(sK4(sK0)),
inference(global_subsumption_just,[status(thm)],[c_90969,c_50,c_712,c_2287,c_2295,c_2313,c_2392,c_2391,c_2668,c_7211,c_10588,c_11516,c_16432,c_32698,c_32898,c_90969]) ).
tcf(c_92035,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK4(sK0)) != tail_of(X1) )
| ( head_of(sK5(sK0)) != head_of(X0) ) ),
inference(light_normalisation,[status(thm)],[c_91025,c_91176]) ).
tcf(c_92062,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(sK0),X1)
| ( tail_of(sK4(sK0)) != tail_of(X0) ) ),
inference(equality_resolution,[status(thm)],[c_92035]) ).
tcf(c_92120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(X1,X2,X0)
| ~ precedes(sK4(sK0),sK5(sK0),X0) ),
inference(equality_resolution,[status(thm)],[c_92062]) ).
tcf(c_92179,plain,
! [X0: $i,X1: $i] :
( ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK4(sK0),sK0)
| ~ shortest_path(X0,X1,sK0)
| ~ sequential(sK4(sK0),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_2496,c_92120]) ).
tcf(c_92182,plain,
! [X0: $i,X1: $i] : ~ shortest_path(X0,X1,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_92179,c_2295,c_2287,c_2313]) ).
tcf(c_92190,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_92182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA011+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 12:44:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 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
% 0.10/0.44 % Proving...
% 50.07/7.86 % SZS status Started for theBenchmark.p
% 50.07/7.86 % SZS status Theorem for theBenchmark.p
% 50.07/7.86
% 50.07/7.86 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 50.07/7.86
% 50.07/7.86 % ------ iProver source info
% 50.07/7.86
% 50.07/7.86 % git: date: 2026-07-19 20:42:38 +0200
% 50.07/7.86 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 50.07/7.86 % git: non_committed_changes: false
% 50.07/7.86
% 50.07/7.86 % ------ Parsing...
% 50.07/7.86 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 50.07/7.86
% 50.07/7.86 % ------ 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 %
% 50.07/7.86
% 50.07/7.86 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 50.07/7.86
% 50.07/7.86 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 50.07/7.86 % ------ Proving...
% 50.07/7.86 % ------ Problem Properties
% 50.07/7.86
% 50.07/7.86 %
% 50.07/7.86 % clauses 34
% 50.07/7.86 % conjectures 2
% 50.07/7.86 % EPR 12
% 50.07/7.86 % Horn 21
% 50.07/7.86 % unary 4
% 50.07/7.86 % binary 7
% 50.07/7.86 % lits 114
% 50.07/7.86 % lits eq 31
% 50.07/7.86 % fd_pure 0
% 50.07/7.86 % fd_pseudo 0
% 50.07/7.86 % fd_cond 0
% 50.07/7.86 % fd_pseudo_cond 5
% 50.07/7.86 % AC symbols 0
% 50.07/7.86
% 50.07/7.86 % ------ Schedule dynamic 5 is on
% 50.07/7.86
% 50.07/7.86 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 50.07/7.86
% 50.07/7.86
% 50.07/7.86 % ------
% 50.07/7.86 % Current options:
% 50.07/7.86 % ------
% 50.07/7.86
% 50.07/7.86
% 50.07/7.86 %
% 50.07/7.86
% 50.07/7.86 % ------ Proving...
% 50.07/7.86 %
% 50.07/7.86
% 50.07/7.86 % SZS status Theorem for theBenchmark.p
% 50.07/7.86
% 50.07/7.86 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 50.07/7.87
% 50.07/7.87
%------------------------------------------------------------------------------