%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA002+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 : n004.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 01:23:33 PM UTC 2026
% Result : Theorem 58.39s 25.07s
% Output : CNFRefutation 58.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 19
% Syntax : Number of formulae : 340 ( 41 unt; 0 def)
% Number of atoms : 1267 ( 473 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1542 ( 615 ~; 786 |; 114 &)
% ( 4 <=>; 18 =>; 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 : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 594 ( 0 sgn 571 !; 23 ?; 327 :)
% 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(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
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(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
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)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,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(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(flattening,[],[f22]) ).
fof(f24,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(f25,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(ennf_transformation,[],[f15]) ).
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(ennf_transformation,[],[f12]) ).
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(flattening,[],[f26]) ).
fof(f28,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(f29,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,[],[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,
! [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(f36,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,[],[f35]) ).
fof(f37,plain,
( complete
& shortest_path(sK1,sK2,sK0)
& ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f21]) ).
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(nnf_transformation,[],[f23]) ).
fof(f39,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,[],[f38]) ).
fof(f40,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))],[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,[],[f24]) ).
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,sK4(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f43]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sequential(sK5(X0),sK6(X0))
& on_path(sK6(X0),X0)
& on_path(sK5(X0),X0)
& ! [X5] : ~ triangle(sK5(X0),sK6(X0),X5) )
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X3,sK5(X0)),skolemize(X4,sK6(X0))],[f29]) ).
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(nnf_transformation,[],[f32]) ).
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(flattening,[],[f46]) ).
fof(f48,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,[],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f50,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(f51,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,[],[f50]) ).
fof(f52,plain,
complete,
inference(cnf_transformation,[],[f37]) ).
fof(f53,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f37]) ).
fof(f54,plain,
~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK3(X0,X1)) = X1
| tail_of(sK3(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
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,[],[f40]) ).
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,[],[f40]) ).
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,[],[f40]) ).
fof(f60,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f63,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f67,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f68,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,[],[f27]) ).
fof(f69,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f70,plain,
! [X2,X0,X1] :
( sequential(sK5(X0),sK6(X0))
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f71,plain,
! [X2,X0,X1] :
( on_path(sK6(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f72,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,[],[f45]) ).
fof(f73,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK5(X0),sK6(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f45]) ).
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,[],[f49]) ).
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,[],[f49]) ).
fof(f80,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f81,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f49]) ).
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,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f87,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,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,[],[f36]) ).
tcf(c_49,negated_conjecture,
~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f54]) ).
tcf(c_50,negated_conjecture,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f53]) ).
tcf(c_51,negated_conjecture,
complete,
inference(cnf_transformation,[],[f52]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_54,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_55,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_56,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_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( minus(length_of(X2),n1) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_64,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,[],[f68]) ).
tcf(c_65,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,[],[f67]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f69]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ path(X2,X3,X0)
| ~ triangle(sK5(X0),sK6(X0),X1) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK5(X2),X2)
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(sK6(X2),X2)
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(sK5(X2),sK6(X2))
| ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_71,plain,
! [X0: $i] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_72,plain,
! [X0: $i] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_73,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_74,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,[],[f81]) ).
tcf(c_75,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,[],[f80]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| sequential(X3,sK7(X2,X3,X4))
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( sequential(X3,X4)
| precedes(sK7(X2,X3,X4),X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X4,X3,X2)
| ~ sequential(X4,X3)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_86,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,[],[f89]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_51,c_52]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_110,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_86,c_83,c_82,c_86]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_75,c_80]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( precedes(X5,X4,X2)
| ~ sequential(X5,X3)
| ~ on_path(X5,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_112]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_51,c_57]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_114]) ).
tcf(c_117,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_56,c_51,c_56]) ).
tcf(c_118,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_117]) ).
tcf(c_119,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_55,c_51,c_55]) ).
tcf(c_120,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_119]) ).
tcf(c_121,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_54,c_51,c_54]) ).
tcf(c_122,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_121]) ).
tcf(c_151,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_110,c_82]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ sequential(X4,X1)
| ~ sequential(X2,X4)
| ~ sequential(X1,X2)
| ~ path(X5,X6,X0)
| ( X3 != X4 )
| ( sK6(X0) != X2 )
| ( sK5(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_151]) ).
tcf(c_616,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X0) = number_of_in(sequential_pairs,X0) )
| ~ sequential(X3,sK5(X0))
| ~ sequential(sK6(X0),X3)
| ~ path(X1,X2,X0)
| ~ sequential(sK5(X0),sK6(X0)) ),
inference(unflattening,[status(thm)],[c_615]) ).
tcf(c_628,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( number_of_in(triangles,X2) = number_of_in(sequential_pairs,X2) )
| ~ sequential(X3,sK5(X2))
| ~ sequential(sK6(X2),X3)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_616,c_70]) ).
tcf(c_772,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_60]) ).
tcf(c_773,plain,
path(sK1,sK2,sK0),
inference(unflattening,[status(thm)],[c_772]) ).
tcf(c_1658,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1660,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1664,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_or_equal(X0,X2)
| ~ less_or_equal(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1669,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = tail_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1672,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(X0,X2)
| ~ on_path(X1,X2)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1673,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X2)
| ~ sequential(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2353,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_2368,plain,
! [X0: $i,X1: $i] :
( on_path(X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2353,c_74]) ).
tcf(c_2381,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2353,c_75]) ).
tcf(c_2392,plain,
minus(length_of(sK0),n1) = number_of_in(sequential_pairs,sK0),
inference(superposition,[status(thm)],[c_2353,c_63]) ).
tcf(c_2446,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_2455,plain,
( on_path(sK5(sK0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2353,c_68]) ).
tcf(c_2464,plain,
( on_path(sK6(sK0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2353,c_69]) ).
tcf(c_2473,plain,
( sequential(sK5(sK0),sK6(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2353,c_70]) ).
tcf(c_2492,plain,
( ( head_of(sK5(sK0)) = tail_of(sK6(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2473,c_85]) ).
tcf(c_2493,plain,
( edge(sK6(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2473,c_83]) ).
tcf(c_2494,plain,
( edge(sK5(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2473,c_82]) ).
tcf(c_2513,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ edge(sK6(sK0))
| ( head_of(sK5(sK0)) != head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2492,c_71]) ).
tcf(c_2514,plain,
( vertex(head_of(sK5(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ edge(sK6(sK0)) ),
inference(superposition,[status(thm)],[c_2492,c_73]) ).
tcf(c_2521,plain,
( vertex(head_of(sK5(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_2514,c_2493,c_2514]) ).
tcf(c_2527,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK5(sK0)) != head_of(sK6(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_2513,c_2493,c_2513]) ).
tcf(c_2580,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK3(head_of(X0),X1)) = X1 )
| ( tail_of(sK3(head_of(X0),X1)) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_115]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(X0,sK7(sK0,X0,X1))
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2353,c_77]) ).
tcf(c_2673,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2353,c_78]) ).
tcf(c_2739,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| on_path(sK7(sK0,X0,X1),sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2673,c_2368]) ).
tcf(c_2853,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_2353,c_79]) ).
tcf(c_2866,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_or_equal(X0,X3)
| ~ less_or_equal(number_of_in(X1,X2),number_of_in(X1,graph))
| ( X3 != number_of_in(X1,graph) )
| ( X0 != number_of_in(X1,X2) ) ),
inference(instantiation,[status(thm)],[c_1664]) ).
tcf(c_2903,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_2853,c_2446]) ).
tcf(c_2962,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2903,c_2368,c_2381,c_2903]) ).
tcf(c_2968,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2853,c_2962]) ).
tcf(c_2992,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ sequential(sK6(sK0),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_2473,c_2968]) ).
tcf(c_3029,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ sequential(sK6(sK0),sK5(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_2992,c_2455,c_2464,c_2992]) ).
tcf(c_3196,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2353,c_113]) ).
tcf(c_3217,plain,
! [X0: $i] :
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(superposition,[status(thm)],[c_2353,c_628]) ).
tcf(c_3240,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),X0)) = head_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2521,c_118]) ).
tcf(c_3271,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK5(sK0)),X0)) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2521,c_120]) ).
tcf(c_3298,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2853,c_3196]) ).
tcf(c_3341,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_or_equal(X1,number_of_in(X0,graph))
| ~ less_or_equal(number_of_in(X0,X2),number_of_in(X0,graph))
| ( X1 != number_of_in(X0,X2) )
| ( number_of_in(X0,graph) != number_of_in(X0,graph) ) ),
inference(instantiation,[status(thm)],[c_2866]) ).
tcf(c_3342,plain,
! [X0: $i] : number_of_in(X0,graph) = number_of_in(X0,graph),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_3382,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK5(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK5(sK0)),X0)) = head_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2521,c_122]) ).
tcf(c_3414,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_2609,c_3298]) ).
tcf(c_3581,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_3755,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_3581,c_75]) ).
tcf(c_3828,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = head_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(X0),head_of(sK5(sK0)))) = head_of(X0) )
| ( tail_of(sK3(head_of(X0),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2521,c_2580]) ).
tcf(c_3987,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3414,c_2368,c_2739,c_3414]) ).
tcf(c_3988,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_3987]) ).
tcf(c_4000,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| precedes(X3,sK7(sK0,X0,X1),sK0)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X3,X2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_3988,c_3196]) ).
tcf(c_4109,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_4136,plain,
( sequential(sK5(sK0),sK6(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_3581,c_70]) ).
tcf(c_4511,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| precedes(X1,sK7(sK0,sK6(sK0),X0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ on_path(X1,sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0) ),
inference(superposition,[status(thm)],[c_2473,c_4000]) ).
tcf(c_5037,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3 = number_of_in(X0,X1) )
| ( X3 != X2 )
| ( number_of_in(X0,X1) != X2 ) ),
inference(instantiation,[status(thm)],[c_1660]) ).
tcf(c_5128,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| sequential(X0,sK7(sK0,X0,X1))
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_3581,c_77]) ).
tcf(c_5553,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| precedes(sK7(sK0,X0,X1),X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_3581,c_78]) ).
tcf(c_6688,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_3581,c_79]) ).
tcf(c_7453,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( X4 = number_of_in(X0,X1) )
| ( X4 != number_of_in(X2,X3) )
| ( number_of_in(X0,X1) != number_of_in(X2,X3) ) ),
inference(instantiation,[status(thm)],[c_5037]) ).
tcf(c_8600,plain,
! [X0: $i,X1: $i] :
( ( minus(length_of(sK0),n1) = number_of_in(X0,X1) )
| ( number_of_in(X0,X1) != number_of_in(sequential_pairs,sK0) )
| ( minus(length_of(sK0),n1) != number_of_in(sequential_pairs,sK0) ) ),
inference(instantiation,[status(thm)],[c_7453]) ).
tcf(c_8665,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_3581,c_113]) ).
tcf(c_8778,plain,
( ( minus(length_of(sK0),n1) = number_of_in(triangles,sK0) )
| ( number_of_in(triangles,sK0) != number_of_in(sequential_pairs,sK0) )
| ( minus(length_of(sK0),n1) != number_of_in(sequential_pairs,sK0) ) ),
inference(instantiation,[status(thm)],[c_8600]) ).
tcf(c_8808,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = tail_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_3271]) ).
tcf(c_9552,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,X1,sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_6688,c_8665]) ).
tcf(c_10056,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(X2,sK6(sK0),sK0)
| ~ on_path(X2,sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ sequential(X2,sK6(sK0))
| ~ path(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_10074,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0)
| ~ on_path(sK7(sK0,X0,X1),sK0) ),
inference(superposition,[status(thm)],[c_5128,c_9552]) ).
tcf(c_10100,plain,
! [X0: $i] :
( on_path(X0,sK0)
| ~ on_path(sK5(sK0),sK0)
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1672]) ).
tcf(c_11260,plain,
( ( head_of(sK5(sK0)) = head_of(sK6(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2493,c_3828]) ).
tcf(c_11320,plain,
number_of_in(triangles,graph) = number_of_in(triangles,graph),
inference(instantiation,[status(thm)],[c_3342]) ).
tcf(c_11491,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = tail_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = head_of(sK5(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_3382]) ).
tcf(c_11617,plain,
( ~ edge(sK6(sK0))
| ( head_of(sK6(sK0)) != tail_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_11618,plain,
( vertex(tail_of(sK6(sK0)))
| ~ edge(sK6(sK0)) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_11619,plain,
( vertex(head_of(sK6(sK0)))
| ~ edge(sK6(sK0)) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_12099,plain,
( ~ edge(sK5(sK0))
| ( head_of(sK5(sK0)) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_12100,plain,
( vertex(tail_of(sK5(sK0)))
| ~ edge(sK5(sK0)) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_12325,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_81]) ).
tcf(c_12788,plain,
sK5(sK0) = sK5(sK0),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_12791,plain,
! [X0: $i,X1: $i] :
( precedes(sK5(sK0),sK6(sK0),sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ path(X0,X1,sK0)
| ~ sequential(sK5(sK0),sK6(sK0)) ),
inference(instantiation,[status(thm)],[c_10056]) ).
tcf(c_12831,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ precedes(X0,X1,sK0)
| ~ sequential(X2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_10074,c_3988]) ).
tcf(c_12832,plain,
! [X0: $i,X1: $i,X2: $i] :
( sequential(X0,X1)
| precedes(X2,sK7(sK0,X0,X1),sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(renaming,[status(thm)],[c_12831]) ).
tcf(c_12844,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X1)
| precedes(X3,sK7(sK0,X0,X1),sK0)
| ~ on_path(X3,sK0)
| ~ on_path(X2,sK0)
| ~ sequential(X3,X2)
| ~ sequential(X2,X0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_12832,c_8665]) ).
tcf(c_12940,plain,
( less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph))
| ~ less_or_equal(number_of_in(triangles,sK0),number_of_in(triangles,graph))
| ( number_of_in(triangles,graph) != number_of_in(triangles,graph) )
| ( minus(length_of(sK0),n1) != number_of_in(triangles,sK0) ) ),
inference(instantiation,[status(thm)],[c_3341]) ).
tcf(c_12958,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_11260,c_2527,c_11260]) ).
tcf(c_12959,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_12958]) ).
tcf(c_12973,plain,
( vertex(head_of(sK6(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK6(sK0)),head_of(sK5(sK0)))) ),
inference(superposition,[status(thm)],[c_12959,c_73]) ).
tcf(c_13015,plain,
( vertex(head_of(sK6(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_12973,c_2493,c_11619]) ).
tcf(c_13023,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK6(sK0)),X0)) = head_of(sK6(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_13015,c_122]) ).
tcf(c_13024,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_13015,c_120]) ).
tcf(c_13027,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = head_of(sK6(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_13015,c_115]) ).
tcf(c_13230,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = tail_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_13024]) ).
tcf(c_13276,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = tail_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = head_of(sK6(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_13023]) ).
tcf(c_13364,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = tail_of(X0) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(X0))) = head_of(sK6(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_13027]) ).
tcf(c_13911,plain,
! [X0: $i] : less_or_equal(number_of_in(triangles,X0),number_of_in(triangles,graph)),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_14026,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2494,c_8808]) ).
tcf(c_14180,plain,
( ( head_of(sK6(sK0)) = tail_of(sK6(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) = tail_of(sK6(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) = tail_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2493,c_13230]) ).
tcf(c_14181,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2494,c_13230]) ).
tcf(c_14915,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ vertex(tail_of(sK5(sK0)))
| ~ vertex(head_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_14925,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK5(sK0)) != X0 )
| ( head_of(sK5(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1660]) ).
tcf(c_15272,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_2494,c_11491]) ).
tcf(c_15373,plain,
( ( head_of(sK5(sK0)) = head_of(sK6(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_13015,c_3240]) ).
tcf(c_15406,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| precedes(X1,sK7(sK0,sK6(sK0),X0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ on_path(X1,sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0) ),
inference(superposition,[status(thm)],[c_4136,c_12844]) ).
tcf(c_15881,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2494,c_13276]) ).
tcf(c_16067,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2494,c_13364]) ).
tcf(c_17004,plain,
( ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_14026,c_2494,c_12099,c_14026]) ).
tcf(c_17005,plain,
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_17004]) ).
tcf(c_17018,plain,
( vertex(tail_of(sK5(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) ),
inference(superposition,[status(thm)],[c_17005,c_73]) ).
tcf(c_17070,plain,
! [X0: $i,X1: $i] :
( ( sK5(sK0) = X1 )
| ( X1 != X0 )
| ( sK5(sK0) != X0 ) ),
inference(instantiation,[status(thm)],[c_1660]) ).
tcf(c_17072,plain,
( vertex(tail_of(sK5(sK0)))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_17018,c_2494,c_12100]) ).
tcf(c_18644,plain,
less_or_equal(number_of_in(triangles,sK0),number_of_in(triangles,graph)),
inference(instantiation,[status(thm)],[c_13911]) ).
tcf(c_18808,plain,
! [X0: $i] :
( edge(sK3(X0,tail_of(sK5(sK0))))
| ( X0 = tail_of(sK5(sK0)) )
| ~ vertex(X0)
| ~ vertex(tail_of(sK5(sK0))) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_18856,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| precedes(X1,sK7(sK0,sK6(sK0),X0),sK0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0)
| ~ on_path(X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_15406,c_49,c_2392,c_2455,c_4511,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_18857,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| precedes(X1,sK7(sK0,sK6(sK0),X0),sK0)
| ~ on_path(X1,sK0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0) ),
inference(renaming,[status(thm)],[c_18856]) ).
tcf(c_18880,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| ~ on_path(X1,sK0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0)
| ~ precedes(sK7(sK0,sK6(sK0),X0),X1,sK0) ),
inference(superposition,[status(thm)],[c_18857,c_4109]) ).
tcf(c_18994,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) = tail_of(sK6(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) = tail_of(sK6(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_14180,c_49,c_2392,c_2493,c_8778,c_11320,c_11617,c_12940,c_14180,c_18644]) ).
tcf(c_19007,plain,
( vertex(tail_of(sK6(sK0)))
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) = tail_of(sK6(sK0)) )
| ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK6(sK0)))) ),
inference(superposition,[status(thm)],[c_18994,c_73]) ).
tcf(c_19039,plain,
vertex(tail_of(sK6(sK0))),
inference(global_subsumption_just,[status(thm)],[c_19007,c_49,c_2392,c_2493,c_8778,c_11320,c_11618,c_12940,c_18644]) ).
tcf(c_19054,plain,
! [X0: $i] :
( ( tail_of(sK6(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK6(sK0)),X0)) = tail_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK6(sK0)),X0)) = tail_of(sK6(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_19039,c_118]) ).
tcf(c_19383,plain,
sK6(sK0) = sK6(sK0),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_19398,plain,
! [X0: $i] :
( ( sK5(sK0) = X0 )
| ( X0 != sK5(sK0) )
| ( sK5(sK0) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_17070]) ).
tcf(c_19464,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK5(sK0)) != tail_of(sK6(sK0)) )
| ( head_of(sK5(sK0)) != tail_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_14925]) ).
tcf(c_20027,plain,
! [X0: $i,X1: $i] :
( sequential(sK6(sK0),X0)
| ~ sequential(X1,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0)
| ~ precedes(sK7(sK0,sK6(sK0),X0),X1,sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18880,c_3755]) ).
tcf(c_20041,plain,
! [X0: $i] :
( sequential(sK6(sK0),X0)
| ~ sequential(X0,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0) ),
inference(superposition,[status(thm)],[c_5553,c_20027]) ).
tcf(c_20142,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_14181,c_49,c_2392,c_8778,c_11320,c_12940,c_14181,c_18644]) ).
tcf(c_20143,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_20142]) ).
tcf(c_20225,plain,
! [X0: $i] :
( ~ precedes(sK6(sK0),X0,sK0)
| ~ sequential(X0,sK5(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_20041,c_49,c_2392,c_3217,c_8778,c_11320,c_12940,c_18644,c_20041]) ).
tcf(c_20226,plain,
! [X0: $i] :
( ~ sequential(X0,sK5(sK0))
| ~ precedes(sK6(sK0),X0,sK0) ),
inference(renaming,[status(thm)],[c_20225]) ).
tcf(c_20232,plain,
! [X0: $i] :
( ~ on_path(X0,sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(superposition,[status(thm)],[c_6688,c_20226]) ).
tcf(c_21999,plain,
! [X0: $i] :
( ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(global_subsumption_just,[status(thm)],[c_20232,c_49,c_2392,c_3217,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_22549,plain,
( ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_15272,c_49,c_2392,c_2494,c_2521,c_8778,c_11320,c_12099,c_12940,c_14915,c_17072,c_18644]) ).
tcf(c_22559,plain,
( vertex(tail_of(sK5(sK0)))
| ( head_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) ),
inference(superposition,[status(thm)],[c_22549,c_72]) ).
tcf(c_22587,plain,
vertex(tail_of(sK5(sK0))),
inference(global_subsumption_just,[status(thm)],[c_22559,c_49,c_2392,c_8778,c_11320,c_12940,c_17072,c_18644]) ).
tcf(c_23762,plain,
( ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_15373,c_49,c_2392,c_2527,c_8778,c_11320,c_12940,c_15373,c_18644]) ).
tcf(c_23776,plain,
( vertex(head_of(sK5(sK0)))
| ( head_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) ),
inference(superposition,[status(thm)],[c_23762,c_73]) ).
tcf(c_23814,plain,
vertex(head_of(sK5(sK0))),
inference(global_subsumption_just,[status(thm)],[c_23776,c_49,c_2392,c_2521,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_23820,plain,
( ( head_of(sK5(sK0)) = tail_of(sK6(sK0)) )
| ( tail_of(sK3(tail_of(sK6(sK0)),head_of(sK5(sK0)))) = tail_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK6(sK0)),head_of(sK5(sK0)))) = tail_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_23814,c_19054]) ).
tcf(c_23835,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = X0 )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = head_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_23814,c_115]) ).
tcf(c_24457,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_22587,c_23835]) ).
tcf(c_25119,plain,
( precedes(sK5(sK0),sK6(sK0),sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ path(sK1,sK2,sK0)
| ~ sequential(sK5(sK0),sK6(sK0)) ),
inference(instantiation,[status(thm)],[c_12791]) ).
tcf(c_27115,plain,
( ( tail_of(sK5(sK0)) = tail_of(sK6(sK0)) )
| ( sK5(sK0) != sK6(sK0) ) ),
inference(instantiation,[status(thm)],[c_1669]) ).
tcf(c_27431,plain,
( sequential(sK6(sK0),sK5(sK0))
| ( sK6(sK0) = sK5(sK0) )
| ~ edge(sK6(sK0))
| ~ edge(sK5(sK0))
| ( head_of(sK6(sK0)) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_12325]) ).
tcf(c_29167,plain,
( edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ~ vertex(tail_of(sK5(sK0)))
| ~ vertex(head_of(sK6(sK0))) ),
inference(instantiation,[status(thm)],[c_18808]) ).
tcf(c_44465,plain,
head_of(sK6(sK0)) = head_of(sK6(sK0)),
inference(instantiation,[status(thm)],[c_1658]) ).
tcf(c_49392,plain,
( ( sK5(sK0) = sK6(sK0) )
| ( sK6(sK0) != sK5(sK0) )
| ( sK5(sK0) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_19398]) ).
tcf(c_51118,plain,
head_of(sK5(sK0)) = tail_of(sK6(sK0)),
inference(global_subsumption_just,[status(thm)],[c_23820,c_49,c_2392,c_2492,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_51204,plain,
( ~ edge(sK6(sK0))
| ( head_of(sK5(sK0)) != head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_51118,c_71]) ).
tcf(c_51976,plain,
head_of(sK5(sK0)) != head_of(sK6(sK0)),
inference(global_subsumption_just,[status(thm)],[c_51204,c_49,c_2392,c_2527,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_66017,plain,
( on_path(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK0)
| ~ on_path(sK5(sK0),sK0)
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_10100]) ).
tcf(c_81069,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_50,c_60]) ).
tcf(c_81133,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_50,c_65]) ).
tcf(c_81151,plain,
( on_path(sK6(sK0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_81069,c_69]) ).
tcf(c_81160,plain,
( sequential(sK5(sK0),sK6(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_81069,c_70]) ).
tcf(c_81178,plain,
on_path(sK6(sK0),sK0),
inference(global_subsumption_just,[status(thm)],[c_81151,c_49,c_2392,c_2464,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_81180,plain,
sequential(sK5(sK0),sK6(sK0)),
inference(global_subsumption_just,[status(thm)],[c_81160,c_49,c_2392,c_2473,c_8778,c_11320,c_12940,c_18644]) ).
tcf(c_81182,plain,
head_of(sK5(sK0)) = tail_of(sK6(sK0)),
inference(superposition,[status(thm)],[c_81180,c_85]) ).
tcf(c_81183,plain,
edge(sK6(sK0)),
inference(superposition,[status(thm)],[c_81180,c_83]) ).
tcf(c_81184,plain,
edge(sK5(sK0)),
inference(superposition,[status(thm)],[c_81180,c_82]) ).
tcf(c_81194,plain,
( vertex(head_of(sK5(sK0)))
| ~ edge(sK6(sK0)) ),
inference(superposition,[status(thm)],[c_81182,c_73]) ).
tcf(c_81195,plain,
vertex(head_of(sK5(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_81194,c_81183]) ).
tcf(c_81335,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_81069,c_79]) ).
tcf(c_81386,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_81335,c_81133]) ).
tcf(c_81409,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_81386,c_2962]) ).
tcf(c_81415,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_81335,c_81409]) ).
tcf(c_81475,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = X0 )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = X0 )
| ( tail_of(sK3(head_of(sK5(sK0)),X0)) = head_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_81195,c_115]) ).
tcf(c_81772,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = head_of(X0) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(X0))) = head_of(X0) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(X0))) = head_of(sK5(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_81475]) ).
tcf(c_81773,plain,
! [X0: $i] :
( ( head_of(sK5(sK0)) = tail_of(X0) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = tail_of(X0) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(X0))) = head_of(sK5(sK0)) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_73,c_81475]) ).
tcf(c_81817,plain,
! [X0: $i] :
( ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) )
| ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(superposition,[status(thm)],[c_81069,c_628]) ).
tcf(c_81914,plain,
! [X0: $i] :
( ~ sequential(sK6(sK0),X0)
| ~ sequential(X0,sK5(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_81817,c_21999]) ).
tcf(c_81915,plain,
! [X0: $i] :
( ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(renaming,[status(thm)],[c_81914]) ).
tcf(c_82155,plain,
( ( head_of(sK5(sK0)) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_81183,c_81772]) ).
tcf(c_82158,plain,
( ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82155,c_51976]) ).
tcf(c_82269,plain,
( vertex(head_of(sK6(sK0)))
| ( tail_of(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK5(sK0)),head_of(sK6(sK0)))) ),
inference(superposition,[status(thm)],[c_82158,c_73]) ).
tcf(c_82290,plain,
vertex(head_of(sK6(sK0))),
inference(global_subsumption_just,[status(thm)],[c_82269,c_49,c_2392,c_8778,c_11320,c_12940,c_13015,c_18644]) ).
tcf(c_82293,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ( head_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_82290,c_120]) ).
tcf(c_82296,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = X0 )
| ( tail_of(sK3(head_of(sK6(sK0)),X0)) = head_of(sK6(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_82290,c_115]) ).
tcf(c_82543,plain,
( ( head_of(sK5(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_81184,c_81773]) ).
tcf(c_82770,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK5(sK0),sK6(sK0))
| ( X1 != sK6(sK0) )
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1673]) ).
tcf(c_83144,plain,
( ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_82543,c_49,c_2392,c_2494,c_8778,c_11320,c_12099,c_12940,c_18644,c_24457]) ).
tcf(c_83145,plain,
( ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_83144]) ).
tcf(c_83156,plain,
( vertex(tail_of(sK5(sK0)))
| ( tail_of(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) = head_of(sK5(sK0)) )
| ~ edge(sK3(head_of(sK5(sK0)),tail_of(sK5(sK0)))) ),
inference(superposition,[status(thm)],[c_83145,c_73]) ).
tcf(c_83198,plain,
vertex(tail_of(sK5(sK0))),
inference(global_subsumption_just,[status(thm)],[c_83156,c_49,c_2392,c_8778,c_11320,c_12940,c_17072,c_18644]) ).
tcf(c_83396,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_83198,c_82293]) ).
tcf(c_84474,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK6(sK0)) = head_of(X1) )
| ( head_of(X1) != X0 )
| ( head_of(sK6(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1660]) ).
tcf(c_84594,plain,
( ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_83396,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_18644,c_19464,c_20143,c_27115,c_27431,c_49392]) ).
tcf(c_84595,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_84594]) ).
tcf(c_84601,plain,
! [X0: $i] :
( sequential(X0,sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = X0 )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ~ edge(X0)
| ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( tail_of(sK5(sK0)) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_84595,c_81]) ).
tcf(c_85823,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_83198,c_82296]) ).
tcf(c_87141,plain,
! [X0: $i] :
( sequential(X0,sK6(sK0))
| ~ sequential(sK5(sK0),sK6(sK0))
| ( X0 != sK5(sK0) )
| ( sK6(sK0) != sK6(sK0) ) ),
inference(instantiation,[status(thm)],[c_82770]) ).
tcf(c_88761,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_85823,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_16067,c_18644,c_19464,c_27115,c_27431,c_49392]) ).
tcf(c_88762,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) ) ),
inference(renaming,[status(thm)],[c_88761]) ).
tcf(c_88772,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_88762,c_71]) ).
tcf(c_90279,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = head_of(X0) )
| ( head_of(X0) != head_of(sK6(sK0)) )
| ( head_of(sK6(sK0)) != head_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_84474]) ).
tcf(c_90768,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(X1,X2,sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( tail_of(X0) != tail_of(sK5(sK0)) )
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_95699,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_88772,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_13015,c_17072,c_18644,c_19464,c_27115,c_27431,c_29167,c_49392,c_88772]) ).
tcf(c_100860,plain,
! [X0: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( tail_of(X0) != tail_of(sK5(sK0)) )
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(instantiation,[status(thm)],[c_90768]) ).
tcf(c_114516,plain,
( ( head_of(sK6(sK0)) = head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) )
| ( head_of(sK6(sK0)) != head_of(sK6(sK0)) )
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) != head_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_90279]) ).
tcf(c_122524,plain,
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( head_of(sK6(sK0)) != head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) )
| ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_100860]) ).
tcf(c_124410,plain,
( sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK6(sK0))
| ~ sequential(sK5(sK0),sK6(sK0))
| ( sK6(sK0) != sK6(sK0) )
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_87141]) ).
tcf(c_124907,plain,
head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = tail_of(sK5(sK0)),
inference(global_subsumption_just,[status(thm)],[c_84601,c_50,c_49,c_773,c_2392,c_2455,c_2464,c_2473,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_14181,c_15881,c_18644,c_19464,c_25119,c_27115,c_27431,c_44465,c_49392,c_114516,c_122524]) ).
tcf(c_124911,plain,
( ( tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)) )
| ( tail_of(sK5(sK0)) != tail_of(sK5(sK0)) ) ),
inference(demodulation,[status(thm)],[c_95699,c_124907]) ).
tcf(c_124916,plain,
tail_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) = head_of(sK6(sK0)),
inference(equality_resolution_simp,[status(thm)],[c_124911]) ).
tcf(c_124939,plain,
! [X0: $i] :
( sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),X0)
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = X0 )
| ~ edge(X0)
| ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( tail_of(sK5(sK0)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_124907,c_81]) ).
tcf(c_125105,plain,
! [X0: $i] :
( sequential(X0,sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = X0 )
| ~ edge(X0)
| ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_124916,c_81]) ).
tcf(c_125121,plain,
( ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( head_of(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0)))) != head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_124916,c_71]) ).
tcf(c_125123,plain,
( ~ edge(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( head_of(sK6(sK0)) != tail_of(sK5(sK0)) ) ),
inference(light_normalisation,[status(thm)],[c_125121,c_124907]) ).
tcf(c_125178,plain,
head_of(sK6(sK0)) != tail_of(sK5(sK0)),
inference(global_subsumption_just,[status(thm)],[c_125123,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_18644,c_19464,c_27115,c_27431,c_49392]) ).
tcf(c_126908,plain,
! [X0: $i] :
( sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),X0)
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = X0 )
| ~ edge(X0)
| ( tail_of(sK5(sK0)) != tail_of(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_124939,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_13015,c_17072,c_18644,c_19464,c_27115,c_27431,c_29167,c_49392,c_124939]) ).
tcf(c_126938,plain,
( sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK5(sK0))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK5(sK0) )
| ~ edge(sK5(sK0)) ),
inference(equality_resolution,[status(thm)],[c_126908]) ).
tcf(c_126939,plain,
( sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK5(sK0))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK5(sK0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126938,c_81184]) ).
tcf(c_127093,plain,
! [X0: $i] :
( sequential(X0,sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = X0 )
| ~ edge(X0)
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(global_subsumption_just,[status(thm)],[c_125105,c_49,c_2392,c_2494,c_2493,c_2492,c_3029,c_8778,c_11320,c_12099,c_12788,c_12940,c_13015,c_17072,c_18644,c_19464,c_27115,c_27431,c_29167,c_49392,c_125105]) ).
tcf(c_127110,plain,
( sequential(sK6(sK0),sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0) )
| ~ edge(sK6(sK0)) ),
inference(equality_resolution,[status(thm)],[c_127093]) ).
tcf(c_127111,plain,
( sequential(sK6(sK0),sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))))
| ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_127110,c_81183]) ).
tcf(c_127495,plain,
( ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0) )
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK0)
| ~ sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK6(sK0)) ),
inference(superposition,[status(thm)],[c_127111,c_81415]) ).
tcf(c_127501,plain,
( ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0) )
| ~ sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_127111,c_81915]) ).
tcf(c_127505,plain,
( ( sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0) )
| ~ on_path(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK0)
| ~ sequential(sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))),sK6(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_127495,c_81178]) ).
tcf(c_127570,plain,
sK3(head_of(sK6(sK0)),tail_of(sK5(sK0))) = sK6(sK0),
inference(global_subsumption_just,[status(thm)],[c_127501,c_49,c_2392,c_2455,c_2473,c_8778,c_11320,c_12940,c_18644,c_19383,c_66017,c_124410,c_126939,c_127501,c_127505]) ).
tcf(c_127579,plain,
head_of(sK6(sK0)) = tail_of(sK5(sK0)),
inference(demodulation,[status(thm)],[c_124907,c_127570]) ).
tcf(c_127580,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_127579,c_125178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.40 % Computer : n004.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Wed Sep 23 12:42:05 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.45 Running first-order theorem proving
% 0.11/10.45 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
% 0.11/10.46
% 0.11/10.46 % ======== iProver multi-core TPTP/SMT =========
% 0.11/10.46
% 0.11/10.46 % Detected problem language: tptp
% 0.11/10.47 % Proving...
% 58.39/25.07 % SZS status Started for theBenchmark.p
% 58.39/25.07 % SZS status Theorem for theBenchmark.p
% 58.39/25.07
% 58.39/25.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 58.39/25.07
% 58.39/25.07 % ------ iProver source info
% 58.39/25.07
% 58.39/25.07 % git: date: 2026-07-19 20:42:38 +0200
% 58.39/25.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 58.39/25.07 % git: non_committed_changes: false
% 58.39/25.07
% 58.39/25.07 % ------ Parsing...
% 58.39/25.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 58.39/25.07
% 58.39/25.07 % ------ 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 %
% 58.39/25.07
% 58.39/25.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 58.39/25.07
% 58.39/25.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 58.39/25.07 % ------ Proving...
% 58.39/25.07 % ------ Problem Properties
% 58.39/25.07
% 58.39/25.07 %
% 58.39/25.07 % clauses 36
% 58.39/25.07 % conjectures 2
% 58.39/25.07 % EPR 12
% 58.39/25.07 % Horn 23
% 58.39/25.07 % unary 5
% 58.39/25.07 % binary 8
% 58.39/25.07 % lits 117
% 58.39/25.07 % lits eq 31
% 58.39/25.07 % fd_pure 0
% 58.39/25.07 % fd_pseudo 0
% 58.39/25.07 % fd_cond 0
% 58.39/25.07 % fd_pseudo_cond 5
% 58.39/25.07 % AC symbols 0
% 58.39/25.07
% 58.39/25.07 % ------ Schedule dynamic 5 is on
% 58.39/25.07
% 58.39/25.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 58.39/25.07
% 58.39/25.07
% 58.39/25.07 % ------
% 58.39/25.07 % Current options:
% 58.39/25.07 % ------
% 58.39/25.07
% 58.39/25.07
% 58.39/25.07 %
% 58.39/25.07
% 58.39/25.07 % ------ Proving...
% 58.39/25.07 % Proof_search_loop: time out after: 2384 full_loop iterations
% 58.39/25.07
% 58.39/25.07 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 58.39/25.07
% 58.39/25.07
% 58.39/25.07 % ------
% 58.39/25.07 % Current options:
% 58.39/25.07 % ------
% 58.39/25.07
% 58.39/25.07
% 58.39/25.07 %
% 58.39/25.07
% 58.39/25.07 % ------ Proving...
% 58.39/25.07 %
% 58.39/25.07
% 58.39/25.07 % SZS status Theorem for theBenchmark.p
% 58.39/25.07
% 58.39/25.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 58.39/25.07
% 58.39/25.07
%------------------------------------------------------------------------------