%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA008+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:23:34 PM UTC 2026
% Result : Theorem 31.75s 5.41s
% Output : CNFRefutation 31.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of formulae : 240 ( 34 unt; 0 def)
% Number of atoms : 937 ( 380 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1130 ( 433 ~; 559 |; 114 &)
% ( 4 <=>; 15 =>; 0 <=; 5 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 420 ( 0 sgn 393 !; 27 ?; 191 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',no_loops) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',edge_ends_are_vertices) ).
fof(f3,axiom,
( complete
=> ! [X0,X1] :
( ( X0 != X1
& vertex(X1)
& vertex(X0) )
=> ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',complete_properties) ).
fof(f8,axiom,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',sequential_defn) ).
fof(f9,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_defn) ).
fof(f10,axiom,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',precedes_properties) ).
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X5) = head_of(X3)
& tail_of(X5) = tail_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_properties) ).
fof(f13,axiom,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,conjecture,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f21,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] : ~ triangle(X2,X3,X5) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
( complete
& ? [X0,X1,X2,X3,X4] :
( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4)
& ! [X5] : ~ triangle(X2,X3,X5) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f24,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ 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(f26,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(f27,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,[],[f26]) ).
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(ennf_transformation,[],[f12]) ).
fof(f29,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,[],[f28]) ).
fof(f30,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(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] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f34,plain,
! [X0] :
( ~ edge(X0)
| ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f35,plain,
( complete
& sequential(sK2,sK3)
& precedes(sK2,sK3,sK4)
& shortest_path(sK0,sK1,sK4)
& ! [X5] : ~ triangle(sK2,sK3,X5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f22]) ).
fof(f36,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(nnf_transformation,[],[f24]) ).
fof(f37,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
| ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& ( tail_of(X2) != X1
| head_of(X2) != X0
| tail_of(X2) != X0
| head_of(X2) != X1 )
& edge(X2) ) ) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ( ( ( tail_of(sK5(X0,X1)) = X1
& head_of(sK5(X0,X1)) = X0 )
| ( tail_of(sK5(X0,X1)) = X0
& head_of(sK5(X0,X1)) = X1 ) )
& ( tail_of(sK5(X0,X1)) != X1
| head_of(sK5(X0,X1)) != X0
| tail_of(sK5(X0,X1)) != X0
| head_of(sK5(X0,X1)) != X1 )
& edge(sK5(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f37]) ).
fof(f39,plain,
! [X0,X1,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,[],[f25]) ).
fof(f40,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,[],[f39]) ).
fof(f41,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,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ! [X3,X4] :
( ~ precedes(X3,X4,X0)
| ( ( sequential(X3,X4)
| ( precedes(sK6(X0,X3,X4),X4,X0)
& sequential(X3,sK6(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,[sK6]),skolemize(X6,sK6(X0,X3,X4))],[f41]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f45,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,[],[f30]) ).
fof(f46,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,[],[f45]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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,sK7(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK7(X0,X1,X2))) )
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f47]) ).
fof(f49,plain,
complete,
inference(cnf_transformation,[],[f35]) ).
fof(f50,plain,
sequential(sK2,sK3),
inference(cnf_transformation,[],[f35]) ).
fof(f51,plain,
precedes(sK2,sK3,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f52,plain,
shortest_path(sK0,sK1,sK4),
inference(cnf_transformation,[],[f35]) ).
fof(f53,plain,
! [X5] : ~ triangle(sK2,sK3,X5),
inference(cnf_transformation,[],[f35]) ).
fof(f54,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK5(X0,X1)) = X1
| tail_of(sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK5(X0,X1)) = X0
| tail_of(sK5(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f38]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK5(X0,X1)) = X1
| head_of(sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK5(X0,X1)) = X0
| head_of(sK5(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f38]) ).
fof(f59,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK5(X0,X1)) ),
inference(cnf_transformation,[],[f38]) ).
fof(f62,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) ),
inference(cnf_transformation,[],[f42]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f64,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X3,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f66,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,[],[f27]) ).
fof(f67,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f68,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f44]) ).
fof(f69,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f70,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f71,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f72,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f29]) ).
fof(f73,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,[],[f29]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f48]) ).
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(f80,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f82,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f83,plain,
! [X1] : ~ sequential(X1,X1),
inference(equality_resolution,[],[f68]) ).
tcf(c_49,negated_conjecture,
! [X0: $i] : ~ triangle(sK2,sK3,X0),
inference(cnf_transformation,[],[f53]) ).
tcf(c_50,negated_conjecture,
shortest_path(sK0,sK1,sK4),
inference(cnf_transformation,[],[f52]) ).
tcf(c_51,negated_conjecture,
precedes(sK2,sK3,sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,negated_conjecture,
sequential(sK2,sK3),
inference(cnf_transformation,[],[f50]) ).
tcf(c_53,negated_conjecture,
complete,
inference(cnf_transformation,[],[f49]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X0,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( on_path(X1,X2)
| ~ path(X3,X4,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ~ sequential(X3,X1)
| ~ sequential(X3,X0)
| ~ path(X4,X5,X2)
| ~ precedes(X3,X1,X2)
| ~ precedes(X0,X1,X2) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X3,X4,X2)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ sequential(X3,X4)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_70,plain,
! [X0: $i] : ~ sequential(X0,X0),
inference(cnf_transformation,[],[f83]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_72,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,[],[f73]) ).
tcf(c_73,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,[],[f72]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_79,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_80,plain,
! [X0: $i] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_81,plain,
! [X0: $i] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_82,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_83,plain,
~ sequential(sK2,sK2),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_86,plain,
( vertex(tail_of(sK2))
| ~ edge(sK2) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_87,plain,
( vertex(head_of(sK2))
| ~ edge(sK2) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_88,plain,
( ~ edge(sK2)
| ( head_of(sK2) != tail_of(sK2) ) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_54,c_53,c_54]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( edge(sK5(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_98]) ).
tcf(c_101,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_79,c_69,c_68,c_79]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_53,c_59]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_53,c_58]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X0 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_108]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_53,c_57]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_110]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_53,c_56]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK5(X0,X1)) = X1 )
| ( head_of(sK5(X0,X1)) = X0 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_112]) ).
tcf(c_136,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_101,c_68]) ).
tcf(c_549,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ sequential(X3,X1)
| ~ sequential(X2,X3)
| ~ sequential(X1,X2)
| ( X3 != sK3 )
| ( X2 != sK2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_136]) ).
tcf(c_550,plain,
! [X0: $i] :
( ~ sequential(sK2,sK3)
| ~ sequential(sK3,X0)
| ~ sequential(X0,sK2) ),
inference(unflattening,[status(thm)],[c_549]) ).
tcf(c_551,plain,
! [X0: $i] :
( ~ sequential(X0,sK2)
| ~ sequential(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_550,c_52,c_550]) ).
tcf(c_552,plain,
! [X0: $i] :
( ~ sequential(sK3,X0)
| ~ sequential(X0,sK2) ),
inference(renaming,[status(thm)],[c_551]) ).
tcf(c_1432,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1434,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1437,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X2)
| ~ sequential(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1440,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1448,plain,
sK2 = sK2,
inference(instantiation,[status(thm)],[c_1432]) ).
tcf(c_2022,plain,
edge(sK2),
inference(superposition,[status(thm)],[c_52,c_68]) ).
tcf(c_2029,plain,
! [X0: $i,X1: $i] :
( on_path(sK2,sK4)
| ~ path(X0,X1,sK4) ),
inference(superposition,[status(thm)],[c_51,c_60]) ).
tcf(c_2037,plain,
edge(sK3),
inference(superposition,[status(thm)],[c_52,c_69]) ).
tcf(c_2050,plain,
path(sK0,sK1,sK4),
inference(superposition,[status(thm)],[c_50,c_76]) ).
tcf(c_2055,plain,
on_path(sK2,sK4),
inference(superposition,[status(thm)],[c_2050,c_2029]) ).
tcf(c_2060,plain,
head_of(sK2) = tail_of(sK3),
inference(superposition,[status(thm)],[c_52,c_71]) ).
tcf(c_2061,plain,
( vertex(head_of(sK2))
| ~ edge(sK3) ),
inference(superposition,[status(thm)],[c_2060,c_82]) ).
tcf(c_2062,plain,
vertex(head_of(sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_2061,c_2037]) ).
tcf(c_2067,plain,
( ~ edge(sK3)
| ( head_of(sK2) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2060,c_80]) ).
tcf(c_2068,plain,
head_of(sK2) != head_of(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_2067,c_2037]) ).
tcf(c_2075,plain,
! [X0: $i,X1: $i] :
( on_path(sK3,sK4)
| ~ path(X0,X1,sK4) ),
inference(superposition,[status(thm)],[c_51,c_61]) ).
tcf(c_2083,plain,
on_path(sK3,sK4),
inference(superposition,[status(thm)],[c_2050,c_2075]) ).
tcf(c_2094,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ sequential(X2,sK3)
| ~ sequential(X2,sK2)
| ~ precedes(X2,sK3,sK4)
| ~ path(X0,X1,sK4) ),
inference(superposition,[status(thm)],[c_51,c_62]) ).
tcf(c_2105,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK4)
| ~ precedes(X0,X1,sK4) ),
inference(superposition,[status(thm)],[c_50,c_73]) ).
tcf(c_2145,plain,
~ precedes(sK3,sK2,sK4),
inference(superposition,[status(thm)],[c_51,c_2105]) ).
tcf(c_2166,plain,
! [X0: $i] :
( ~ sequential(X0,sK3)
| ~ sequential(X0,sK2)
| ~ precedes(X0,sK3,sK4) ),
inference(superposition,[status(thm)],[c_2050,c_2094]) ).
tcf(c_2307,plain,
! [X0: $i,X1: $i] :
( precedes(X0,X1,sK4)
| ~ on_path(X1,sK4)
| ~ on_path(X0,sK4)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2050,c_65]) ).
tcf(c_2345,plain,
! [X0: $i] :
( ~ on_path(sK3,sK4)
| ~ on_path(X0,sK4)
| ~ sequential(X0,sK3)
| ~ sequential(X0,sK2) ),
inference(superposition,[status(thm)],[c_2307,c_2166]) ).
tcf(c_2346,plain,
( ~ on_path(sK3,sK4)
| ~ on_path(sK2,sK4)
| ~ sequential(sK3,sK2) ),
inference(superposition,[status(thm)],[c_2307,c_2145]) ).
tcf(c_2348,plain,
~ sequential(sK3,sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_2346,c_2083,c_2055]) ).
tcf(c_2353,plain,
! [X0: $i] :
( ~ on_path(X0,sK4)
| ~ sequential(X0,sK3)
| ~ sequential(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2345,c_2083]) ).
tcf(c_2572,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_81,c_106]) ).
tcf(c_2574,plain,
! [X0: $i] :
( ( head_of(sK2) = X0 )
| ( tail_of(sK5(X0,head_of(sK2))) = X0 )
| ( tail_of(sK5(X0,head_of(sK2))) = head_of(sK2) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2062,c_106]) ).
tcf(c_2642,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK2,sK3)
| ( X1 != sK3 )
| ( X0 != sK2 ) ),
inference(instantiation,[status(thm)],[c_1437]) ).
tcf(c_2643,plain,
( sequential(sK2,sK2)
| ~ sequential(sK2,sK3)
| ( sK2 != sK3 )
| ( sK2 != sK2 ) ),
inference(instantiation,[status(thm)],[c_2642]) ).
tcf(c_2695,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK2) )
| ( tail_of(sK5(tail_of(X0),head_of(sK2))) = head_of(sK2) )
| ( tail_of(sK5(tail_of(X0),head_of(sK2))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_2574]) ).
tcf(c_2757,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = X1 )
| ( head_of(sK5(X1,head_of(X0))) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_81,c_109]) ).
tcf(c_2788,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ( head_of(sK5(X1,head_of(X0))) = head_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_81,c_111]) ).
tcf(c_2822,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = X1 )
| ( head_of(sK5(X1,tail_of(X0))) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_113]) ).
tcf(c_3045,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(X0))) = tail_of(X0) )
| ( head_of(sK5(head_of(X0),tail_of(X0))) = head_of(X0) )
| ~ vertex(tail_of(X0))
| ~ vertex(head_of(X0)) ),
inference(instantiation,[status(thm)],[c_113]) ).
tcf(c_3046,plain,
( ( head_of(sK2) = tail_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = tail_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) )
| ~ vertex(tail_of(sK2))
| ~ vertex(head_of(sK2)) ),
inference(instantiation,[status(thm)],[c_3045]) ).
tcf(c_3153,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK3 )
| ( sK3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_1434]) ).
tcf(c_3154,plain,
( ( sK2 = sK3 )
| ( sK3 != sK2 )
| ( sK2 != sK2 ) ),
inference(instantiation,[status(thm)],[c_3153]) ).
tcf(c_3263,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_2757]) ).
tcf(c_3264,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK2) )
| ( tail_of(sK5(head_of(sK2),head_of(X0))) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),head_of(X0))) = head_of(sK2) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2062,c_2757]) ).
tcf(c_3328,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_2572]) ).
tcf(c_3454,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(X0))) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(X0))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2062,c_2822]) ).
tcf(c_3548,plain,
( ( head_of(sK2) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_2037,c_3264]) ).
tcf(c_3550,plain,
( ( tail_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3548,c_2068]) ).
tcf(c_3580,plain,
! [X0: $i] :
( sequential(X0,sK5(head_of(sK2),head_of(sK3)))
| ( sK5(head_of(sK2),head_of(sK3)) = X0 )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) )
| ~ edge(X0)
| ~ edge(sK5(head_of(sK2),head_of(sK3)))
| ( head_of(X0) != head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_3550,c_67]) ).
tcf(c_3781,plain,
( ( head_of(sK2) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_2022,c_2695]) ).
tcf(c_3817,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ( head_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_2788]) ).
tcf(c_3818,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK2) )
| ( tail_of(sK5(head_of(sK2),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(head_of(sK2),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2062,c_2788]) ).
tcf(c_3992,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = head_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = tail_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_3781,c_88,c_2022,c_3781]) ).
tcf(c_3993,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = head_of(sK2) ) ),
inference(renaming,[status(thm)],[c_3992]) ).
tcf(c_4004,plain,
( vertex(tail_of(sK2))
| ( tail_of(sK5(tail_of(sK2),head_of(sK2))) = head_of(sK2) )
| ~ edge(sK5(tail_of(sK2),head_of(sK2))) ),
inference(superposition,[status(thm)],[c_3993,c_82]) ).
tcf(c_4061,plain,
vertex(tail_of(sK2)),
inference(global_subsumption_just,[status(thm)],[c_4004,c_86,c_2022]) ).
tcf(c_4064,plain,
! [X0: $i] :
( ( head_of(X0) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(X0))) = head_of(X0) )
| ( head_of(sK5(tail_of(sK2),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_4061,c_2788]) ).
tcf(c_4190,plain,
! [X0: $i,X1: $i] :
( edge(sK5(head_of(X0),X1))
| ( head_of(X0) = X1 )
| ~ vertex(X1)
| ~ vertex(head_of(X0)) ),
inference(instantiation,[status(thm)],[c_99]) ).
tcf(c_4774,plain,
( ( head_of(sK2) = tail_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = tail_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_2022,c_3454]) ).
tcf(c_4813,plain,
( ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = tail_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_4774,c_86,c_87,c_88,c_2022,c_3046]) ).
tcf(c_4814,plain,
( ( head_of(sK5(head_of(sK2),tail_of(sK2))) = tail_of(sK2) )
| ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) ) ),
inference(renaming,[status(thm)],[c_4813]) ).
tcf(c_4820,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) )
| ~ shortest_path(X3,X4,X2)
| ~ precedes(X1,sK5(head_of(sK2),tail_of(sK2)),X2)
| ( tail_of(X0) != tail_of(X1) )
| ( head_of(X0) != tail_of(sK2) ) ),
inference(superposition,[status(thm)],[c_4814,c_72]) ).
tcf(c_4880,plain,
( ( head_of(sK2) = head_of(sK3) )
| ( tail_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2037,c_3818]) ).
tcf(c_4882,plain,
( ( tail_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4880,c_2068]) ).
tcf(c_4911,plain,
( vertex(head_of(sK3))
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(head_of(sK2),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_4882,c_82]) ).
tcf(c_4948,plain,
! [X0: $i] :
( sequential(sK3,X0)
| ( sK3 = X0 )
| ~ edge(sK3)
| ~ edge(X0)
| ( head_of(sK3) != tail_of(X0) ) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_4949,plain,
( sequential(sK3,sK2)
| ( sK3 = sK2 )
| ~ edge(sK3)
| ~ edge(sK2)
| ( head_of(sK3) != tail_of(sK2) ) ),
inference(instantiation,[status(thm)],[c_4948]) ).
tcf(c_6282,plain,
! [X0: $i,X1: $i] :
( edge(sK5(head_of(X0),head_of(X1)))
| ( head_of(X0) = head_of(X1) )
| ~ vertex(head_of(X1))
| ~ vertex(head_of(X0)) ),
inference(instantiation,[status(thm)],[c_4190]) ).
tcf(c_7098,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2037,c_4064]) ).
tcf(c_7114,plain,
( ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_7098,c_52,c_83,c_1448,c_2022,c_2037,c_2348,c_2643,c_3154,c_4949,c_7098]) ).
tcf(c_7115,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_7114]) ).
tcf(c_7121,plain,
! [X0: $i] :
( sequential(X0,sK5(tail_of(sK2),head_of(sK3)))
| ( sK5(tail_of(sK2),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK2),head_of(sK3)))
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_7115,c_67]) ).
tcf(c_7623,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2037,c_3263]) ).
tcf(c_7865,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(superposition,[status(thm)],[c_2022,c_7623]) ).
tcf(c_7884,plain,
( ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_7865,c_52,c_83,c_1448,c_2022,c_2037,c_2348,c_2643,c_3154,c_4949,c_7865]) ).
tcf(c_7885,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(renaming,[status(thm)],[c_7884]) ).
tcf(c_7906,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_7885,c_7115]) ).
tcf(c_7968,plain,
( ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_7906,c_52,c_83,c_1448,c_2022,c_2037,c_2348,c_2643,c_3154,c_4949,c_7906]) ).
tcf(c_7969,plain,
( ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_7968]) ).
tcf(c_7977,plain,
! [X0: $i] :
( sequential(sK5(tail_of(sK2),head_of(sK3)),X0)
| ( sK5(tail_of(sK2),head_of(sK3)) = X0 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0)
| ~ edge(sK5(tail_of(sK2),head_of(sK3)))
| ( tail_of(X0) != tail_of(sK2) ) ),
inference(superposition,[status(thm)],[c_7969,c_67]) ).
tcf(c_8278,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = tail_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2037,c_3328]) ).
tcf(c_8534,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2022,c_8278]) ).
tcf(c_8572,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_8534,c_52,c_83,c_1448,c_2022,c_2037,c_2348,c_2643,c_3154,c_4949,c_8534]) ).
tcf(c_8573,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(renaming,[status(thm)],[c_8572]) ).
tcf(c_9670,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2037,c_3817]) ).
tcf(c_9899,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK5(X0,X1)) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X0,X1)),head_of(sK3))) = head_of(sK3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_99,c_9670]) ).
tcf(c_10473,plain,
( vertex(head_of(sK3))
| ~ edge(sK3) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_13199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK5(head_of(sK2),tail_of(sK2))) = head_of(sK2) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(X0,sK5(head_of(sK2),tail_of(sK2)),X1)
| ( head_of(sK3) != tail_of(sK2) )
| ( tail_of(X0) != head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_2060,c_4820]) ).
tcf(c_14794,plain,
head_of(sK3) != tail_of(sK2),
inference(global_subsumption_just,[status(thm)],[c_13199,c_52,c_83,c_1448,c_2022,c_2037,c_2348,c_2643,c_3154,c_4949]) ).
tcf(c_16077,plain,
( sequential(sK2,sK5(head_of(sK2),head_of(sK3)))
| ( sK5(head_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) )
| ~ edge(sK2)
| ~ edge(sK5(head_of(sK2),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_3580]) ).
tcf(c_16078,plain,
( sequential(sK2,sK5(head_of(sK2),head_of(sK3)))
| ( sK5(head_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) )
| ~ edge(sK5(head_of(sK2),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16077,c_2022]) ).
tcf(c_16671,plain,
! [X0: $i] :
( edge(sK5(head_of(X0),head_of(sK3)))
| ( head_of(X0) = head_of(sK3) )
| ~ vertex(head_of(sK3))
| ~ vertex(head_of(X0)) ),
inference(instantiation,[status(thm)],[c_6282]) ).
tcf(c_16674,plain,
( edge(sK5(head_of(sK2),head_of(sK3)))
| ( head_of(sK2) = head_of(sK3) )
| ~ vertex(head_of(sK3))
| ~ vertex(head_of(sK2)) ),
inference(instantiation,[status(thm)],[c_16671]) ).
tcf(c_16744,plain,
( sequential(sK2,sK5(head_of(sK2),head_of(sK3)))
| ( sK5(head_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) ) ),
inference(global_subsumption_just,[status(thm)],[c_16078,c_87,c_2022,c_2037,c_2068,c_10473,c_16078,c_16674]) ).
tcf(c_16758,plain,
( edge(sK5(head_of(sK2),head_of(sK3)))
| ( sK5(head_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK2) ) ),
inference(superposition,[status(thm)],[c_16744,c_69]) ).
tcf(c_16887,plain,
edge(sK5(head_of(sK2),head_of(sK3))),
inference(global_subsumption_just,[status(thm)],[c_16758,c_87,c_2022,c_2037,c_2068,c_10473,c_16674]) ).
tcf(c_16889,plain,
( vertex(head_of(sK3))
| ( head_of(sK5(head_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_4911,c_16887]) ).
tcf(c_18342,plain,
vertex(head_of(sK3)),
inference(global_subsumption_just,[status(thm)],[c_16889,c_2037,c_10473]) ).
tcf(c_25601,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK5(tail_of(X0),head_of(X1))) = head_of(X1) )
| ( sK5(tail_of(X0),head_of(X1)) != X1 ) ),
inference(instantiation,[status(thm)],[c_1440]) ).
tcf(c_26738,plain,
( sequential(sK3,sK5(tail_of(sK2),head_of(sK3)))
| ( sK5(tail_of(sK2),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK3)
| ~ edge(sK5(tail_of(sK2),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_7121]) ).
tcf(c_26739,plain,
( sequential(sK3,sK5(tail_of(sK2),head_of(sK3)))
| ( sK5(tail_of(sK2),head_of(sK3)) = sK3 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK2),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26738,c_2037]) ).
tcf(c_26882,plain,
( sequential(sK5(tail_of(sK2),head_of(sK3)),sK2)
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK2)
| ~ edge(sK5(tail_of(sK2),head_of(sK3))) ),
inference(equality_resolution,[status(thm)],[c_7977]) ).
tcf(c_26883,plain,
( sequential(sK5(tail_of(sK2),head_of(sK3)),sK2)
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK2),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26882,c_2022]) ).
tcf(c_31088,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK2),head_of(sK3)))
| ~ on_path(sK5(tail_of(sK2),head_of(sK3)),sK4)
| ~ sequential(sK5(tail_of(sK2),head_of(sK3)),sK3) ),
inference(superposition,[status(thm)],[c_26883,c_2353]) ).
tcf(c_31089,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK2),head_of(sK3)))
| ~ sequential(sK3,sK5(tail_of(sK2),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_26883,c_552]) ).
tcf(c_31125,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ sequential(sK3,sK5(tail_of(sK2),head_of(sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31089,c_69]) ).
tcf(c_31135,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK3 )
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ edge(sK5(tail_of(sK2),head_of(sK3))) ),
inference(superposition,[status(thm)],[c_26739,c_31125]) ).
tcf(c_31184,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( sK5(tail_of(sK2),head_of(sK3)) = sK3 )
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ vertex(tail_of(sK2))
| ~ vertex(head_of(sK3)) ),
inference(superposition,[status(thm)],[c_99,c_31135]) ).
tcf(c_31185,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK3 )
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_31184,c_14794,c_4061,c_18342]) ).
tcf(c_43110,plain,
! [X0: $i] :
( ( head_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(X0),head_of(sK3)) != sK3 ) ),
inference(instantiation,[status(thm)],[c_25601]) ).
tcf(c_43114,plain,
( ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( sK5(tail_of(sK2),head_of(sK3)) != sK3 ) ),
inference(instantiation,[status(thm)],[c_43110]) ).
tcf(c_58480,plain,
( ( sK5(tail_of(sK2),head_of(sK3)) = sK2 )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) ) ),
inference(global_subsumption_just,[status(thm)],[c_31088,c_31185,c_43114]) ).
tcf(c_63398,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = X1 )
| ( tail_of(sK5(X1,head_of(X0))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(X1,head_of(X0))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(X1,head_of(X0))),head_of(sK3))) = head_of(sK3) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_81,c_9899]) ).
tcf(c_64283,plain,
! [X0: $i,X1: $i] :
( ( head_of(X1) = tail_of(X0) )
| ( tail_of(sK5(tail_of(X0),head_of(X1))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(X0),head_of(X1))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(X0),head_of(X1))),head_of(sK3))) = head_of(sK3) )
| ~ edge(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_82,c_63398]) ).
tcf(c_68227,plain,
! [X0: $i] :
( ( tail_of(X0) = head_of(sK3) )
| ( tail_of(sK5(tail_of(X0),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(X0),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(X0),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_2037,c_64283]) ).
tcf(c_68984,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_2022,c_68227]) ).
tcf(c_68994,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_68984,c_14794]) ).
tcf(c_69042,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_8573,c_68994]) ).
tcf(c_69141,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ( head_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) = head_of(sK3) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69042,c_14794]) ).
tcf(c_69154,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( head_of(X1) != head_of(sK3) )
| ( tail_of(sK5(tail_of(sK5(tail_of(sK2),head_of(sK3))),head_of(sK3))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_69141,c_72]) ).
tcf(c_70745,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(X1) != tail_of(sK2) )
| ( head_of(X0) != head_of(sK3) ) ),
inference(superposition,[status(thm)],[c_8573,c_69154]) ).
tcf(c_72246,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ precedes(X0,sK3,X3)
| ~ shortest_path(X1,X2,X3)
| ( tail_of(X0) != tail_of(sK2) ) ),
inference(equality_resolution,[status(thm)],[c_70745]) ).
tcf(c_72334,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ precedes(sK2,sK3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c_72246]) ).
tcf(c_72550,plain,
( ( tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3) )
| ~ precedes(sK2,sK3,sK4) ),
inference(superposition,[status(thm)],[c_50,c_72334]) ).
tcf(c_72551,plain,
tail_of(sK5(tail_of(sK2),head_of(sK3))) = head_of(sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_72550,c_51]) ).
tcf(c_72554,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2) ) ),
inference(demodulation,[status(thm)],[c_7885,c_72551]) ).
tcf(c_72555,plain,
head_of(sK5(tail_of(sK2),head_of(sK3))) = tail_of(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_72554,c_14794]) ).
tcf(c_72557,plain,
( ( head_of(sK3) = tail_of(sK2) )
| ( sK5(tail_of(sK2),head_of(sK3)) = sK2 ) ),
inference(demodulation,[status(thm)],[c_58480,c_72555]) ).
tcf(c_72670,plain,
sK5(tail_of(sK2),head_of(sK3)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_72557,c_14794]) ).
tcf(c_72673,plain,
head_of(sK3) = tail_of(sK2),
inference(light_normalisation,[status(thm)],[c_72551,c_72670]) ).
tcf(c_72674,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_72673,c_14794]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA008+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n009.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 12:43:43 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.46 % Proving...
% 31.75/5.41 % SZS status Started for theBenchmark.p
% 31.75/5.41 % SZS status Theorem for theBenchmark.p
% 31.75/5.41
% 31.75/5.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.75/5.41
% 31.75/5.41 % ------ iProver source info
% 31.75/5.41
% 31.75/5.41 % git: date: 2026-07-19 20:42:38 +0200
% 31.75/5.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.75/5.41 % git: non_committed_changes: false
% 31.75/5.41
% 31.75/5.41 % ------ Parsing...
% 31.75/5.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.75/5.41
% 31.75/5.41 % ------ 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 %
% 31.75/5.41
% 31.75/5.41 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.75/5.41
% 31.75/5.41 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.75/5.41 % ------ Proving...
% 31.75/5.41 % ------ Problem Properties
% 31.75/5.41
% 31.75/5.41 %
% 31.75/5.41 % clauses 32
% 31.75/5.41 % conjectures 3
% 31.75/5.41 % EPR 15
% 31.75/5.41 % Horn 22
% 31.75/5.41 % unary 5
% 31.75/5.41 % binary 8
% 31.75/5.41 % lits 104
% 31.75/5.41 % lits eq 26
% 31.75/5.41 % fd_pure 0
% 31.75/5.41 % fd_pseudo 0
% 31.75/5.41 % fd_cond 0
% 31.75/5.41 % fd_pseudo_cond 5
% 31.75/5.41 % AC symbols 0
% 31.75/5.41
% 31.75/5.41 % ------ Schedule dynamic 5 is on
% 31.75/5.41
% 31.75/5.41 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.75/5.41
% 31.75/5.41
% 31.75/5.41 % ------
% 31.75/5.41 % Current options:
% 31.75/5.41 % ------
% 31.75/5.41
% 31.75/5.41
% 31.75/5.41 %
% 31.75/5.41
% 31.75/5.41 % ------ Proving...
% 31.75/5.41 %
% 31.75/5.41
% 31.75/5.41 % SZS status Theorem for theBenchmark.p
% 31.75/5.41
% 31.75/5.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.75/5.42
% 31.75/5.42
%------------------------------------------------------------------------------