%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRA012+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 01:23:38 PM UTC 2026
% Result : Theorem 71.22s 10.72s
% Output : CNFRefutation 71.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 233 ( 28 unt; 0 def)
% Number of atoms : 924 ( 357 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1152 ( 461 ~; 550 |; 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 : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 457 ( 0 sgn 434 !; 23 ?; 210 :)
% 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(f18,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(triangles,X0) = minus(length_of(X0),n1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_on_a_path) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(triangles,X0) = minus(length_of(X0),n1) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f21,plain,
( complete
& ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& number_of_in(triangles,X0) != minus(length_of(X0),n1) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f22,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f24,plain,
( ~ complete
| ! [X0,X1] :
( X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ? [X2] :
( ( ( X1 = tail_of(X2)
& X0 = head_of(X2) )
<~> ( X0 = tail_of(X2)
& X1 = head_of(X2) ) )
& edge(X2) ) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ 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] :
( 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(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(ennf_transformation,[],[f16]) ).
fof(f30,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,[],[f29]) ).
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)
& number_of_in(triangles,sK0) != minus(length_of(sK0),n1) ),
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,[],[f24]) ).
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,[],[f28]) ).
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))],[f30]) ).
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,
number_of_in(triangles,sK0) != minus(length_of(sK0),n1),
inference(cnf_transformation,[],[f37]) ).
fof(f55,plain,
! [X0] :
( ~ edge(X0)
| head_of(X0) != tail_of(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK3(X0,X1)) = X1
| tail_of(sK3(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f40]) ).
fof(f57,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(f58,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(f59,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(f61,plain,
! [X0,X1] :
( ~ complete
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| edge(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f40]) ).
fof(f62,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f63,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X3,X2,X4) ),
inference(cnf_transformation,[],[f27]) ).
fof(f64,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(f67,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
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)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f75,plain,
! [X0] :
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f79,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ precedes(X3,X4,X0)
| on_path(X4,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f80,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] :
( ~ path(X1,X2,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f83,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f85,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f87,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f88,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,
minus(length_of(sK0),n1) != number_of_in(triangles,sK0),
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] :
( ~ edge(X0)
| ( head_of(X0) != tail_of(X0) ) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ complete
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_58,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,[],[f56]) ).
tcf(c_59,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,[],[f62]) ).
tcf(c_60,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,[],[f64]) ).
tcf(c_61,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,[],[f63]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
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] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_72,plain,
! [X0: $i] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_73,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,[],[f80]) ).
tcf(c_74,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,[],[f79]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( precedes(X3,X4,X2)
| ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ( X0 = X1 )
| ~ edge(X1)
| ~ edge(X0)
| ( head_of(X0) != tail_of(X1) ) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = tail_of(X1) )
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_85,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,[],[f88]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_51,c_53]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( edge(sK3(X0,X1))
| ( X0 = X1 )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(renaming,[status(thm)],[c_105]) ).
tcf(c_108,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_85,c_82,c_81,c_85]) ).
tcf(c_112,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_58,c_51,c_58]) ).
tcf(c_113,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_112]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X0 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_51,c_57]) ).
tcf(c_116,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_115]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( tail_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_51,c_56]) ).
tcf(c_118,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_117]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( head_of(sK3(X0,X1)) = X1 )
| ( head_of(sK3(X0,X1)) = X0 )
| ~ vertex(X0)
| ~ vertex(X1) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_51,c_55]) ).
tcf(c_120,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_119]) ).
tcf(c_147,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_108,c_81]) ).
tcf(c_640,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_147]) ).
tcf(c_641,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_640]) ).
tcf(c_653,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_641,c_70]) ).
tcf(c_722,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_64]) ).
tcf(c_723,plain,
path(sK1,sK2,sK0),
inference(unflattening,[status(thm)],[c_722]) ).
tcf(c_1558,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1560,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1565,plain,
! [X0: $i,X1: $i] :
( ( head_of(X0) = head_of(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1570,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( precedes(X0,X2,X3)
| ~ precedes(X1,X2,X3)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1572,plain,
! [X0: $i,X1: $i,X2: $i] :
( on_path(X0,X2)
| ~ on_path(X1,X2)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1573,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sequential(X0,X2)
| ~ sequential(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2253,plain,
path(sK1,sK2,sK0),
inference(superposition,[status(thm)],[c_50,c_64]) ).
tcf(c_2268,plain,
! [X0: $i,X1: $i] :
( on_path(X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2253,c_73]) ).
tcf(c_2281,plain,
! [X0: $i,X1: $i] :
( on_path(X1,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_2253,c_74]) ).
tcf(c_2292,plain,
minus(length_of(sK0),n1) = number_of_in(sequential_pairs,sK0),
inference(superposition,[status(thm)],[c_2253,c_59]) ).
tcf(c_2293,plain,
number_of_in(triangles,sK0) != number_of_in(sequential_pairs,sK0),
inference(demodulation,[status(thm)],[c_49,c_2292]) ).
tcf(c_2308,plain,
! [X0: $i,X1: $i] :
( ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_2347,plain,
( on_path(sK5(sK0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2253,c_68]) ).
tcf(c_2348,plain,
on_path(sK5(sK0),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2347,c_2293]) ).
tcf(c_2355,plain,
( on_path(sK6(sK0),sK0)
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2253,c_69]) ).
tcf(c_2356,plain,
on_path(sK6(sK0),sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2355,c_2293]) ).
tcf(c_2363,plain,
( sequential(sK5(sK0),sK6(sK0))
| ( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ) ),
inference(superposition,[status(thm)],[c_2253,c_70]) ).
tcf(c_2364,plain,
sequential(sK5(sK0),sK6(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2363,c_2293]) ).
tcf(c_2377,plain,
head_of(sK5(sK0)) = tail_of(sK6(sK0)),
inference(superposition,[status(thm)],[c_2364,c_84]) ).
tcf(c_2378,plain,
edge(sK6(sK0)),
inference(superposition,[status(thm)],[c_2364,c_82]) ).
tcf(c_2379,plain,
edge(sK5(sK0)),
inference(superposition,[status(thm)],[c_2364,c_81]) ).
tcf(c_2406,plain,
( ~ edge(sK6(sK0))
| ( head_of(sK5(sK0)) != head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2377,c_52]) ).
tcf(c_2407,plain,
( vertex(head_of(sK5(sK0)))
| ~ edge(sK6(sK0)) ),
inference(superposition,[status(thm)],[c_2377,c_72]) ).
tcf(c_2408,plain,
vertex(head_of(sK5(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_2407,c_2378]) ).
tcf(c_2409,plain,
head_of(sK5(sK0)) != head_of(sK6(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2406,c_2378]) ).
tcf(c_2526,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_2253,c_78]) ).
tcf(c_2580,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_2526,c_2308]) ).
tcf(c_2603,plain,
! [X0: $i,X1: $i] :
( ~ sequential(X1,X0)
| ~ precedes(X0,X1,sK0) ),
inference(global_subsumption_just,[status(thm)],[c_2580,c_2268,c_2281,c_2580]) ).
tcf(c_2609,plain,
! [X0: $i,X1: $i] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X1,X0)
| ~ sequential(X0,X1) ),
inference(superposition,[status(thm)],[c_2526,c_2603]) ).
tcf(c_2636,plain,
( ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ sequential(sK6(sK0),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_2364,c_2609]) ).
tcf(c_2638,plain,
~ sequential(sK6(sK0),sK5(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2636,c_2356,c_2348]) ).
tcf(c_2664,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_71,c_113]) ).
tcf(c_2665,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_113]) ).
tcf(c_2812,plain,
! [X0: $i,X1: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(X1,X0,sK0)
| ~ precedes(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2813,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(X2,X0,sK0)
| ( tail_of(X1) != tail_of(X2) )
| ( head_of(X0) != head_of(X1) ) ),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_3034,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_2253,c_653]) ).
tcf(c_3035,plain,
! [X0: $i] :
( ~ sequential(X0,sK5(sK0))
| ~ sequential(sK6(sK0),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3034,c_2293]) ).
tcf(c_3056,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ( head_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_116]) ).
tcf(c_3086,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( tail_of(sK3(tail_of(X0),X1)) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = X1 )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_118]) ).
tcf(c_3419,plain,
! [X0: $i,X1: $i] :
( ( tail_of(X0) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = X1 )
| ( head_of(sK3(tail_of(X0),X1)) = tail_of(X0) )
| ~ vertex(X1)
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_72,c_120]) ).
tcf(c_3906,plain,
! [X0: $i,X1: $i] :
( sequential(X0,X1)
| ~ sequential(sK5(sK0),sK6(sK0))
| ( X1 != sK6(sK0) )
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1573]) ).
tcf(c_3952,plain,
! [X0: $i] :
( ( tail_of(sK5(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK5(sK0)),X0)) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),X0)) = X0 )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2379,c_3086]) ).
tcf(c_4015,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_2378,c_2664]) ).
tcf(c_4081,plain,
! [X0: $i,X1: $i,X2: $i] :
( precedes(sK5(sK0),X2,sK0)
| ~ on_path(X2,sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ sequential(sK5(sK0),X2)
| ~ path(X0,X1,sK0) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_4084,plain,
! [X0: $i] :
( on_path(X0,sK0)
| ~ on_path(sK5(sK0),sK0)
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1572]) ).
tcf(c_4523,plain,
! [X0: $i] :
( ( tail_of(sK5(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK5(sK0)),X0)) = X0 )
| ( tail_of(sK3(tail_of(sK5(sK0)),X0)) = tail_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2379,c_2665]) ).
tcf(c_4594,plain,
! [X0: $i] :
( ( tail_of(sK5(sK0)) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),X0)) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),X0)) = tail_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2379,c_3419]) ).
tcf(c_5079,plain,
! [X0: $i] :
( ( tail_of(sK5(sK0)) = X0 )
| ( tail_of(sK3(tail_of(sK5(sK0)),X0)) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),X0)) = tail_of(sK5(sK0)) )
| ~ vertex(X0) ),
inference(superposition,[status(thm)],[c_2379,c_3056]) ).
tcf(c_5268,plain,
! [X0: $i] :
( ( tail_of(sK5(sK0)) = head_of(X0) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(X0))) = head_of(X0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(X0))) = head_of(X0) )
| ~ edge(X0) ),
inference(superposition,[status(thm)],[c_71,c_3952]) ).
tcf(c_5285,plain,
( vertex(head_of(sK6(sK0)))
| ~ edge(sK6(sK0)) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_5380,plain,
( vertex(tail_of(sK5(sK0)))
| ~ edge(sK5(sK0)) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_5687,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_80]) ).
tcf(c_5966,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_2378,c_5268]) ).
tcf(c_6016,plain,
( ( head_of(sK5(sK0)) = head_of(sK6(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_2408,c_4015]) ).
tcf(c_6025,plain,
( ( 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(forward_subsumption_resolution,[status(thm)],[c_6016,c_2409]) ).
tcf(c_6055,plain,
( vertex(head_of(sK6(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_6025,c_72]) ).
tcf(c_6889,plain,
vertex(head_of(sK6(sK0))),
inference(global_subsumption_just,[status(thm)],[c_6055,c_2378,c_5285]) ).
tcf(c_7188,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_4081]) ).
tcf(c_7247,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_6889,c_4523]) ).
tcf(c_7289,plain,
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK6(sK0),sK6(sK0),sK0) ),
inference(instantiation,[status(thm)],[c_2812]) ).
tcf(c_7629,plain,
! [X0: $i] :
( precedes(X0,sK6(sK0),sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( X0 != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_1570]) ).
tcf(c_7631,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_2813]) ).
tcf(c_8266,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_6889,c_4594]) ).
tcf(c_8973,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(X0)
| ~ edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(superposition,[status(thm)],[c_5966,c_80]) ).
tcf(c_9156,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_5687]) ).
tcf(c_10372,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_7188]) ).
tcf(c_10391,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK5(sK0)) != X0 )
| ( head_of(sK6(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1560]) ).
tcf(c_10551,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_6889,c_5079]) ).
tcf(c_11769,plain,
! [X0: $i] :
( edge(sK3(X0,head_of(sK6(sK0))))
| ( X0 = head_of(sK6(sK0)) )
| ~ vertex(X0)
| ~ vertex(head_of(sK6(sK0))) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_11779,plain,
! [X0: $i] :
( ( head_of(X0) = head_of(sK6(sK0)) )
| ( X0 != sK6(sK0) ) ),
inference(instantiation,[status(thm)],[c_1565]) ).
tcf(c_12015,plain,
! [X0: $i,X1: $i] :
( ( head_of(sK6(sK0)) = X1 )
| ( X1 != X0 )
| ( head_of(sK6(sK0)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1560]) ).
tcf(c_12112,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_7247,c_52]) ).
tcf(c_12927,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),X0)
| ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(X0)
| ~ edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( tail_of(sK5(sK0)) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_8266,c_80]) ).
tcf(c_12930,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK5(sK0)) != head_of(X1) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(X0) ) ),
inference(superposition,[status(thm)],[c_8266,c_60]) ).
tcf(c_13591,plain,
sK6(sK0) = sK6(sK0),
inference(instantiation,[status(thm)],[c_1558]) ).
tcf(c_13770,plain,
head_of(sK6(sK0)) = head_of(sK6(sK0)),
inference(instantiation,[status(thm)],[c_1558]) ).
tcf(c_16199,plain,
( edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( tail_of(sK5(sK0)) = head_of(sK6(sK0)) )
| ~ vertex(tail_of(sK5(sK0)))
| ~ vertex(head_of(sK6(sK0))) ),
inference(instantiation,[status(thm)],[c_11769]) ).
tcf(c_21540,plain,
! [X0: $i] :
( ( head_of(sK6(sK0)) = X0 )
| ( X0 != head_of(sK6(sK0)) )
| ( head_of(sK6(sK0)) != head_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_12015]) ).
tcf(c_21542,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK5(sK0)) != head_of(sK6(sK0)) )
| ( head_of(sK6(sK0)) != head_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_10391]) ).
tcf(c_22008,plain,
( precedes(sK6(sK0),sK6(sK0),sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( sK6(sK0) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_7629]) ).
tcf(c_23131,plain,
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK5(sK0))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ~ edge(sK5(sK0))
| ~ edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_5687]) ).
tcf(c_40388,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(X0) )
| ( tail_of(sK5(sK0)) != head_of(X1) )
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4)
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_12930,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_7289,c_9156,c_10372,c_12930,c_22008]) ).
tcf(c_40389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ precedes(X0,X1,X4)
| ~ shortest_path(X2,X3,X4)
| ( tail_of(sK5(sK0)) != head_of(X1) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(X0) ) ),
inference(renaming,[status(thm)],[c_40388]) ).
tcf(c_40407,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ shortest_path(X2,X3,X1)
| ~ precedes(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),X0,X1)
| ( tail_of(sK5(sK0)) != head_of(X0) ) ),
inference(equality_resolution,[status(thm)],[c_40389]) ).
tcf(c_42611,plain,
( ( head_of(sK6(sK0)) = head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) )
| ( head_of(sK6(sK0)) != head_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != head_of(sK6(sK0)) ) ),
inference(instantiation,[status(thm)],[c_21540]) ).
tcf(c_43763,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),X0)
| ~ sequential(sK5(sK0),sK6(sK0))
| ( X0 != sK6(sK0) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_3906]) ).
tcf(c_43764,plain,
( on_path(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK0)
| ~ on_path(sK5(sK0),sK0)
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_4084]) ).
tcf(c_49853,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( head_of(sK6(sK0)) != head_of(X0) )
| ~ edge(X0)
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_8973,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_5285,c_5380,c_7289,c_8973,c_9156,c_10372,c_13770,c_16199,c_21542,c_22008]) ).
tcf(c_49854,plain,
! [X0: $i] :
( sequential(X0,sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(X0)
| ( head_of(sK6(sK0)) != head_of(X0) ) ),
inference(renaming,[status(thm)],[c_49853]) ).
tcf(c_49875,plain,
( sequential(sK6(sK0),sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(sK6(sK0)) ),
inference(equality_resolution,[status(thm)],[c_49854]) ).
tcf(c_49876,plain,
( sequential(sK6(sK0),sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49875,c_2378]) ).
tcf(c_50097,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK0)
| ~ sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK6(sK0)) ),
inference(superposition,[status(thm)],[c_49876,c_2609]) ).
tcf(c_50099,plain,
( edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_49876,c_82]) ).
tcf(c_50103,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK5(sK0)) ),
inference(superposition,[status(thm)],[c_49876,c_3035]) ).
tcf(c_50113,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ on_path(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK0)
| ~ sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK6(sK0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50097,c_2356]) ).
tcf(c_50168,plain,
edge(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_50099,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_5285,c_5380,c_7289,c_9156,c_10372,c_13770,c_16199,c_21542,c_22008]) ).
tcf(c_50170,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12112,c_50168]) ).
tcf(c_50904,plain,
( ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(global_subsumption_just,[status(thm)],[c_50170,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_5285,c_5380,c_7289,c_9156,c_10372,c_12112,c_13770,c_16199,c_21542,c_22008]) ).
tcf(c_50905,plain,
( ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(renaming,[status(thm)],[c_50904]) ).
tcf(c_50911,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK6(sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_50113,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_5285,c_5380,c_7289,c_8266,c_9156,c_10372,c_13770,c_16199,c_21542,c_22008,c_23131,c_43764,c_50103,c_50113]) ).
tcf(c_53210,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),X0)
| ( tail_of(sK5(sK0)) != tail_of(X0) )
| ~ edge(X0)
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_12927,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_5285,c_5380,c_7289,c_9156,c_10372,c_12927,c_13770,c_16199,c_21542,c_22008]) ).
tcf(c_53211,plain,
! [X0: $i] :
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),X0)
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = X0 )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(X0)
| ( tail_of(sK5(sK0)) != tail_of(X0) ) ),
inference(renaming,[status(thm)],[c_53210]) ).
tcf(c_53247,plain,
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK5(sK0))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ~ edge(sK5(sK0)) ),
inference(equality_resolution,[status(thm)],[c_53211]) ).
tcf(c_53248,plain,
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK5(sK0))
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_53247,c_2379]) ).
tcf(c_54336,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK6(sK0) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(superposition,[status(thm)],[c_53248,c_50103]) ).
tcf(c_61536,plain,
( ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) != sK6(sK0) ) ),
inference(instantiation,[status(thm)],[c_11779]) ).
tcf(c_61564,plain,
( ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) ) ),
inference(global_subsumption_just,[status(thm)],[c_54336,c_54336,c_61536]) ).
tcf(c_61565,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) ) ),
inference(renaming,[status(thm)],[c_61564]) ).
tcf(c_61604,plain,
( ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) = sK5(sK0) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)) )
| ( head_of(sK6(sK0)) != tail_of(sK5(sK0)) ) ),
inference(superposition,[status(thm)],[c_61565,c_50905]) ).
tcf(c_61882,plain,
head_of(sK6(sK0)) != tail_of(sK5(sK0)),
inference(global_subsumption_just,[status(thm)],[c_61604,c_50,c_723,c_2348,c_2356,c_2364,c_2379,c_2378,c_2638,c_7289,c_9156,c_10372,c_22008]) ).
tcf(c_61885,plain,
( ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) )
| ( head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_10551,c_61882]) ).
tcf(c_80751,plain,
( sequential(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))),sK6(sK0))
| ~ sequential(sK5(sK0),sK6(sK0))
| ( sK6(sK0) != sK6(sK0) )
| ( sK3(tail_of(sK5(sK0)),head_of(sK6(sK0))) != sK5(sK0) ) ),
inference(instantiation,[status(thm)],[c_43763]) ).
tcf(c_81742,plain,
( ~ shortest_path(sK1,sK2,sK0)
| ~ precedes(sK5(sK0),sK6(sK0),sK0)
| ( head_of(sK6(sK0)) != head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) != tail_of(sK5(sK0)) ) ),
inference(instantiation,[status(thm)],[c_7631]) ).
tcf(c_81957,plain,
head_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = head_of(sK6(sK0)),
inference(global_subsumption_just,[status(thm)],[c_40407,c_2364,c_13591,c_50911,c_54336,c_61536,c_80751]) ).
tcf(c_81964,plain,
( ( head_of(sK6(sK0)) = tail_of(sK5(sK0)) )
| ( tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)) ) ),
inference(demodulation,[status(thm)],[c_61885,c_81957]) ).
tcf(c_81982,plain,
tail_of(sK3(tail_of(sK5(sK0)),head_of(sK6(sK0)))) = tail_of(sK5(sK0)),
inference(forward_subsumption_resolution,[status(thm)],[c_81964,c_61882]) ).
tcf(c_81995,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_81982,c_81957,c_81742,c_42611,c_13770,c_10372,c_2364,c_2356,c_2348,c_723,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRA012+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n004.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Wed Sep 23 12:45:07 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.49 Running first-order theorem proving
% 0.16/0.49 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
% 0.16/0.50
% 0.16/0.50 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.50
% 0.16/0.51 % Detected problem language: tptp
% 0.25/0.53 % Proving...
% 71.22/10.72 % SZS status Started for theBenchmark.p
% 71.22/10.72 % SZS status Theorem for theBenchmark.p
% 71.22/10.72
% 71.22/10.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 71.22/10.72
% 71.22/10.72 % ------ iProver source info
% 71.22/10.72
% 71.22/10.72 % git: date: 2026-07-19 20:42:38 +0200
% 71.22/10.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 71.22/10.72 % git: non_committed_changes: false
% 71.22/10.72
% 71.22/10.72 % ------ Parsing...
% 71.22/10.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 71.22/10.72
% 71.22/10.72 % ------ 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 %
% 71.22/10.72
% 71.22/10.72 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 71.22/10.72
% 71.22/10.72 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 71.22/10.72 % ------ Proving...
% 71.22/10.72 % ------ Problem Properties
% 71.22/10.72
% 71.22/10.72 %
% 71.22/10.72 % clauses 35
% 71.22/10.72 % conjectures 2
% 71.22/10.72 % EPR 12
% 71.22/10.72 % Horn 22
% 71.22/10.72 % unary 4
% 71.22/10.72 % binary 8
% 71.22/10.72 % lits 116
% 71.22/10.72 % lits eq 32
% 71.22/10.72 % fd_pure 0
% 71.22/10.72 % fd_pseudo 0
% 71.22/10.72 % fd_cond 0
% 71.22/10.72 % fd_pseudo_cond 5
% 71.22/10.72 % AC symbols 0
% 71.22/10.72
% 71.22/10.72 % ------ Schedule dynamic 5 is on
% 71.22/10.72
% 71.22/10.72 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 71.22/10.72
% 71.22/10.72
% 71.22/10.72 % ------
% 71.22/10.72 % Current options:
% 71.22/10.72 % ------
% 71.22/10.72
% 71.22/10.72
% 71.22/10.72 %
% 71.22/10.72
% 71.22/10.72 % ------ Proving...
% 71.22/10.72 %
% 71.22/10.72
% 71.22/10.72 % SZS status Theorem for theBenchmark.p
% 71.22/10.72
% 71.22/10.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 71.22/10.72
% 71.22/10.72
%------------------------------------------------------------------------------