%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA006+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 12:30:39 PM UTC 2026
% Result : Theorem 5.25s 1.33s
% Output : CNFRefutation 5.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 146
% Syntax : Number of formulae : 608 ( 15 unt; 133 def)
% Number of atoms : 2714 ( 379 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 3791 (1685 ~;1769 |; 172 &)
% ( 137 <=>; 16 =>; 2 <=; 10 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 145 ( 143 usr; 133 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 1138 (1088 !; 50 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E] :
( edge(E)
=> head_of(E) != tail_of(E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E] :
( edge(E)
=> ( vertex(tail_of(E))
& vertex(head_of(E)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( complete
=> ! [V1,V2] :
( ( V1 != V2
& vertex(V2)
& vertex(V1) )
=> ? [E] :
( ( ( V2 = tail_of(E)
& V1 = head_of(E) )
<~> ( V1 = tail_of(E)
& V2 = head_of(E) ) )
& edge(E) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
<= ( ? [E] :
( ( ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) )
| ( P = path_cons(E,empty)
& V2 = head_of(E) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> ( ? [E] :
( ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V1,V2,P,E] :
( ( on_path(E,P)
& path(V1,V2,P) )
=> ( in_path(tail_of(E),P)
& in_path(head_of(E),P)
& edge(E) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V1,V2,P,V] :
( ( in_path(V,P)
& path(V1,V2,P) )
=> ( ? [E] :
( ( V = tail_of(E)
| V = head_of(E) )
& on_path(E,P) )
& vertex(V) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [E1,E2] :
( sequential(E1,E2)
<=> ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [P,V1,V2] :
( path(V1,V2,P)
=> ! [E1,E2] :
( precedes(E1,E2,P)
<= ( ( ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) )
| sequential(E1,E2) )
& on_path(E2,P)
& on_path(E1,P) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [P,V1,V2] :
( path(V1,V2,P)
=> ! [E1,E2] :
( precedes(E1,E2,P)
=> ( ( sequential(E1,E2)
<~> ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) ) )
& on_path(E2,P)
& on_path(E1,P) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) )
& V1 != V2
& path(V1,V2,SP) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( ~ precedes(E2,E1,P)
& ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
( complete
=> ! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) )
<~> ? [E3] :
( head_of(E3) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) )
<~> ? [E3] :
( head_of(E3) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [E] :
( head_of(E) != tail_of(E)
| ~ edge(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [E] :
( ( vertex(tail_of(E))
& vertex(head_of(E)) )
| ~ edge(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
( ! [V1,V2] :
( ? [E] :
( ( ( V2 = tail_of(E)
& V1 = head_of(E) )
<~> ( V1 = tail_of(E)
& V2 = head_of(E) ) )
& edge(E) )
| V1 = V2
| ~ vertex(V2)
| ~ vertex(V1) )
| ~ complete ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f26,definition,
! [V1,V2,E] :
( sP0_prd(E,V2,V1)
<=> ( V2 = tail_of(E)
& V1 = head_of(E) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f27,plain,
( ! [V1,V2] :
( ? [E] :
( ( sP0_prd(E,V2,V1)
<~> ( V1 = tail_of(E)
& V2 = head_of(E) ) )
& edge(E) )
| V1 = V2
| ~ vertex(V2)
| ~ vertex(V1) )
| ~ complete ),
inference(formula_renaming,[status(thm)],[f25,f26]) ).
fof(f28,plain,
( ! [V1,V2] :
( ? [E] :
( ( V1 != tail_of(E)
| V2 != head_of(E)
| ~ sP0_prd(E,V2,V1) )
& ( ( V1 = tail_of(E)
& V2 = head_of(E) )
| sP0_prd(E,V2,V1) )
& edge(E) )
| V1 = V2
| ~ vertex(V2)
| ~ vertex(V1) )
| ~ complete ),
inference(NNF_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [V1,V2] :
( ( ( V1 != tail_of(sK0_skl(V2,V1))
| V2 != head_of(sK0_skl(V2,V1))
| ~ sP0_prd(sK0_skl(V2,V1),V2,V1) )
& ( ( V1 = tail_of(sK0_skl(V2,V1))
& V2 = head_of(sK0_skl(V2,V1)) )
| sP0_prd(sK0_skl(V2,V1),V2,V1) )
& edge(sK0_skl(V2,V1)) )
| V1 = V2
| ~ vertex(V2)
| ~ vertex(V1) )
| ~ complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(E,sK0_skl(V2,V1))],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( edge(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( X1 = head_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( X0 = tail_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( X0 != tail_of(sK0_skl(X1,X0))
| X1 != head_of(sK0_skl(X1,X0))
| ~ sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f34,plain,
! [V1,V2,P] :
( ! [E] :
( ( ! [TP] :
( P != path_cons(E,TP)
| ~ path(head_of(E),V2,TP) )
& ( P != path_cons(E,empty)
| V2 != head_of(E) ) )
| V1 != tail_of(E)
| ~ edge(E) )
| ~ vertex(V2)
| ~ vertex(V1)
| path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( X2 != path_cons(X3,empty)
| X1 != head_of(X3)
| X0 != tail_of(X3)
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0)
| path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f38,definition,
! [V2,P,E] :
( sP1_prd(E,P,V2)
<=> ( P = path_cons(E,empty)
& V2 = head_of(E) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f39,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( sP1_prd(E,P,V2)
<~> ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) ) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(formula_renaming,[status(thm)],[f37,f38]) ).
fof(f40,plain,
! [V1,V2,P] :
( ( ? [E] :
( ( ! [TP] :
( P != path_cons(E,TP)
| ~ path(head_of(E),V2,TP) )
| ~ sP1_prd(E,P,V2) )
& ( ? [TP] :
( P = path_cons(E,TP)
& path(head_of(E),V2,TP) )
| sP1_prd(E,P,V2) )
& V1 = tail_of(E)
& edge(E) )
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(NNF_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [V1,V2,P] :
( ( ( ! [TP] :
( P != path_cons(sK1_skl(P,V2,V1),TP)
| ~ path(head_of(sK1_skl(P,V2,V1)),V2,TP) )
| ~ sP1_prd(sK1_skl(P,V2,V1),P,V2) )
& ( ( P = path_cons(sK1_skl(P,V2,V1),sK2_skl(P,V2,V1))
& path(head_of(sK1_skl(P,V2,V1)),V2,sK2_skl(P,V2,V1)) )
| sP1_prd(sK1_skl(P,V2,V1),P,V2) )
& V1 = tail_of(sK1_skl(P,V2,V1))
& edge(sK1_skl(P,V2,V1))
& vertex(V2)
& vertex(V1) )
| ~ path(V1,V2,P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(E,sK1_skl(P,V2,V1)),skolemize(TP,sK2_skl(P,V2,V1))],[f40]) ).
fof(f44,plain,
! [X0,X1,X2] :
( edge(sK1_skl(X2,X1,X0))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1,X2] :
( X0 = tail_of(sK1_skl(X2,X1,X0))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f49,plain,
! [V1,V2,P,E] :
( ( in_path(tail_of(E),P)
& in_path(head_of(E),P)
& edge(E) )
| ~ on_path(E,P)
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f50,plain,
! [P,E] :
( ( in_path(tail_of(E),P)
& in_path(head_of(E),P)
& edge(E) )
| ~ on_path(E,P)
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( in_path(head_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( in_path(tail_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
! [V1,V2,P,V] :
( ( ? [E] :
( ( V = tail_of(E)
| V = head_of(E) )
& on_path(E,P) )
& vertex(V) )
| ~ in_path(V,P)
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f55,plain,
! [P,V] :
( ( ? [E] :
( ( V = tail_of(E)
| V = head_of(E) )
& on_path(E,P) )
& vertex(V) )
| ~ in_path(V,P)
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f56,plain,
! [P,V] :
( ( ( V = tail_of(sK3_skl(V,P))
| V = head_of(sK3_skl(V,P)) )
& on_path(sK3_skl(V,P),P)
& vertex(V) )
| ~ in_path(V,P)
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(E,sK3_skl(V,P))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2,X3] :
( vertex(X3)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( on_path(sK3_skl(X3,X2),X2)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( X3 = tail_of(sK3_skl(X3,X2))
| X3 = head_of(sK3_skl(X3,X2))
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f60,plain,
! [E1,E2] :
( ( head_of(E1) != tail_of(E2)
| E1 = E2
| ~ edge(E2)
| ~ edge(E1)
| sequential(E1,E2) )
& ( ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) )
| ~ sequential(E1,E2) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f61,plain,
( ! [E1,E2] :
( head_of(E1) != tail_of(E2)
| E1 = E2
| ~ edge(E2)
| ~ edge(E1)
| sequential(E1,E2) )
& ! [E1,E2] :
( ( head_of(E1) = tail_of(E2)
& E1 != E2
& edge(E2)
& edge(E1) )
| ~ sequential(E1,E2) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
! [X0,X1] :
( head_of(X0) = tail_of(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f67,plain,
! [P,V1,V2] :
( ! [E1,E2] :
( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ~ on_path(E2,P)
| ~ on_path(E1,P)
| precedes(E1,E2,P) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
! [P] :
( ! [E1,E2] :
( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ~ on_path(E2,P)
| ~ on_path(E1,P)
| precedes(E1,E2,P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(X3,X4)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ precedes(X5,X4,X2)
| ~ sequential(X3,X5)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f71,plain,
! [P,V1,V2] :
( ! [E1,E2] :
( ( ( sequential(E1,E2)
<~> ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) ) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P) )
| ~ path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f72,plain,
! [P,V1,V2] :
( ! [E1,E2] :
( ( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
| ~ sequential(E1,E2) )
& ( ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) )
| sequential(E1,E2) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P) )
| ~ path(V1,V2,P) ),
inference(NNF_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
! [P] :
( ! [E1,E2] :
( ( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
| ~ sequential(E1,E2) )
& ( ? [E3] :
( precedes(E3,E2,P)
& sequential(E1,E3) )
| sequential(E1,E2) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f74,plain,
! [P] :
( ! [E1,E2] :
( ( ( ! [E3] :
( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
| ~ sequential(E1,E2) )
& ( ( precedes(sK4_skl(E2,E1,P),E2,P)
& sequential(E1,sK4_skl(E2,E1,P)) )
| sequential(E1,E2) )
& on_path(E2,P)
& on_path(E1,P) )
| ~ precedes(E1,E2,P) )
| ! [V1,V2] : ~ path(V1,V2,P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(E3,sK4_skl(E2,E1,P))],[f73]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0,X1,X2,X3,X4] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4] :
( sequential(X3,sK4_skl(X4,X3,X2))
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4] :
( precedes(sK4_skl(X4,X3,X2),X4,X2)
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ precedes(X5,X4,X2)
| ~ sequential(X3,X5)
| ~ sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f80,plain,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) ) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f81,plain,
! [V1,V2,SP] :
( ( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [V1,V2,SP] :
( ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
( ! [V1,V2,SP] :
( ( ~ less_or_equal(length_of(SP),length_of(sK5_skl(SP,V2,V1)))
& path(V1,V2,sK5_skl(SP,V2,V1)) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ! [V1,V2,SP] :
( ( ! [P] :
( less_or_equal(length_of(SP),length_of(P))
| ~ path(V1,V2,P) )
& V1 != V2
& path(V1,V2,SP) )
| ~ shortest_path(V1,V2,SP) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(P,sK5_skl(SP,V2,V1))],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f89,plain,
! [V1,V2,E1,E2,P] :
( ( ~ precedes(E2,E1,P)
& ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f90,plain,
! [E1,E2,P] :
( ( ~ precedes(E2,E1,P)
& ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4,X5] :
( head_of(X5) != head_of(X4)
| tail_of(X5) != tail_of(X3)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X4,X3,X2)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f116,plain,
( ? [V1,V2,E1,E2,P] :
( ( ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) )
<=> ? [E3] :
( head_of(E3) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) ) )
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
& complete ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f117,plain,
( ? [V1,V2,E1,E2,P] :
( ( ! [E3] :
( head_of(E3) != tail_of(E1)
| tail_of(E3) != head_of(E2)
| ~ edge(E3) )
| ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) ) )
& ( ? [E3] :
( head_of(E3) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) )
| ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1)
| ~ edge(E3) ) )
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
& complete ),
inference(NNF_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
( ? [E1,E2] :
( ( ! [E3] :
( head_of(E3) != tail_of(E1)
| tail_of(E3) != head_of(E2)
| ~ edge(E3) )
| ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1)
& edge(E3) ) )
& ( ? [E3] :
( head_of(E3) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) )
| ! [E3] :
( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1)
| ~ edge(E3) ) )
& ? [P] :
( precedes(E1,E2,P)
& ? [V1,V2] : shortest_path(V1,V2,P) ) )
& complete ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f119,plain,
( ( ! [E3] :
( head_of(E3) != tail_of(sK8_skl)
| tail_of(E3) != head_of(sK9_skl)
| ~ edge(E3) )
| ( head_of(sK14_skl) = head_of(sK9_skl)
& tail_of(sK14_skl) = tail_of(sK8_skl)
& edge(sK14_skl) ) )
& ( ( head_of(sK13_skl) = tail_of(sK8_skl)
& tail_of(sK13_skl) = head_of(sK9_skl)
& edge(sK13_skl) )
| ! [E3] :
( head_of(E3) != head_of(sK9_skl)
| tail_of(E3) != tail_of(sK8_skl)
| ~ edge(E3) ) )
& precedes(sK8_skl,sK9_skl,sK10_skl)
& shortest_path(sK11_skl,sK12_skl,sK10_skl)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl,sK14_skl]),skolemize(E1,sK8_skl),skolemize(E2,sK9_skl),skolemize(P,sK10_skl),skolemize(V1,sK11_skl),skolemize(V2,sK12_skl),skolemize(E3,sK13_skl),skolemize(E3,sK14_skl)],[f118]) ).
fof(f120,plain,
complete,
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
shortest_path(sK11_skl,sK12_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
precedes(sK8_skl,sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f123,plain,
! [X0] :
( edge(sK13_skl)
| head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f124,plain,
! [X0] :
( tail_of(sK13_skl) = head_of(sK9_skl)
| head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f125,plain,
! [X0] :
( head_of(sK13_skl) = tail_of(sK8_skl)
| head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f127,plain,
! [X0] :
( head_of(X0) != tail_of(sK8_skl)
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0)
| tail_of(sK14_skl) = tail_of(sK8_skl) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f128,plain,
! [X0] :
( head_of(X0) != tail_of(sK8_skl)
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0)
| head_of(sK14_skl) = head_of(sK9_skl) ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f129,plain,
! [V1,V2,E] :
( ( V2 != tail_of(E)
| V1 != head_of(E)
| sP0_prd(E,V2,V1) )
& ( ( V2 = tail_of(E)
& V1 = head_of(E) )
| ~ sP0_prd(E,V2,V1) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f130,plain,
( ! [V1,V2,E] :
( V2 != tail_of(E)
| V1 != head_of(E)
| sP0_prd(E,V2,V1) )
& ! [V1,V2,E] :
( ( V2 = tail_of(E)
& V1 = head_of(E) )
| ~ sP0_prd(E,V2,V1) ) ),
inference(miniscoping,[status(thm)],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( X2 = head_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f132,plain,
! [X0,X1,X2] :
( X1 = tail_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f133,plain,
! [X0,X1,X2] :
( X1 != tail_of(X0)
| X2 != head_of(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f139,definition,
( sQ0_spl
<=> complete ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( sQ0_spl
| ~ complete ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X0,X1] :
( sQ1_spl
<=> ( edge(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ1_spl
| edge(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f139,f142]) ).
fof(f146,definition,
! [X0,X1] :
( sQ2_spl
<=> ( X1 = head_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f147,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = head_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f139,f146]) ).
fof(f150,definition,
! [X0,X1] :
( sQ3_spl
<=> ( X0 = tail_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f151,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = tail_of(sK0_skl(X1,X0))
| sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f139,f150]) ).
fof(f154,definition,
! [X0,X1] :
( sQ4_spl
<=> ( X0 != tail_of(sK0_skl(X1,X0))
| X1 != head_of(sK0_skl(X1,X0))
| ~ sP0_prd(sK0_skl(X1,X0),X1,X0)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f139,f154]) ).
fof(f158,definition,
! [X0] :
( sQ5_spl
<=> ( head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl)
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f159,plain,
! [X0] :
( ~ sQ5_spl
| head_of(X0) != head_of(sK9_skl)
| tail_of(X0) != tail_of(sK8_skl)
| ~ edge(X0) ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,definition,
( sQ6_spl
<=> edge(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f123,f158,f161]) ).
fof(f165,definition,
( sQ7_spl
<=> tail_of(sK13_skl) = head_of(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ7_spl
| tail_of(sK13_skl) = head_of(sK9_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ7_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f124,f158,f165]) ).
fof(f169,definition,
( sQ8_spl
<=> head_of(sK13_skl) = tail_of(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ8_spl
| head_of(sK13_skl) = tail_of(sK8_skl) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f125,f158,f169]) ).
fof(f176,definition,
! [X0] :
( sQ10_spl
<=> ( head_of(X0) != tail_of(sK8_skl)
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f177,plain,
! [X0] :
( ~ sQ10_spl
| head_of(X0) != tail_of(sK8_skl)
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f180,definition,
( sQ11_spl
<=> tail_of(sK14_skl) = tail_of(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ11_spl
| tail_of(sK14_skl) = tail_of(sK8_skl) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f127,f180,f176]) ).
fof(f184,definition,
( sQ12_spl
<=> head_of(sK14_skl) = head_of(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ12_spl
| head_of(sK14_skl) = head_of(sK9_skl) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f128,f184,f176]) ).
fof(f188,plain,
! [X0] :
( ~ edge(X0)
| ~ vertex(head_of(X0))
| ~ vertex(tail_of(X0))
| path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
inference(destructive_equality_resolution,[status(thm)],[f35]) ).
fof(f192,plain,
! [X0] : sP0_prd(X0,tail_of(X0),head_of(X0)),
inference(destructive_equality_resolution,[status(thm)],[f133]) ).
fof(f194,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f120]) ).
fof(f195,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
path(sK11_skl,sK12_skl,sK10_skl),
inference(resolution,[status(thm)],[f84,f121]) ).
fof(f199,plain,
! [X0,X1,X2] :
( ~ sequential(X2,sK8_skl)
| ~ sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f79,f122]) ).
fof(f201,definition,
! [X0,X1] :
( sQ13_spl
<=> ~ path(X0,X1,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ path(X0,X1,sK10_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f207,definition,
( sQ15_spl
<=> sequential(sK8_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f215,definition,
! [X2] :
( sQ17_spl
<=> ( ~ sequential(X2,sK8_skl)
| ~ sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f216,plain,
! [X0] :
( ~ sQ17_spl
| ~ sequential(X0,sK8_skl)
| ~ sequential(X0,sK9_skl)
| ~ precedes(X0,sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( sQ17_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f199,f201,f215]) ).
fof(f219,plain,
! [X0,X1,X2,X3,X4] :
( head_of(X3) != head_of(X4)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f91]) ).
fof(f220,plain,
! [X0] :
( ~ edge(X0)
| ~ vertex(head_of(X0))
| path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f24]) ).
fof(f224,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f196,f202]) ).
fof(f225,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f224]) ).
fof(f227,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK10_skl)
| ~ precedes(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f92,f121]) ).
fof(f229,definition,
( sQ18_spl
<=> edge(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ18_spl
| ~ edge(sK8_skl) ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f239,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( head_of(X0) != head_of(X6)
| ~ precedes(sK1_skl(X2,X1,tail_of(X0)),X6,X5)
| ~ shortest_path(X3,X4,X5)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f45,f91]) ).
fof(f241,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( head_of(sK1_skl(X2,X1,tail_of(X0))) != head_of(X6)
| ~ precedes(X0,X6,X5)
| ~ shortest_path(X3,X4,X5)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f45,f91]) ).
fof(f245,plain,
~ precedes(sK9_skl,sK8_skl,sK10_skl),
inference(resolution,[status(thm)],[f227,f122]) ).
fof(f248,plain,
! [X0,X1,X2,X3] :
( ~ precedes(X3,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f219]) ).
fof(f249,plain,
! [X0] : ~ precedes(X0,X0,sK10_skl),
inference(resolution,[status(thm)],[f248,f121]) ).
fof(f250,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = tail_of(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| X0 = head_of(sK0_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f131,f151]) ).
fof(f251,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = head_of(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| X0 = head_of(sK0_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f131,f147]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ3_spl
| X1 = tail_of(sK0_skl(X0,X1))
| X1 = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = tail_of(sK0_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f132,f151]) ).
fof(f253,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = head_of(sK0_skl(X0,X1))
| X1 = X0
| ~ vertex(X0)
| ~ vertex(X1)
| X0 = tail_of(sK0_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f132,f147]) ).
fof(f258,plain,
! [X0] :
( edge(X0)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f51,f196]) ).
fof(f261,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ precedes(sK1_skl(X2,X1,tail_of(X0)),X0,X5)
| ~ shortest_path(X3,X4,X5)
| ~ path(tail_of(X0),X1,X2) ),
inference(equality_resolution,[status(thm)],[f239]) ).
fof(f270,definition,
( sQ21_spl
<=> vertex(tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f274,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ2_spl
| ~ precedes(sK1_skl(X3,X2,tail_of(X1)),sK0_skl(head_of(X1),X0),X6)
| ~ shortest_path(X4,X5,X6)
| ~ path(tail_of(X1),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f251,f239]) ).
fof(f275,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ2_spl
| ~ precedes(X1,sK0_skl(head_of(X1),X0),X4)
| ~ shortest_path(X2,X3,X4)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f251,f219]) ).
fof(f276,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ2_spl
| ~ precedes(sK1_skl(X3,X2,tail_of(sK0_skl(head_of(X1),X0))),X1,X6)
| ~ shortest_path(X4,X5,X6)
| ~ path(tail_of(sK0_skl(head_of(X1),X0)),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f251,f239]) ).
fof(f277,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ2_spl
| ~ precedes(sK0_skl(head_of(X1),X0),X1,X4)
| ~ shortest_path(X2,X3,X4)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f251,f219]) ).
fof(f287,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| head_of(sK0_skl(X0,tail_of(sK8_skl))) != head_of(sK9_skl)
| ~ edge(sK0_skl(X0,tail_of(sK8_skl)))
| tail_of(sK8_skl) = X0
| ~ vertex(X0)
| ~ vertex(tail_of(sK8_skl))
| X0 = tail_of(sK0_skl(X0,tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f252,f159]) ).
fof(f288,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ3_spl
| head_of(sK0_skl(X0,tail_of(X1))) != head_of(X5)
| ~ precedes(X1,X5,X4)
| ~ shortest_path(X2,X3,X4)
| tail_of(X1) = X0
| ~ vertex(X0)
| ~ vertex(tail_of(X1))
| X0 = tail_of(sK0_skl(X0,tail_of(X1))) ),
inference(resolution,[status(thm)],[f252,f91]) ).
fof(f291,definition,
! [X0] :
( sQ23_spl
<=> ( head_of(sK0_skl(X0,tail_of(sK8_skl))) != head_of(sK9_skl)
| ~ edge(sK0_skl(X0,tail_of(sK8_skl)))
| tail_of(sK8_skl) = X0
| ~ vertex(X0)
| X0 = tail_of(sK0_skl(X0,tail_of(sK8_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f292,plain,
! [X0] :
( ~ sQ23_spl
| head_of(sK0_skl(X0,tail_of(sK8_skl))) != head_of(sK9_skl)
| ~ edge(sK0_skl(X0,tail_of(sK8_skl)))
| tail_of(sK8_skl) = X0
| ~ vertex(X0)
| X0 = tail_of(sK0_skl(X0,tail_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f287,f291,f270,f150,f158]) ).
fof(f300,plain,
( ~ sQ7_spl
| head_of(sK13_skl) != head_of(sK9_skl)
| ~ edge(sK13_skl) ),
inference(paramodulation,[status(thm)],[f166,f21]) ).
fof(f308,definition,
( sQ26_spl
<=> vertex(head_of(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( sQ26_spl
| ~ vertex(head_of(sK9_skl)) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f312,definition,
( sQ27_spl
<=> head_of(sK13_skl) = head_of(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ27_spl
| head_of(sK13_skl) != head_of(sK9_skl) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f300,f161,f312,f165]) ).
fof(f316,plain,
! [X0] :
( ~ sQ10_spl
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0)
| ~ sequential(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f65,f177]) ).
fof(f320,plain,
! [X0] :
( ~ sQ10_spl
| tail_of(X0) != head_of(sK9_skl)
| ~ sequential(X0,sK8_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f62]) ).
fof(f322,plain,
! [X0] :
( in_path(head_of(X0),sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f52,f196]) ).
fof(f326,plain,
! [X0] :
( in_path(tail_of(X0),sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f53,f196]) ).
fof(f330,plain,
! [X0] :
( vertex(X0)
| ~ in_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f57,f196]) ).
fof(f333,plain,
! [X0] :
( ~ sQ10_spl
| ~ sequential(sK9_skl,X0)
| ~ sequential(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f320,f65]) ).
fof(f354,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| head_of(sK14_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f181,f91]) ).
fof(f385,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ2_spl
| X6 = head_of(sK1_skl(X2,X1,tail_of(X0)))
| ~ vertex(head_of(sK1_skl(X2,X1,tail_of(X0))))
| ~ vertex(X6)
| X6 = head_of(sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X6))
| ~ precedes(X0,sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X6),X5)
| ~ shortest_path(X3,X4,X5)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f241,f251]) ).
fof(f386,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ precedes(X0,sK1_skl(X2,X1,tail_of(X0)),X5)
| ~ shortest_path(X3,X4,X5)
| ~ path(tail_of(X0),X1,X2) ),
inference(equality_resolution,[status(thm)],[f241]) ).
fof(f389,plain,
! [X0] :
( vertex(head_of(X0))
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f322,f330]) ).
fof(f390,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f326,f330]) ).
fof(f397,plain,
! [X0,X1,X2] :
( vertex(tail_of(sK3_skl(X2,sK10_skl)))
| ~ in_path(X2,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f58,f390]) ).
fof(f398,plain,
! [X0,X1,X2] :
( vertex(head_of(sK3_skl(X2,sK10_skl)))
| ~ in_path(X2,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f58,f389]) ).
fof(f399,plain,
! [X0,X1,X2] :
( edge(sK3_skl(X2,sK10_skl))
| ~ in_path(X2,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f58,f258]) ).
fof(f400,definition,
! [X2] :
( sQ34_spl
<=> ( vertex(tail_of(sK3_skl(X2,sK10_skl)))
| ~ in_path(X2,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( sQ34_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f397,f201,f400]) ).
fof(f404,definition,
! [X2] :
( sQ35_spl
<=> ( vertex(head_of(sK3_skl(X2,sK10_skl)))
| ~ in_path(X2,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f407,plain,
( sQ35_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f398,f201,f404]) ).
fof(f408,definition,
! [X2] :
( sQ36_spl
<=> ( edge(sK3_skl(X2,sK10_skl))
| ~ in_path(X2,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( sQ36_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f399,f201,f408]) ).
fof(f417,plain,
! [X0,X1,X2,X3] :
( head_of(X0) = head_of(sK3_skl(head_of(X0),X1))
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f66,f59]) ).
fof(f420,plain,
! [X0,X1,X2] :
( ~ path(head_of(X0),X2,X1)
| X0 = sK1_skl(X1,X2,head_of(X0))
| ~ edge(sK1_skl(X1,X2,head_of(X0)))
| ~ edge(X0)
| sequential(X0,sK1_skl(X1,X2,head_of(X0))) ),
inference(resolution,[status(thm)],[f66,f45]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ path(head_of(X0),X2,X1)
| X0 = sK1_skl(X1,X2,head_of(X0))
| ~ edge(X0)
| sequential(X0,sK1_skl(X1,X2,head_of(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f44]) ).
fof(f427,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = sK0_skl(head_of(X1),X0)
| ~ edge(sK0_skl(head_of(X1),X0))
| ~ edge(X1)
| sequential(X1,sK0_skl(head_of(X1),X0))
| head_of(X1) = head_of(sK0_skl(head_of(X1),X0))
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f253,f66]) ).
fof(f429,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sequential(sK0_skl(head_of(sK9_skl),X0),sK8_skl)
| head_of(sK9_skl) = head_of(sK0_skl(head_of(sK9_skl),X0))
| X0 = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f253,f320]) ).
fof(f432,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = sK0_skl(head_of(X1),X0)
| ~ edge(sK0_skl(head_of(X1),X0))
| ~ edge(X1)
| sequential(X1,sK0_skl(head_of(X1),X0))
| head_of(X1) = head_of(sK0_skl(head_of(X1),X0))
| X0 = head_of(X1)
| ~ vertex(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f23]) ).
fof(f433,definition,
! [X0] :
( sQ37_spl
<=> ( ~ sequential(sK0_skl(head_of(sK9_skl),X0),sK8_skl)
| head_of(sK9_skl) = head_of(sK0_skl(head_of(sK9_skl),X0))
| X0 = head_of(sK9_skl)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f434,plain,
! [X0] :
( ~ sQ37_spl
| ~ sequential(sK0_skl(head_of(sK9_skl),X0),sK8_skl)
| head_of(sK9_skl) = head_of(sK0_skl(head_of(sK9_skl),X0))
| X0 = head_of(sK9_skl)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ26_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f429,f433,f308,f146,f176]) ).
fof(f443,plain,
( ~ sQ8_spl
| sK13_skl = sK8_skl
| ~ edge(sK8_skl)
| ~ edge(sK13_skl)
| sequential(sK13_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f170,f66]) ).
fof(f454,plain,
( ~ sQ8_spl
| head_of(sK8_skl) != head_of(sK13_skl)
| ~ edge(sK8_skl) ),
inference(paramodulation,[status(thm)],[f170,f21]) ).
fof(f455,definition,
( sQ39_spl
<=> sequential(sK13_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ39_spl
| sequential(sK13_skl,sK8_skl) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,definition,
( sQ40_spl
<=> sK13_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ40_spl
| sK13_skl = sK8_skl ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( ~ sQ8_spl
| sQ40_spl
| ~ sQ18_spl
| ~ sQ6_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f443,f455,f161,f229,f458,f169]) ).
fof(f467,definition,
( sQ42_spl
<=> on_path(sK8_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ42_spl
| on_path(sK8_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f478,definition,
( sQ45_spl
<=> vertex(head_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ45_spl
| ~ vertex(head_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f483,definition,
( sQ46_spl
<=> head_of(sK8_skl) = head_of(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ46_spl
| head_of(sK8_skl) != head_of(sK13_skl) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( ~ sQ8_spl
| ~ sQ46_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f454,f229,f483,f169]) ).
fof(f495,plain,
( ~ sQ7_spl
| sK9_skl = sK13_skl
| ~ edge(sK13_skl)
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK13_skl) ),
inference(resolution,[status(thm)],[f166,f66]) ).
fof(f506,definition,
( sQ47_spl
<=> sequential(sK9_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ47_spl
| sequential(sK9_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ48_spl
<=> edge(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( sQ48_spl
| ~ edge(sK9_skl) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,definition,
( sQ49_spl
<=> sK9_skl = sK13_skl ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ49_spl
| sK9_skl = sK13_skl ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f515,plain,
( ~ sQ7_spl
| sQ49_spl
| ~ sQ6_spl
| ~ sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f495,f506,f509,f161,f512,f165]) ).
fof(f532,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl)
| precedes(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f69,f196]) ).
fof(f536,definition,
! [X2] :
( sQ53_spl
<=> ( ~ sequential(X2,sK8_skl)
| ~ on_path(X2,sK10_skl)
| precedes(X2,sK9_skl,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f537,plain,
! [X0] :
( ~ sQ53_spl
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl)
| precedes(X0,sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,definition,
( sQ54_spl
<=> on_path(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( ~ sQ54_spl
| on_path(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f543,plain,
! [X0,X1] :
( on_path(sK8_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f75,f122]) ).
fof(f544,plain,
( sQ42_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f543,f201,f467]) ).
fof(f550,plain,
( sQ26_spl
| ~ edge(sK9_skl) ),
inference(resolution,[status(thm)],[f310,f23]) ).
fof(f563,plain,
( ~ sQ42_spl
| vertex(tail_of(sK8_skl)) ),
inference(resolution,[status(thm)],[f468,f390]) ).
fof(f564,plain,
( ~ sQ42_spl
| vertex(head_of(sK8_skl)) ),
inference(resolution,[status(thm)],[f468,f389]) ).
fof(f565,plain,
( ~ sQ42_spl
| edge(sK8_skl) ),
inference(resolution,[status(thm)],[f468,f258]) ).
fof(f566,plain,
( ~ sQ42_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f563,f270,f467]) ).
fof(f567,plain,
( ~ sQ42_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f565,f231]) ).
fof(f568,plain,
( ~ sQ42_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f570,plain,
( sQ27_spl
| ~ sQ49_spl
| head_of(sK9_skl) != head_of(sK9_skl) ),
inference(backward_demodulation,[status(thm)],[f513,f314]) ).
fof(f571,plain,
( sQ27_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f570]) ).
fof(f572,plain,
( sQ27_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f573,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ precedes(X5,X4,X2)
| ~ sequential(X3,X5)
| ~ on_path(X3,X2)
| precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f70,f76]) ).
fof(f574,plain,
! [X0,X1] :
( on_path(sK9_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f76,f122]) ).
fof(f575,plain,
( sQ54_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f574,f201,f539]) ).
fof(f577,plain,
! [X0,X1,X2,X3,X4] :
( edge(X3)
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f77,f62]) ).
fof(f578,plain,
! [X0,X1,X2,X3,X4] :
( edge(X3)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f62]) ).
fof(f579,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK8_skl)
| ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK9_skl)
| sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f78,f216]) ).
fof(f580,plain,
! [X0,X1,X2,X3] :
( ~ precedes(X3,sK4_skl(X3,X2,sK10_skl),sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f78,f227]) ).
fof(f582,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( on_path(sK4_skl(X4,X3,X2),X2)
| ~ path(X5,X6,X2)
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f75]) ).
fof(f586,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ precedes(X7,X4,X2)
| ~ sequential(sK4_skl(X4,X3,X2),X7)
| ~ sequential(sK4_skl(X4,X3,X2),X4)
| ~ path(X5,X6,X2)
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f79]) ).
fof(f587,definition,
! [X2] :
( sQ55_spl
<=> ( ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK8_skl)
| ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK9_skl)
| sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( ~ sQ17_spl
| sQ55_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f579,f201,f587,f215]) ).
fof(f591,definition,
! [X2,X3] :
( sQ56_spl
<=> ( ~ precedes(X3,sK4_skl(X3,X2,sK10_skl),sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f594,plain,
( sQ56_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f580,f201,f591]) ).
fof(f674,plain,
( ~ sQ54_spl
| edge(sK9_skl) ),
inference(resolution,[status(thm)],[f540,f258]) ).
fof(f765,plain,
( ~ sQ47_spl
| ~ sQ10_spl
| ~ sequential(sK13_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f333,f507]) ).
fof(f767,plain,
( ~ sQ47_spl
| ~ sQ10_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f765,f456]) ).
fof(f768,plain,
( ~ sQ47_spl
| ~ sQ10_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f771,plain,
( sQ46_spl
| ~ sQ40_spl
| head_of(sK8_skl) != head_of(sK8_skl) ),
inference(backward_demodulation,[status(thm)],[f459,f485]) ).
fof(f778,plain,
( sQ46_spl
| ~ sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f771]) ).
fof(f779,plain,
( sQ46_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f798,plain,
( ~ sQ54_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f674,f511]) ).
fof(f799,plain,
( ~ sQ54_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f798]) ).
fof(f893,plain,
! [X0,X1,X2] :
( ~ sequential(X2,sK8_skl)
| ~ on_path(X2,sK10_skl)
| precedes(X2,sK9_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f573,f122]) ).
fof(f894,plain,
( sQ53_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f893,f201,f536]) ).
fof(f987,definition,
( sQ75_spl
<=> sequential(sK9_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1101,plain,
! [X0] :
( ~ sQ53_spl
| ~ precedes(sK9_skl,X0,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f227]) ).
fof(f1102,plain,
! [X0,X1,X2,X3] :
( ~ sQ53_spl
| ~ sequential(X3,X0)
| ~ on_path(X3,sK10_skl)
| precedes(X3,sK9_skl,sK10_skl)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f573]) ).
fof(f1104,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| on_path(X0,sK10_skl)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f75]) ).
fof(f1105,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| ~ sequential(X0,X0)
| ~ sequential(X0,sK9_skl)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f79]) ).
fof(f1106,plain,
! [X0,X1,X2,X3] :
( ~ sQ53_spl
| ~ sequential(X3,X0)
| ~ sequential(X3,sK9_skl)
| ~ precedes(X3,sK9_skl,sK10_skl)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f79]) ).
fof(f1108,plain,
! [X0,X1,X2,X3] :
( ~ sQ53_spl
| ~ precedes(X3,sK9_skl,sK10_skl)
| ~ sequential(X0,X3)
| ~ sequential(X0,sK9_skl)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f79]) ).
fof(f1111,definition,
! [X0,X3] :
( sQ80_spl
<=> ( ~ sequential(X3,X0)
| ~ on_path(X3,sK10_skl)
| precedes(X3,sK9_skl,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
! [X0,X1] :
( ~ sQ80_spl
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| precedes(X1,sK9_skl,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f1111]) ).
fof(f1114,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1102,f1111,f201,f536]) ).
fof(f1119,definition,
! [X0] :
( sQ82_spl
<=> ( on_path(X0,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1122,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ82_spl ),
inference(split_clause,[status(thm)],[f1104,f1119,f201,f536]) ).
fof(f1123,definition,
! [X0] :
( sQ83_spl
<=> ( ~ sequential(X0,X0)
| ~ sequential(X0,sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1126,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1105,f1123,f201,f536]) ).
fof(f1127,definition,
! [X0,X3] :
( sQ84_spl
<=> ( ~ sequential(X3,X0)
| ~ sequential(X3,sK9_skl)
| ~ precedes(X3,sK9_skl,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1128,plain,
! [X0,X1] :
( ~ sQ84_spl
| ~ sequential(X1,X0)
| ~ sequential(X1,sK9_skl)
| ~ precedes(X1,sK9_skl,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f1127]) ).
fof(f1130,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1106,f1127,f201,f536]) ).
fof(f1132,definition,
! [X0,X3] :
( sQ85_spl
<=> ( ~ precedes(X3,sK9_skl,sK10_skl)
| ~ sequential(X0,X3)
| ~ sequential(X0,sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1135,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1108,f1132,f201,f536]) ).
fof(f1151,definition,
( sQ86_spl
<=> sK9_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1152,plain,
( ~ sQ86_spl
| sK9_skl = sK8_skl ),
inference(component_clause,[status(thm)],[f1151]) ).
fof(f1192,plain,
( ~ sQ86_spl
| precedes(sK8_skl,sK8_skl,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f1152,f122]) ).
fof(f1196,plain,
( ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1192,f249]) ).
fof(f1197,plain,
~ sQ86_spl,
inference(contradiction_clause,[status(thm)],[f1196]) ).
fof(f1304,definition,
( sQ94_spl
<=> head_of(sK13_skl) = head_of(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( sQ94_spl
| head_of(sK13_skl) != head_of(sK13_skl) ),
inference(component_clause,[status(thm)],[f1304]) ).
fof(f1312,plain,
( sQ94_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1306]) ).
fof(f1313,plain,
sQ94_spl,
inference(contradiction_clause,[status(thm)],[f1312]) ).
fof(f1442,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ precedes(sK1_skl(X5,X4,tail_of(X0)),sK3_skl(head_of(X0),X1),X8)
| ~ shortest_path(X6,X7,X8)
| ~ path(tail_of(X0),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f417,f239]) ).
fof(f1443,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ precedes(X0,sK3_skl(head_of(X0),X1),X6)
| ~ shortest_path(X4,X5,X6)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f417,f219]) ).
fof(f1445,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ precedes(sK1_skl(X5,X4,tail_of(sK3_skl(head_of(X0),X1))),X0,X8)
| ~ shortest_path(X6,X7,X8)
| ~ path(tail_of(sK3_skl(head_of(X0),X1)),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f417,f239]) ).
fof(f1446,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ precedes(sK3_skl(head_of(X0),X1),X0,X6)
| ~ shortest_path(X4,X5,X6)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f417,f219]) ).
fof(f1494,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( sequential(sK4_skl(X4,X3,X2),X7)
| ~ precedes(sK4_skl(X4,X3,X2),X7,X8)
| ~ path(X9,X10,X8)
| ~ precedes(sK4_skl(X7,sK4_skl(X4,X3,X2),X8),X4,X2)
| ~ sequential(sK4_skl(X4,X3,X2),X4)
| ~ path(X5,X6,X2)
| sequential(X3,X4)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(resolution,[status(thm)],[f586,f77]) ).
fof(f1511,definition,
! [X1,X2] :
( sQ120_spl
<=> ~ path(X1,X2,path_cons(sK8_skl,empty)) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1512,plain,
! [X0,X1] :
( ~ sQ120_spl
| ~ path(X0,X1,path_cons(sK8_skl,empty)) ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1538,plain,
! [X0,X1,X2,X3,X4,X5] :
( vertex(tail_of(sK4_skl(X3,X2,sK10_skl)))
| ~ path(X4,X5,sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f582,f390]) ).
fof(f1539,plain,
! [X0,X1,X2,X3,X4,X5] :
( vertex(head_of(sK4_skl(X3,X2,sK10_skl)))
| ~ path(X4,X5,sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f582,f389]) ).
fof(f1540,plain,
! [X0,X1,X2,X3,X4,X5] :
( edge(sK4_skl(X3,X2,sK10_skl))
| ~ path(X4,X5,sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f582,f258]) ).
fof(f1549,definition,
! [X2,X3] :
( sQ123_spl
<=> ( vertex(tail_of(sK4_skl(X3,X2,sK10_skl)))
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( sQ123_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1538,f201,f1549]) ).
fof(f1553,definition,
! [X2,X3] :
( sQ124_spl
<=> ( vertex(head_of(sK4_skl(X3,X2,sK10_skl)))
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1556,plain,
( sQ124_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1539,f201,f1553]) ).
fof(f1557,definition,
! [X2,X3] :
( sQ125_spl
<=> ( edge(sK4_skl(X3,X2,sK10_skl))
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
( sQ125_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f1540,f201,f1557]) ).
fof(f1582,plain,
( ~ sQ120_spl
| ~ edge(sK8_skl)
| ~ vertex(head_of(sK8_skl)) ),
inference(resolution,[status(thm)],[f1512,f220]) ).
fof(f1816,definition,
! [X0,X1,X2,X3] :
( sQ160_spl
<=> ( head_of(sK9_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1817,plain,
! [X0,X1,X2,X3] :
( ~ sQ160_spl
| head_of(sK9_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f1816]) ).
fof(f1821,plain,
! [X0,X1,X2,X3] :
( ~ sQ11_spl
| ~ sQ12_spl
| head_of(sK9_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f185,f354]) ).
fof(f1830,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ precedes(sK8_skl,sK9_skl,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f1821]) ).
fof(f1835,definition,
! [X0,X1,X2] :
( sQ162_spl
<=> ( ~ precedes(sK8_skl,sK9_skl,X2)
| ~ shortest_path(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1836,plain,
! [X0,X1,X2] :
( ~ sQ162_spl
| ~ precedes(sK8_skl,sK9_skl,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f1835]) ).
fof(f1858,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ precedes(sK8_skl,sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f1830,f121]) ).
fof(f1859,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1858,f122]) ).
fof(f1860,plain,
( ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1859]) ).
fof(f1861,plain,
( sQ45_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f564]) ).
fof(f1862,plain,
( sQ45_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f1861]) ).
fof(f1869,plain,
( sQ26_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f550,f509,f308]) ).
fof(f1875,plain,
( ~ sQ120_spl
| ~ sQ18_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f1582,f478,f229,f1511]) ).
fof(f1912,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| edge(X0)
| ~ path(X1,X2,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f537,f578]) ).
fof(f1921,definition,
! [X0] :
( sQ170_spl
<=> ( edge(X0)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1924,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1912,f1921,f201,f536]) ).
fof(f2108,plain,
( ~ sequential(sK9_skl,sK8_skl)
| ~ on_path(sK8_skl,sK10_skl)
| ~ on_path(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f245]) ).
fof(f2109,plain,
! [X0] :
( ~ sQ53_spl
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl)
| ~ sequential(sK9_skl,X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f1101]) ).
fof(f2110,plain,
! [X0] :
( ~ sQ17_spl
| ~ sequential(X0,sK8_skl)
| ~ sequential(X0,sK9_skl)
| ~ sequential(X0,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f216]) ).
fof(f2112,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f227]) ).
fof(f2113,plain,
! [X0,X1,X2,X3] :
( edge(X0)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f578]) ).
fof(f2114,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(X4,X0)
| ~ on_path(X4,sK10_skl)
| precedes(X4,X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f573]) ).
fof(f2115,plain,
! [X0,X1,X2,X3] :
( on_path(X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f76]) ).
fof(f2116,plain,
! [X0,X1,X2,X3] :
( on_path(X0,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f75]) ).
fof(f2117,plain,
! [X0,X1,X2,X3] :
( ~ sequential(X0,X0)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f79]) ).
fof(f2118,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(X4,X0)
| ~ sequential(X4,X1)
| ~ precedes(X4,X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f79]) ).
fof(f2120,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X4,X1,sK10_skl)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f532,f79]) ).
fof(f2129,plain,
( ~ sQ75_spl
| ~ sQ42_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2108,f539,f467,f987]) ).
fof(f2130,definition,
! [X0] :
( sQ185_spl
<=> ( ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl)
| ~ sequential(sK9_skl,X0)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2133,plain,
( ~ sQ53_spl
| sQ185_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2109,f539,f2130,f536]) ).
fof(f2134,definition,
! [X0] :
( sQ186_spl
<=> ( ~ sequential(X0,sK8_skl)
| ~ sequential(X0,sK9_skl)
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( ~ sQ17_spl
| ~ sQ54_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f2110,f2134,f539,f215]) ).
fof(f2139,definition,
! [X0,X1] :
( sQ187_spl
<=> ( edge(X0)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2142,plain,
( sQ13_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f2113,f2139,f201]) ).
fof(f2143,definition,
! [X0,X1,X4] :
( sQ188_spl
<=> ( ~ sequential(X4,X0)
| ~ on_path(X4,sK10_skl)
| precedes(X4,X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f2146,plain,
( sQ13_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f2114,f2143,f201]) ).
fof(f2147,definition,
! [X0,X1] :
( sQ189_spl
<=> ( on_path(X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2150,plain,
( sQ13_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f2115,f2147,f201]) ).
fof(f2151,definition,
! [X0,X1] :
( sQ190_spl
<=> ( on_path(X0,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2154,plain,
( sQ13_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f2116,f2151,f201]) ).
fof(f2155,definition,
! [X0,X1] :
( sQ191_spl
<=> ( ~ sequential(X0,X0)
| ~ sequential(X0,X1)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2158,plain,
( sQ13_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f2117,f2155,f201]) ).
fof(f2159,definition,
! [X0,X1,X4] :
( sQ192_spl
<=> ( ~ sequential(X4,X0)
| ~ sequential(X4,X1)
| ~ precedes(X4,X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2162,plain,
( sQ13_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f2118,f2159,f201]) ).
fof(f2164,definition,
! [X0,X1,X4] :
( sQ193_spl
<=> ( ~ precedes(X4,X1,sK10_skl)
| ~ sequential(X0,X4)
| ~ sequential(X0,X1)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2165,plain,
! [X0,X1,X2] :
( ~ sQ193_spl
| ~ precedes(X2,X1,sK10_skl)
| ~ sequential(X0,X2)
| ~ sequential(X0,X1)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f2164]) ).
fof(f2167,plain,
( sQ13_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f2120,f2164,f201]) ).
fof(f2171,plain,
! [X0,X1,X2] :
( ~ sQ193_spl
| ~ precedes(X2,X1,sK10_skl)
| ~ sequential(X0,X2)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f2165]) ).
fof(f2173,plain,
! [X0,X1,X2,X3] :
( sequential(X1,X0)
| ~ precedes(X1,X0,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X0,sK4_skl(X0,X1,sK10_skl))
| ~ on_path(sK4_skl(X0,X1,sK10_skl),sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2112,f78]) ).
fof(f2175,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2112,f532]) ).
fof(f2177,definition,
! [X0,X1] :
( sQ194_spl
<=> ( sequential(X1,X0)
| ~ precedes(X1,X0,sK10_skl)
| ~ sequential(X0,sK4_skl(X0,X1,sK10_skl))
| ~ on_path(sK4_skl(X0,X1,sK10_skl),sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2180,plain,
( sQ13_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f2173,f2177,f201]) ).
fof(f2182,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f2175]) ).
fof(f2183,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ path(X5,X6,sK10_skl)
| sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ path(X3,X4,sK10_skl)
| ~ sequential(sK4_skl(X1,X2,sK10_skl),X0)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2182,f582]) ).
fof(f2184,plain,
! [X0] :
( ~ sQ54_spl
| ~ sequential(sK9_skl,X0)
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2182,f540]) ).
fof(f2185,plain,
! [X0] :
( ~ sQ42_spl
| ~ sequential(sK8_skl,X0)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2182,f468]) ).
fof(f2186,plain,
! [X0,X1,X2,X3] :
( ~ in_path(X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(sK3_skl(X1,sK10_skl),X0)
| ~ sequential(X0,sK3_skl(X1,sK10_skl))
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2182,f58]) ).
fof(f2192,definition,
! [X0,X1,X2] :
( sQ195_spl
<=> ( sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ sequential(sK4_skl(X1,X2,sK10_skl),X0)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( sQ13_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f2183,f2192,f201]) ).
fof(f2196,definition,
! [X0,X1] :
( sQ196_spl
<=> ( ~ in_path(X1,sK10_skl)
| ~ sequential(sK3_skl(X1,sK10_skl),X0)
| ~ sequential(X0,sK3_skl(X1,sK10_skl))
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2199,plain,
( sQ13_spl
| sQ196_spl ),
inference(split_clause,[status(thm)],[f2186,f2196,f201]) ).
fof(f2203,plain,
! [X0,X1] :
( ~ sQ54_spl
| ~ path(head_of(sK9_skl),X1,X0)
| sK9_skl = sK1_skl(X0,X1,head_of(sK9_skl))
| ~ edge(sK9_skl)
| ~ sequential(sK1_skl(X0,X1,head_of(sK9_skl)),sK9_skl)
| ~ on_path(sK1_skl(X0,X1,head_of(sK9_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f2184,f424]) ).
fof(f2205,plain,
( ~ sQ54_spl
| ~ sequential(sK9_skl,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl) ),
inference(factoring,[status(thm)],[f2184]) ).
fof(f2206,definition,
! [X0,X1] :
( sQ197_spl
<=> ( ~ path(head_of(sK9_skl),X1,X0)
| sK9_skl = sK1_skl(X0,X1,head_of(sK9_skl))
| ~ sequential(sK1_skl(X0,X1,head_of(sK9_skl)),sK9_skl)
| ~ on_path(sK1_skl(X0,X1,head_of(sK9_skl)),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2209,plain,
( ~ sQ54_spl
| ~ sQ48_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f2203,f2206,f509,f539]) ).
fof(f2210,definition,
( sQ198_spl
<=> sequential(sK9_skl,sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2213,plain,
( ~ sQ198_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2205,f539,f2210]) ).
fof(f2214,plain,
! [X0,X1,X2,X3] :
( ~ sQ53_spl
| ~ sequential(sK1_skl(X1,X0,tail_of(sK9_skl)),sK8_skl)
| ~ on_path(sK1_skl(X1,X0,tail_of(sK9_skl)),sK10_skl)
| ~ shortest_path(X2,X3,sK10_skl)
| ~ path(tail_of(sK9_skl),X0,X1) ),
inference(resolution,[status(thm)],[f261,f537]) ).
fof(f2215,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(sK1_skl(X2,X1,tail_of(X0)),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK1_skl(X2,X1,tail_of(X0)),sK10_skl)
| ~ shortest_path(X3,X4,sK10_skl)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f261,f532]) ).
fof(f2219,definition,
! [X0,X1] :
( sQ199_spl
<=> ( ~ sequential(sK1_skl(X1,X0,tail_of(sK9_skl)),sK8_skl)
| ~ on_path(sK1_skl(X1,X0,tail_of(sK9_skl)),sK10_skl)
| ~ path(tail_of(sK9_skl),X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2222,definition,
! [X2,X3] :
( sQ200_spl
<=> ~ shortest_path(X2,X3,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2223,plain,
! [X0,X1] :
( ~ sQ200_spl
| ~ shortest_path(X0,X1,sK10_skl) ),
inference(component_clause,[status(thm)],[f2222]) ).
fof(f2225,plain,
( ~ sQ53_spl
| sQ200_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f2214,f2219,f2222,f536]) ).
fof(f2226,definition,
! [X0,X1,X2] :
( sQ201_spl
<=> ( ~ sequential(sK1_skl(X2,X1,tail_of(X0)),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK1_skl(X2,X1,tail_of(X0)),sK10_skl)
| ~ path(tail_of(X0),X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2229,plain,
( sQ200_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f2215,f2226,f2222]) ).
fof(f2244,plain,
( ~ sQ200_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f121,f2223]) ).
fof(f2245,plain,
~ sQ200_spl,
inference(contradiction_clause,[status(thm)],[f2244]) ).
fof(f2249,plain,
! [X0,X1] :
( ~ sQ42_spl
| ~ path(head_of(sK8_skl),X1,X0)
| sK8_skl = sK1_skl(X0,X1,head_of(sK8_skl))
| ~ edge(sK8_skl)
| ~ sequential(sK1_skl(X0,X1,head_of(sK8_skl)),sK8_skl)
| ~ on_path(sK1_skl(X0,X1,head_of(sK8_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f2185,f424]) ).
fof(f2251,plain,
( ~ sQ42_spl
| ~ sequential(sK8_skl,sK8_skl)
| ~ on_path(sK8_skl,sK10_skl) ),
inference(factoring,[status(thm)],[f2185]) ).
fof(f2252,definition,
! [X0,X1] :
( sQ204_spl
<=> ( ~ path(head_of(sK8_skl),X1,X0)
| sK8_skl = sK1_skl(X0,X1,head_of(sK8_skl))
| ~ sequential(sK1_skl(X0,X1,head_of(sK8_skl)),sK8_skl)
| ~ on_path(sK1_skl(X0,X1,head_of(sK8_skl)),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2255,plain,
( ~ sQ42_spl
| ~ sQ18_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2249,f2252,f229,f467]) ).
fof(f2256,plain,
( ~ sQ15_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f2251,f467,f207]) ).
fof(f2258,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| ~ sequential(sK1_skl(X3,X2,tail_of(X1)),sK0_skl(head_of(X1),X0))
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| ~ on_path(sK1_skl(X3,X2,tail_of(X1)),sK10_skl)
| ~ shortest_path(X4,X5,sK10_skl)
| ~ path(tail_of(X1),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f274,f532]) ).
fof(f2262,definition,
! [X0,X1,X2,X3] :
( sQ205_spl
<=> ( ~ sequential(sK1_skl(X3,X2,tail_of(X1)),sK0_skl(head_of(X1),X0))
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| ~ on_path(sK1_skl(X3,X2,tail_of(X1)),sK10_skl)
| ~ path(tail_of(X1),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2265,plain,
( ~ sQ2_spl
| sQ200_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f2258,f2262,f2222,f146]) ).
fof(f2266,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ sequential(X1,sK0_skl(head_of(X1),X0))
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| ~ on_path(X1,sK10_skl)
| ~ shortest_path(X2,X3,sK10_skl)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f275,f532]) ).
fof(f2270,definition,
! [X0,X1] :
( sQ206_spl
<=> ( ~ sequential(X1,sK0_skl(head_of(X1),X0))
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| ~ on_path(X1,sK10_skl)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2273,plain,
( ~ sQ2_spl
| sQ200_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2266,f2270,f2222,f146]) ).
fof(f2287,plain,
! [X0,X1,X2,X3,X4] :
( ~ sequential(X0,sK1_skl(X2,X1,tail_of(X0)))
| ~ on_path(sK1_skl(X2,X1,tail_of(X0)),sK10_skl)
| ~ on_path(X0,sK10_skl)
| ~ shortest_path(X3,X4,sK10_skl)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f386,f532]) ).
fof(f2291,definition,
! [X0,X1,X2] :
( sQ207_spl
<=> ( ~ sequential(X0,sK1_skl(X2,X1,tail_of(X0)))
| ~ on_path(sK1_skl(X2,X1,tail_of(X0)),sK10_skl)
| ~ on_path(X0,sK10_skl)
| ~ path(tail_of(X0),X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2294,plain,
( sQ200_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2287,f2291,f2222]) ).
fof(f2295,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| ~ sQ2_spl
| ~ sequential(sK1_skl(X2,X1,tail_of(sK0_skl(head_of(sK9_skl),X0))),sK8_skl)
| ~ on_path(sK1_skl(X2,X1,tail_of(sK0_skl(head_of(sK9_skl),X0))),sK10_skl)
| ~ shortest_path(X3,X4,sK10_skl)
| ~ path(tail_of(sK0_skl(head_of(sK9_skl),X0)),X1,X2)
| X0 = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(sK9_skl),X0)) ),
inference(resolution,[status(thm)],[f276,f537]) ).
fof(f2296,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| ~ sequential(sK1_skl(X3,X2,tail_of(sK0_skl(head_of(X1),X0))),X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(sK1_skl(X3,X2,tail_of(sK0_skl(head_of(X1),X0))),sK10_skl)
| ~ shortest_path(X4,X5,sK10_skl)
| ~ path(tail_of(sK0_skl(head_of(X1),X0)),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f276,f532]) ).
fof(f2300,definition,
! [X0,X1,X2] :
( sQ208_spl
<=> ( ~ sequential(sK1_skl(X2,X1,tail_of(sK0_skl(head_of(sK9_skl),X0))),sK8_skl)
| ~ on_path(sK1_skl(X2,X1,tail_of(sK0_skl(head_of(sK9_skl),X0))),sK10_skl)
| ~ path(tail_of(sK0_skl(head_of(sK9_skl),X0)),X1,X2)
| X0 = head_of(sK9_skl)
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(sK9_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2303,plain,
( ~ sQ53_spl
| ~ sQ2_spl
| sQ200_spl
| ~ sQ26_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f2295,f2300,f308,f2222,f146,f536]) ).
fof(f2304,definition,
! [X0,X1,X2,X3] :
( sQ209_spl
<=> ( ~ sequential(sK1_skl(X3,X2,tail_of(sK0_skl(head_of(X1),X0))),X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(sK1_skl(X3,X2,tail_of(sK0_skl(head_of(X1),X0))),sK10_skl)
| ~ path(tail_of(sK0_skl(head_of(X1),X0)),X2,X3)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2307,plain,
( ~ sQ2_spl
| sQ200_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2296,f2304,f2222,f146]) ).
fof(f2310,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| ~ sQ2_spl
| ~ sequential(sK0_skl(head_of(sK9_skl),X0),sK8_skl)
| ~ on_path(sK0_skl(head_of(sK9_skl),X0),sK10_skl)
| ~ shortest_path(X1,X2,sK10_skl)
| X0 = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(sK9_skl),X0)) ),
inference(resolution,[status(thm)],[f277,f537]) ).
fof(f2311,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ sequential(sK0_skl(head_of(X1),X0),X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| ~ shortest_path(X2,X3,sK10_skl)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ),
inference(resolution,[status(thm)],[f277,f532]) ).
fof(f2315,definition,
! [X0] :
( sQ210_spl
<=> ( ~ sequential(sK0_skl(head_of(sK9_skl),X0),sK8_skl)
| ~ on_path(sK0_skl(head_of(sK9_skl),X0),sK10_skl)
| X0 = head_of(sK9_skl)
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(sK9_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2318,plain,
( ~ sQ53_spl
| ~ sQ2_spl
| sQ200_spl
| ~ sQ26_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f2310,f2315,f308,f2222,f146,f536]) ).
fof(f2319,definition,
! [X0,X1] :
( sQ211_spl
<=> ( ~ sequential(sK0_skl(head_of(X1),X0),X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(sK0_skl(head_of(X1),X0),sK10_skl)
| X0 = head_of(X1)
| ~ vertex(head_of(X1))
| ~ vertex(X0)
| X0 = head_of(sK0_skl(head_of(X1),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2322,plain,
( ~ sQ2_spl
| sQ200_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f2311,f2319,f2222,f146]) ).
fof(f2352,plain,
! [X0] :
( ~ sQ193_spl
| ~ sequential(X0,sK8_skl)
| ~ sequential(X0,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2171,f122]) ).
fof(f2353,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ193_spl
| sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ path(X3,X4,sK10_skl)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2171,f78]) ).
fof(f2354,plain,
! [X0,X1] :
( ~ sQ53_spl
| ~ sQ193_spl
| ~ sequential(X1,sK8_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ sequential(X0,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2171,f537]) ).
fof(f2356,definition,
! [X0] :
( sQ216_spl
<=> ( ~ sequential(X0,sK8_skl)
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2359,plain,
( ~ sQ193_spl
| ~ sQ54_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f2352,f2356,f539,f2164]) ).
fof(f2360,definition,
! [X0,X1,X2] :
( sQ217_spl
<=> ( sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ sequential(X0,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( ~ sQ193_spl
| sQ13_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f2353,f2360,f201,f2164]) ).
fof(f2364,definition,
! [X0,X1] :
( sQ218_spl
<=> ( ~ sequential(X1,sK8_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
! [X0,X1] :
( ~ sQ218_spl
| ~ sequential(X1,sK8_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,X1)
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f2364]) ).
fof(f2367,plain,
( ~ sQ53_spl
| ~ sQ193_spl
| ~ sQ54_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2354,f2364,f539,f2164,f536]) ).
fof(f2371,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ218_spl
| ~ path(X5,X6,sK10_skl)
| sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ path(X3,X4,sK10_skl)
| ~ sequential(sK4_skl(X1,X2,sK10_skl),sK8_skl)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2365,f582]) ).
fof(f2374,plain,
! [X0,X1,X2,X3] :
( ~ sQ218_spl
| ~ in_path(X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(sK3_skl(X1,sK10_skl),sK8_skl)
| ~ sequential(X0,sK3_skl(X1,sK10_skl))
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f2365,f58]) ).
fof(f2377,definition,
! [X0,X1,X2] :
( sQ219_spl
<=> ( sequential(X2,X1)
| ~ precedes(X2,X1,sK10_skl)
| ~ sequential(sK4_skl(X1,X2,sK10_skl),sK8_skl)
| ~ sequential(X0,sK4_skl(X1,X2,sK10_skl))
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2380,plain,
( ~ sQ218_spl
| sQ13_spl
| sQ219_spl ),
inference(split_clause,[status(thm)],[f2371,f2377,f201,f2364]) ).
fof(f2386,definition,
! [X0,X1] :
( sQ221_spl
<=> ( ~ in_path(X1,sK10_skl)
| ~ sequential(sK3_skl(X1,sK10_skl),sK8_skl)
| ~ sequential(X0,sK3_skl(X1,sK10_skl))
| ~ sequential(X0,sK9_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2389,plain,
( ~ sQ218_spl
| sQ13_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2374,f2386,f201,f2364]) ).
fof(f2402,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| ~ sequential(X0,sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5))
| ~ on_path(sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5),sK10_skl)
| ~ on_path(X0,sK10_skl)
| X5 = head_of(sK1_skl(X2,X1,tail_of(X0)))
| ~ vertex(head_of(sK1_skl(X2,X1,tail_of(X0))))
| ~ vertex(X5)
| X5 = head_of(sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5))
| ~ shortest_path(X3,X4,sK10_skl)
| ~ path(tail_of(X0),X1,X2) ),
inference(resolution,[status(thm)],[f385,f532]) ).
fof(f2406,definition,
! [X0,X1,X2,X5] :
( sQ223_spl
<=> ( ~ sequential(X0,sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5))
| ~ on_path(sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5),sK10_skl)
| ~ on_path(X0,sK10_skl)
| X5 = head_of(sK1_skl(X2,X1,tail_of(X0)))
| ~ vertex(head_of(sK1_skl(X2,X1,tail_of(X0))))
| ~ vertex(X5)
| X5 = head_of(sK0_skl(head_of(sK1_skl(X2,X1,tail_of(X0))),X5))
| ~ path(tail_of(X0),X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( ~ sQ2_spl
| sQ200_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f2402,f2406,f2222,f146]) ).
fof(f2454,plain,
! [X0,X1,X2,X3] :
( ~ sQ2_spl
| ~ sQ80_spl
| ~ shortest_path(X2,X3,sK10_skl)
| X1 = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(X1)
| X1 = head_of(sK0_skl(head_of(sK9_skl),X1))
| ~ sequential(sK0_skl(head_of(sK9_skl),X1),X0)
| ~ on_path(sK0_skl(head_of(sK9_skl),X1),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f277]) ).
fof(f2455,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| ~ sQ80_spl
| ~ shortest_path(X4,X5,sK10_skl)
| ~ path(tail_of(sK0_skl(head_of(sK9_skl),X3)),X2,X1)
| X3 = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(X3)
| X3 = head_of(sK0_skl(head_of(sK9_skl),X3))
| ~ sequential(sK1_skl(X1,X2,tail_of(sK0_skl(head_of(sK9_skl),X3))),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK0_skl(head_of(sK9_skl),X3))),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f276]) ).
fof(f2456,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ80_spl
| ~ shortest_path(X3,X4,sK10_skl)
| ~ path(tail_of(sK9_skl),X2,X1)
| ~ sequential(sK1_skl(X1,X2,tail_of(sK9_skl)),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK9_skl)),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f261]) ).
fof(f2459,plain,
! [X0,X1,X2] :
( ~ sQ193_spl
| ~ sQ80_spl
| ~ sequential(X2,X1)
| ~ sequential(X2,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(X2,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f2171]) ).
fof(f2460,plain,
! [X0,X1] :
( ~ sQ80_spl
| ~ sequential(sK9_skl,X1)
| ~ on_path(X1,sK10_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f2112]) ).
fof(f2461,plain,
! [X0] :
( ~ sQ80_spl
| ~ sequential(sK9_skl,X0)
| ~ on_path(sK9_skl,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f249]) ).
fof(f2463,plain,
! [X0,X1,X2,X3] :
( ~ sQ80_spl
| edge(X1)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f578]) ).
fof(f2464,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ80_spl
| ~ sequential(X4,X1)
| ~ on_path(X4,sK10_skl)
| precedes(X4,sK9_skl,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f573]) ).
fof(f2466,plain,
! [X0,X1,X2,X3] :
( ~ sQ80_spl
| on_path(X1,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f75]) ).
fof(f2467,plain,
! [X0,X1,X2,X3] :
( ~ sQ80_spl
| ~ sequential(X1,X1)
| ~ sequential(X1,sK9_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f79]) ).
fof(f2468,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ80_spl
| ~ sequential(X4,X1)
| ~ sequential(X4,sK9_skl)
| ~ precedes(X4,sK9_skl,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f79]) ).
fof(f2470,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ80_spl
| ~ precedes(X4,sK9_skl,sK10_skl)
| ~ sequential(X1,X4)
| ~ sequential(X1,sK9_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f79]) ).
fof(f2471,definition,
! [X0,X1] :
( sQ227_spl
<=> ( X1 = head_of(sK9_skl)
| ~ vertex(X1)
| X1 = head_of(sK0_skl(head_of(sK9_skl),X1))
| ~ sequential(sK0_skl(head_of(sK9_skl),X1),X0)
| ~ on_path(sK0_skl(head_of(sK9_skl),X1),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2474,plain,
( ~ sQ2_spl
| ~ sQ80_spl
| sQ200_spl
| ~ sQ26_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2454,f2471,f308,f2222,f1111,f146]) ).
fof(f2475,definition,
! [X0,X1,X2,X3] :
( sQ228_spl
<=> ( ~ path(tail_of(sK0_skl(head_of(sK9_skl),X3)),X2,X1)
| X3 = head_of(sK9_skl)
| ~ vertex(X3)
| X3 = head_of(sK0_skl(head_of(sK9_skl),X3))
| ~ sequential(sK1_skl(X1,X2,tail_of(sK0_skl(head_of(sK9_skl),X3))),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK0_skl(head_of(sK9_skl),X3))),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2478,plain,
( ~ sQ2_spl
| ~ sQ80_spl
| sQ200_spl
| ~ sQ26_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2455,f2475,f308,f2222,f1111,f146]) ).
fof(f2479,definition,
! [X0,X1,X2] :
( sQ229_spl
<=> ( ~ path(tail_of(sK9_skl),X2,X1)
| ~ sequential(sK1_skl(X1,X2,tail_of(sK9_skl)),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK9_skl)),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2482,plain,
( ~ sQ80_spl
| sQ200_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2456,f2479,f2222,f1111]) ).
fof(f2483,definition,
! [X0] :
( sQ230_spl
<=> ( ~ sequential(sK9_skl,X0)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2487,definition,
! [X0,X1,X2] :
( sQ231_spl
<=> ( ~ sequential(X2,X1)
| ~ sequential(X2,sK9_skl)
| ~ on_path(X2,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2490,plain,
( ~ sQ193_spl
| ~ sQ80_spl
| ~ sQ54_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2459,f2487,f539,f1111,f2164]) ).
fof(f2491,definition,
! [X0,X1] :
( sQ232_spl
<=> ( ~ sequential(sK9_skl,X1)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2494,plain,
( ~ sQ80_spl
| ~ sQ54_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2460,f2491,f539,f1111]) ).
fof(f2495,plain,
( ~ sQ80_spl
| ~ sQ54_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2461,f2483,f539,f1111]) ).
fof(f2496,definition,
! [X0,X1] :
( sQ233_spl
<=> ( edge(X1)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2499,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2463,f2496,f201,f1111]) ).
fof(f2500,definition,
! [X0,X1,X4] :
( sQ234_spl
<=> ( ~ sequential(X4,X1)
| ~ on_path(X4,sK10_skl)
| precedes(X4,sK9_skl,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2503,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2464,f2500,f201,f1111]) ).
fof(f2508,definition,
! [X0,X1] :
( sQ236_spl
<=> ( on_path(X1,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2511,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2466,f2508,f201,f1111]) ).
fof(f2512,definition,
! [X0,X1] :
( sQ237_spl
<=> ( ~ sequential(X1,X1)
| ~ sequential(X1,sK9_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2515,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2467,f2512,f201,f1111]) ).
fof(f2516,definition,
! [X0,X1,X4] :
( sQ238_spl
<=> ( ~ sequential(X4,X1)
| ~ sequential(X4,sK9_skl)
| ~ precedes(X4,sK9_skl,sK10_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2519,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2468,f2516,f201,f1111]) ).
fof(f2521,definition,
! [X0,X1,X4] :
( sQ239_spl
<=> ( ~ precedes(X4,sK9_skl,sK10_skl)
| ~ sequential(X1,X4)
| ~ sequential(X1,sK9_skl)
| ~ sequential(X1,X0)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2524,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f2470,f2521,f201,f1111]) ).
fof(f2671,definition,
( sQ259_spl
<=> head_of(sK9_skl) = tail_of(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2672,plain,
( ~ sQ259_spl
| head_of(sK9_skl) = tail_of(sK9_skl) ),
inference(component_clause,[status(thm)],[f2671]) ).
fof(f2687,definition,
( sQ262_spl
<=> sP0_prd(sK9_skl,head_of(sK9_skl),head_of(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2688,plain,
( ~ sQ262_spl
| sP0_prd(sK9_skl,head_of(sK9_skl),head_of(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2687]) ).
fof(f2693,plain,
( ~ sQ162_spl
| ~ precedes(sK8_skl,sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f1836,f121]) ).
fof(f2694,plain,
( ~ sQ162_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2693,f122]) ).
fof(f2695,plain,
~ sQ162_spl,
inference(contradiction_clause,[status(thm)],[f2694]) ).
fof(f2696,plain,
( ~ sQ262_spl
| head_of(sK9_skl) = tail_of(sK9_skl) ),
inference(resolution,[status(thm)],[f2688,f132]) ).
fof(f2723,plain,
( ~ sQ262_spl
| ~ edge(sK9_skl) ),
inference(resolution,[status(thm)],[f2696,f21]) ).
fof(f2758,plain,
( ~ sQ262_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f2723,f509,f2687]) ).
fof(f2762,definition,
( sQ266_spl
<=> vertex(tail_of(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2764,plain,
( sQ266_spl
| ~ vertex(tail_of(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2762]) ).
fof(f2801,definition,
( sQ274_spl
<=> head_of(sK9_skl) = tail_of(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2802,plain,
( ~ sQ274_spl
| head_of(sK9_skl) = tail_of(sK8_skl) ),
inference(component_clause,[status(thm)],[f2801]) ).
fof(f2827,plain,
( sQ266_spl
| ~ edge(sK9_skl) ),
inference(resolution,[status(thm)],[f2764,f24]) ).
fof(f2828,plain,
( sQ266_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f2827,f509,f2762]) ).
fof(f2882,definition,
( sQ284_spl
<=> edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2884,plain,
( sQ284_spl
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f2882]) ).
fof(f2888,definition,
( sQ286_spl
<=> tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) = head_of(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ286_spl
| tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) = head_of(sK9_skl) ),
inference(component_clause,[status(thm)],[f2888]) ).
fof(f2901,plain,
( ~ sQ274_spl
| sK9_skl = sK8_skl
| ~ edge(sK8_skl)
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f2802,f66]) ).
fof(f2938,plain,
( ~ sQ274_spl
| sQ86_spl
| ~ sQ18_spl
| ~ sQ48_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2901,f987,f509,f229,f1151,f2801]) ).
fof(f3066,definition,
( sQ302_spl
<=> sequential(sK9_skl,sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f3067,plain,
( ~ sQ302_spl
| sequential(sK9_skl,sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f3066]) ).
fof(f3069,definition,
( sQ303_spl
<=> sK9_skl = sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f3070,plain,
( ~ sQ303_spl
| sK9_skl = sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f3069]) ).
fof(f3073,definition,
( sQ304_spl
<=> tail_of(sK8_skl) = head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f3074,plain,
( ~ sQ304_spl
| tail_of(sK8_skl) = head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f3073]) ).
fof(f3119,definition,
( sQ315_spl
<=> tail_of(sK8_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f3120,plain,
( ~ sQ315_spl
| tail_of(sK8_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f3119]) ).
fof(f3127,plain,
( ~ sQ1_spl
| sQ284_spl
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(tail_of(sK8_skl)) ),
inference(resolution,[status(thm)],[f2884,f143]) ).
fof(f3128,plain,
( ~ sQ1_spl
| sQ284_spl
| sQ274_spl
| ~ sQ26_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f3127,f270,f308,f2801,f2882,f142]) ).
fof(f3203,plain,
! [X0,X1,X2,X3] :
( ~ sQ303_spl
| ~ sQ3_spl
| head_of(sK9_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2)
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(tail_of(sK8_skl))
| head_of(sK9_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(paramodulation,[status(thm)],[f3070,f288]) ).
fof(f3223,plain,
( ~ sQ303_spl
| ~ sQ3_spl
| sQ160_spl
| sQ274_spl
| ~ sQ26_spl
| ~ sQ21_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f3203,f2888,f270,f308,f2801,f1816,f150,f3069]) ).
fof(f3235,definition,
( sQ322_spl
<=> sP0_prd(sK9_skl,head_of(sK9_skl),tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f3236,plain,
( ~ sQ322_spl
| sP0_prd(sK9_skl,head_of(sK9_skl),tail_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f3235]) ).
fof(f3257,plain,
( ~ sQ322_spl
| tail_of(sK8_skl) = head_of(sK9_skl) ),
inference(resolution,[status(thm)],[f3236,f131]) ).
fof(f3258,plain,
( ~ sQ322_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f3257,f2801,f3235]) ).
fof(f3263,definition,
( sQ323_spl
<=> on_path(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f3265,plain,
( sQ323_spl
| ~ on_path(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK10_skl) ),
inference(component_clause,[status(thm)],[f3263]) ).
fof(f3303,plain,
( ~ sQ259_spl
| sP0_prd(sK9_skl,head_of(sK9_skl),head_of(sK9_skl)) ),
inference(paramodulation,[status(thm)],[f2672,f192]) ).
fof(f3353,plain,
( ~ sQ259_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f3303,f2687,f2671]) ).
fof(f3380,plain,
( ~ sQ302_spl
| ~ sequential(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f3067,f2182]) ).
fof(f3384,definition,
( sQ330_spl
<=> sequential(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f3387,plain,
( ~ sQ302_spl
| ~ sQ330_spl
| ~ sQ54_spl
| ~ sQ323_spl ),
inference(split_clause,[status(thm)],[f3380,f3263,f539,f3384,f3066]) ).
fof(f3495,definition,
( sQ350_spl
<=> tail_of(sK8_skl) = head_of(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f3496,plain,
( ~ sQ350_spl
| tail_of(sK8_skl) = head_of(sK8_skl) ),
inference(component_clause,[status(thm)],[f3495]) ).
fof(f3514,definition,
( sQ354_spl
<=> sP0_prd(sK8_skl,head_of(sK13_skl),tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3515,plain,
( ~ sQ354_spl
| sP0_prd(sK8_skl,head_of(sK13_skl),tail_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f3514]) ).
fof(f3539,plain,
( ~ sQ350_spl
| ~ edge(sK8_skl) ),
inference(resolution,[status(thm)],[f3496,f21]) ).
fof(f3582,plain,
( ~ sQ350_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f3539,f229,f3495]) ).
fof(f3934,plain,
( ~ sQ354_spl
| tail_of(sK8_skl) = head_of(sK8_skl) ),
inference(resolution,[status(thm)],[f3515,f131]) ).
fof(f3936,plain,
( ~ sQ354_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f3934,f3495,f3514]) ).
fof(f4295,definition,
( sQ442_spl
<=> edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f4297,plain,
( sQ442_spl
| ~ edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
inference(component_clause,[status(thm)],[f4295]) ).
fof(f4348,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sequential(sK1_skl(X5,X4,tail_of(X0)),sK3_skl(head_of(X0),X1))
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ on_path(sK1_skl(X5,X4,tail_of(X0)),sK10_skl)
| ~ shortest_path(X6,X7,sK10_skl)
| ~ path(tail_of(X0),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f1442,f532]) ).
fof(f4352,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ446_spl
<=> ( ~ sequential(sK1_skl(X5,X4,tail_of(X0)),sK3_skl(head_of(X0),X1))
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ on_path(sK1_skl(X5,X4,tail_of(X0)),sK10_skl)
| ~ path(tail_of(X0),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f4355,plain,
( sQ200_spl
| sQ446_spl ),
inference(split_clause,[status(thm)],[f4348,f4352,f2222]) ).
fof(f4360,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sequential(X0,sK3_skl(head_of(X0),X1))
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ on_path(X0,sK10_skl)
| ~ shortest_path(X4,X5,sK10_skl)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f1443,f532]) ).
fof(f4364,definition,
! [X0,X1,X2,X3] :
( sQ447_spl
<=> ( ~ sequential(X0,sK3_skl(head_of(X0),X1))
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ on_path(X0,sK10_skl)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f4367,plain,
( sQ200_spl
| sQ447_spl ),
inference(split_clause,[status(thm)],[f4360,f4364,f2222]) ).
fof(f4368,plain,
( ~ sQ1_spl
| sQ442_spl
| head_of(sK9_skl) = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(head_of(sK9_skl)) ),
inference(resolution,[status(thm)],[f4297,f143]) ).
fof(f4369,plain,
( ~ sQ1_spl
| sQ442_spl
| sQ274_spl
| ~ sQ21_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f4368,f308,f270,f2801,f4295,f142]) ).
fof(f4370,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sequential(sK1_skl(X5,X4,tail_of(sK3_skl(head_of(X0),X1))),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK1_skl(X5,X4,tail_of(sK3_skl(head_of(X0),X1))),sK10_skl)
| ~ shortest_path(X6,X7,sK10_skl)
| ~ path(tail_of(sK3_skl(head_of(X0),X1)),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f1445,f532]) ).
fof(f4374,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ448_spl
<=> ( ~ sequential(sK1_skl(X5,X4,tail_of(sK3_skl(head_of(X0),X1))),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK1_skl(X5,X4,tail_of(sK3_skl(head_of(X0),X1))),sK10_skl)
| ~ path(tail_of(sK3_skl(head_of(X0),X1)),X4,X5)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4377,plain,
( sQ200_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f4370,f4374,f2222]) ).
fof(f4382,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sequential(sK3_skl(head_of(X0),X1),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ shortest_path(X4,X5,sK10_skl)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ),
inference(resolution,[status(thm)],[f1446,f532]) ).
fof(f4386,definition,
! [X0,X1,X2,X3] :
( sQ449_spl
<=> ( ~ sequential(sK3_skl(head_of(X0),X1),X0)
| ~ on_path(X0,sK10_skl)
| ~ on_path(sK3_skl(head_of(X0),X1),sK10_skl)
| ~ in_path(head_of(X0),X1)
| ~ path(X2,X3,X1)
| X0 = sK3_skl(head_of(X0),X1)
| ~ edge(sK3_skl(head_of(X0),X1))
| ~ edge(X0)
| sequential(X0,sK3_skl(head_of(X0),X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4389,plain,
( sQ200_spl
| sQ449_spl ),
inference(split_clause,[status(thm)],[f4382,f4386,f2222]) ).
fof(f4447,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sequential(sK4_skl(X9,sK4_skl(X3,X2,sK10_skl),X8),X3)
| ~ on_path(X3,sK10_skl)
| ~ on_path(sK4_skl(X9,sK4_skl(X3,X2,sK10_skl),X8),sK10_skl)
| sequential(sK4_skl(X3,X2,sK10_skl),X9)
| ~ precedes(sK4_skl(X3,X2,sK10_skl),X9,X8)
| ~ path(X6,X7,X8)
| ~ sequential(sK4_skl(X3,X2,sK10_skl),X3)
| ~ path(X4,X5,sK10_skl)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f1494,f532]) ).
fof(f4451,definition,
! [X2,X3,X6,X7,X8,X9] :
( sQ457_spl
<=> ( ~ sequential(sK4_skl(X9,sK4_skl(X3,X2,sK10_skl),X8),X3)
| ~ on_path(X3,sK10_skl)
| ~ on_path(sK4_skl(X9,sK4_skl(X3,X2,sK10_skl),X8),sK10_skl)
| sequential(sK4_skl(X3,X2,sK10_skl),X9)
| ~ precedes(sK4_skl(X3,X2,sK10_skl),X9,X8)
| ~ path(X6,X7,X8)
| ~ sequential(sK4_skl(X3,X2,sK10_skl),X3)
| sequential(X2,X3)
| ~ precedes(X2,X3,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f4454,plain,
( sQ457_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f4447,f201,f4451]) ).
fof(f4889,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| sK9_skl = sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| head_of(sK9_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f292,f432]) ).
fof(f4890,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(tail_of(sK8_skl))
| tail_of(sK8_skl) = head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| head_of(sK9_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f292,f251]) ).
fof(f4891,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| sQ303_spl
| ~ sQ48_spl
| sQ302_spl
| ~ sQ21_spl
| ~ sQ284_spl
| sQ274_spl
| ~ sQ26_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f4889,f2888,f308,f2801,f2882,f270,f3066,f509,f3069,f291,f146]) ).
fof(f4892,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| ~ sQ21_spl
| sQ304_spl
| ~ sQ284_spl
| sQ274_spl
| ~ sQ26_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f4890,f2888,f308,f2801,f2882,f3073,f270,f291,f146]) ).
fof(f4893,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ sQ53_spl
| sequential(sK4_skl(sK9_skl,X1,sK10_skl),X0)
| ~ precedes(sK4_skl(sK9_skl,X1,sK10_skl),X0,X2)
| ~ path(X7,X8,X2)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),sK9_skl)
| ~ path(X5,X6,sK10_skl)
| sequential(X1,sK9_skl)
| ~ precedes(X1,sK9_skl,sK10_skl)
| ~ path(X3,X4,sK10_skl)
| ~ sequential(sK4_skl(X0,sK4_skl(sK9_skl,X1,sK10_skl),X2),sK8_skl)
| ~ on_path(sK4_skl(X0,sK4_skl(sK9_skl,X1,sK10_skl),X2),sK10_skl) ),
inference(resolution,[status(thm)],[f537,f1494]) ).
fof(f4894,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ53_spl
| ~ shortest_path(X3,X4,sK10_skl)
| ~ in_path(head_of(sK9_skl),X0)
| ~ path(X1,X2,X0)
| sK9_skl = sK3_skl(head_of(sK9_skl),X0)
| ~ edge(sK3_skl(head_of(sK9_skl),X0))
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X0))
| ~ sequential(sK3_skl(head_of(sK9_skl),X0),sK8_skl)
| ~ on_path(sK3_skl(head_of(sK9_skl),X0),sK10_skl) ),
inference(resolution,[status(thm)],[f537,f1446]) ).
fof(f4896,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sQ53_spl
| ~ shortest_path(X5,X6,sK10_skl)
| ~ path(tail_of(sK3_skl(head_of(sK9_skl),X2)),X1,X0)
| ~ in_path(head_of(sK9_skl),X2)
| ~ path(X3,X4,X2)
| sK9_skl = sK3_skl(head_of(sK9_skl),X2)
| ~ edge(sK3_skl(head_of(sK9_skl),X2))
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X2))
| ~ sequential(sK1_skl(X0,X1,tail_of(sK3_skl(head_of(sK9_skl),X2))),sK8_skl)
| ~ on_path(sK1_skl(X0,X1,tail_of(sK3_skl(head_of(sK9_skl),X2))),sK10_skl) ),
inference(resolution,[status(thm)],[f537,f1445]) ).
fof(f4912,definition,
! [X0,X1,X2,X7,X8] :
( sQ491_spl
<=> ( sequential(sK4_skl(sK9_skl,X1,sK10_skl),X0)
| ~ precedes(sK4_skl(sK9_skl,X1,sK10_skl),X0,X2)
| ~ path(X7,X8,X2)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),sK9_skl)
| sequential(X1,sK9_skl)
| ~ precedes(X1,sK9_skl,sK10_skl)
| ~ sequential(sK4_skl(X0,sK4_skl(sK9_skl,X1,sK10_skl),X2),sK8_skl)
| ~ on_path(sK4_skl(X0,sK4_skl(sK9_skl,X1,sK10_skl),X2),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f4915,plain,
( ~ sQ53_spl
| sQ13_spl
| sQ491_spl ),
inference(split_clause,[status(thm)],[f4893,f4912,f201,f536]) ).
fof(f4916,definition,
! [X0,X1,X2] :
( sQ492_spl
<=> ( ~ in_path(head_of(sK9_skl),X0)
| ~ path(X1,X2,X0)
| sK9_skl = sK3_skl(head_of(sK9_skl),X0)
| ~ edge(sK3_skl(head_of(sK9_skl),X0))
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X0))
| ~ sequential(sK3_skl(head_of(sK9_skl),X0),sK8_skl)
| ~ on_path(sK3_skl(head_of(sK9_skl),X0),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f4919,plain,
( ~ sQ53_spl
| sQ200_spl
| ~ sQ48_spl
| sQ492_spl ),
inference(split_clause,[status(thm)],[f4894,f4916,f509,f2222,f536]) ).
fof(f4921,definition,
! [X0,X1,X2,X3,X4] :
( sQ493_spl
<=> ( ~ path(tail_of(sK3_skl(head_of(sK9_skl),X2)),X1,X0)
| ~ in_path(head_of(sK9_skl),X2)
| ~ path(X3,X4,X2)
| sK9_skl = sK3_skl(head_of(sK9_skl),X2)
| ~ edge(sK3_skl(head_of(sK9_skl),X2))
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X2))
| ~ sequential(sK1_skl(X0,X1,tail_of(sK3_skl(head_of(sK9_skl),X2))),sK8_skl)
| ~ on_path(sK1_skl(X0,X1,tail_of(sK3_skl(head_of(sK9_skl),X2))),sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f4924,plain,
( ~ sQ53_spl
| sQ200_spl
| ~ sQ48_spl
| sQ493_spl ),
inference(split_clause,[status(thm)],[f4896,f4921,f509,f2222,f536]) ).
fof(f4998,definition,
( sQ499_spl
<=> sequential(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f5237,plain,
! [X0,X1,X2] :
( ~ sQ160_spl
| ~ precedes(sK8_skl,sK9_skl,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f1817]) ).
fof(f5252,plain,
( ~ sQ160_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f5237,f1835,f1816]) ).
fof(f5315,definition,
( sQ535_spl
<=> precedes(sK8_skl,sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f5317,plain,
( sQ535_spl
| ~ precedes(sK8_skl,sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f5315]) ).
fof(f5319,plain,
( sQ535_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5317,f122]) ).
fof(f5320,plain,
sQ535_spl,
inference(contradiction_clause,[status(thm)],[f5319]) ).
fof(f5321,plain,
( ~ sQ10_spl
| ~ sQ304_spl
| tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) != head_of(sK9_skl)
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f3074,f177]) ).
fof(f5322,plain,
( ~ sQ304_spl
| sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)) = sK8_skl
| ~ edge(sK8_skl)
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| sequential(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK8_skl) ),
inference(resolution,[status(thm)],[f3074,f66]) ).
fof(f5323,plain,
( ~ sQ304_spl
| ~ sQ37_spl
| ~ sequential(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)),sK8_skl)
| head_of(sK9_skl) = tail_of(sK8_skl)
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(tail_of(sK8_skl)) ),
inference(paramodulation,[status(thm)],[f3074,f434]) ).
fof(f5369,plain,
( ~ sQ10_spl
| ~ sQ304_spl
| ~ sQ286_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f5321,f2882,f2888,f3073,f176]) ).
fof(f5370,definition,
( sQ536_spl
<=> sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)) = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f5371,plain,
( ~ sQ536_spl
| sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)) = sK8_skl ),
inference(component_clause,[status(thm)],[f5370]) ).
fof(f5373,plain,
( ~ sQ304_spl
| sQ536_spl
| ~ sQ18_spl
| ~ sQ284_spl
| sQ499_spl ),
inference(split_clause,[status(thm)],[f5322,f4998,f2882,f229,f5370,f3073]) ).
fof(f5374,plain,
( ~ sQ304_spl
| ~ sQ37_spl
| ~ sQ499_spl
| sQ274_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5323,f270,f2801,f4998,f433,f3073]) ).
fof(f5413,definition,
( sQ545_spl
<=> vertex(head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f5415,plain,
( sQ545_spl
| ~ vertex(head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))) ),
inference(component_clause,[status(thm)],[f5413]) ).
fof(f5898,plain,
( sQ323_spl
| ~ sQ536_spl
| ~ on_path(sK8_skl,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f5371,f3265]) ).
fof(f5919,plain,
( ~ sQ536_spl
| ~ sQ3_spl
| tail_of(sK8_skl) = tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))
| sP0_prd(sK8_skl,head_of(sK9_skl),tail_of(sK8_skl))
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(tail_of(sK8_skl)) ),
inference(paramodulation,[status(thm)],[f5371,f151]) ).
fof(f5922,plain,
( sQ323_spl
| ~ sQ536_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f5898,f467,f5370,f3263]) ).
fof(f5949,definition,
( sQ566_spl
<=> sP0_prd(sK8_skl,head_of(sK9_skl),tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f5950,plain,
( ~ sQ566_spl
| sP0_prd(sK8_skl,head_of(sK9_skl),tail_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f5949]) ).
fof(f5952,plain,
( ~ sQ536_spl
| ~ sQ3_spl
| sQ315_spl
| sQ566_spl
| sQ274_spl
| ~ sQ26_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5919,f270,f308,f2801,f5949,f3119,f150,f5370]) ).
fof(f5991,plain,
! [X0,X1,X2,X3] :
( ~ sQ84_spl
| sequential(X1,sK9_skl)
| ~ precedes(X1,sK9_skl,sK10_skl)
| ~ path(X2,X3,sK10_skl)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),X0)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1128,f78]) ).
fof(f5993,plain,
! [X0,X1] :
( ~ sQ84_spl
| ~ sequential(X1,sK9_skl)
| ~ on_path(sK9_skl,sK10_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X1,X0)
| ~ sequential(X1,sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1128,f532]) ).
fof(f5998,definition,
! [X0,X1] :
( sQ569_spl
<=> ( sequential(X1,sK9_skl)
| ~ precedes(X1,sK9_skl,sK10_skl)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),X0)
| ~ sequential(sK4_skl(sK9_skl,X1,sK10_skl),sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f6001,plain,
( ~ sQ84_spl
| sQ13_spl
| sQ569_spl ),
inference(split_clause,[status(thm)],[f5991,f5998,f201,f1127]) ).
fof(f6002,definition,
! [X0,X1] :
( sQ570_spl
<=> ( ~ sequential(X1,sK9_skl)
| ~ on_path(X1,sK10_skl)
| ~ sequential(X1,X0)
| ~ sequential(X1,sK9_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f6005,plain,
( ~ sQ84_spl
| ~ sQ54_spl
| sQ570_spl ),
inference(split_clause,[status(thm)],[f5993,f6002,f539,f1127]) ).
fof(f6012,plain,
( ~ sQ566_spl
| tail_of(sK8_skl) = head_of(sK8_skl) ),
inference(resolution,[status(thm)],[f5950,f131]) ).
fof(f6014,plain,
( ~ sQ566_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f6012,f3495,f5949]) ).
fof(f6062,definition,
( sQ576_spl
<=> edge(sK0_skl(tail_of(sK8_skl),head_of(sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ576_spl])],[split_symbol_definition]) ).
fof(f6064,plain,
( sQ576_spl
| ~ edge(sK0_skl(tail_of(sK8_skl),head_of(sK8_skl))) ),
inference(component_clause,[status(thm)],[f6062]) ).
fof(f6183,definition,
( sQ599_spl
<=> sP0_prd(sK8_skl,head_of(sK8_skl),head_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f6184,plain,
( ~ sQ599_spl
| sP0_prd(sK8_skl,head_of(sK8_skl),head_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f6183]) ).
fof(f6189,plain,
( ~ sQ1_spl
| sQ576_spl
| head_of(sK8_skl) = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(head_of(sK8_skl)) ),
inference(resolution,[status(thm)],[f6064,f143]) ).
fof(f6190,plain,
( ~ sQ1_spl
| sQ576_spl
| sQ350_spl
| ~ sQ21_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f6189,f478,f270,f3495,f6062,f142]) ).
fof(f6191,plain,
( ~ sQ599_spl
| head_of(sK8_skl) = tail_of(sK8_skl) ),
inference(resolution,[status(thm)],[f6184,f132]) ).
fof(f6193,plain,
( ~ sQ599_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f6191,f3495,f6183]) ).
fof(f6206,plain,
( sQ545_spl
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f5415,f23]) ).
fof(f6207,plain,
( sQ545_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f6206,f2882,f5413]) ).
fof(f6446,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ sQ80_spl
| sequential(sK4_skl(sK9_skl,X2,sK10_skl),X1)
| ~ precedes(sK4_skl(sK9_skl,X2,sK10_skl),X1,X3)
| ~ path(X8,X9,X3)
| ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK9_skl)
| ~ path(X6,X7,sK10_skl)
| sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl)
| ~ path(X4,X5,sK10_skl)
| ~ sequential(sK4_skl(X1,sK4_skl(sK9_skl,X2,sK10_skl),X3),X0)
| ~ on_path(sK4_skl(X1,sK4_skl(sK9_skl,X2,sK10_skl),X3),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f1494]) ).
fof(f6447,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ80_spl
| ~ shortest_path(X4,X5,sK10_skl)
| ~ in_path(head_of(sK9_skl),X1)
| ~ path(X2,X3,X1)
| sK9_skl = sK3_skl(head_of(sK9_skl),X1)
| ~ edge(sK3_skl(head_of(sK9_skl),X1))
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X1))
| ~ sequential(sK3_skl(head_of(sK9_skl),X1),X0)
| ~ on_path(sK3_skl(head_of(sK9_skl),X1),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f1446]) ).
fof(f6449,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ sQ80_spl
| ~ shortest_path(X6,X7,sK10_skl)
| ~ path(tail_of(sK3_skl(head_of(sK9_skl),X3)),X2,X1)
| ~ in_path(head_of(sK9_skl),X3)
| ~ path(X4,X5,X3)
| sK9_skl = sK3_skl(head_of(sK9_skl),X3)
| ~ edge(sK3_skl(head_of(sK9_skl),X3))
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X3))
| ~ sequential(sK1_skl(X1,X2,tail_of(sK3_skl(head_of(sK9_skl),X3))),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK3_skl(head_of(sK9_skl),X3))),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f1112,f1445]) ).
fof(f6467,definition,
! [X0,X1,X2,X3,X8,X9] :
( sQ629_spl
<=> ( sequential(sK4_skl(sK9_skl,X2,sK10_skl),X1)
| ~ precedes(sK4_skl(sK9_skl,X2,sK10_skl),X1,X3)
| ~ path(X8,X9,X3)
| ~ sequential(sK4_skl(sK9_skl,X2,sK10_skl),sK9_skl)
| sequential(X2,sK9_skl)
| ~ precedes(X2,sK9_skl,sK10_skl)
| ~ sequential(sK4_skl(X1,sK4_skl(sK9_skl,X2,sK10_skl),X3),X0)
| ~ on_path(sK4_skl(X1,sK4_skl(sK9_skl,X2,sK10_skl),X3),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f6470,plain,
( ~ sQ80_spl
| sQ13_spl
| sQ629_spl ),
inference(split_clause,[status(thm)],[f6446,f6467,f201,f1111]) ).
fof(f6471,definition,
! [X0,X1,X2,X3] :
( sQ630_spl
<=> ( ~ in_path(head_of(sK9_skl),X1)
| ~ path(X2,X3,X1)
| sK9_skl = sK3_skl(head_of(sK9_skl),X1)
| ~ edge(sK3_skl(head_of(sK9_skl),X1))
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X1))
| ~ sequential(sK3_skl(head_of(sK9_skl),X1),X0)
| ~ on_path(sK3_skl(head_of(sK9_skl),X1),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f6474,plain,
( ~ sQ80_spl
| sQ200_spl
| ~ sQ48_spl
| sQ630_spl ),
inference(split_clause,[status(thm)],[f6447,f6471,f509,f2222,f1111]) ).
fof(f6476,definition,
! [X0,X1,X2,X3,X4,X5] :
( sQ631_spl
<=> ( ~ path(tail_of(sK3_skl(head_of(sK9_skl),X3)),X2,X1)
| ~ in_path(head_of(sK9_skl),X3)
| ~ path(X4,X5,X3)
| sK9_skl = sK3_skl(head_of(sK9_skl),X3)
| ~ edge(sK3_skl(head_of(sK9_skl),X3))
| sequential(sK9_skl,sK3_skl(head_of(sK9_skl),X3))
| ~ sequential(sK1_skl(X1,X2,tail_of(sK3_skl(head_of(sK9_skl),X3))),X0)
| ~ on_path(sK1_skl(X1,X2,tail_of(sK3_skl(head_of(sK9_skl),X3))),sK10_skl)
| ~ sequential(X0,sK8_skl)
| ~ on_path(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ631_spl])],[split_symbol_definition]) ).
fof(f6479,plain,
( ~ sQ80_spl
| sQ200_spl
| ~ sQ48_spl
| sQ631_spl ),
inference(split_clause,[status(thm)],[f6449,f6476,f509,f2222,f1111]) ).
fof(f6569,plain,
( ~ sQ315_spl
| head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) != tail_of(sK8_skl)
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(paramodulation,[status(thm)],[f3120,f21]) ).
fof(f6608,definition,
( sQ637_spl
<=> vertex(tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f6610,plain,
( sQ637_spl
| ~ vertex(tail_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl)))) ),
inference(component_clause,[status(thm)],[f6608]) ).
fof(f6676,plain,
( ~ sQ315_spl
| ~ sQ304_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f6569,f2882,f3073,f3119]) ).
fof(f6677,plain,
( sQ637_spl
| ~ edge(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(resolution,[status(thm)],[f6610,f24]) ).
fof(f6678,plain,
( sQ637_spl
| ~ sQ284_spl ),
inference(split_clause,[status(thm)],[f6677,f2882,f6608]) ).
fof(f6686,plain,
( ~ sQ286_spl
| ~ sQ3_spl
| tail_of(sK8_skl) = head_of(sK9_skl)
| tail_of(sK8_skl) = head_of(sK9_skl)
| ~ vertex(head_of(sK9_skl))
| ~ vertex(tail_of(sK8_skl))
| tail_of(sK8_skl) = head_of(sK0_skl(head_of(sK9_skl),tail_of(sK8_skl))) ),
inference(paramodulation,[status(thm)],[f2889,f250]) ).
fof(f6733,plain,
( ~ sQ286_spl
| ~ sQ3_spl
| sQ274_spl
| ~ sQ26_spl
| ~ sQ21_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f6686,f3073,f270,f308,f2801,f150,f2888]) ).
fof(f6831,plain,
$false,
inference(sat_refutation,[status(thm)],[f145,f149,f153,f157,f164,f168,f172,f183,f187,f195,f218,f225,f294,f315,f403,f407,f411,f436,f461,f486,f515,f544,f566,f568,f572,f575,f590,f594,f768,f779,f799,f894,f1114,f1122,f1126,f1130,f1135,f1197,f1313,f1552,f1556,f1560,f1860,f1862,f1869,f1875,f1924,f2129,f2133,f2137,f2142,f2146,f2150,f2154,f2158,f2162,f2167,f2180,f2195,f2199,f2209,f2213,f2225,f2229,f2245,f2255,f2256,f2265,f2273,f2294,f2303,f2307,f2318,f2322,f2359,f2363,f2367,f2380,f2389,f2409,f2474,f2478,f2482,f2490,f2494,f2495,f2499,f2503,f2511,f2515,f2519,f2524,f2695,f2758,f2828,f2938,f3128,f3223,f3258,f3353,f3387,f3582,f3936,f4355,f4367,f4369,f4377,f4389,f4454,f4891,f4892,f4915,f4919,f4924,f5252,f5320,f5369,f5373,f5374,f5922,f5952,f6001,f6005,f6014,f6190,f6193,f6207,f6470,f6474,f6479,f6676,f6678,f6733]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRA006+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n005.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 20 18:19:03 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 5.25/1.33 % Refutation found
% 5.25/1.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.25/1.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.50/1.38 % Elapsed time: 0.960694 seconds
% 1.50/1.38 % CPU time: 7.295730 seconds
% 1.50/1.38 % Total memory used: 191.454 MB
% 1.50/1.38 % Net memory used: 183.714 MB
%------------------------------------------------------------------------------