%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRA007+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 : n016.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 0.74s 0.56s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 29
% Syntax : Number of formulae : 151 ( 11 unt; 20 def)
% Number of atoms : 610 ( 130 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 767 ( 308 ~; 317 |; 100 &)
% ( 23 <=>; 13 =>; 1 <=; 5 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 21 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 292 ( 268 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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) = 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) = tail_of(E1)
& tail_of(E3) = head_of(E2)
& edge(E3) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
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(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(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(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(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(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) != 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,
( ? [E1,E2] :
( ! [E3] :
( head_of(E3) != tail_of(E1)
| tail_of(E3) != head_of(E2)
| ~ edge(E3) )
& ? [P] :
( precedes(E1,E2,P)
& ? [V1,V2] : shortest_path(V1,V2,P) ) )
& complete ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f118,plain,
( ! [E3] :
( head_of(E3) != tail_of(sK8_skl)
| tail_of(E3) != head_of(sK9_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]),skolemize(E1,sK8_skl),skolemize(E2,sK9_skl),skolemize(P,sK10_skl),skolemize(V1,sK11_skl),skolemize(V2,sK12_skl)],[f117]) ).
fof(f119,plain,
complete,
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
shortest_path(sK11_skl,sK12_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f121,plain,
precedes(sK8_skl,sK9_skl,sK10_skl),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f122,plain,
! [X0] :
( head_of(X0) != tail_of(sK8_skl)
| tail_of(X0) != head_of(sK9_skl)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f123,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(f124,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)],[f123]) ).
fof(f125,plain,
! [X0,X1,X2] :
( X2 = head_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f126,plain,
! [X0,X1,X2] :
( X1 = tail_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f133,definition,
( sQ0_spl
<=> complete ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( sQ0_spl
| ~ complete ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,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(f137,plain,
! [X0,X1] :
( ~ sQ1_spl
| edge(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f133,f136]) ).
fof(f140,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(f141,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)],[f140]) ).
fof(f143,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f133,f140]) ).
fof(f144,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(f145,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)],[f144]) ).
fof(f147,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f133,f144]) ).
fof(f158,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f119]) ).
fof(f159,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f164,plain,
path(sK11_skl,sK12_skl,sK10_skl),
inference(resolution,[status(thm)],[f84,f120]) ).
fof(f166,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK10_skl)
| ~ precedes(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f92,f120]) ).
fof(f167,plain,
~ precedes(sK9_skl,sK8_skl,sK10_skl),
inference(resolution,[status(thm)],[f166,f121]) ).
fof(f173,definition,
! [X0,X1] :
( sQ5_spl
<=> ~ path(X0,X1,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f174,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ path(X0,X1,sK10_skl) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f191,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f164,f174]) ).
fof(f192,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f203,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(f204,plain,
! [X0,X1,X2,X3] :
( ~ precedes(X3,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f203]) ).
fof(f205,plain,
! [X0] : ~ precedes(X0,X0,sK10_skl),
inference(resolution,[status(thm)],[f204,f120]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ2_spl
| X1 = tail_of(sK0_skl(X1,X0))
| X1 = head_of(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f141,f126]) ).
fof(f207,plain,
! [X0,X1] :
( ~ sQ2_spl
| X0 = head_of(sK0_skl(X1,X0))
| X1 = head_of(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f141,f125]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ3_spl
| X0 = head_of(sK0_skl(X1,X0))
| X0 = tail_of(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f145,f125]) ).
fof(f212,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ2_spl
| head_of(sK0_skl(tail_of(X1),X0)) != head_of(X5)
| ~ precedes(X1,X5,X4)
| ~ shortest_path(X2,X3,X4)
| tail_of(X1) = head_of(sK0_skl(tail_of(X1),X0))
| X0 = tail_of(X1)
| ~ vertex(tail_of(X1))
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f206,f91]) ).
fof(f218,definition,
( sQ11_spl
<=> vertex(head_of(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ11_spl
| ~ vertex(head_of(sK9_skl)) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f224,plain,
! [X0] :
( ~ sQ2_spl
| tail_of(sK0_skl(tail_of(sK8_skl),X0)) != head_of(sK9_skl)
| ~ edge(sK0_skl(tail_of(sK8_skl),X0))
| X0 = head_of(sK0_skl(tail_of(sK8_skl),X0))
| X0 = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(X0) ),
inference(resolution,[status(thm)],[f207,f122]) ).
fof(f227,definition,
! [X0] :
( sQ12_spl
<=> ( tail_of(sK0_skl(tail_of(sK8_skl),X0)) != head_of(sK9_skl)
| ~ edge(sK0_skl(tail_of(sK8_skl),X0))
| X0 = head_of(sK0_skl(tail_of(sK8_skl),X0))
| X0 = tail_of(sK8_skl)
| ~ vertex(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f228,plain,
! [X0] :
( ~ sQ12_spl
| tail_of(sK0_skl(tail_of(sK8_skl),X0)) != head_of(sK9_skl)
| ~ edge(sK0_skl(tail_of(sK8_skl),X0))
| X0 = head_of(sK0_skl(tail_of(sK8_skl),X0))
| X0 = tail_of(sK8_skl)
| ~ vertex(X0) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ13_spl
<=> vertex(tail_of(sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( sQ13_spl
| ~ vertex(tail_of(sK8_skl)) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f224,f227,f230,f140]) ).
fof(f245,plain,
( sQ11_spl
| ~ edge(sK9_skl) ),
inference(resolution,[status(thm)],[f220,f23]) ).
fof(f261,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| head_of(sK9_skl) = head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))
| head_of(sK9_skl) = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(head_of(sK9_skl))
| ~ edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))
| head_of(sK9_skl) = head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl)))
| head_of(sK9_skl) = tail_of(sK8_skl)
| ~ vertex(head_of(sK9_skl)) ),
inference(resolution,[status(thm)],[f228,f209]) ).
fof(f263,definition,
( sQ16_spl
<=> head_of(sK9_skl) = tail_of(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ16_spl
| head_of(sK9_skl) = tail_of(sK8_skl) ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ17_spl
<=> head_of(sK9_skl) = head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ17_spl
| head_of(sK9_skl) = head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,definition,
( sQ18_spl
<=> edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ18_spl
| ~ edge(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f261,f218,f263,f266,f269,f230,f227,f144]) ).
fof(f273,plain,
( sQ13_spl
| ~ edge(sK8_skl) ),
inference(resolution,[status(thm)],[f232,f24]) ).
fof(f292,plain,
! [X0] :
( edge(X0)
| ~ on_path(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f51,f164]) ).
fof(f305,plain,
! [X0,X1] :
( on_path(sK8_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f75,f121]) ).
fof(f306,definition,
( sQ20_spl
<=> on_path(sK8_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( ~ sQ20_spl
| on_path(sK8_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( sQ20_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f305,f173,f306]) ).
fof(f310,plain,
( ~ sQ20_spl
| edge(sK8_skl) ),
inference(resolution,[status(thm)],[f307,f292]) ).
fof(f311,plain,
( ~ sQ20_spl
| sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f273]) ).
fof(f312,plain,
( ~ sQ20_spl
| sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f311]) ).
fof(f313,plain,
! [X0,X1] :
( on_path(sK9_skl,sK10_skl)
| ~ path(X0,X1,sK10_skl) ),
inference(resolution,[status(thm)],[f76,f121]) ).
fof(f314,definition,
( sQ21_spl
<=> on_path(sK9_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ21_spl
| on_path(sK9_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( sQ21_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f313,f173,f314]) ).
fof(f318,plain,
( ~ sQ21_spl
| edge(sK9_skl) ),
inference(resolution,[status(thm)],[f315,f292]) ).
fof(f319,plain,
( ~ sQ21_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f245]) ).
fof(f320,plain,
( ~ sQ21_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f326,plain,
( ~ sQ1_spl
| sQ18_spl
| head_of(sK9_skl) = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(head_of(sK9_skl)) ),
inference(resolution,[status(thm)],[f271,f137]) ).
fof(f327,plain,
( ~ sQ1_spl
| sQ18_spl
| sQ16_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f326,f218,f230,f263,f269,f136]) ).
fof(f330,plain,
( ~ sQ16_spl
| sK9_skl = sK8_skl
| ~ edge(sK8_skl)
| ~ edge(sK9_skl)
| sequential(sK9_skl,sK8_skl) ),
inference(resolution,[status(thm)],[f264,f66]) ).
fof(f343,definition,
( sQ22_spl
<=> sequential(sK9_skl,sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f346,definition,
( sQ23_spl
<=> edge(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ23_spl
| ~ edge(sK9_skl) ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ24_spl
<=> edge(sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ24_spl
| ~ edge(sK8_skl) ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,definition,
( sQ25_spl
<=> sK9_skl = sK8_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ25_spl
| sK9_skl = sK8_skl ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( ~ sQ16_spl
| sQ25_spl
| ~ sQ24_spl
| ~ sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f330,f343,f346,f349,f352,f263]) ).
fof(f384,plain,
( sQ24_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f310]) ).
fof(f385,plain,
( sQ24_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f384]) ).
fof(f400,plain,
( ~ sQ25_spl
| precedes(sK8_skl,sK8_skl,sK10_skl) ),
inference(backward_demodulation,[status(thm)],[f353,f121]) ).
fof(f403,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f205]) ).
fof(f404,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f496,plain,
( sQ23_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f318]) ).
fof(f497,plain,
( sQ23_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f541,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,f164]) ).
fof(f648,definition,
! [X1,X2] :
( sQ56_spl
<=> ~ shortest_path(X1,X2,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f649,plain,
! [X0,X1] :
( ~ sQ56_spl
| ~ shortest_path(X0,X1,sK10_skl) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f690,plain,
( ~ sequential(sK9_skl,sK8_skl)
| ~ on_path(sK8_skl,sK10_skl)
| ~ on_path(sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f541,f167]) ).
fof(f704,plain,
( ~ sQ22_spl
| ~ sQ20_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f690,f314,f306,f343]) ).
fof(f751,plain,
( ~ sQ56_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f120,f649]) ).
fof(f752,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f751]) ).
fof(f2314,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ sQ2_spl
| head_of(sK0_skl(tail_of(sK8_skl),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)
| head_of(sK9_skl) = tail_of(sK8_skl)
| ~ vertex(tail_of(sK8_skl))
| ~ vertex(head_of(sK9_skl)) ),
inference(paramodulation,[status(thm)],[f267,f212]) ).
fof(f2321,definition,
! [X0,X1,X2,X3] :
( sQ274_spl
<=> ( head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2322,plain,
! [X0,X1,X2,X3] :
( ~ sQ274_spl
| head_of(sK0_skl(tail_of(sK8_skl),head_of(sK9_skl))) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(component_clause,[status(thm)],[f2321]) ).
fof(f2324,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| sQ274_spl
| sQ16_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2314,f218,f230,f263,f2321,f140,f266]) ).
fof(f2325,plain,
! [X0,X1,X2,X3] :
( ~ sQ274_spl
| ~ sQ17_spl
| head_of(sK9_skl) != head_of(X3)
| ~ precedes(sK8_skl,X3,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f267,f2322]) ).
fof(f2370,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| ~ sQ17_spl
| ~ precedes(sK8_skl,sK9_skl,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[f2325]) ).
fof(f2391,plain,
( ~ sQ274_spl
| ~ sQ17_spl
| ~ precedes(sK8_skl,sK9_skl,sK10_skl) ),
inference(resolution,[status(thm)],[f2370,f120]) ).
fof(f2392,plain,
( ~ sQ274_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2391,f121]) ).
fof(f2393,plain,
( ~ sQ274_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f2392]) ).
fof(f2394,plain,
$false,
inference(sat_refutation,[status(thm)],[f139,f143,f147,f159,f192,f233,f272,f309,f312,f317,f320,f327,f355,f385,f404,f497,f704,f752,f2324,f2393]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA007+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 18:29:07 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.74/0.56 % Refutation found
% 0.74/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.74/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.74/0.60 % Elapsed time: 0.216099 seconds
% 0.74/0.60 % CPU time: 1.293930 seconds
% 0.74/0.60 % Total memory used: 102.626 MB
% 0.74/0.60 % Net memory used: 101.313 MB
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