%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRA075+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:31:17 PM UTC 2026
% Result : Satisfiable 0.13s 0.39s
% Output : Saturation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E] :
( edge(E)
=> head_of(E) != tail_of(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E] :
( edge(E)
=> ( vertex(tail_of(E))
& vertex(head_of(E)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [E] :
( head_of(E) != tail_of(E)
| ~ edge(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [E] :
( ( vertex(tail_of(E))
& vertex(head_of(E)) )
| ~ edge(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,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(f19,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(f20,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)],[f18,f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( edge(sK0_skl(X1,X0))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,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)],[f22]) ).
fof(f25,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)],[f22]) ).
fof(f26,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)],[f22]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3,X4] :
( X2 != path_cons(X3,X4)
| ~ path(head_of(X3),X1,X4)
| X0 != tail_of(X3)
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0)
| path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f30,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(f31,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(f32,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)],[f30,f31]) ).
fof(f33,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)],[f32]) ).
fof(f34,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))],[f33]) ).
fof(f35,plain,
! [X0,X1,X2] :
( vertex(X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1,X2] :
( edge(sK1_skl(X2,X1,X0))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1,X2] :
( X0 = tail_of(sK1_skl(X2,X1,X0))
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( path(head_of(sK1_skl(X2,X1,X0)),X1,sK2_skl(X2,X1,X0))
| sP1_prd(sK1_skl(X2,X1,X0),X2,X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f40,plain,
! [X0,X1,X2] :
( X2 = path_cons(sK1_skl(X2,X1,X0),sK2_skl(X2,X1,X0))
| sP1_prd(sK1_skl(X2,X1,X0),X2,X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( X2 != path_cons(sK1_skl(X2,X1,X0),X3)
| ~ path(head_of(sK1_skl(X2,X1,X0)),X1,X3)
| ~ sP1_prd(sK1_skl(X2,X1,X0),X2,X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f42,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(f43,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)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( in_path(head_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( in_path(tail_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f47,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(f48,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)],[f47]) ).
fof(f49,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))],[f48]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( vertex(X3)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,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)],[f49]) ).
fof(f52,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)],[f49]) ).
fof(f53,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(f54,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)],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f57,plain,
! [X0,X1] :
( X0 != X1
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f58,plain,
! [X0,X1] :
( head_of(X0) = tail_of(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f59,plain,
! [X0,X1] :
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f60,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(f61,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)],[f60]) ).
fof(f62,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)],[f61]) ).
fof(f63,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)],[f61]) ).
fof(f64,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(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,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))],[f66]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( on_path(X3,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( on_path(X4,X2)
| ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,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)],[f67]) ).
fof(f71,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)],[f67]) ).
fof(f72,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)],[f67]) ).
fof(f73,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(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [X0,X1,X2] :
( path(X0,X1,sK5_skl(X2,X1,X0))
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ less_or_equal(length_of(X2),length_of(sK5_skl(X2,X1,X0)))
| X0 = X1
| ~ path(X0,X1,X2)
| shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f82,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(f83,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)],[f82]) ).
fof(f84,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)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X4,X3,X2)
| ~ precedes(X3,X4,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,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)],[f19]) ).
fof(f87,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)],[f86]) ).
fof(f88,plain,
! [X0,X1,X2] :
( X2 = head_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [X0,X1,X2] :
( X1 = tail_of(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,plain,
! [X0,X1,X2] :
( X1 != tail_of(X0)
| X2 != head_of(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f91,plain,
! [V2,P,E] :
( ( P != path_cons(E,empty)
| V2 != head_of(E)
| sP1_prd(E,P,V2) )
& ( ( P = path_cons(E,empty)
& V2 = head_of(E) )
| ~ sP1_prd(E,P,V2) ) ),
inference(NNF_transformation,[status(thm)],[f31]) ).
fof(f92,plain,
( ! [V2,P,E] :
( P != path_cons(E,empty)
| V2 != head_of(E)
| sP1_prd(E,P,V2) )
& ! [V2,P,E] :
( ( P = path_cons(E,empty)
& V2 = head_of(E) )
| ~ sP1_prd(E,P,V2) ) ),
inference(miniscoping,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( X2 = head_of(X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( X1 = path_cons(X0,empty)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0,X1,X2] :
( X1 != path_cons(X0,empty)
| X2 != head_of(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f96,definition,
( sQ0_spl
<=> complete ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( sQ0_spl
| ~ complete ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,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(f102,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f23,f96,f99]) ).
fof(f103,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(f106,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f24,f96,f103]) ).
fof(f107,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(f110,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f96,f107]) ).
fof(f111,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(f114,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f26,f96,f111]) ).
fof(f115,plain,
! [X3] :
( ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(tail_of(X3))
| path(tail_of(X3),head_of(X3),path_cons(X3,empty)) ),
inference(destructive_equality_resolution,[status(thm)],[f28]) ).
fof(f116,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)],[f115,f17]) ).
fof(f117,plain,
! [X3,X1,X4] :
( ~ path(head_of(X3),X1,X4)
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(tail_of(X3))
| path(tail_of(X3),X1,path_cons(X3,X4)) ),
inference(destructive_equality_resolution,[status(thm)],[f29]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ~ path(head_of(X0),X1,X2)
| ~ edge(X0)
| ~ vertex(X1)
| path(tail_of(X0),X1,path_cons(X0,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f17]) ).
fof(f119,plain,
! [X0,X1,X2] :
( ~ path(head_of(X0),X1,X2)
| ~ edge(X0)
| path(tail_of(X0),X1,path_cons(X0,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[f118,f36]) ).
fof(f120,plain,
! [X0] : ~ sequential(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f57]) ).
fof(f121,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)],[f63,f69]) ).
fof(f122,plain,
! [X0,X1] : ~ shortest_path(X0,X0,X1),
inference(destructive_equality_resolution,[status(thm)],[f78]) ).
fof(f123,plain,
! [X0] : sP0_prd(X0,tail_of(X0),head_of(X0)),
inference(destructive_equality_resolution,[status(thm)],[f90]) ).
fof(f124,plain,
! [X0] : sP1_prd(X0,path_cons(X0,empty),head_of(X0)),
inference(destructive_equality_resolution,[status(thm)],[f95]) ).
fof(model,axiom,
~ sQ0_spl ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA075+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 19:09:16 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 0.13/0.39 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.13/0.39 % SZS output start Saturation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.033321 seconds
% 0.13/0.41 % CPU time: 0.092009 seconds
% 0.13/0.41 % Total memory used: 3.401 MB
% 0.13/0.41 % Net memory used: 3.323 MB
%------------------------------------------------------------------------------