%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:22:52 PM UTC 2026
% Result : Theorem 36.22s 5.91s
% Output : Proof 36.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 65 ( 13 unt; 0 def)
% Number of atoms : 252 ( 76 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 301 ( 114 ~; 110 |; 65 &)
% ( 2 <=>; 8 =>; 1 <=; 1 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-5 aty)
% Number of variables : 157 ( 16 sgn 91 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,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',shortest_path_properties) ).
fof(f11_nnf,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(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [V1,V2,P,E1,E2,E3] :
( ( ~ precedes(E2,E1,P)
& ( head_of(E3) != head_of(E2)
| tail_of(E3) != tail_of(E1) ) )
| ~ precedes(E1,E2,P)
| ~ shortest_path(V1,V2,P) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c54,plain,
( head_of(X5) != head_of(X3)
| tail_of(X5) != tail_of(X2)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f17,conjecture,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( head_of(E2) != head_of(E1)
& head_of(E2) != tail_of(E1)
& ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties_lemma) ).
fof(f17_neg,negated_conjecture,
~ ! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( head_of(E2) != head_of(E1)
& head_of(E2) != tail_of(E1)
& ~ ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
? [V1,V2,E1,E2,P] :
( ( head_of(E2) = head_of(E1)
| head_of(E2) = tail_of(E1)
| ? [E3] :
( head_of(E3) = head_of(E2)
& tail_of(E3) = tail_of(E1) ) )
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
( ( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10)
| ( head_of(sk13) = head_of(sk11)
& tail_of(sk13) = tail_of(sk10) ) )
& precedes(sk10,sk11,sk12)
& shortest_path(sk8,sk9,sk12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10,sk11,sk12,sk13])],[f17_nnf]) ).
cnf(c70,plain,
shortest_path(sk8,sk9,sk12),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p657,plain,
( head_of(X2) != head_of(X1)
| tail_of(X2) != tail_of(X0)
| ~ precedes(X0,X1,sk12) ),
inference(resolution,[status(thm)],[c54,c70]) ).
cnf(c71,plain,
precedes(sk10,sk11,sk12),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1173,plain,
( head_of(X0) != head_of(sk11)
| tail_of(X0) != tail_of(sk10) ),
inference(resolution,[status(thm)],[p657,c71]) ).
cnf(c72,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10)
| tail_of(sk13) = tail_of(sk10) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1213,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10)
| head_of(sk13) != head_of(sk11) ),
inference(resolution,[status(thm)],[p1173,c72]) ).
cnf(c73,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10)
| head_of(sk13) = head_of(sk11) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1402,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10)
| head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10) ),
inference(resolution,[status(thm)],[p1213,c73]) ).
cnf(p6453,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10) ),
inference(factoring,[status(thm)],[p1402]) ).
cnf(p6456,plain,
( head_of(sk11) = head_of(sk10)
| head_of(sk11) = tail_of(sk10) ),
inference(factoring,[status(thm)],[p6453]) ).
fof(f9,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',precedes_properties) ).
fof(f9_nnf,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)],[f9]) ).
fof(f9_sk,plain,
! [V1,V2,P,E1,E2,E3] :
( ( ( ( precedes(sk4(P,V1,V2,E1,E2),E2,P)
& sequential(E1,sk4(P,V1,V2,E1,E2))
& ~ sequential(E1,E2) )
| ( ( ~ 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(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f9_nnf]) ).
cnf(c42,plain,
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f10,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',shortest_path_defn) ).
fof(f10_nnf,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)],[f10]) ).
fof(f10_sk,plain,
! [V1,V2,SP,P] :
( ( ( ~ less_or_equal(length_of(SP),length_of(sk5(V1,V2,SP)))
& path(V1,V2,sk5(V1,V2,SP)) )
| V1 = V2
| ~ path(V1,V2,SP)
| shortest_path(V1,V2,SP) )
& ( ( ( 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(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f10_nnf]) ).
cnf(c49,plain,
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p89,plain,
path(sk8,sk9,sk12),
inference(resolution,[status(thm)],[c49,c70]) ).
cnf(p379,plain,
( on_path(X1,sk12)
| ~ precedes(X0,X1,sk12) ),
inference(resolution,[status(thm)],[c42,p89]) ).
cnf(p397,plain,
on_path(sk11,sk12),
inference(resolution,[status(thm)],[p379,c71]) ).
fof(f5,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',on_path_properties) ).
fof(f5_nnf,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(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,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(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c28,plain,
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p98,plain,
( edge(X0)
| ~ on_path(X0,sk12) ),
inference(resolution,[status(thm)],[c28,p89]) ).
cnf(p398,plain,
edge(sk11),
inference(resolution,[status(thm)],[p397,p98]) ).
fof(f7,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',sequential_defn) ).
fof(f7_nnf,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)],[f7]) ).
fof(f7_sk,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(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c38,plain,
( head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0)
| sequential(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p414,plain,
( head_of(sk11) != tail_of(X0)
| sk11 = X0
| ~ edge(X0)
| sequential(sk11,X0) ),
inference(resolution,[status(thm)],[p398,c38]) ).
cnf(c41,plain,
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p346,plain,
( on_path(X0,sk12)
| ~ precedes(X0,X1,sk12) ),
inference(resolution,[status(thm)],[c41,p89]) ).
cnf(p350,plain,
on_path(sk10,sk12),
inference(resolution,[status(thm)],[p346,c71]) ).
cnf(p351,plain,
edge(sk10),
inference(resolution,[status(thm)],[p350,p98]) ).
cnf(p1158,plain,
( head_of(sk11) != tail_of(sk10)
| sk11 = sk10
| sequential(sk11,sk10) ),
inference(resolution,[status(thm)],[p414,p351]) ).
cnf(p6466,plain,
( sk11 = sk10
| sequential(sk11,sk10)
| head_of(sk11) = head_of(sk10) ),
inference(resolution,[status(thm)],[p6456,p1158]) ).
cnf(p1171,plain,
( head_of(X0) != head_of(X1)
| ~ precedes(X0,X1,sk12) ),
inference(equality_resolution,[status(thm)],[p657]) ).
cnf(p1174,plain,
head_of(sk10) != head_of(sk11),
inference(resolution,[status(thm)],[p1171,c71]) ).
cnf(p6509,plain,
( head_of(sk10) != head_of(sk10)
| sk11 = sk10
| sequential(sk11,sk10) ),
inference(superposition,[status(thm)],[p6466,p1174]) ).
cnf(p6539,plain,
( sk11 = sk10
| sequential(sk11,sk10) ),
inference(equality_resolution,[status(thm)],[p6509]) ).
fof(f8,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',precedes_defn) ).
fof(f8_nnf,plain,
! [P,V1,V2] :
( ! [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) )
| ~ path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [V1,V2,P,E1,E2,E3] :
( precedes(E1,E2,P)
| ( ( ~ precedes(E3,E2,P)
| ~ sequential(E1,E3) )
& ~ sequential(E1,E2) )
| ~ on_path(E2,P)
| ~ on_path(E1,P)
| ~ path(V1,V2,P) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c39,plain,
( precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p305,plain,
( precedes(X0,X1,sk12)
| ~ sequential(X0,X1)
| ~ on_path(X1,sk12)
| ~ on_path(X0,sk12) ),
inference(resolution,[status(thm)],[c39,p89]) ).
cnf(p1038,plain,
( precedes(sk11,X0,sk12)
| ~ sequential(sk11,X0)
| ~ on_path(X0,sk12) ),
inference(resolution,[status(thm)],[p305,p397]) ).
cnf(p1063,plain,
( precedes(sk11,sk10,sk12)
| ~ sequential(sk11,sk10) ),
inference(resolution,[status(thm)],[p1038,p350]) ).
cnf(p6541,plain,
( precedes(sk11,sk10,sk12)
| sk11 = sk10 ),
inference(resolution,[status(thm)],[p6539,p1063]) ).
cnf(c55,plain,
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p695,plain,
( ~ precedes(X1,X0,sk12)
| ~ precedes(X0,X1,sk12) ),
inference(resolution,[status(thm)],[c55,c70]) ).
cnf(p697,plain,
~ precedes(sk11,sk10,sk12),
inference(resolution,[status(thm)],[p695,c71]) ).
cnf(p6544,plain,
sk11 = sk10,
inference(resolution,[status(thm)],[p6541,p697]) ).
cnf(p6545,plain,
precedes(sk10,sk10,sk12),
inference(demodulation,[status(thm)],[p6544,c71]) ).
cnf(p696,plain,
~ precedes(X0,X0,sk12),
inference(factoring,[status(thm)],[p695]) ).
cnf(p7410,plain,
$false,
inference(resolution,[status(thm)],[p6545,p696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA004+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.39 % Computer : n014.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Wed Sep 23 12:42:49 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 36.22/5.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.22/5.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------