%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 07:19:21 AM UTC 2026
% Result : Theorem 0.14s 0.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 143 ( 34 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 167 ( 68 ~; 53 |; 35 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 82 ( 17 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(path_properties,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('theBenchmark.p',path_properties) ).
fof(on_path_properties,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('theBenchmark.p',on_path_properties) ).
fof(precedes_properties,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('theBenchmark.p',precedes_properties) ).
fof(shortest_path_defn,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('theBenchmark.p',shortest_path_defn) ).
fof(shortest_path_properties,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('theBenchmark.p',shortest_path_properties) ).
fof(vertices_and_edges,conjecture,
! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( path(V1,V2,P)
& E1 != E2
& edge(E2)
& edge(E1)
& V1 != V2
& vertex(V2)
& vertex(V1) ) ),
file('theBenchmark.p',vertices_and_edges) ).
fof(vertices_and_edges_neg,negated_conjecture,
~ ! [V1,V2,E1,E2,P] :
( ( precedes(E1,E2,P)
& shortest_path(V1,V2,P) )
=> ( path(V1,V2,P)
& E1 != E2
& edge(E2)
& edge(E1)
& V1 != V2
& vertex(V2)
& vertex(V1) ) ),
inference(assume_negation,[status(cth)],[vertices_and_edges]) ).
fof(nnf_18,plain,
? [V1,V2,E1,E2,P] :
( ( ~ path(V1,V2,P)
| E2 = E1
| ~ edge(E2)
| ~ edge(E1)
| V2 = V1
| ~ vertex(V2)
| ~ vertex(V1) )
& precedes(E1,E2,P)
& shortest_path(V1,V2,P) ),
inference(fof_nnf,[status(thm)],[vertices_and_edges_neg]) ).
fof(sk_vertices_and_edges_neg,plain,
( ( ~ path(sK0,sK1,sK2)
| sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3)
| sK1 = sK0
| ~ vertex(sK1)
| ~ vertex(sK0) )
& precedes(sK3,sK4,sK2)
& shortest_path(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(V1,sK0),skolemize(V2,sK1),skolemize(E1,sK3),skolemize(E2,sK4),skolemize(P,sK2)],[nnf_18]) ).
cnf(c_25,negated_conjecture,
shortest_path(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_vertices_and_edges_neg]) ).
cnf(c_26,plain,
( head_of(F) != head_of(E)
| tail_of(F) != tail_of(D)
| ~ precedes(D,E,C)
| ~ shortest_path(A,B,C) ),
inference(clausify,[status(thm)],[shortest_path_properties]) ).
cnf(c_30,plain,
( B != A
| ~ shortest_path(A,B,C) ),
inference(clausify,[status(thm)],[shortest_path_defn]) ).
cnf(c_31,plain,
( path(A,B,C)
| ~ shortest_path(A,B,C) ),
inference(clausify,[status(thm)],[shortest_path_defn]) ).
cnf(c_32,negated_conjecture,
path(sK0,sK1,sK2),
inference(resolve,[status(thm)],[c_31,c_25]) ).
cnf(c_33,negated_conjecture,
sK1 != sK0,
inference(resolve,[status(thm)],[c_30,c_25]) ).
cnf(c_41,negated_conjecture,
( head_of(C) != head_of(B)
| tail_of(C) != tail_of(A)
| ~ precedes(A,B,sK2) ),
inference(resolve,[status(thm)],[c_26,c_25]) ).
cnf(c_54,plain,
( vertex(A)
| ~ path(A,B,C) ),
inference(clausify,[status(thm)],[path_properties]) ).
cnf(c_55,plain,
( vertex(B)
| ~ path(A,B,C) ),
inference(clausify,[status(thm)],[path_properties]) ).
cnf(c_63,plain,
( edge(D)
| ~ on_path(D,C)
| ~ path(A,B,C) ),
inference(clausify,[status(thm)],[on_path_properties]) ).
cnf(c_71,plain,
( on_path(D,C)
| ~ precedes(D,E,C)
| ~ path(A,B,C) ),
inference(clausify,[status(thm)],[precedes_properties]) ).
cnf(c_72,plain,
( on_path(E,C)
| ~ precedes(D,E,C)
| ~ path(A,B,C) ),
inference(clausify,[status(thm)],[precedes_properties]) ).
cnf(c_90,negated_conjecture,
precedes(sK3,sK4,sK2),
inference(split_conjunct,[status(thm)],[sk_vertices_and_edges_neg]) ).
cnf(c_91,negated_conjecture,
( ~ path(sK0,sK1,sK2)
| sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3)
| sK1 = sK0
| ~ vertex(sK1)
| ~ vertex(sK0) ),
inference(split_conjunct,[status(thm)],[sk_vertices_and_edges_neg]) ).
cnf(c_222,negated_conjecture,
( ~ path(sK0,sK1,sK2)
| sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3)
| ~ vertex(sK1)
| ~ vertex(sK0) ),
inference(resolve,[status(thm)],[c_33,c_91]) ).
cnf(c_92,negated_conjecture,
( sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3)
| ~ vertex(sK1)
| ~ vertex(sK0) ),
inference(resolve,[status(thm)],[c_32,c_222]) ).
cnf(c_125,plain,
vertex(sK0),
inference(resolve,[status(thm)],[c_54,c_32]) ).
cnf(c_126,negated_conjecture,
( sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3)
| ~ vertex(sK1) ),
inference(resolve,[status(thm)],[c_125,c_92]) ).
cnf(c_127,plain,
vertex(sK1),
inference(resolve,[status(thm)],[c_55,c_32]) ).
cnf(c_128,negated_conjecture,
( sK4 = sK3
| ~ edge(sK4)
| ~ edge(sK3) ),
inference(resolve,[status(thm)],[c_127,c_126]) ).
cnf(c_223,negated_conjecture,
( on_path(B,sK2)
| ~ precedes(A,B,sK2) ),
inference(resolve,[status(thm)],[c_72,c_32]) ).
cnf(c_154,negated_conjecture,
on_path(sK4,sK2),
inference(resolve,[status(thm)],[c_223,c_90]) ).
cnf(c_224,negated_conjecture,
( on_path(A,sK2)
| ~ precedes(A,B,sK2) ),
inference(resolve,[status(thm)],[c_71,c_32]) ).
cnf(c_155,negated_conjecture,
on_path(sK3,sK2),
inference(resolve,[status(thm)],[c_224,c_90]) ).
cnf(c_225,negated_conjecture,
( head_of(A) != head_of(sK4)
| tail_of(A) != tail_of(sK3) ),
inference(resolve,[status(thm)],[c_41,c_90]) ).
cnf(c_226,plain,
head_of(sK3) != head_of(sK4),
inference(xxres,[status(thm)],[c_225]) ).
cnf(c_157,plain,
head_of(sK4) != head_of(sK3),
inference(copy,[status(thm)],[c_226]) ).
cnf(c_227,negated_conjecture,
( edge(A)
| ~ on_path(A,sK2) ),
inference(resolve,[status(thm)],[c_63,c_32]) ).
cnf(c_199,negated_conjecture,
edge(sK4),
inference(resolve,[status(thm)],[c_227,c_154]) ).
cnf(c_201,negated_conjecture,
( sK4 = sK3
| ~ edge(sK3) ),
inference(resolve,[status(thm)],[c_199,c_128]) ).
cnf(c_228,negated_conjecture,
( edge(A)
| ~ on_path(A,sK2) ),
inference(resolve,[status(thm)],[c_63,c_32]) ).
cnf(c_213,negated_conjecture,
edge(sK3),
inference(resolve,[status(thm)],[c_228,c_155]) ).
cnf(c_214,negated_conjecture,
sK4 = sK3,
inference(resolve,[status(thm)],[c_213,c_201]) ).
cnf(c_229,plain,
head_of(sK3) != head_of(sK3),
inference(paramod,[status(thm)],[c_214,c_157]) ).
cnf(c_221,plain,
$false,
inference(copy,[status(thm)],[c_229]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA003+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n026.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Fri Sep 25 13:50:11 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.53 % Process 2670666 was started by sandbox on n026,
% 0.10/0.53 % Fri Sep 25 13:50:11 2026
% 0.10/0.53 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.54
% 0.10/0.54 % From the command line: assign(max_seconds, 300).
% 0.14/0.57
% 0.14/0.57 % SZS status Theorem for theBenchmark
% 0.14/0.57
% 0.14/0.57 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.57 % Length of proof is 33.
% 0.14/0.57 % Level of proof is 8.
% 0.14/0.57 % Maximum clause weight is 24.000.
% 0.14/0.57 % Given clauses 85.
% 0.14/0.57
% 0.14/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------