%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 3.99s 0.94s
% Output : Proof 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 74 ( 16 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 71 ( 27 ~; 21 |; 14 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 60 ( 7 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,lemma,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f17_nnf,plain,
( ! [P,V1,V2] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ~ shortest_path(V1,V2,P) )
| ~ complete ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [V1,V2,P] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ~ shortest_path(V1,V2,P)
| ~ complete ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c70,plain,
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0)
| ~ complete ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f18,conjecture,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f18_neg,negated_conjecture,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
( ? [P,V1,V2] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& shortest_path(V1,V2,P) )
& complete ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
( ~ less_or_equal(minus(length_of(sk8),n1),number_of_in(triangles,graph))
& shortest_path(sk9,sk10,sk8)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8,sk9,sk10])],[f18_nnf]) ).
cnf(c71,plain,
complete,
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1800,plain,
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(resolution,[status(thm)],[c70,c71]) ).
cnf(c72,plain,
shortest_path(sk9,sk10,sk8),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1882,plain,
number_of_in(sequential_pairs,sk8) = number_of_in(triangles,sk8),
inference(resolution,[status(thm)],[p1800,c72]) ).
fof(f16,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f16_nnf,plain,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c69,plain,
less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p1883,plain,
less_or_equal(number_of_in(sequential_pairs,sk8),number_of_in(triangles,graph)),
inference(superposition,[status(thm)],[p1882,c69]) ).
fof(f14,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f14_nnf,plain,
! [V1,V2,P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ~ path(V1,V2,P) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [V1,V2,P] :
( number_of_in(sequential_pairs,P) = minus(length_of(P),n1)
| ~ path(V1,V2,P) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c64,plain,
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_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/sandbox/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(p132,plain,
path(sk9,sk10,sk8),
inference(resolution,[status(thm)],[c49,c72]) ).
cnf(p1554,plain,
number_of_in(sequential_pairs,sk8) = minus(length_of(sk8),n1),
inference(resolution,[status(thm)],[c64,p132]) ).
cnf(c73,plain,
~ less_or_equal(minus(length_of(sk8),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1556,plain,
~ less_or_equal(number_of_in(sequential_pairs,sk8),number_of_in(triangles,graph)),
inference(superposition,[status(thm)],[p1554,c73]) ).
cnf(p1884,plain,
$false,
inference(resolution,[status(thm)],[p1883,p1556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 12:43:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.99/0.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.99/0.94 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------