TSTP Solution File: GRA002+4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 07:19:50 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 21 unt; 0 def)
% Number of atoms : 118 ( 33 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 113 ( 48 ~; 40 |; 12 &)
% ( 3 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 81 ( 7 sgn 50 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(shortest_path_defn,axiom,
! [V1,V2,SP] :
( shortest_path(V1,V2,SP)
<=> ( path(V1,V2,SP)
& V1 != V2
& ! [P] :
( path(V1,V2,P)
=> less_or_equal(length_of(SP),length_of(P)) ) ) ) ).
fof(path_length_sequential_pairs,axiom,
! [V1,V2,P] :
( path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ) ).
fof(graph_has_them_all,axiom,
! [Things,InThese] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)) ).
fof(triangles_and_sequential_pairs,lemma,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ).
fof(maximal_path_length,conjecture,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ) ).
fof(subgoal_0,plain,
( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(strip,[],[maximal_path_length]) ).
fof(negate_0_0,plain,
~ ( complete
=> ! [P,V1,V2] :
( shortest_path(V1,V2,P)
=> less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [InThese,Things] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
inference(canonicalize,[],[graph_has_them_all]) ).
fof(normalize_0_1,plain,
! [InThese,Things] : less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( complete
& ? [P] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& ? [V1,V2] : shortest_path(V1,V2,P) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
? [P] :
( ~ less_or_equal(minus(length_of(P),n1),number_of_in(triangles,graph))
& ? [V1,V2] : shortest_path(V1,V2,P) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph))
& ? [V1,V2] : shortest_path(V1,V2,skolemFOFtoCNF_P_1) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [V1,V2] : shortest_path(V1,V2,skolemFOFtoCNF_P_1),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ complete
| ! [P] :
( number_of_in(sequential_pairs,P) = number_of_in(triangles,P)
| ! [V1,V2] : ~ shortest_path(V1,V2,P) ) ),
inference(canonicalize,[],[triangles_and_sequential_pairs]) ).
fof(normalize_0_8,plain,
! [P,V1,V2] :
( ~ complete
| ~ shortest_path(V1,V2,P)
| number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
complete,
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,plain,
~ less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_11,plain,
! [SP,V1,V2] :
( ~ shortest_path(V1,V2,SP)
<=> ( ~ path(V1,V2,SP)
| V1 = V2
| ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) ) ) ),
inference(canonicalize,[],[shortest_path_defn]) ).
fof(normalize_0_12,plain,
! [SP,V1,V2] :
( ~ shortest_path(V1,V2,SP)
<=> ( ~ path(V1,V2,SP)
| V1 = V2
| ? [P] :
( ~ less_or_equal(length_of(SP),length_of(P))
& path(V1,V2,P) ) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [P,SP,V1,V2] :
( ( V1 != V2
| ~ shortest_path(V1,V2,SP) )
& ( ~ shortest_path(V1,V2,SP)
| path(V1,V2,SP) )
& ( ~ path(V1,V2,P)
| ~ shortest_path(V1,V2,SP)
| less_or_equal(length_of(SP),length_of(P)) )
& ( ~ less_or_equal(length_of(SP),length_of(skolemFOFtoCNF_P(SP,V1,V2)))
| ~ path(V1,V2,SP)
| V1 = V2
| shortest_path(V1,V2,SP) )
& ( ~ path(V1,V2,SP)
| V1 = V2
| path(V1,V2,skolemFOFtoCNF_P(SP,V1,V2))
| shortest_path(V1,V2,SP) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [SP,V1,V2] :
( ~ shortest_path(V1,V2,SP)
| path(V1,V2,SP) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [P,V1,V2] :
( ~ path(V1,V2,P)
| number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
inference(canonicalize,[],[path_length_sequential_pairs]) ).
fof(normalize_0_16,plain,
! [P,V1,V2] :
( ~ path(V1,V2,P)
| number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
inference(specialize,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
less_or_equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)),
inference(subst,[],[refute_0_0:[bind(InThese,$fot(skolemFOFtoCNF_P_1)),bind(Things,$fot(triangles))]]) ).
cnf(refute_0_2,plain,
shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ complete
| ~ shortest_path(V1,V2,P)
| number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
complete,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ shortest_path(V1,V2,P)
| number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ),
inference(resolve,[$cnf( complete )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1)
| number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) = number_of_in(triangles,skolemFOFtoCNF_P_1) ),
inference(subst,[],[refute_0_5:[bind(P,$fot(skolemFOFtoCNF_P_1)),bind(V1,$fot(skolemFOFtoCNF_V1)),bind(V2,$fot(skolemFOFtoCNF_V2))]]) ).
cnf(refute_0_7,plain,
number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) = number_of_in(triangles,skolemFOFtoCNF_P_1),
inference(resolve,[$cnf( shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) != number_of_in(triangles,skolemFOFtoCNF_P_1)
| number_of_in(triangles,skolemFOFtoCNF_P_1) = number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1))),bind(Y,$fot(number_of_in(triangles,skolemFOFtoCNF_P_1)))]]) ).
cnf(refute_0_12,plain,
number_of_in(triangles,skolemFOFtoCNF_P_1) = number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),
inference(resolve,[$cnf( $equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,skolemFOFtoCNF_P_1)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( number_of_in(triangles,skolemFOFtoCNF_P_1) != number_of_in(sequential_pairs,skolemFOFtoCNF_P_1)
| ~ less_or_equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(triangles,graph))
| less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)) ),
introduced(tautology,[equality,[$cnf( less_or_equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)) ),[0],$fot(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1))]]) ).
cnf(refute_0_14,plain,
( ~ less_or_equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(triangles,graph))
| less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)) ),
inference(resolve,[$cnf( $equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(sequential_pairs,skolemFOFtoCNF_P_1)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)),
inference(resolve,[$cnf( less_or_equal(number_of_in(triangles,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
~ less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_17,plain,
( ~ shortest_path(V1,V2,SP)
| path(V1,V2,SP) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_18,plain,
( ~ shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1)
| path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1) ),
inference(subst,[],[refute_0_17:[bind(SP,$fot(skolemFOFtoCNF_P_1)),bind(V1,$fot(skolemFOFtoCNF_V1)),bind(V2,$fot(skolemFOFtoCNF_V2))]]) ).
cnf(refute_0_19,plain,
path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1),
inference(resolve,[$cnf( shortest_path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ path(V1,V2,P)
| number_of_in(sequential_pairs,P) = minus(length_of(P),n1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_21,plain,
( ~ path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1)
| number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) = minus(length_of(skolemFOFtoCNF_P_1),n1) ),
inference(subst,[],[refute_0_20:[bind(P,$fot(skolemFOFtoCNF_P_1)),bind(V1,$fot(skolemFOFtoCNF_V1)),bind(V2,$fot(skolemFOFtoCNF_V2))]]) ).
cnf(refute_0_22,plain,
number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) = minus(length_of(skolemFOFtoCNF_P_1),n1),
inference(resolve,[$cnf( path(skolemFOFtoCNF_V1,skolemFOFtoCNF_V2,skolemFOFtoCNF_P_1) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) != minus(length_of(skolemFOFtoCNF_P_1),n1)
| minus(length_of(skolemFOFtoCNF_P_1),n1) = number_of_in(sequential_pairs,skolemFOFtoCNF_P_1) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1))),bind(Y,$fot(minus(length_of(skolemFOFtoCNF_P_1),n1)))]]) ).
cnf(refute_0_24,plain,
minus(length_of(skolemFOFtoCNF_P_1),n1) = number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),
inference(resolve,[$cnf( $equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),minus(length_of(skolemFOFtoCNF_P_1),n1)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( minus(length_of(skolemFOFtoCNF_P_1),n1) != number_of_in(sequential_pairs,skolemFOFtoCNF_P_1)
| ~ less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph))
| less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)) ),
introduced(tautology,[equality,[$cnf( ~ less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)) ),[0],$fot(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1))]]) ).
cnf(refute_0_26,plain,
( ~ less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph))
| less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)) ),
inference(resolve,[$cnf( $equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(sequential_pairs,skolemFOFtoCNF_P_1)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
~ less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)),
inference(resolve,[$cnf( less_or_equal(minus(length_of(skolemFOFtoCNF_P_1),n1),number_of_in(triangles,graph)) )],[refute_0_26,refute_0_16]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( less_or_equal(number_of_in(sequential_pairs,skolemFOFtoCNF_P_1),number_of_in(triangles,graph)) )],[refute_0_15,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA002+4 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 02:29:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.41
%------------------------------------------------------------------------------