%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEV664+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 : 300s
% DateTime : Tue May 5 06:54:14 PM UTC 2026
% Result : Theorem 8.53s 8.77s
% Output : CNFRefutation 8.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 55 ( 19 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 15 ~; 7 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( cProp___24t(V1__Q)
=> ( V0__P = V1__Q
=> ( p(V0__P)
=> p(V1__Q) ) ) ) ) ).
fof(subgoal_0,plain,
! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( ( cProp___24t(V1__Q)
& V0__P = V1__Q
& p(V0__P) )
=> p(V1__Q) ) ),
inference(strip,[],['_HAMMER_GOAL']) ).
fof(negate_0_0,plain,
~ ! [V0__P] :
( cProp___24t(V0__P)
=> ! [V1__Q] :
( ( cProp___24t(V1__Q)
& V0__P = V1__Q
& p(V0__P) )
=> p(V1__Q) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [V0__P] :
( cProp___24t(V0__P)
& ? [V1__Q] :
( ~ p(V1__Q)
& V0__P = V1__Q
& cProp___24t(V1__Q)
& p(V0__P) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( cProp___24t(skolemFOFtoCNF_V0__P)
& ? [V1__Q] :
( ~ p(V1__Q)
& skolemFOFtoCNF_V0__P = V1__Q
& cProp___24t(V1__Q)
& p(skolemFOFtoCNF_V0__P) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [V1__Q] :
( ~ p(V1__Q)
& skolemFOFtoCNF_V0__P = V1__Q
& cProp___24t(V1__Q)
& p(skolemFOFtoCNF_V0__P) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ p(skolemFOFtoCNF_V1__Q)
& skolemFOFtoCNF_V0__P = skolemFOFtoCNF_V1__Q
& cProp___24t(skolemFOFtoCNF_V1__Q)
& p(skolemFOFtoCNF_V0__P) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
p(skolemFOFtoCNF_V0__P),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
~ p(skolemFOFtoCNF_V1__Q),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
skolemFOFtoCNF_V0__P = skolemFOFtoCNF_V1__Q,
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
p(skolemFOFtoCNF_V0__P),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
~ p(skolemFOFtoCNF_V1__Q),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_V0__P = skolemFOFtoCNF_V1__Q,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_4,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_5,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
( skolemFOFtoCNF_V0__P != skolemFOFtoCNF_V1__Q
| skolemFOFtoCNF_V1__Q = skolemFOFtoCNF_V0__P ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_V0__P)),bind(Y,$fot(skolemFOFtoCNF_V1__Q))]]) ).
cnf(refute_0_7,plain,
skolemFOFtoCNF_V1__Q = skolemFOFtoCNF_V0__P,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V0__P,skolemFOFtoCNF_V1__Q) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( skolemFOFtoCNF_V1__Q != skolemFOFtoCNF_V0__P
| ~ p(skolemFOFtoCNF_V0__P)
| p(skolemFOFtoCNF_V1__Q) ),
introduced(tautology,[equality,[$cnf( ~ p(skolemFOFtoCNF_V1__Q) ),[0],$fot(skolemFOFtoCNF_V0__P)]]) ).
cnf(refute_0_9,plain,
( ~ p(skolemFOFtoCNF_V0__P)
| p(skolemFOFtoCNF_V1__Q) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_V1__Q,skolemFOFtoCNF_V0__P) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ p(skolemFOFtoCNF_V0__P),
inference(resolve,[$cnf( p(skolemFOFtoCNF_V1__Q) )],[refute_0_9,refute_0_1]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( p(skolemFOFtoCNF_V0__P) )],[refute_0_0,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV664+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 07:53:43 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.53/8.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.53/8.77
% 8.53/8.77 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.53/8.78
%------------------------------------------------------------------------------