%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEV678+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 06:54:15 PM UTC 2026
% Result : Theorem 95.74s 96.02s
% Output : CNFRefutation 95.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 49 ( 18 ~; 15 |; 6 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 10 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('$_def_UseAuto.myFact',axiom,
( p(cUseAuto_2emyFact)
<=> ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
=> cUseAuto_2eP___24a1(V0__x) ) ) ) ).
fof('_HAMMER_GOAL',conjecture,
( ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cUseAuto_2eP___24a1(V0__x) )
=> p(cUseAuto_2emyFact) ) ).
fof(subgoal_0,plain,
( ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cUseAuto_2eP___24a1(V0__x) )
=> p(cUseAuto_2emyFact) ),
inference(strip,[],['_HAMMER_GOAL']) ).
fof(negate_0_0,plain,
~ ( ! [V0__x] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
=> cUseAuto_2eP___24a1(V0__x) )
=> p(cUseAuto_2emyFact) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ p(cUseAuto_2emyFact)
<=> ? [V0__x] :
( ~ cUseAuto_2eP___24a1(V0__x)
& cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
& cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO)))) ) ),
inference(canonicalize,[],['$_def_UseAuto.myFact']) ).
fof(normalize_0_1,plain,
! [V0__x] :
( ( ~ cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) )
& ( cCoq_2eInit_2ePeano_2ele___24a2(skolemFOFtoCNF_V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| p(cUseAuto_2emyFact) )
& ( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(V0__x,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ p(cUseAuto_2emyFact)
| cUseAuto_2eP___24a1(V0__x) ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ p(cUseAuto_2emyFact)
& ! [V0__x] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
| cUseAuto_2eP___24a1(V0__x) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
~ p(cUseAuto_2emyFact),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [V0__x] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
| cUseAuto_2eP___24a1(V0__x) ),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [V0__x] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
| cUseAuto_2eP___24a1(V0__x) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ~ cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) ),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ p(cUseAuto_2emyFact),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x),
inference(resolve,[$cnf( p(cUseAuto_2emyFact) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__x)
| cUseAuto_2eP___24a1(V0__x) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x)
| cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x) ),
inference(subst,[],[refute_0_3:[bind(V0__x,$fot(skolemFOFtoCNF_V0__x))]]) ).
cnf(refute_0_5,plain,
cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x),
inference(resolve,[$cnf( cCoq_2eInit_2eDatatypes_2enat___24t(skolemFOFtoCNF_V0__x) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x)
| p(cUseAuto_2emyFact) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x),
inference(resolve,[$cnf( p(cUseAuto_2emyFact) )],[refute_0_6,refute_0_1]) ).
cnf(refute_0_8,plain,
$false,
inference(resolve,[$cnf( cUseAuto_2eP___24a1(skolemFOFtoCNF_V0__x) )],[refute_0_5,refute_0_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV678+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.14 % Command : metis --show proof --show saturation %s
% 0.19/0.35 % Computer : n028.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Tue May 5 08:24:45 EDT 2026
% 0.19/0.35 % CPUTime :
% 0.19/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 95.74/96.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.74/96.02
% 95.74/96.02 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 95.86/96.03
%------------------------------------------------------------------------------