%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEV608+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 06:54:11 PM UTC 2026
% Result : Theorem 33.97s 34.49s
% Output : CNFRefutation 33.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 2 unt; 0 def)
% Number of atoms : 37 ( 7 equ)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 38 ( 10 ~; 8 |; 6 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 7 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 18 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof('Color.select_terminates',axiom,
! [V0__K] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
=> ! [V1__g] :
( cColor_2egraph___24t(V1__g)
=> ! [V2__n] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ) ) ).
fof('_HAMMER_GOAL',conjecture,
! [V0__K] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
=> ! [V1__g] :
( cColor_2egraph___24t(V1__g)
=> ! [V2__n] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ) ) ).
fof(subgoal_0,plain,
! [V0__K] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
=> ! [V1__g] :
( cColor_2egraph___24t(V1__g)
=> ! [V2__n] :
( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n) )
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ),
inference(strip,[],['_HAMMER_GOAL']) ).
fof(negate_0_0,plain,
~ ! [V0__K] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
=> ! [V1__g] :
( cColor_2egraph___24t(V1__g)
=> ! [V2__n] :
( ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n) )
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [V0__K] :
( cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
& ? [V1__g] :
( cColor_2egraph___24t(V1__g)
& ? [V2__n] :
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [V0__K] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
| ! [V1__g] :
( ~ cColor_2egraph___24t(V1__g)
| ! [V2__n] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ),
inference(canonicalize,[],['Color.select_terminates']) ).
fof(normalize_0_2,plain,
! [V0__K] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__K)
| ! [V1__g] :
( ~ cColor_2egraph___24t(V1__g)
| ! [V2__n] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(V0__K),V1__g)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,V2__n)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(V2__n)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(V2__n,V1__g)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,V1__g)) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
$false,
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
cnf(refute_0_0,plain,
$false,
inference(canonicalize,[],[normalize_0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV608+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.16/0.34 % Computer : n027.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 05:25:19 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 33.97/34.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.97/34.49
% 33.97/34.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.97/34.49
%------------------------------------------------------------------------------