%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 : Thu Sep 24 02:33:05 PM UTC 2026
% Result : Theorem 121.09s 121.49s
% Output : CNFRefutation 121.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 10 unt; 4 def)
% Number of atoms : 77 ( 8 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 24 ~; 22 |; 8 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1538,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)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2868,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)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2869,negated_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)) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2868]) ).
fof(f10124,plain,
! [V0__K] :
( ! [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) )
| ~ cColor_2egraph___24t(V1__g) )
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(V0__K) ),
inference(pre_NNF_transformation,[status(thm)],[f1538]) ).
fof(f10125,plain,
! [X0,X1,X2] :
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X2,X1)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X1))
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X0),X1)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X2)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X2)
| ~ cColor_2egraph___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ),
inference(cnf_transformation,[status(thm)],[f10124]) ).
fof(f13607,plain,
? [V0__K] :
( ? [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) )
& cColor_2egraph___24t(V1__g) )
& cCoq_2eInit_2eDatatypes_2enat___24t(V0__K) ),
inference(pre_NNF_transformation,[status(thm)],[f2869]) ).
fof(f13608,plain,
( ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK1739_skl,sK1738_skl)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1738_skl))
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(sK1737_skl),sK1738_skl)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK1739_skl)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK1739_skl)
& cColor_2egraph___24t(sK1738_skl)
& cCoq_2eInit_2eDatatypes_2enat___24t(sK1737_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1737_skl,sK1738_skl,sK1739_skl]),skolemize(V0__K,sK1737_skl),skolemize(V1__g,sK1738_skl),skolemize(V2__n,sK1739_skl)],[f13607]) ).
fof(f13609,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(sK1737_skl),
inference(cnf_transformation,[status(thm)],[f13608]) ).
fof(f13610,plain,
cColor_2egraph___24t(sK1738_skl),
inference(cnf_transformation,[status(thm)],[f13608]) ).
fof(f13611,plain,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK1739_skl),
inference(cnf_transformation,[status(thm)],[f13608]) ).
fof(f13612,plain,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(sK1737_skl),sK1738_skl)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,sK1739_skl),
inference(cnf_transformation,[status(thm)],[f13608]) ).
fof(f13613,plain,
~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK1739_skl,sK1738_skl)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1738_skl)),
inference(cnf_transformation,[status(thm)],[f13608]) ).
fof(f23572,plain,
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK1739_skl,sK1738_skl)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1738_skl))
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK1739_skl)
| ~ cColor_2egraph___24t(sK1738_skl)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(sK1737_skl) ),
inference(resolution,[status(thm)],[f10125,f13612]) ).
fof(f23574,definition,
( sQ107_spl
<=> cCoq_2eInit_2eDatatypes_2enat___24t(sK1737_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f23576,plain,
( sQ107_spl
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(sK1737_skl) ),
inference(component_clause,[status(thm)],[f23574]) ).
fof(f23577,definition,
( sQ108_spl
<=> cColor_2egraph___24t(sK1738_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f23579,plain,
( sQ108_spl
| ~ cColor_2egraph___24t(sK1738_skl) ),
inference(component_clause,[status(thm)],[f23577]) ).
fof(f23580,definition,
( sQ109_spl
<=> cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK1739_skl) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f23582,plain,
( sQ109_spl
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(sK1739_skl) ),
inference(component_clause,[status(thm)],[f23580]) ).
fof(f23583,definition,
( sQ110_spl
<=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK1739_skl,sK1738_skl)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1738_skl)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f23584,plain,
( ~ sQ110_spl
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(sK1739_skl,sK1738_skl)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,sK1738_skl)) ),
inference(component_clause,[status(thm)],[f23583]) ).
fof(f23586,plain,
( sQ110_spl
| ~ sQ109_spl
| ~ sQ108_spl
| ~ sQ107_spl ),
inference(split_clause,[status(thm)],[f23572,f23574,f23577,f23580,f23583]) ).
fof(f23591,plain,
( sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23579,f13610]) ).
fof(f23592,plain,
sQ108_spl,
inference(contradiction_clause,[status(thm)],[f23591]) ).
fof(f23593,plain,
( sQ107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23576,f13609]) ).
fof(f23594,plain,
sQ107_spl,
inference(contradiction_clause,[status(thm)],[f23593]) ).
fof(f23595,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23582,f13611]) ).
fof(f23596,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f23595]) ).
fof(f23597,plain,
( ~ sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23584,f13613]) ).
fof(f23598,plain,
~ sQ110_spl,
inference(contradiction_clause,[status(thm)],[f23597]) ).
fof(f23599,plain,
$false,
inference(sat_refutation,[status(thm)],[f23586,f23592,f23594,f23596,f23598]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV608+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 07:28:52 UTC 2026
% 0.09/0.37 % CPUTime :
% 120.99/121.30 % Drodi V4.1.1
% 121.09/121.49 % Refutation found
% 121.09/121.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 121.09/121.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 121.19/121.73 % Elapsed time: 121.329790 seconds
% 121.19/121.73 % CPU time: 122.507550 seconds
% 121.19/121.73 % Total memory used: 3.138 GB
% 121.19/121.73 % Net memory used: 3.134 GB
%------------------------------------------------------------------------------