%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV608+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n011.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 05:15:25 PM UTC 2026
% Result : Theorem 3.98s 4.15s
% Output : CNFRefutation 3.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 13 ( 6 unt; 0 def)
% Number of atoms : 39 ( 8 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 39 ( 13 ~; 10 |; 4 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Color.select_terminates',axiom,
! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Color.select_terminates') ).
fof(c_0_2,negated_conjecture,
~ ! [X76] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X76)
=> ! [X82] :
( cColor_2egraph___24t(X82)
=> ! [X95] :
( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X95)
=> ( cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X76),X82)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X95)
=> cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X95,X82)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X82)) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_3,plain,
! [X3053,X3054,X3055] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X3053)
| ~ cColor_2egraph___24t(X3054)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X3055)
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X3053),X3054)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X3055)
| cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X3055,X3054)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X3054)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Color.select_terminates'])])]) ).
fof(c_0_4,negated_conjecture,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0)
& cColor_2egraph___24t(esk2_0)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(esk3_0)
& cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(esk1_0),esk2_0)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0)
& ~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(esk3_0,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
cnf(c_0_5,plain,
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X3,X2)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,X2))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ cColor_2egraph___24t(X2)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X3)
| cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(X1),X2)) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2echoose___24a1(cColor_2esubset__nodes___24a2(cColor_2elow__deg___24a1(esk1_0),esk2_0)) = cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,negated_conjecture,
cColor_2egraph___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,negated_conjecture,
~ cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(esk3_0,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( cCoq_2eInit_2ePeano_2elt___24a2(cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,cColor_2eremove__node___24a2(X1,esk2_0)),cCoq_2eFSets_2eFMapPositive_2ePositiveMap_2ecardinal___24a2(cColor_2enodeset,esk2_0))
| cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,esk3_0) != cCoq_2eInit_2eDatatypes_2eSome___24a2(cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt,X1)
| ~ cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7]),c_0_8])]) ).
cnf(c_0_11,negated_conjecture,
cCoq_2eFSets_2eFSetPositive_2ePositiveSet_2eelt___24t(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV608+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:02:17 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.98/4.15 % Version : CSE_E---1.7
% 3.98/4.15 % Problem : theBenchmark.p
% 3.98/4.15 % SZS status Theorem for theBenchmark.p
% 3.98/4.15 % SZS output start CNFRefutation
% See solution above
% 3.98/4.15 % Total time : 3.724s
%------------------------------------------------------------------------------