%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV677+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 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 05:15:56 PM UTC 2026
% Result : Theorem 5.19s 5.40s
% Output : CNFRefutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 141 ( 66 equ)
% Maximal formula atoms : 74 ( 4 avg)
% Number of connectives : 156 ( 47 ~; 82 |; 22 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-1 aty)
% Number of variables : 19 ( 1 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof('$_def_UrysohnsLemma.Urysohns_Lemma_construction.Un',axiom,
! [X99] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X99)
=> ( ( X99 = cCoq_2eInit_2eDatatypes_2eO
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X99) = cU0 )
| ? [X473] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X473)
& ( cCoq_2eInit_2eDatatypes_2enat___24t(X473)
=> ( X99 = cCoq_2eInit_2eDatatypes_2eS___24a1(X473)
& ( ( X473 = cCoq_2eInit_2eDatatypes_2eO
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X99) = cU1 )
| ? [X474] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X474)
& X473 = cCoq_2eInit_2eDatatypes_2eS___24a1(X474)
& cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X99) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_UrysohnsLemma.Urysohns_Lemma_construction.Un') ).
fof('_HAMMER_GOAL',conjecture,
! [X99] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X99)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Topology.TopologicalSpaces.open_full',axiom,
! [X460] :
( cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(X460)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(X460,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(X460))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Topology.TopologicalSpaces.open_full') ).
fof('$_typeof_X',axiom,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cX),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_X') ).
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [X482] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X482),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S') ).
fof('U1_open',axiom,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','U1_open') ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.O') ).
fof('U0_open',axiom,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','U0_open') ).
fof(c_0_8,plain,
! [X2386] :
( ( cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( X2386 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_1(X2386))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk3_1(X2386))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eS___24a1(esk3_1(X2386))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk3_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eS___24a1(esk3_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| X2386 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( X2386 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_1(X2386))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk3_1(X2386))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eS___24a1(esk3_1(X2386))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk3_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( esk2_1(X2386) = cCoq_2eInit_2eDatatypes_2eS___24a1(esk3_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) )
& ( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU1
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X2386))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X2386) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2386) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_UrysohnsLemma.Urysohns_Lemma_construction.Un'])])])])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X99] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X99)
=> cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X99)) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_10,plain,
! [X2393] :
( ~ cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(X2393)
| cTopology_2eTopologicalSpaces_2eopen___24a2(X2393,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(X2393))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Topology.TopologicalSpaces.open_full'])]) ).
cnf(c_0_11,plain,
( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU1
| X1 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X1))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X1))
| X1 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,negated_conjecture,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0)
& ~ cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( cTopology_2eTopologicalSpaces_2eopen___24a2(X1,cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(X1)))
| ~ cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cCoq_2eSets_2eEnsembles_2eFull__set___24a1(cTopology_2eTopologicalSpaces_2epoint__set___24a1(cX))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU1
| X1 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
cTopology_2eTopologicalSpaces_2eTopologicalSpace___24t(cX),
inference(split_conjunct,[status(thm)],['$_typeof_X']) ).
cnf(c_0_17,negated_conjecture,
~ cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU1
| X1 = cCoq_2eInit_2eDatatypes_2eO
| cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_20,plain,
! [X2396] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X2396),
inference(variable_rename,[status(thm)],['$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S']) ).
cnf(c_0_21,plain,
( X1 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_1(X1))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X1))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_22,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk2_1(X1))
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_23,negated_conjecture,
( cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(esk1_0) = cU1
| esk1_0 = cCoq_2eInit_2eDatatypes_2eO ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_24,plain,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU1),
inference(split_conjunct,[status(thm)],['U1_open']) ).
cnf(c_0_25,plain,
cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,plain,
( cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_1(X1)) = X1
| cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(X1) = cU0
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(csr,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
inference(split_conjunct,[status(thm)],['$_typeof_Coq.Init.Datatypes.O']) ).
cnf(c_0_28,negated_conjecture,
esk1_0 = cCoq_2eInit_2eDatatypes_2eO,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_24])]) ).
cnf(c_0_29,plain,
cUrysohnsLemma_2eUrysohns__Lemma__construction_2eUn___24a1(cCoq_2eInit_2eDatatypes_2eO) = cU0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26])]),c_0_27])]) ).
cnf(c_0_30,plain,
cTopology_2eTopologicalSpaces_2eopen___24a2(cX,cU0),
inference(split_conjunct,[status(thm)],['U0_open']) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_28]),c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV677+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:07:50 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 5.19/5.40 % Version : CSE_E---1.7
% 5.19/5.40 % Problem : theBenchmark.p
% 5.19/5.40 % SZS status Theorem for theBenchmark.p
% 5.19/5.40 % SZS output start CNFRefutation
% See solution above
% 5.19/5.41 % Total time : 5.038s
%------------------------------------------------------------------------------