%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV673+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 : n015.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 05:15:55 PM UTC 2026
% Result : Theorem 203.89s 173.78s
% Output : CNFRefutation 204.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 77 ( 28 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 82 ( 27 ~; 29 |; 12 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 1 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S',axiom,
! [X555] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X555),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S') ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [X61,X62] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X61)
=> ( ( X61 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(X61,X62) = X62 )
| ? [X154] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X154)
& X61 = cCoq_2eInit_2eDatatypes_2eS___24a1(X154)
& cCoq_2eInit_2eNat_2eadd___24a2(X61,X62) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X154,X62)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_Coq.Init.Nat.add') ).
fof('_HAMMER_GOAL',conjecture,
! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,cCoq_2eInit_2eDatatypes_2eO),X1505,X68) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(X68)),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Substitution.subst_rec_subst_rec',axiom,
! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> ! [X375] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X375)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,X375),X1505,cCoq_2eInit_2eNat_2eadd___24a2(X375,X68)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X375,X68))),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),X375) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Substitution.subst_rec_subst_rec') ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.O') ).
fof(c_0_5,plain,
! [X2097] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X2097),
inference(variable_rename,[status(thm)],['$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S']) ).
fof(c_0_6,plain,
! [X2165,X2166] :
( ( cCoq_2eInit_2eDatatypes_2enat___24t(esk9_2(X2165,X2166))
| X2165 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) )
& ( X2165 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk9_2(X2165,X2166))
| X2165 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) )
& ( cCoq_2eInit_2eNat_2eadd___24a2(X2165,X2166) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(esk9_2(X2165,X2166),X2166))
| X2165 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk9_2(X2165,X2166))
| cCoq_2eInit_2eNat_2eadd___24a2(X2165,X2166) = X2166
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) )
& ( X2165 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk9_2(X2165,X2166))
| cCoq_2eInit_2eNat_2eadd___24a2(X2165,X2166) = X2166
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) )
& ( cCoq_2eInit_2eNat_2eadd___24a2(X2165,X2166) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(esk9_2(X2165,X2166),X2166))
| cCoq_2eInit_2eNat_2eadd___24a2(X2165,X2166) = X2166
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2165) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_Coq.Init.Nat.add'])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1503] :
( cLambda_2eRedexes_2eredexes___24t(X1503)
=> ! [X1504] :
( cLambda_2eRedexes_2eredexes___24t(X1504)
=> ! [X1505] :
( cLambda_2eRedexes_2eredexes___24t(X1505)
=> ! [X68] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X68)
=> cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1503,cCoq_2eInit_2eDatatypes_2eO),X1505,X68) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1504,X1505,cCoq_2eInit_2eDatatypes_2eS___24a1(X68)),cSubstitution_2esubst__rec__r___24a3(X1503,X1505,X68),cCoq_2eInit_2eDatatypes_2eO) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_8,plain,
! [X2092,X2093,X2094,X2095,X2096] :
( ~ cLambda_2eRedexes_2eredexes___24t(X2092)
| ~ cLambda_2eRedexes_2eredexes___24t(X2093)
| ~ cLambda_2eRedexes_2eredexes___24t(X2094)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2095)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2096)
| cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2093,X2092,X2096),X2094,cCoq_2eInit_2eNat_2eadd___24a2(X2096,X2095)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2093,X2094,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X2096,X2095))),cSubstitution_2esubst__rec__r___24a3(X2092,X2094,X2095),X2096) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Substitution.subst_rec_subst_rec'])])]) ).
cnf(c_0_9,plain,
cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( X1 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk9_2(X1,X2))
| cCoq_2eInit_2eNat_2eadd___24a2(X1,X2) = X2
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
inference(split_conjunct,[status(thm)],['$_typeof_Coq.Init.Datatypes.O']) ).
fof(c_0_12,negated_conjecture,
( cLambda_2eRedexes_2eredexes___24t(esk1_0)
& cLambda_2eRedexes_2eredexes___24t(esk2_0)
& cLambda_2eRedexes_2eredexes___24t(esk3_0)
& cCoq_2eInit_2eDatatypes_2enat___24t(esk4_0)
& cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk1_0,cCoq_2eInit_2eDatatypes_2eO),esk3_0,esk4_0) != cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk3_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk4_0)),cSubstitution_2esubst__rec__r___24a3(esk1_0,esk3_0,esk4_0),cCoq_2eInit_2eDatatypes_2eO) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2,X1,X5),X3,cCoq_2eInit_2eNat_2eadd___24a2(X5,X4)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X2,X3,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X5,X4))),cSubstitution_2esubst__rec__r___24a3(X1,X3,X4),X5)
| ~ cLambda_2eRedexes_2eredexes___24t(X1)
| ~ cLambda_2eRedexes_2eredexes___24t(X2)
| ~ cLambda_2eRedexes_2eredexes___24t(X3)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X4)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X5) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
cCoq_2eInit_2eNat_2eadd___24a2(cCoq_2eInit_2eDatatypes_2eO,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10])]),c_0_11])]) ).
cnf(c_0_15,negated_conjecture,
cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk1_0,cCoq_2eInit_2eDatatypes_2eO),esk3_0,esk4_0) != cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(esk2_0,esk3_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk4_0)),cSubstitution_2esubst__rec__r___24a3(esk1_0,esk3_0,esk4_0),cCoq_2eInit_2eDatatypes_2eO),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1,X2,cCoq_2eInit_2eDatatypes_2eS___24a1(X3)),cSubstitution_2esubst__rec__r___24a3(X4,X2,X3),cCoq_2eInit_2eDatatypes_2eO) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1,X4,cCoq_2eInit_2eDatatypes_2eO),X2,X3)
| ~ cLambda_2eRedexes_2eredexes___24t(X2)
| ~ cLambda_2eRedexes_2eredexes___24t(X1)
| ~ cLambda_2eRedexes_2eredexes___24t(X4)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11])]) ).
cnf(c_0_17,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
cLambda_2eRedexes_2eredexes___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18]),c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV673+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
% 0.12/0.32 % Computer : n015.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 04:06:16 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 89.35/59.23 % Warning 104: No lemmas were extracted from the log file '/export/starexec/sandbox2/solver/bin/output/initial_lemmas_CSE.log'. Continuing with baseline prover only.
% 203.89/173.78 % Version : CSE_E---1.7
% 203.89/173.78 % Problem : theBenchmark.p
% 203.89/173.78 % SZS status Theorem for theBenchmark.p
% 203.89/173.78 % SZS output start CNFRefutation
% See solution above
% 204.99/174.85 % Total time : 129.438s
%------------------------------------------------------------------------------