%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SEV673+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n020.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 06:51:39 PM UTC 2026
% Result : Theorem 193.03s 36.16s
% Output : CNFRefutation 193.03s
% 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/sandbox/benchmark/theBenchmark.p','$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S') ).
fof('$_def_Coq.Init.Nat.add',axiom,
! [X61,X62] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X61)
=> ( ( X61 = cCoq_2eInit_2eDatatypes_2eO
& cCoq_2eInit_2eNat_2eadd___24a2(X61,X62) = X62 )
| ? [X154] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X154)
& X61 = cCoq_2eInit_2eDatatypes_2eS___24a1(X154)
& cCoq_2eInit_2eNat_2eadd___24a2(X61,X62) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X154,X62)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_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/sandbox/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/sandbox/benchmark/theBenchmark.p','Substitution.subst_rec_subst_rec') ).
fof('$_typeof_Coq.Init.Datatypes.O',axiom,
cCoq_2eInit_2eDatatypes_2enat___24t(cCoq_2eInit_2eDatatypes_2eO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_typeof_Coq.Init.Datatypes.O') ).
fof(c_0_5,plain,
! [X1565] : cCoq_2eInit_2eDatatypes_2eO != cCoq_2eInit_2eDatatypes_2eS___24a1(X1565),
inference(variable_rename,[status(thm)],['$_discrim_Coq.Init.Datatypes.O$Coq.Init.Datatypes.S']) ).
fof(c_0_6,plain,
! [X1633,X1634] :
( ( cCoq_2eInit_2eDatatypes_2enat___24t(esk9_2(X1633,X1634))
| X1633 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) )
& ( X1633 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk9_2(X1633,X1634))
| X1633 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) )
& ( cCoq_2eInit_2eNat_2eadd___24a2(X1633,X1634) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(esk9_2(X1633,X1634),X1634))
| X1633 = cCoq_2eInit_2eDatatypes_2eO
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk9_2(X1633,X1634))
| cCoq_2eInit_2eNat_2eadd___24a2(X1633,X1634) = X1634
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) )
& ( X1633 = cCoq_2eInit_2eDatatypes_2eS___24a1(esk9_2(X1633,X1634))
| cCoq_2eInit_2eNat_2eadd___24a2(X1633,X1634) = X1634
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) )
& ( cCoq_2eInit_2eNat_2eadd___24a2(X1633,X1634) = cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(esk9_2(X1633,X1634),X1634))
| cCoq_2eInit_2eNat_2eadd___24a2(X1633,X1634) = X1634
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1633) ) ),
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,
! [X1560,X1561,X1562,X1563,X1564] :
( ~ cLambda_2eRedexes_2eredexes___24t(X1560)
| ~ cLambda_2eRedexes_2eredexes___24t(X1561)
| ~ cLambda_2eRedexes_2eredexes___24t(X1562)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1563)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1564)
| cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1561,X1560,X1564),X1562,cCoq_2eInit_2eNat_2eadd___24a2(X1564,X1563)) = cSubstitution_2esubst__rec__r___24a3(cSubstitution_2esubst__rec__r___24a3(X1561,X1562,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eNat_2eadd___24a2(X1564,X1563))),cSubstitution_2esubst__rec__r___24a3(X1560,X1562,X1563),X1564) ),
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
% 0.00/0.12 % Problem : SEV673+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : enigmatic-eprover.py %s %d 1
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 08:13:51 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.29/0.48 # ENIGMATIC: Selected SinE mode:
% 0.45/0.66 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.45/0.66 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.45/0.66 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.45/0.66 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 193.03/36.16 # ENIGMATIC: Solved by autoschedule:
% 193.03/36.16 # SinE strategy is gf120_h_gu_RUU_F100_L00500
% 193.03/36.16 # Trying AutoSched0 for 144 seconds
% 193.03/36.16 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S0Y
% 193.03/36.16 # and selection function SelectMaxLComplexAvoidPosPred.
% 193.03/36.16 #
% 193.03/36.16 # Preprocessing time : 0.039 s
% 193.03/36.16 # Presaturation interreduction done
% 193.03/36.16
% 193.03/36.16 # Proof found!
% 193.03/36.16 # SZS status Theorem
% 193.03/36.16 # SZS output start CNFRefutation
% See solution above
% 193.03/36.16 # Training examples: 0 positive, 0 negative
% 193.03/36.16
% 193.03/36.16 # -------------------------------------------------
% 193.03/36.16 # User time : 20.792 s
% 193.03/36.16 # System time : 0.756 s
% 193.03/36.16 # Total time : 21.548 s
% 193.03/36.16 # Maximum resident set size: 12236 pages
% 193.03/36.16
%------------------------------------------------------------------------------