%------------------------------------------------------------------------------
% File : Enigma---0.5.1
% Problem : SEV637+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : enigmatic-eprover.py %s %d 1
% Computer : n026.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 06:51:36 PM UTC 2026
% Result : Theorem 20.57s 13.65s
% Output : CNFRefutation 20.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 52 ( 20 ~; 16 |; 5 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X37] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X37)
=> ! [X38] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X38)
=> ( cIndProp_2elt___24a2(X37,X38)
=> cIndProp_2elt___24a2(X37,cCoq_2eInit_2eDatatypes_2eS___24a1(X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('$_def_IndProp.lt',axiom,
! [X37,X38] :
( cIndProp_2elt___24a2(X37,X38)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X37),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_IndProp.lt') ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [X37,X38] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(X37,X38))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X37),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_Coq.Init.Peano.lt') ).
fof('Coq.Arith.PeanoNat.Nat.lt_lt_succ_r',axiom,
! [X37] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X37)
=> ! [X38] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X38)
=> ( p(cCoq_2eInit_2ePeano_2elt___24a2(X37,X38))
=> p(cCoq_2eInit_2ePeano_2elt___24a2(X37,cCoq_2eInit_2eDatatypes_2eS___24a1(X38))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Coq.Arith.PeanoNat.Nat.lt_lt_succ_r') ).
fof(c_0_4,negated_conjecture,
~ ! [X37] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X37)
=> ! [X38] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X38)
=> ( cIndProp_2elt___24a2(X37,X38)
=> cIndProp_2elt___24a2(X37,cCoq_2eInit_2eDatatypes_2eS___24a1(X38)) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_5,plain,
! [X2160,X2161] :
( ( ~ cIndProp_2elt___24a2(X2160,X2161)
| p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2160),X2161)) )
& ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2160),X2161))
| cIndProp_2elt___24a2(X2160,X2161) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_IndProp.lt'])]) ).
fof(c_0_6,plain,
! [X2447,X2448] :
( ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X2447,X2448))
| p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2447),X2448)) )
& ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2447),X2448))
| p(cCoq_2eInit_2ePeano_2elt___24a2(X2447,X2448)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_Coq.Init.Peano.lt'])]) ).
fof(c_0_7,negated_conjecture,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0)
& cCoq_2eInit_2eDatatypes_2enat___24t(esk2_0)
& cIndProp_2elt___24a2(esk1_0,esk2_0)
& ~ cIndProp_2elt___24a2(esk1_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( cIndProp_2elt___24a2(X1,X2)
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X1),X2))
| ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2))
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X1),X2))
| ~ cIndProp_2elt___24a2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
~ cIndProp_2elt___24a2(esk1_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( cIndProp_2elt___24a2(X1,X2)
| ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_14,plain,
! [X2515,X2516] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2515)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2516)
| ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X2515,X2516))
| p(cCoq_2eInit_2ePeano_2elt___24a2(X2515,cCoq_2eInit_2eDatatypes_2eS___24a1(X2516))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.Arith.PeanoNat.Nat.lt_lt_succ_r'])])]) ).
cnf(c_0_15,plain,
( p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2))
| ~ cIndProp_2elt___24a2(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
cIndProp_2elt___24a2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
~ p(cCoq_2eInit_2ePeano_2elt___24a2(esk1_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_0))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
( p(cCoq_2eInit_2ePeano_2elt___24a2(X1,cCoq_2eInit_2eDatatypes_2eS___24a1(X2)))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
p(cCoq_2eInit_2ePeano_2elt___24a2(esk1_0,esk2_0)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV637+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : enigmatic-eprover.py %s %d 1
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 06:47:55 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.29/0.46 # ENIGMATIC: Selected SinE mode:
% 0.44/0.67 # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.44/0.67 # Filter: axfilter_auto 0 goes into file theBenchmark_axfilter_auto 0.p
% 0.44/0.67 # Filter: axfilter_auto 1 goes into file theBenchmark_axfilter_auto 1.p
% 0.44/0.67 # Filter: axfilter_auto 2 goes into file theBenchmark_axfilter_auto 2.p
% 20.57/13.65 # ENIGMATIC: Solved by autoschedule:
% 20.57/13.65 # SinE strategy is gf120_h_gu_RUU_F100_L00500
% 20.57/13.65 # Trying AutoSched0 for 145 seconds
% 20.57/13.65 # AutoSched0-Mode selected heuristic G_E___207_C18_F1_SE_CS_SP_PI_PS_S0Y
% 20.57/13.65 # and selection function SelectMaxLComplexAvoidPosPred.
% 20.57/13.65 #
% 20.57/13.65 # Preprocessing time : 0.036 s
% 20.57/13.65 # Presaturation interreduction done
% 20.57/13.65
% 20.57/13.65 # Proof found!
% 20.57/13.65 # SZS status Theorem
% 20.57/13.65 # SZS output start CNFRefutation
% See solution above
% 20.57/13.65 # Training examples: 0 positive, 0 negative
% 20.57/13.65
% 20.57/13.65 # -------------------------------------------------
% 20.57/13.65 # User time : 0.294 s
% 20.57/13.65 # System time : 0.021 s
% 20.57/13.65 # Total time : 0.315 s
% 20.57/13.65 # Maximum resident set size: 13800 pages
% 20.57/13.65
%------------------------------------------------------------------------------