%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV678+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 : n021.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 3.90s 4.16s
% Output : CNFRefutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 32 ( 11 ~; 10 |; 4 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
( ! [X70] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X70)
=> cUseAuto_2eP___24a1(X70) )
=> p(cUseAuto_2emyFact) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('$_def_UseAuto.myFact',axiom,
( p(cUseAuto_2emyFact)
<=> ! [X70] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X70)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(X70,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
=> cUseAuto_2eP___24a1(X70) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_def_UseAuto.myFact') ).
fof(c_0_2,negated_conjecture,
~ ( ! [X70] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X70)
=> cUseAuto_2eP___24a1(X70) )
=> p(cUseAuto_2emyFact) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_3,plain,
! [X2939] :
( ( ~ p(cUseAuto_2emyFact)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2939)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X2939,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| cUseAuto_2eP___24a1(X2939) )
& ( cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0)
| p(cUseAuto_2emyFact) )
& ( cCoq_2eInit_2ePeano_2ele___24a2(esk1_0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| p(cUseAuto_2emyFact) )
& ( ~ cUseAuto_2eP___24a1(esk1_0)
| p(cUseAuto_2emyFact) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_UseAuto.myFact'])])])])]) ).
fof(c_0_4,negated_conjecture,
! [X2938] :
( ( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2938)
| cUseAuto_2eP___24a1(X2938) )
& ~ p(cUseAuto_2emyFact) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])]) ).
cnf(c_0_5,plain,
( p(cUseAuto_2emyFact)
| ~ cUseAuto_2eP___24a1(esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
~ p(cUseAuto_2emyFact),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0)
| p(cUseAuto_2emyFact) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_8,plain,
~ cUseAuto_2eP___24a1(esk1_0),
inference(sr,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( cUseAuto_2eP___24a1(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(sr,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_11,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV678+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 : n021.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 04:06:55 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.90/4.16 % Version : CSE_E---1.7
% 3.90/4.16 % Problem : theBenchmark.p
% 3.90/4.16 % SZS status Theorem for theBenchmark.p
% 3.90/4.16 % SZS output start CNFRefutation
% See solution above
% 3.90/4.16 % Total time : 3.800s
%------------------------------------------------------------------------------