%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV606+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 : n025.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 05:15:25 PM UTC 2026
% Result : Theorem 11.62s 8.05s
% Output : CNFRefutation 11.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 12 unt; 0 def)
% Number of atoms : 50 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 47 ( 16 ~; 12 |; 5 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('_HAMMER_GOAL',conjecture,
! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X25))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X51,X25)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Coq.ZArith.BinInt.Z.square_le_simpl_nonneg',axiom,
! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X25,X51)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.ZArith.BinInt.Z.square_le_simpl_nonneg') ).
fof('$adef_Coq.ZArith.BinInt.Z.le_$a2',axiom,
! [X789,X790] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,X789),X790) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X789,X790),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_Coq.ZArith.BinInt.Z.le_$a2') ).
fof(c_0_3,negated_conjecture,
~ ! [X25] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X25)
=> ! [X51] :
( cCoq_2eNumbers_2eBinNums_2eZ___24t(X51)
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X25))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X51))
=> ( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X51,X51),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X25,X25)))
=> p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X51,X25)) ) ) ) ) ),
inference(assume_negation,[status(cth)],['_HAMMER_GOAL']) ).
fof(c_0_4,plain,
! [X4017,X4018] :
( ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X4017)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X4018)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X4018))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X4017,X4017),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X4018,X4018)))
| p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X4017,X4018)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.ZArith.BinInt.Z.square_le_simpl_nonneg'])])]) ).
fof(c_0_5,plain,
! [X6442,X6443] : happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,X6442),X6443) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X6442,X6443),
inference(variable_rename,[status(thm)],['$adef_Coq.ZArith.BinInt.Z.le_$a2']) ).
fof(c_0_6,negated_conjecture,
( cCoq_2eNumbers_2eBinNums_2eZ___24t(esk1_0)
& cCoq_2eNumbers_2eBinNums_2eZ___24t(esk2_0)
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk1_0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk2_0))
& p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk2_0,esk2_0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk1_0,esk1_0)))
& ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(esk2_0,esk1_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_7,plain,
( p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X2))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X2)
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,X2))
| ~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X2,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,X1),X2) = cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk2_0,esk2_0),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk1_0,esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(cCoq_2eNumbers_2eBinNums_2eZ0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
~ p(cCoq_2eZArith_2eBinInt_2eZ_2ele___24a2(esk2_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,X1),X2))
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X2)
| ~ cCoq_2eNumbers_2eBinNums_2eZ___24t(X1)
| ~ p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eNumbers_2eBinNums_2eZ0),X2))
| ~ p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X1,X1)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(X2,X2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]),c_0_8]) ).
cnf(c_0_13,negated_conjecture,
p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk2_0,esk2_0)),cCoq_2eZArith_2eBinIntDef_2eZ_2emul___24a2(esk1_0,esk1_0))),
inference(rw,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,negated_conjecture,
cCoq_2eNumbers_2eBinNums_2eZ___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,cCoq_2eNumbers_2eBinNums_2eZ0),esk1_0)),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_17,negated_conjecture,
~ p(happ(happ(cCoq_2eZArith_2eBinInt_2eZ_2ele,esk2_0),esk1_0)),
inference(rw,[status(thm)],[c_0_11,c_0_8]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16])]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV606+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
% 0.15/0.32 % Computer : n025.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 04:02:43 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 11.62/8.05 % Version : CSE_E---1.7
% 11.62/8.05 % Problem : theBenchmark.p
% 11.62/8.05 % SZS status Theorem for theBenchmark.p
% 11.62/8.05 % SZS output start CNFRefutation
% See solution above
% 11.62/8.07 % Total time : 6.670s
%------------------------------------------------------------------------------