%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV637+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 : n019.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 05:15:53 PM UTC 2026
% Result : Theorem 31.93s 27.68s
% Output : CNFRefutation 32.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 31 ( 6 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 105 ( 41 ~; 39 |; 6 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 45 ( 0 sgn 26 !; 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/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof('Coq.Arith.PeanoNat.Nat.lt_nge',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_2ele___24a2(X38,X37)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Arith.PeanoNat.Nat.lt_nge') ).
fof('$_def_Coq.Init.Peano.lt',axiom,
! [X37,X38] :
( p(cCoq_2eInit_2ePeano_2elt___24a2(X37,X38))
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X37),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_Coq.Init.Peano.lt') ).
fof('$_def_IndProp.lt',axiom,
! [X37,X38] :
( cIndProp_2elt___24a2(X37,X38)
<=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X37),X38)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_IndProp.lt') ).
fof('Coq.Arith.PeanoNat.Nat.le_ge_cases',axiom,
! [X37] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X37)
=> ! [X38] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X38)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(X37,X38))
| p(cCoq_2eInit_2ePeano_2ele___24a2(X38,X37)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Arith.PeanoNat.Nat.le_ge_cases') ).
fof('Coq.Arith.Le.le_n_S',axiom,
! [X37] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X37)
=> ! [X38] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X38)
=> ( p(cCoq_2eInit_2ePeano_2ele___24a2(X37,X38))
=> p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X37),cCoq_2eInit_2eDatatypes_2eS___24a1(X38))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Arith.Le.le_n_S') ).
fof(c_0_6,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_7,plain,
! [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_2ele___24a2(X38,X37)) ) ) ),
inference(fof_simplification,[status(thm)],['Coq.Arith.PeanoNat.Nat.lt_nge']) ).
fof(c_0_8,plain,
! [X2826,X2827] :
( ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X2826,X2827))
| p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2826),X2827)) )
& ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2826),X2827))
| p(cCoq_2eInit_2ePeano_2elt___24a2(X2826,X2827)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_Coq.Init.Peano.lt'])]) ).
fof(c_0_9,plain,
! [X2539,X2540] :
( ( ~ cIndProp_2elt___24a2(X2539,X2540)
| p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2539),X2540)) )
& ( ~ p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2539),X2540))
| cIndProp_2elt___24a2(X2539,X2540) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['$_def_IndProp.lt'])]) ).
fof(c_0_10,plain,
! [X2608,X2609] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2608)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2609)
| p(cCoq_2eInit_2ePeano_2ele___24a2(X2608,X2609))
| p(cCoq_2eInit_2ePeano_2ele___24a2(X2609,X2608)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.Arith.PeanoNat.Nat.le_ge_cases'])])]) ).
fof(c_0_11,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_6])])]) ).
fof(c_0_12,plain,
! [X2898,X2899] :
( ( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X2898,X2899))
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X2899,X2898))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2899)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2898) )
& ( p(cCoq_2eInit_2ePeano_2ele___24a2(X2899,X2898))
| p(cCoq_2eInit_2ePeano_2elt___24a2(X2898,X2899))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2899)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2898) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_13,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_8]) ).
cnf(c_0_14,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_9]) ).
cnf(c_0_15,plain,
( p(cCoq_2eInit_2ePeano_2ele___24a2(X1,X2))
| p(cCoq_2eInit_2ePeano_2ele___24a2(X2,X1))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,plain,
! [X2592,X2593] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2592)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2593)
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X2592,X2593))
| p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X2592),cCoq_2eInit_2eDatatypes_2eS___24a1(X2593))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Coq.Arith.Le.le_n_S'])])]) ).
cnf(c_0_18,plain,
( ~ p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2))
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X2,X1))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( p(cCoq_2eInit_2ePeano_2elt___24a2(X1,X2))
| ~ cIndProp_2elt___24a2(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( p(cCoq_2eInit_2ePeano_2ele___24a2(esk2_0,X1))
| p(cCoq_2eInit_2ePeano_2ele___24a2(X1,esk2_0))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
cCoq_2eInit_2eDatatypes_2enat___24t(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_22,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_9]) ).
cnf(c_0_23,plain,
( p(cCoq_2eInit_2ePeano_2ele___24a2(cCoq_2eInit_2eDatatypes_2eS___24a1(X1),cCoq_2eInit_2eDatatypes_2eS___24a1(X2)))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
( ~ cIndProp_2elt___24a2(X1,X2)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,negated_conjecture,
( p(cCoq_2eInit_2ePeano_2ele___24a2(esk1_0,esk2_0))
| p(cCoq_2eInit_2ePeano_2ele___24a2(esk2_0,esk1_0)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
cIndProp_2elt___24a2(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( cIndProp_2elt___24a2(X1,cCoq_2eInit_2eDatatypes_2eS___24a1(X2))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X2)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1)
| ~ p(cCoq_2eInit_2ePeano_2ele___24a2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
p(cCoq_2eInit_2ePeano_2ele___24a2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_16]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
~ cIndProp_2elt___24a2(esk1_0,cCoq_2eInit_2eDatatypes_2eS___24a1(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16]),c_0_21])]),c_0_29]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV637+1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n019.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 04:03:29 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 31.93/27.68 % Version : CSE_E---1.7
% 31.93/27.68 % Problem : theBenchmark.p
% 31.93/27.68 % SZS status Theorem for theBenchmark.p
% 31.93/27.68 % SZS output start CNFRefutation
% See solution above
% 32.03/27.73 % Total time : 25.362s
%------------------------------------------------------------------------------