%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : SWW347+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:12:00 PM UTC 2026
% Result : ContradictoryAxioms 25.11s 8.89s
% Output : CNFRefutation 25.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 104 ( 78 unt; 0 def)
% Number of atoms : 138 ( 105 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 73 ( 39 ~; 25 |; 2 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-3 aty)
% Number of variables : 172 ( 22 sgn 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_empty__def,axiom,
! [X5] : c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(fact_Collect__def,axiom,
! [X24,X5] : hAPP(c_Set_OCollect(X5),X24) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(help_c__COMBK__1,axiom,
! [X331,X330,X18,X5] : hAPP(hAPP(c_COMBK(X5,X18),X330),X331) = X330,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(fact_bot__fun__def,axiom,
! [X17,X18,X5] :
( class_Orderings_Obot(X5)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X18,X5)),X17) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(fact_Collect__empty__eq,axiom,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_inf__bot__left,axiom,
! [X90,X5] :
( class_Lattices_Obounded__lattice__bot(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Obot__class_Obot(X5)),X90) = c_Orderings_Obot__class_Obot(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(arity_HOL__Obool__Orderings_Obot,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(fact_Collect__neg__eq,axiom,
! [X24,X5] : hAPP(c_Set_OCollect(X5),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5),c_fNot),X24)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).
fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(fact_Zero__neq__Suc,axiom,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_double__complement,axiom,
! [X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X20)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(help_c__fNot__1,axiom,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(fact_UNIV__def,axiom,
! [X5] : c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X5),hAPP(c_COMBK(tc_HOL_Obool,X5),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(fact_Diff__empty,axiom,
! [X20,X5] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),X20),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(fact_Compl__eq__Diff__UNIV,axiom,
! [X20,X5] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5,tc_HOL_Obool)),X20) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool))),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).
fof(fact_transfer__nat__int__numerals_I1_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(help_c__COMBB__1,axiom,
! [X35,X23,X24,X64,X5,X18] : hAPP(hAPP(hAPP(c_COMBB(X18,X5,X64),X24),X23),X35) = hAPP(X24,hAPP(X23,X35)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(fact_add__0__iff,axiom,
! [X6,X22,X5] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5)
=> ( X22 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X22),X6)
<=> X6 = c_Groups_Ozero__class_Ozero(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_add__Suc__right,axiom,
! [X91,X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),hAPP(c_Nat_OSuc,X91)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),X91)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_rev__rev__ident,axiom,
! [X275,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X275)) = X275,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X109),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X109,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_n__not__Suc__n,axiom,
! [X91] : X91 != hAPP(c_Nat_OSuc,X91),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(c_0_25,plain,
! [X802] : c_Orderings_Obot__class_Obot(tc_fun(X802,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X802),hAPP(c_COMBK(tc_HOL_Obool,X802),c_fFalse)),
inference(variable_rename,[status(thm)],[fact_empty__def]) ).
fof(c_0_26,plain,
! [X770,X771] : hAPP(c_Set_OCollect(X771),X770) = X770,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_27,plain,
! [X17779,X17780,X17781,X17782] : hAPP(hAPP(c_COMBK(X17782,X17781),X17780),X17779) = X17780,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_28,plain,
c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_30,plain,
! [X361,X362,X363] :
( hAPP(c_Orderings_Obot__class_Obot(tc_fun(X362,X363)),X361) = c_Orderings_Obot__class_Obot(X363)
| ~ class_Orderings_Obot(X363) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])])]) ).
cnf(c_0_31,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_33,plain,
! [X24,X5] :
( hAPP(c_Set_OCollect(X5),X24) = c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))
<=> ! [X3] : ~ hBOOL(hAPP(X24,X3)) ),
inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).
fof(c_0_34,plain,
! [X332,X333] :
( X333 = X332
| hAPP(X333,esk1_2(X332,X333)) != hAPP(X332,esk1_2(X332,X333)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])])]) ).
fof(c_0_35,plain,
! [X1974,X1975] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1975),c_Orderings_Obot__class_Obot(X1975)),X1974) = c_Orderings_Obot__class_Obot(X1975)
| ~ class_Lattices_Obounded__lattice__bot(X1975) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])])]) ).
cnf(c_0_36,plain,
( ~ class_Orderings_Obot(X1)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,X1)),X3) = c_Orderings_Obot__class_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]) ).
cnf(c_0_38,plain,
hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X2) = c_fFalse,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_39,plain,
! [X5439,X5440] : hAPP(c_Set_OCollect(X5440),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X5440),c_fNot),X5439)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5440,tc_HOL_Obool)),hAPP(c_Set_OCollect(X5440),X5439)),
inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).
fof(c_0_40,plain,
! [X790,X791,X792,X793,X795] :
( ( hAPP(c_Set_OCollect(X795),X793) = c_Orderings_Obot__class_Obot(tc_fun(X795,tc_HOL_Obool))
| hBOOL(hAPP(X793,esk20_1(X793))) )
& ( ~ hBOOL(hAPP(X790,X792))
| hAPP(c_Set_OCollect(X791),X790) != c_Orderings_Obot__class_Obot(tc_fun(X791,tc_HOL_Obool)) ) ),
inference(fof_nnf,[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)],[c_0_33])])])])])]) ).
cnf(c_0_41,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( ~ class_Lattices_Obounded__lattice__bot(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X2) = c_Orderings_Obot__class_Obot(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice__bot]) ).
cnf(c_0_44,plain,
c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_fFalse,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
fof(c_0_45,plain,
! [X109] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X109),
inference(fof_simplification,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(c_0_46,plain,
! [X5190,X5191] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5191,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5191,tc_HOL_Obool)),X5190)) = X5190,
inference(variable_rename,[status(thm)],[fact_double__complement]) ).
cnf(c_0_47,plain,
hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_48,plain,
! [X24] :
( ~ hBOOL(X24)
| ~ hBOOL(hAPP(c_fNot,X24)) ),
inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).
cnf(c_0_49,plain,
( hAPP(c_Set_OCollect(X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| hBOOL(hAPP(X1,esk20_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_50,plain,
! [X8868] : c_Orderings_Otop__class_Otop(tc_fun(X8868,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8868),hAPP(c_COMBK(tc_HOL_Obool,X8868),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_51,plain,
! [X2026,X2027] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2027,tc_HOL_Obool)),X2026),c_Orderings_Obot__class_Obot(tc_fun(X2027,tc_HOL_Obool))) = X2026,
inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).
cnf(c_0_52,plain,
( hAPP(X1,esk1_2(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),X1)) != c_fFalse
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(spm,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_53,plain,
hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_fFalse),X1) = c_fFalse,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_44]) ).
fof(c_0_54,plain,
! [X9006,X9007] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X9007,tc_HOL_Obool)),X9006) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X9007,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X9007,tc_HOL_Obool))),X9006),
inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).
fof(c_0_55,plain,
! [X5390] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X5390),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_45])]) ).
cnf(c_0_56,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I1_J]) ).
cnf(c_0_57,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_58,plain,
! [X17783,X17784,X17785,X17786,X17787,X17788] : hAPP(hAPP(hAPP(c_COMBB(X17788,X17787,X17786),X17785),X17784),X17783) = hAPP(X17785,hAPP(X17784,X17783)),
inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_0_59,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_29]),c_0_29]) ).
fof(c_0_61,plain,
! [X17805] :
( ~ hBOOL(X17805)
| ~ hBOOL(hAPP(c_fNot,X17805)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_48])]) ).
cnf(c_0_62,plain,
( hBOOL(hAPP(X1,esk20_1(X1)))
| X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
inference(rw,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_63,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X1),hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue)),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_64,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X2,
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,plain,
hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),c_fFalse) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_67,plain,
! [X5347,X5348,X5349] :
( ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5349)
| X5348 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5349),X5348),X5347)
| X5347 != c_Groups_Ozero__class_Ozero(X5349) )
& ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5349)
| X5347 = c_Groups_Ozero__class_Ozero(X5349)
| X5348 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5349),X5348),X5347) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])])]) ).
fof(c_0_68,plain,
! [X4035,X4036] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4036),hAPP(c_Nat_OSuc,X4035)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4036),X4035)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
cnf(c_0_69,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_71,plain,
hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_72,plain,
hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]) ).
fof(c_0_73,plain,
! [X16820,X16821] : hAPP(c_List_Orev(X16821),hAPP(c_List_Orev(X16821),X16820)) = X16820,
inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).
cnf(c_0_74,plain,
( ~ hBOOL(X1)
| ~ hBOOL(hAPP(c_fNot,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
( hBOOL(X1)
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_38]),c_0_31]) ).
cnf(c_0_76,plain,
hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),
inference(rw,[status(thm)],[c_0_63,c_0_29]) ).
cnf(c_0_77,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_65]) ).
cnf(c_0_78,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X2) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2),
inference(rw,[status(thm)],[c_0_66,c_0_60]) ).
cnf(c_0_79,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
| X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(X2) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_80,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X2)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_81,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
cnf(c_0_82,plain,
hAPP(c_Int_Onat,c_Int_OPls) != hAPP(c_Nat_OSuc,X1),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
fof(c_0_83,plain,
! [X5402] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X5402),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5402,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(c_0_84,plain,
! [X91] : X91 != hAPP(c_Nat_OSuc,X91),
inference(fof_simplification,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_0_85,plain,
hAPP(c_fNot,hAPP(c_fNot,hAPP(X1,X2))) = hAPP(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_71]) ).
cnf(c_0_86,plain,
hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_87,plain,
( ~ hBOOL(X1)
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_88,plain,
hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2) = c_fTrue,
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_89,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),c_Orderings_Obot__class_Obot(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_90,plain,
hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)) != X1,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_70]),c_0_81])]),c_0_82]) ).
cnf(c_0_91,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_83]) ).
fof(c_0_92,plain,
! [X4000] : X4000 != hAPP(c_Nat_OSuc,X4000),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_84])]) ).
cnf(c_0_93,plain,
hAPP(c_fNot,hAPP(c_fNot,X1)) = X1,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_94,plain,
( c_fFalse = X1
| hAPP(c_fNot,X1) = c_fFalse ),
inference(spm,[status(thm)],[c_0_87,c_0_75]) ).
cnf(c_0_95,plain,
hAPP(c_fNot,c_fFalse) = c_fTrue,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_71]),c_0_38]) ).
cnf(c_0_96,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2))) != X1,
inference(spm,[status(thm)],[c_0_90,c_0_80]) ).
cnf(c_0_97,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Int_Onat,c_Int_OPls)) = X1,
inference(rw,[status(thm)],[c_0_91,c_0_70]) ).
cnf(c_0_98,plain,
X1 != hAPP(c_Nat_OSuc,X1),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_99,plain,
( c_fTrue = X1
| c_fFalse = X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]) ).
cnf(c_0_100,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X1)) != X1,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_101,plain,
hAPP(c_Nat_OSuc,c_fTrue) = c_fFalse,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99])]) ).
cnf(c_0_102,plain,
hAPP(c_Nat_OSuc,c_fFalse) != c_fTrue,
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_103,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_99]),c_0_98]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWW347+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Mon Sep 21 09:48:22 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.35 Running first-order theorem proving
% 0.04/0.35 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.11/8.89 % Version: 3.5.1
% 25.11/8.89 % Preprocessing class: FMLMSLSMSSSNFFN.
% 25.11/8.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.11/8.89 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 25.11/8.89 % Starting new_bool_3 with 300s (1) cores
% 25.11/8.89 % Starting new_bool_1 with 300s (1) cores
% 25.11/8.89 % Starting sh5l with 300s (1) cores
% 25.11/8.89 % SAT001_MinMin_p005000_rr_RG with pid 2106342 completed with status 0
% 25.11/8.89 % Result found by SAT001_MinMin_p005000_rr_RG
% 25.11/8.89 % Preprocessing class: FMLMSLSMSSSNFFN.
% 25.11/8.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.11/8.89 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 25.11/8.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.11/8.89 % No SInE strategy applied
% 25.11/8.89 % Search class: FGHSM-SMLM33-DFFFFFNN
% 25.11/8.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.11/8.89 % Starting SubtermCWHack with 136s (1) cores
% 25.11/8.89 % Starting SAT001_MinMin_p005000_rr_RG with 151s (1) cores
% 25.11/8.89 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 25.11/8.89 % Starting SAT001_CA_MinMin_p005000_rr with 136s (1) cores
% 25.11/8.89 % Starting G-E--_208_B07_F1_S5PRR_SE_CS_SP_PS_S0Y with 136s (1) cores
% 25.11/8.89 % SAT001_MinMin_p005000_rr_RG with pid 2106350 completed with status 0
% 25.11/8.89 % Result found by SAT001_MinMin_p005000_rr_RG
% 25.11/8.89 % Preprocessing class: FMLMSLSMSSSNFFN.
% 25.11/8.89 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 25.11/8.89 % Starting SAT001_MinMin_p005000_rr_RG with 1500s (5) cores
% 25.11/8.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 25.11/8.89 % No SInE strategy applied
% 25.11/8.89 % Search class: FGHSM-SMLM33-DFFFFFNN
% 25.11/8.89 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 25.11/8.89 % Starting SubtermCWHack with 136s (1) cores
% 25.11/8.89 % Starting SAT001_MinMin_p005000_rr_RG with 151s (1) cores
% 25.11/8.89 % Preprocessing time : 0.133 s
% 25.11/8.89 % Presaturation interreduction done
% 25.11/8.89
% 25.11/8.89 % Proof found!
% 25.11/8.89 % SZS status ContradictoryAxioms
% 25.11/8.89 % SZS output start CNFRefutation
% See solution above
% 25.11/8.89 % Parsed axioms : 5243
% 25.11/8.89 % Removed by relevancy pruning/SinE : 0
% 25.11/8.89 % Initial clauses : 7567
% 25.11/8.89 % Removed in clause preprocessing : 236
% 25.11/8.89 % Initial clauses in saturation : 7331
% 25.11/8.89 % Processed clauses : 21684
% 25.11/8.89 % ...of these trivial : 425
% 25.11/8.89 % ...subsumed : 7790
% 25.11/8.89 % ...remaining for further processing : 13469
% 25.11/8.89 % Other redundant clauses eliminated : 1689
% 25.11/8.89 % Clauses deleted for lack of memory : 0
% 25.11/8.89 % Backward-subsumed : 290
% 25.11/8.89 % Backward-rewritten : 455
% 25.11/8.89 % Generated clauses : 200203
% 25.11/8.89 % ...of the previous two non-redundant : 190266
% 25.11/8.89 % ...aggressively subsumed : 0
% 25.11/8.89 % Contextual simplify-reflections : 64
% 25.11/8.89 % Paramodulations : 198524
% 25.11/8.89 % Factorizations : 6
% 25.11/8.89 % NegExts : 0
% 25.11/8.89 % Equation resolutions : 1739
% 25.11/8.89 % Disequality decompositions : 0
% 25.11/8.89 % Total rewrite steps : 66195
% 25.11/8.89 % ...of those cached : 47936
% 25.11/8.89 % Propositional unsat checks : 3
% 25.11/8.89 % Propositional check models : 2
% 25.11/8.89 % Propositional check unsatisfiable : 0
% 25.11/8.89 % Propositional clauses : 0
% 25.11/8.89 % Propositional clauses after purity: 0
% 25.11/8.89 % Propositional unsat core size : 0
% 25.11/8.89 % Propositional preprocessing time : 0.000
% 25.11/8.89 % Propositional encoding time : 0.149
% 25.11/8.89 % Propositional solver time : 0.061
% 25.11/8.89 % Success case prop preproc time : 0.000
% 25.11/8.89 % Success case prop encoding time : 0.000
% 25.11/8.89 % Success case prop solver time : 0.000
% 25.11/8.89 % Current number of processed clauses : 6315
% 25.11/8.89 % Positive orientable unit clauses : 1582
% 25.11/8.89 % Positive unorientable unit clauses: 127
% 25.11/8.89 % Negative unit clauses : 716
% 25.11/8.89 % Non-unit-clauses : 3890
% 25.11/8.89 % Current number of unprocessed clauses: 174127
% 25.11/8.89 % ...number of literals in the above : 352999
% 25.11/8.89 % Current number of archived formulas : 0
% 25.11/8.89 % Current number of archived clauses : 6707
% 25.11/8.89 % Clause-clause subsumption calls (NU) : 5459965
% 25.11/8.89 % Rec. Clause-clause subsumption calls : 2452060
% 25.11/8.89 % Non-unit clause-clause subsumptions : 5358
% 25.11/8.89 % Unit Clause-clause subsumption calls : 257267
% 25.11/8.89 % Rewrite failures with RHS unbound : 0
% 25.11/8.89 % BW rewrite match attempts : 38762
% 25.11/8.89 % BW rewrite match successes : 1159
% 25.11/8.89 % Condensation attempts : 0
% 25.11/8.89 % Condensation successes : 0
% 25.11/8.89 % Termbank termtop insertions : 6985462
% 25.11/8.89 % Search garbage collected termcells : 100626
% 25.11/8.89
% 25.11/8.89 % -------------------------------------------------
% 25.11/8.90 % User time : 8.030 s
% 25.11/8.90 % System time : 0.231 s
% 25.11/8.90 % Total time : 8.262 s
% 25.11/8.90 % Maximum resident set size: 42900 pages
% 25.11/8.90
% 25.11/8.90 % -------------------------------------------------
% 25.11/8.90 % User time : 36.996 s
% 25.11/8.90 % System time : 0.972 s
% 25.11/8.90 % Total time : 37.968 s
% 25.11/8.90 % Maximum resident set size: 12288 pages
% 25.11/8.90 % E exiting
%------------------------------------------------------------------------------