TSTP Solution File: SWW380+1 by ET---2.0
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%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SWW380+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n024.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 : 600s
% DateTime : Thu Jul 21 00:10:42 EDT 2022
% Result : Theorem 1.26s 70.44s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 44
% Syntax : Number of formulae : 157 ( 138 unt; 0 def)
% Number of atoms : 184 ( 142 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 41 ( 41 usr; 9 con; 0-3 aty)
% Number of variables : 217 ( 14 sgn 120 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_singleton__conv2,axiom,
! [X39,X6] : hAPP(c_Set_OCollect(X6),hAPP(c_fequal,X39)) = hAPP(hAPP(c_Set_Oinsert(X6),X39),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_singleton__conv2) ).
fof(fact_List_Oset_Osimps_I1_J,axiom,
! [X6] : hAPP(c_List_Oset(X6),c_List_Olist_ONil(X6)) = c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(fact_Collect__def,axiom,
! [X32,X6] : hAPP(c_Set_OCollect(X6),X32) = X32,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_Collect__def) ).
fof(fact_UNIV__def,axiom,
! [X6] : c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X6),hAPP(c_COMBK(tc_HOL_Obool,X6),c_fTrue)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_UNIV__def) ).
fof(fact_insert__is__Un,axiom,
! [X13,X39,X6] : hAPP(hAPP(c_Set_Oinsert(X6),X39),X13) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6),X39),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),X13),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_insert__is__Un) ).
fof(fact_succ__def,axiom,
! [X108] : c_Int_Osucc(X108) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X108),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_succ__def) ).
fof(fact_diff__bin__simps_I2_J,axiom,
! [X108] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X108),c_Int_OMin) = c_Int_Osucc(X108),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(fact_pred__def,axiom,
! [X108] : c_Int_Opred(X108) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X108),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_pred__def) ).
fof(fact_add__Min__right,axiom,
! [X108] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X108),c_Int_OMin) = c_Int_Opred(X108),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_add__Min__right) ).
fof(fact_succ__Bit0,axiom,
! [X108] : c_Int_Osucc(c_Int_OBit0(X108)) = c_Int_OBit1(X108),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_succ__Bit0) ).
fof(fact_Bit0__def,axiom,
! [X108] : c_Int_OBit0(X108) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X108),X108),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_Bit0__def) ).
fof(fact_UNIV__enum,axiom,
! [X6] :
( class_Enum_Oenum(X6)
=> c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) = hAPP(c_List_Oset(X6),c_Enum_Oenum__class_Oenum(X6)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_UNIV__enum) ).
fof(fact_ivl__disj__un_I3_J,axiom,
! [X117,X131,X6] :
( class_Orderings_Olinorder(X6)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X6),X131),X117))
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X6),X131),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X6,X131,X117)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X6,X131),X117) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_ivl__disj__un_I3_J) ).
fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
! [X117,X131] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),c_Groups_Oone__class_Oone(tc_Int_Oint))),X117) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X131,X117),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).
fof(fact_add__Pls,axiom,
! [X108] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X108) = X108,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_add__Pls) ).
fof(fact_upto__empty,axiom,
! [X110,X109] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X109),X110))
=> c_List_Oupto(X110,X109) = c_List_Olist_ONil(tc_Int_Oint) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_upto__empty) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19)),X19) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_minus__Min,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_minus__Min) ).
fof(fact_Bit1__def,axiom,
! [X108] : c_Int_OBit1(X108) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X108)),X108),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).
fof(fact_card__atLeastAtMost__int,axiom,
! [X117,X131] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X131,X117)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X117),X131)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(fact_atLeastAtMost__upto,axiom,
! [X115,X116] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X116,X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X116,X115)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(fact_succ__Min,axiom,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_succ__Min) ).
fof(fact_atLeastLessThan__upto,axiom,
! [X115,X116] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X116),X115) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X116,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X115),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_atLeastLessThan__upto) ).
fof(fact_rel__simps_I6_J,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_Pls__def) ).
fof(fact_zadd__commute,axiom,
! [X128,X19] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X128),X19),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_zadd__commute) ).
fof(fact_diff__int__def,axiom,
! [X128,X19] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X128) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X128)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_diff__int__def) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_one__is__num__one) ).
fof(fact_number__of__is__id,axiom,
! [X108] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108) = X108,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_eq__int__code_I14_J,axiom,
! [X315,X314] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X314)),c_Int_OBit1(X315))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_eq__int__code_I14_J) ).
fof(fact_zadd__assoc,axiom,
! [X129,X126,X127] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),X126)),X129) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X127),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X126),X129)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
! [X13,X6] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X6),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool))))
=> ( hAPP(c_Finite__Set_Ocard(X6),X13) = hAPP(c_Finite__Set_Ocard(X6),c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)))
=> X13 = c_Orderings_Otop__class_Otop(tc_fun(X6,tc_HOL_Obool)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).
fof(fact_card__UNIV__unit,axiom,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_card__UNIV__unit) ).
fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(fact_card__cartesian__product__singleton,axiom,
! [X13,X16,X10,X6] : hAPP(c_Finite__Set_Ocard(tc_prod(X6,X10)),hAPP(hAPP(c_Product__Type_OSigma(X6,X10),hAPP(hAPP(c_Set_Oinsert(X6),X16),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X6),X13))) = hAPP(c_Finite__Set_Ocard(X10),X13),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_card__cartesian__product__singleton) ).
fof(fact_card__cartesian__product,axiom,
! [X12,X13,X10,X6] : hAPP(c_Finite__Set_Ocard(tc_prod(X6,X10)),hAPP(hAPP(c_Product__Type_OSigma(X6,X10),X13),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X6),X12))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X6),X13)),hAPP(c_Finite__Set_Ocard(X10),X12)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_card__cartesian__product) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(fact_eq__equal,axiom,
! [X6] :
( class_HOL_Oequal(X6)
=> c_fequal = c_HOL_Oequal__class_Oequal(X6) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_eq__equal) ).
fof(fact_finite__set,axiom,
! [X251,X6] : hBOOL(hAPP(c_Finite__Set_Ofinite(X6),hAPP(c_List_Oset(X6),X251))),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_finite__set) ).
fof(fact_transfer__nat__int__numerals_I2_J,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
fof(fact_nat__mult__1__right,axiom,
! [X106] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X106),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X106,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',fact_nat__mult__1__right) ).
fof(arity_Int__Oint__HOL_Oequal,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',arity_Int__Oint__HOL_Oequal) ).
fof(help_c__COMBK__1,axiom,
! [X324,X38,X10,X6] : hAPP(hAPP(c_COMBK(X6,X10),X38),X324) = X38,
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',help_c__COMBK__1) ).
fof(help_c__fTrue__1,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',help_c__fTrue__1) ).
fof(c_0_44,plain,
! [X40,X41] : hAPP(c_Set_OCollect(X41),hAPP(c_fequal,X40)) = hAPP(hAPP(c_Set_Oinsert(X41),X40),c_Orderings_Obot__class_Obot(tc_fun(X41,tc_HOL_Obool))),
inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).
fof(c_0_45,plain,
! [X7] : hAPP(c_List_Oset(X7),c_List_Olist_ONil(X7)) = c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).
fof(c_0_46,plain,
! [X33,X34] : hAPP(c_Set_OCollect(X34),X33) = X33,
inference(variable_rename,[status(thm)],[fact_Collect__def]) ).
fof(c_0_47,plain,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),hAPP(c_COMBK(tc_HOL_Obool,X7),c_fTrue)),
inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).
fof(c_0_48,plain,
! [X40,X41,X42] : hAPP(hAPP(c_Set_Oinsert(X42),X41),X40) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X42,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X42),X41),c_Orderings_Obot__class_Obot(tc_fun(X42,tc_HOL_Obool)))),X40),
inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).
cnf(c_0_49,plain,
hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
hAPP(c_Set_OCollect(X1),X2) = X2,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_52,plain,
! [X109] : c_Int_Osucc(X109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X109),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_succ__def]) ).
fof(c_0_53,plain,
! [X109] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X109),c_Int_OMin) = c_Int_Osucc(X109),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).
fof(c_0_54,plain,
! [X109] : c_Int_Opred(X109) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X109),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(variable_rename,[status(thm)],[fact_pred__def]) ).
fof(c_0_55,plain,
! [X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X109),c_Int_OMin) = c_Int_Opred(X109),
inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).
fof(c_0_56,plain,
! [X109] : c_Int_Osucc(c_Int_OBit0(X109)) = c_Int_OBit1(X109),
inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).
fof(c_0_57,plain,
! [X109] : c_Int_OBit0(X109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X109),X109),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_58,plain,
! [X7] :
( ~ class_Enum_Oenum(X7)
| c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_List_Oset(X7),c_Enum_Oenum__class_Oenum(X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UNIV__enum])]) ).
cnf(c_0_59,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_47]) ).
fof(c_0_60,plain,
! [X132,X133,X134] :
( ~ class_Orderings_Olinorder(X134)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X134),X133),X132))
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X134,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X134),X133),c_Orderings_Obot__class_Obot(tc_fun(X134,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X134,X133,X132)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X134,X133),X132) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).
cnf(c_0_61,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_62,plain,
hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1))) = hAPP(c_fequal,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_51]) ).
fof(c_0_63,plain,
! [X132,X133] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X133),c_Groups_Oone__class_Oone(tc_Int_Oint))),X132) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X133,X132),
inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).
cnf(c_0_64,plain,
c_Int_Osucc(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_65,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Osucc(X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
fof(c_0_66,plain,
! [X109] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X109) = X109,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
cnf(c_0_67,plain,
c_Int_Opred(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_68,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = c_Int_Opred(X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_69,plain,
! [X111,X112] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),X111))
| c_List_Oupto(X111,X112) = c_List_Olist_ONil(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).
fof(c_0_70,plain,
! [X20] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X20)),X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
cnf(c_0_71,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_minus__Min]) ).
cnf(c_0_72,plain,
c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_73,plain,
c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
fof(c_0_74,plain,
! [X109] : c_Int_OBit1(X109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X109)),X109),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
cnf(c_0_75,plain,
( c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))
| ~ class_Enum_Oenum(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_76,plain,
c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue),
inference(rw,[status(thm)],[c_0_59,c_0_51]) ).
fof(c_0_77,plain,
! [X132,X133] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X133,X132)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X132),X133)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).
fof(c_0_78,plain,
! [X117,X118] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X118,X117) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X118,X117)),
inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).
cnf(c_0_79,plain,
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_80,plain,
hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(c_fequal,X2)),X3) = hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_50]),c_0_62]) ).
cnf(c_0_81,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_82,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rw,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_83,plain,
c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).
fof(c_0_84,plain,
! [X117,X118] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X118),X117) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X118,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X117),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).
cnf(c_0_85,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_86,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_87,plain,
( c_List_Oupto(X1,X2) = c_List_Olist_ONil(tc_Int_Oint)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_88,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J]) ).
cnf(c_0_89,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_90,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).
fof(c_0_91,plain,
! [X129,X130] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X130),X129) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X129),X130),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(c_0_92,plain,
! [X129,X130] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X130),X129) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X130),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X129)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
cnf(c_0_93,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_one__is__num__one]) ).
cnf(c_0_94,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_65]) ).
fof(c_0_95,plain,
! [X109] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X109) = X109,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(c_0_96,plain,
! [X316,X317] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X317)),c_Int_OBit1(X316))),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_eq__int__code_I14_J])]) ).
cnf(c_0_97,plain,
c_Int_OBit1(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
fof(c_0_98,plain,
! [X130,X131,X132] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),X131)),X130) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X132),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X131),X130)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(c_0_99,plain,
! [X14,X15] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X15),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool))))
| hAPP(c_Finite__Set_Ocard(X15),X14) != hAPP(c_Finite__Set_Ocard(X15),c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)))
| X14 = c_Orderings_Otop__class_Otop(tc_fun(X15,tc_HOL_Obool)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).
cnf(c_0_100,plain,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_card__UNIV__unit]) ).
cnf(c_0_101,plain,
( hAPP(c_COMBK(tc_HOL_Obool,X1),c_fTrue) = hAPP(c_List_Oset(X1),c_Enum_Oenum__class_Oenum(X1))
| ~ class_Enum_Oenum(X1) ),
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_102,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]) ).
fof(c_0_103,plain,
! [X17,X18,X19,X20] : hAPP(c_Finite__Set_Ocard(tc_prod(X20,X19)),hAPP(hAPP(c_Product__Type_OSigma(X20,X19),hAPP(hAPP(c_Set_Oinsert(X20),X18),c_Orderings_Obot__class_Obot(tc_fun(X20,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X19,tc_HOL_Obool),X20),X17))) = hAPP(c_Finite__Set_Ocard(X19),X17),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).
fof(c_0_104,plain,
! [X14,X15,X16,X17] : hAPP(c_Finite__Set_Ocard(tc_prod(X17,X16)),hAPP(hAPP(c_Product__Type_OSigma(X17,X16),X15),hAPP(c_COMBK(tc_fun(X16,tc_HOL_Obool),X17),X14))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17),X15)),hAPP(c_Finite__Set_Ocard(X16),X14)),
inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).
cnf(c_0_105,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_106,plain,
c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_107,plain,
( hAPP(hAPP(c_Set_Oinsert(X1),X2),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)
| ~ class_Orderings_Olinorder(X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_50]),c_0_62]),c_0_80]) ).
cnf(c_0_108,plain,
c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin)),X2),
inference(rw,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_109,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = c_Int_OPls,
inference(rw,[status(thm)],[c_0_83,c_0_65]) ).
cnf(c_0_110,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
cnf(c_0_111,plain,
hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X2) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_112,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_113,plain,
c_List_Oupto(c_Int_OPls,c_Int_OMin) = c_List_Olist_ONil(tc_Int_Oint),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_114,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)),X1) = c_Int_OPls,
inference(rw,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_115,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_116,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_117,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_72]),c_0_73]),c_0_65]) ).
cnf(c_0_118,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(rw,[status(thm)],[c_0_94,c_0_85]) ).
cnf(c_0_119,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_120,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X2))),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_121,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_72]),c_0_73]),c_0_65]) ).
cnf(c_0_122,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X3)),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
fof(c_0_123,plain,
! [X7] :
( ~ class_HOL_Oequal(X7)
| c_fequal = c_HOL_Oequal__class_Oequal(X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equal])]) ).
cnf(c_0_124,plain,
( X1 = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
| hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Finite__Set_Ocard(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_125,plain,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),hAPP(c_COMBK(tc_HOL_Obool,tc_Product__Type_Ounit),c_fTrue)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_59]),c_0_51]) ).
cnf(c_0_126,plain,
hAPP(c_COMBK(tc_HOL_Obool,tc_Product__Type_Ounit),c_fTrue) = hAPP(c_List_Oset(tc_Product__Type_Ounit),c_Enum_Oenum__class_Oenum(tc_Product__Type_Ounit)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
fof(c_0_127,plain,
! [X252,X253] : hBOOL(hAPP(c_Finite__Set_Ofinite(X253),hAPP(c_List_Oset(X253),X252))),
inference(variable_rename,[status(thm)],[fact_finite__set]) ).
cnf(c_0_128,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(c_Finite__Set_Ocard(X2),X4),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_129,plain,
hAPP(c_Finite__Set_Ocard(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X3)),hAPP(c_Finite__Set_Ocard(X2),X4)),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_130,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X2))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Int_OMin)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106]),c_0_82]) ).
cnf(c_0_131,plain,
hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(c_Int_OMin,c_Int_OMin)) = hAPP(c_fequal,c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_88]),c_0_108]),c_0_109]),c_0_110])]),c_0_111]),c_0_112]),c_0_111]),c_0_112]),c_0_113]),c_0_62]) ).
cnf(c_0_132,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X1) = c_Int_OPls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_133,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_85]),c_0_118]),c_0_119]) ).
cnf(c_0_134,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I2_J]) ).
fof(c_0_135,plain,
! [X107] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X107),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X107,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
cnf(c_0_136,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),c_Int_OMin))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_120,c_0_72]),c_0_73]),c_0_73]),c_0_65]) ).
cnf(c_0_137,plain,
hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),
inference(rw,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_138,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(X1)
| ~ class_HOL_Oequal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_139,plain,
class_HOL_Oequal(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__HOL_Oequal]) ).
cnf(c_0_140,plain,
( X1 = hAPP(c_COMBK(tc_HOL_Obool,X2),c_fTrue)
| hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Finite__Set_Ocard(X2),hAPP(c_COMBK(tc_HOL_Obool,X2),c_fTrue))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),hAPP(c_COMBK(tc_HOL_Obool,X2),c_fTrue))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_124,c_0_76]),c_0_76]),c_0_76]) ).
cnf(c_0_141,plain,
hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),hAPP(c_List_Oset(tc_Product__Type_Ounit),c_Enum_Oenum__class_Oenum(tc_Product__Type_Ounit))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_142,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_143,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(c_fequal,X2))),hAPP(c_Finite__Set_Ocard(X3),X4)) = hAPP(c_Finite__Set_Ocard(X3),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_50]),c_0_62]),c_0_129]) ).
cnf(c_0_144,plain,
hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_fequal,c_Int_OMin)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_132]),c_0_118]),c_0_133]),c_0_134]) ).
cnf(c_0_145,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[c_0_135]) ).
fof(c_0_146,plain,
! [X325,X326,X327,X328] : hAPP(hAPP(c_COMBK(X328,X327),X326),X325) = X326,
inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).
cnf(c_0_147,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))),
inference(rw,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_148,plain,
c_HOL_Oequal__class_Oequal(tc_Int_Oint) = c_fequal,
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_149,plain,
( X1 = hAPP(c_List_Oset(tc_Product__Type_Ounit),c_Enum_Oenum__class_Oenum(tc_Product__Type_Ounit))
| hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_126]),c_0_141]),c_0_142])]) ).
cnf(c_0_150,plain,
hAPP(c_Finite__Set_Ocard(X1),hAPP(c_fequal,X2)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_145]) ).
cnf(c_0_151,plain,
hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
inference(split_conjunct,[status(thm)],[c_0_146]) ).
cnf(c_0_152,plain,
~ hBOOL(hAPP(hAPP(c_fequal,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))),
inference(rw,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_153,plain,
hAPP(c_fequal,X1) = hAPP(c_List_Oset(tc_Product__Type_Ounit),c_Enum_Oenum__class_Oenum(tc_Product__Type_Ounit)),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,plain,
hAPP(hAPP(c_List_Oset(tc_Product__Type_Ounit),c_Enum_Oenum__class_Oenum(tc_Product__Type_Ounit)),X1) = c_fTrue,
inference(spm,[status(thm)],[c_0_151,c_0_126]) ).
cnf(c_0_155,plain,
hBOOL(c_fTrue),
inference(split_conjunct,[status(thm)],[help_c__fTrue__1]) ).
cnf(c_0_156,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_152,c_0_153]),c_0_154]),c_0_155])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW380+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : run_ET %s %d
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 6 01:47:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.03/24.10 eprover: CPU time limit exceeded, terminating
% 1.03/24.11 eprover: CPU time limit exceeded, terminating
% 1.03/24.11 eprover: CPU time limit exceeded, terminating
% 1.03/24.11 eprover: CPU time limit exceeded, terminating
% 1.14/47.12 eprover: CPU time limit exceeded, terminating
% 1.14/47.12 eprover: CPU time limit exceeded, terminating
% 1.14/47.13 eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 1.14/47.13
% 1.26/70.14 eprover: CPU time limit exceeded, terminating
% 1.26/70.14 eprover: CPU time limit exceeded, terminating
% 1.26/70.14 eprover: CPU time limit exceeded, terminating
% 1.26/70.44 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 1.26/70.44
% 1.26/70.44 # Failure: Resource limit exceeded (time)
% 1.26/70.44 # OLD status Res
% 1.26/70.44 # Preprocessing time : 0.929 s
% 1.26/70.44 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 1.26/70.44
% 1.26/70.44 # Failure: Resource limit exceeded (time)
% 1.26/70.44 # OLD status Res
% 1.26/70.44 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 1.26/70.44 # Preprocessing time : 0.324 s
% 1.26/70.44 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 1.26/70.44 # Preprocessing time : 1.087 s
% 1.26/70.44
% 1.26/70.44 # Proof found!
% 1.26/70.44 # SZS status Theorem
% 1.26/70.44 # SZS output start CNFRefutation
% See solution above
% 1.26/70.44 # Proof object total steps : 157
% 1.26/70.44 # Proof object clause steps : 80
% 1.26/70.44 # Proof object formula steps : 77
% 1.26/70.44 # Proof object conjectures : 0
% 1.26/70.44 # Proof object clause conjectures : 0
% 1.26/70.44 # Proof object formula conjectures : 0
% 1.26/70.44 # Proof object initial clauses used : 44
% 1.26/70.44 # Proof object initial formulas used : 44
% 1.26/70.44 # Proof object generating inferences : 10
% 1.26/70.44 # Proof object simplifying inferences : 69
% 1.26/70.44 # Training examples: 0 positive, 0 negative
% 1.26/70.44 # Parsed axioms : 5242
% 1.26/70.44 # Removed by relevancy pruning/SinE : 0
% 1.26/70.44 # Initial clauses : 7572
% 1.26/70.44 # Removed in clause preprocessing : 233
% 1.26/70.44 # Initial clauses in saturation : 7339
% 1.26/70.44 # Processed clauses : 8901
% 1.26/70.44 # ...of these trivial : 392
% 1.26/70.44 # ...subsumed : 1352
% 1.26/70.44 # ...remaining for further processing : 7157
% 1.26/70.44 # Other redundant clauses eliminated : 1005
% 1.26/70.44 # Clauses deleted for lack of memory : 568033
% 1.26/70.44 # Backward-subsumed : 21
% 1.26/70.44 # Backward-rewritten : 755
% 1.26/70.44 # Generated clauses : 668072
% 1.26/70.44 # ...of the previous two non-trivial : 652393
% 1.26/70.44 # Contextual simplify-reflections : 284
% 1.26/70.44 # Paramodulations : 666683
% 1.26/70.44 # Factorizations : 15
% 1.26/70.44 # Equation resolutions : 1380
% 1.26/70.44 # Current number of processed clauses : 6287
% 1.26/70.44 # Positive orientable unit clauses : 1343
% 1.26/70.44 # Positive unorientable unit clauses: 243
% 1.26/70.44 # Negative unit clauses : 91
% 1.26/70.44 # Non-unit-clauses : 4610
% 1.26/70.44 # Current number of unprocessed clauses: 58759
% 1.26/70.44 # ...number of literals in the above : 145324
% 1.26/70.44 # Current number of archived formulas : 0
% 1.26/70.44 # Current number of archived clauses : 814
% 1.26/70.44 # Clause-clause subsumption calls (NU) : 4240951
% 1.26/70.44 # Rec. Clause-clause subsumption calls : 1717874
% 1.26/70.44 # Non-unit clause-clause subsumptions : 1389
% 1.26/70.44 # Unit Clause-clause subsumption calls : 98720
% 1.26/70.44 # Rewrite failures with RHS unbound : 50162
% 1.26/70.44 # BW rewrite match attempts : 38646
% 1.26/70.44 # BW rewrite match successes : 6750
% 1.26/70.44 # Condensation attempts : 0
% 1.26/70.44 # Condensation successes : 0
% 1.26/70.44 # Termbank termtop insertions : 29759819
% 1.26/70.44
% 1.26/70.44 # -------------------------------------------------
% 1.26/70.44 # User time : 22.683 s
% 1.26/70.44 # System time : 0.186 s
% 1.26/70.44 # Total time : 22.869 s
% 1.26/70.44 # Maximum resident set size: 172580 pages
% 1.26/93.15 eprover: CPU time limit exceeded, terminating
% 1.26/93.16 eprover: CPU time limit exceeded, terminating
% 1.26/93.17 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.17 eprover: No such file or directory
% 1.26/93.18 eprover: CPU time limit exceeded, terminating
% 1.26/93.18 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.18 eprover: No such file or directory
% 1.26/93.18 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.18 eprover: No such file or directory
% 1.26/93.18 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.18 eprover: No such file or directory
% 1.26/93.19 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.19 eprover: No such file or directory
% 1.26/93.19 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.19 eprover: No such file or directory
% 1.26/93.19 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.19 eprover: No such file or directory
% 1.26/93.19 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.19 eprover: No such file or directory
% 1.26/93.19 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.19 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.20 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.20 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.21 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.21 eprover: No such file or directory
% 1.26/93.22 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.22 eprover: No such file or directory
% 1.26/93.23 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.23 eprover: No such file or directory
% 1.26/93.23 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.26/93.23 eprover: No such file or directory
%------------------------------------------------------------------------------