%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW196+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n017.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 05:29:28 PM UTC 2026
% Result : Theorem 2.30s 2.78s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1483)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__sum__power2__lt__zero,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_odd__equiv__def,axiom,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
<=> ? [X31] : X15 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__equiv__def) ).
fof(fact_odd__Suc__mult__two__ex,axiom,
! [X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
<=> ? [X1] : X17 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(fact_power2__less__0,axiom,
! [X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).
fof(fact_zmod__number__of__Bit1,axiom,
! [X9,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit1) ).
fof(fact_odd__nat__equiv__def2,axiom,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X31] : X15 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nat__equiv__def2) ).
fof(fact_iszero__number__of__Bit1,axiom,
! [X8,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Int_Oring__char__0(X3) )
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(fact_not__iszero__Numeral1,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(fact_odd__nat__equiv__def,axiom,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nat__equiv__def) ).
fof(fact_odd__nat__mod__two__eq__one,axiom,
! [X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nat__mod__two__eq__one) ).
fof(fact_le__SucE,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> X19 = c_Nat_OSuc(X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_not__less__eq__eq,axiom,
! [X17,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X17,X18] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X18,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> X17 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [X19,X20] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucE,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(fact_even__Suc,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X15))
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__Suc) ).
fof(fact_power2__diff,axiom,
! [X22,X23,X3] :
( class_Int_Onumber__ring(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__diff) ).
fof(fact_Bit0__def,axiom,
! [X7] : c_Int_OBit0(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X7] : c_Int_OBit1(X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_power2__sum,axiom,
! [X22,X23,X3] :
( class_Int_Onumber__ring(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).
fof(fact_real__sum__squared__expand,axiom,
! [X22,X23] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X23,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),X22)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_Suc__eq__plus1,axiom,
! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_sum__power2__gt__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
| X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
& X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_four__x__squared,axiom,
! [X23] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_four__x__squared) ).
fof(fact_neg__zmod__mult__2,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zmod__mult__2) ).
fof(fact_pos__zmod__mult__2,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
fof(fact_odd__power__less__zero,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_sum__power2__ge__zero,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__ge__zero) ).
fof(fact_even__power__le__0__imp__0,axiom,
! [X7,X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X7)),c_Groups_Ozero__class_Ozero(X3))
=> X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).
fof(fact_power2__le__imp__le,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
=> c_Orderings_Oord__class_Oless__eq(X3,X23,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_power2__less__imp__less,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
=> c_Orderings_Oord__class_Oless(X3,X23,X22) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
& X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
fof(fact_realpow__two__sum__zero__iff,axiom,
! [X14,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
fof(fact_power__odd__eq,axiom,
! [X20,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__odd__eq) ).
fof(fact_neg__zdiv__mult__2,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).
fof(fact_pos__zdiv__mult__2,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [X20,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_power__m1__odd,axiom,
! [X20,X3] :
( class_Int_Onumber__ring(X3)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).
fof(fact_zero__le__even__power_H,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_power2__eq__imp__eq,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
=> X23 = X22 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_zero__less__power2,axiom,
! [X25,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> X25 != c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power2) ).
fof(fact_neq__one__mod__two,axiom,
! [X15] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq__one__mod__two) ).
fof(fact_power__even__eq,axiom,
! [X20,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X20,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X23,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_power__m1__even,axiom,
! [X20,X3] :
( class_Int_Onumber__ring(X3)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).
fof(fact_zero__le__power2,axiom,
! [X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power2) ).
fof(fact_two__realpow__ge__one,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).
fof(fact_Suc3__eq__add__3,axiom,
! [X20] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X20))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_power3__eq__cube,axiom,
! [X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( X23 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X23 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).
fof(fact_less__2__cases,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X20 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__2__cases) ).
fof(fact_zero__eq__power2,axiom,
! [X25,X3] :
( class_Rings_Oring__1__no__zero__divisors(X3)
=> ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3)
<=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_even__def,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__def) ).
fof(fact_even__equiv__def,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
<=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__equiv__def) ).
fof(fact_even__mult__two__ex,axiom,
! [X17] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
<=> ? [X1] : X17 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__mult__two__ex) ).
fof(fact_int__even__iff__2__dvd,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__even__iff__2__dvd) ).
fof(fact_nat__even__iff__2__dvd,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__even__iff__2__dvd) ).
fof(conj_0,hypothesis,
( ? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
=> v_thesis____ ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [X8,X9] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_add__2__eq__Suc,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X20) = c_Nat_OSuc(c_Nat_OSuc(X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_power2__eq__square__number__of,axiom,
! [X8,X30] :
( ( class_Groups_Omonoid__mult(X30)
& class_Int_Onumber(X30) )
=> c_Power_Opower__class_Opower(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X8),c_Int_Onumber__class_Onumber__of(X30,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_mult__2,axiom,
! [X10,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
fof(fact_mult__2__right,axiom,
! [X10,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,X10,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3,X10,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_power2__eq__square,axiom,
! [X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X23,X23) = c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_nat__mult__2,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X10) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
fof(fact_nat__mult__2__right,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_one__power2,axiom,
! [X3] :
( class_Rings_Osemiring__1(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
fof(fact_zero__power2,axiom,
! [X3] :
( class_Rings_Osemiring__1(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).
fof(fact_csqrt,axiom,
! [X10] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_csqrt) ).
fof(fact__096EX_Am_O_An_A_061_A2_A_K_Am_096,axiom,
? [X1] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Am_O_An_A_061_A2_A_K_Am_096) ).
fof(fact_realpow__two__diff,axiom,
! [X22,X23,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X3,X22,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),c_Groups_Oplus__class_Oplus(X3,X23,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__two__diff) ).
fof(fact_Suc__diff__eq__diff__pred,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X20)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).
fof(fact_one__add__one__is__two,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).
fof(fact_power__le__imp__le__base,axiom,
! [X21,X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20)))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
fof(fact_less__eq__int__code_I16_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).
fof(fact_rel__simps_I34_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_less__int__code_I16_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit1(X49))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).
fof(fact_rel__simps_I17_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X4))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_diff__bin__simps_I10_J,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).
fof(fact_diff__bin__simps_I9_J,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).
fof(fact_add__Bit1__Bit0,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X7),c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_add__Bit0__Bit1,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_mult__Bit1,axiom,
! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X7),X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).
fof(fact_mod__mult__self4,axiom,
! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19)),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self4) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__ring(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22)),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_number__of1,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X20))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X20)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).
fof(fact_add__special_I3_J,axiom,
! [X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oone__class_Oone(X3)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).
fof(fact_add__special_I2_J,axiom,
! [X8,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_diff__bin__simps_I4_J,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_lemma__realpow__diff,axiom,
! [X22,X20,X38,X3] :
( class_Groups_Omonoid__mult(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X38,X20)
=> c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),X38)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X22,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X38)),X22) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__realpow__diff) ).
fof(fact_less__eq__int__code_I15_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).
fof(fact_rel__simps_I33_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).
fof(fact_less__int__code_I15_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X50),c_Int_OBit0(X49))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).
fof(fact_rel__simps_I16_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X4))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
fof(fact_less__eq__int__code_I14_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).
fof(fact_rel__simps_I32_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_less__int__code_I14_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit1(X49))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).
fof(fact_rel__simps_I15_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).
fof(fact_one__le__mult__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_one__less__mult,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_diff__Suc__diff__eq2,axiom,
! [X19,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)),X19) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X51),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).
fof(fact_diff__Suc__diff__eq1,axiom,
! [X19,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Nat_OSuc(X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).
fof(fact_power__inject__base,axiom,
! [X21,X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Power_Opower__class_Opower(X3,X21,c_Nat_OSuc(X20))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> X2 = X21 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_mult__numeral__1,axiom,
! [X2,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_mult__numeral__1__right,axiom,
! [X2,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_n__less__n__mult__m,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X23 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X23 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).
fof(fact_le__special_I4_J,axiom,
! [X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_less__special_I4_J,axiom,
! [X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Oone__class_Oone(X3))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OBit1(c_Int_OPls)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_le__special_I2_J,axiom,
! [X14,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_less__special_I2_J,axiom,
! [X14,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).
fof(fact_nat__diff__split__asm,axiom,
! [X24,X25,X55] :
( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
& ~ hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X69] :
( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
& ~ hBOOL(hAPP(X55,X69)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
fof(fact_divmod__int__rel__mod__eq,axiom,
! [X22,X78,X79,X80] :
( X80 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X22)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X79) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X22)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X79 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X80,X79) = X22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
fof(fact_Suc__diff__diff,axiom,
! [X7,X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20),c_Nat_OSuc(X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).
fof(fact_rel__simps_I26_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).
fof(fact_rel__simps_I22_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).
fof(fact_rel__simps_I5_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).
fof(fact_rel__simps_I9_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).
fof(fact_rel__simps_I30_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).
fof(fact_rel__simps_I13_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).
fof(fact_rel__simps_I29_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).
fof(fact_rel__simps_I12_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).
fof(fact_even__nat__equiv__def,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__nat__equiv__def) ).
fof(fact_even__nat__equiv__def2,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X31] : X15 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__nat__equiv__def2) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X6)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_number__of__Bit1,axiom,
! [X8,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_power__Suc__less__one,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)),c_Groups_Oone__class_Oone(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_realpow__Suc__le__self,axiom,
! [X20,X54,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X54)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X54,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X54,c_Nat_OSuc(X20)),X54) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_nat__number__of__mult__left,axiom,
! [X7,X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_nat__one__le__power,axiom,
! [X20,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X53)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_mod__Suc__eq__Suc__mod,axiom,
! [X20,X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).
fof(fact_diff__bin__simps_I7_J,axiom,
! [X6,X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).
fof(fact_add__Bit0__Bit0,axiom,
! [X6,X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X7),c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_rel__simps_I51_J,axiom,
! [X4,X5] :
( c_Int_OBit1(X5) = c_Int_OBit1(X4)
<=> X5 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X17,X18,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X17)
<=> X18 = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_power__gt1,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_mod__Suc,axiom,
! [X20,X19] :
( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = X20
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) != X20
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__Suc) ).
fof(fact_Suc__le__mono,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),c_Nat_OSuc(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
fof(fact_Suc__less__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X18),c_Nat_OSuc(X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__less__SucD,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__pred,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).
fof(fact_diff__Suc__less,axiom,
! [X53,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Nat_OSuc(X53)),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_less__eq__int__code_I13_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).
fof(fact_rel__simps_I31_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_less__int__code_I13_J,axiom,
! [X49,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X50),c_Int_OBit0(X49))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).
fof(fact_rel__simps_I14_J,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X4))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
fof(fact_zero__less__power__eq__number__of,axiom,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& X15 != c_Groups_Ozero__class_Ozero(X3) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__eq__number__of) ).
fof(fact_iszero__number__of__Bit0,axiom,
! [X16,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Int_Oring__char__0(X3) )
=> ( c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X16)))
<=> c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,X16)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).
fof(fact_zero__le__power__eq__number__of,axiom,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__eq__number__of) ).
fof(fact_power__le__zero__eq__number__of,axiom,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__zero__eq__number__of) ).
fof(fact_add__eq__if,axiom,
! [X20,X19] :
( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X20 )
& ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).
fof(fact_split__zmod,axiom,
! [X5,X17,X55] :
( hBOOL(hAPP(X55,c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,X5)))
<=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X55,X17)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ! [X77,X58] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X5)
& X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X55,X58)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X77,X58] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X58)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X55,X58)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(fact_even__nat__mod__two__eq__zero,axiom,
! [X23] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__nat__mod__two__eq__zero) ).
fof(fact_mult__Bit0,axiom,
! [X6,X7] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X7),X6) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
fof(fact_diff__bin__simps_I3_J,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X6)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(fact_Suc__diff__le,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).
fof(fact_power__less__zero__eq__number__of,axiom,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__zero__eq__number__of) ).
fof(fact_number__of__Bit0,axiom,
! [X8,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X8)),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_power__mono__odd,axiom,
! [X22,X23,X20,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X23,X22)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono__odd) ).
fof(fact_less__add__Suc1,axiom,
! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X19,X53] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X53))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_le__Suc__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
| X18 = c_Nat_OSuc(X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_dvd_Oless__trans,axiom,
! [X10,X22,X23] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_Suc__mono,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [X16,X61,X3] :
( ( class_Int_Onumber(X3)
& class_Orderings_Olinorder(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X61),c_Int_Onumber__class_Onumber__of(X3,X16))
<=> ~ c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X16),c_Int_Onumber__class_Onumber__of(X3,X61)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_expand__Suc,axiom,
! [X9] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).
fof(fact_zero__less__power__eq,axiom,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& X15 != c_Groups_Ozero__class_Ozero(X3) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__eq) ).
fof(fact_zero__le__power__eq,axiom,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__eq) ).
fof(fact_zero__le__odd__power,axiom,
! [X15,X17,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__odd__power) ).
fof(fact_power__le__zero__eq,axiom,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
<=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__zero__eq) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X58] :
( X18 = c_Nat_OSuc(X58)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_le__less__Suc__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> X17 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_numeral__1__eq__1,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oone__class_Oone(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_rel__simps_I49_J,axiom,
! [X6,X7] : c_Int_OBit0(X7) != c_Int_OBit1(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I50_J,axiom,
! [X6,X7] : c_Int_OBit1(X7) != c_Int_OBit0(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_double__number__of__Bit0,axiom,
! [X8,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit0(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_power__Suc2,axiom,
! [X20,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_power__Suc,axiom,
! [X20,X2,X3] :
( class_Power_Opower(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Nat_OSuc(X20)) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X35,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) = c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X35,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),X23) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
! [X35,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X23,c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Nat_OSuc(X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_power__less__zero__eq,axiom,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__zero__eq) ).
fof(fact_less__trans__Suc,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X53),X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_dvd__1__iff__1,axiom,
! [X18] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).
fof(fact_diff__Suc__Suc,axiom,
! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X19),c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).
fof(fact_add__Suc__shift,axiom,
! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_diff__Suc__eq__diff__pred,axiom,
! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).
fof(fact_add__Suc,axiom,
! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_mult__Suc,axiom,
! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X19),X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_mult__Suc__right,axiom,
! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_add__nat__number__of,axiom,
! [X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X32)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_less__Suc__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
| X18 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__leD,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_Suc__le__lessD,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__le__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X17)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__eq__Suc__le,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__lessD,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_bin__less__0__simps_I3_J,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
fof(fact_less__iff__Suc__add,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
<=> ? [X59] : X17 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [X10,X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [X10,X22,X23] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_Suc__lessI,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> ( c_Nat_OSuc(X19) != X20
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_even__num__iff,axiom,
! [X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__num__iff) ).
fof(fact_mult__eq__1__iff,axiom,
! [X17,X18] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_add__leE,axiom,
! [X20,X7,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_one__is__add,axiom,
! [X17,X18] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17)
<=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [X17,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X18 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X17 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(fact_rel__simps_I21_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).
fof(fact_rel__simps_I25_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).
fof(fact_rel__simps_I8_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).
fof(fact_rel__simps_I4_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X5))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).
fof(fact_rel__simps_I11_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).
fof(fact_rel__simps_I27_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).
fof(fact_rel__simps_I10_J,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OPls)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).
fof(fact_not__square__less__zero,axiom,
! [X2,X3] :
( class_Rings_Olinordered__ring(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_even__difference__nat,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__difference__nat) ).
fof(fact_less__Suc0,axiom,
! [X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(fact_mult__nat__number__of,axiom,
! [X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_diff__less__Suc,axiom,
! [X20,X19] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),c_Nat_OSuc(X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_mod__if,axiom,
! [X20,X19] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__if) ).
fof(fact_mod__geq,axiom,
! [X20,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__geq) ).
fof(fact_le__nat__number__of,axiom,
! [X60,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X60)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_rel__simps_I43_J,axiom,
! [X4] :
( c_Int_OMin = c_Int_OBit1(X4)
<=> c_Int_OMin = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [X5] :
( c_Int_OBit1(X5) = c_Int_OMin
<=> X5 = c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X15] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_zdvd__not__zless,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X20)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_nat__dvd__not__less,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_rel__simps_I46_J,axiom,
! [X7] : c_Int_OBit1(X7) != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [X6] : c_Int_OPls != c_Int_OBit1(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_Suc__diff__1,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).
fof(fact_Suc__pred_H,axiom,
! [X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> X20 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).
fof(fact_Suc__leI,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X19),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_le__SucI,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_less__SucI,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_not__add__less1,axiom,
! [X51,X53] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X53,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X18,X15] :
( c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X18) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X15 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_power__Suc__0,axiom,
! [X20] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(fact_odd__plus__even,axiom,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__plus__even) ).
fof(fact_even__difference,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__difference) ).
fof(fact_even__plus__odd,axiom,
! [X22,X23] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__plus__odd) ).
fof(fact_even__sum,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__sum) ).
fof(fact_odd__add,axiom,
! [X17,X18] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__add) ).
fof(fact_even__sum__nat,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__sum__nat) ).
fof(fact_add__diff__inverse,axiom,
! [X20,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_odd__times__odd,axiom,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__times__odd) ).
fof(fact_odd__pow,axiom,
! [X20,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__pow) ).
fof(fact_power__0__Suc,axiom,
! [X20,X3] :
( ( class_Power_Opower(X3)
& class_Rings_Osemiring__0(X3) )
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Nat_OSuc(X20)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_Suc__inject,axiom,
! [X22,X23] :
( c_Nat_OSuc(X23) = c_Nat_OSuc(X22)
=> X23 = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_nat_Oinject,axiom,
! [X36,X37] :
( c_Nat_OSuc(X37) = c_Nat_OSuc(X36)
<=> X37 = X36 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_mod__1,axiom,
! [X19] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [X21,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
=> ( X2 != X21
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
| X23 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [X21,X2] :
( X2 != X21
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oless__le,axiom,
! [X14,X15] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& X15 != X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Ole__less,axiom,
! [X14,X15] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
| X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd__1__left,axiom,
! [X7] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(fact_rel__simps_I48_J,axiom,
! [X4,X5] :
( c_Int_OBit0(X5) = c_Int_OBit0(X4)
<=> X5 = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_diff__Suc__1,axiom,
! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(fact_zero__less__Suc,axiom,
! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_lessI,axiom,
! [X20] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_gr0__conv__Suc,axiom,
! [X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
<=> ? [X1] : X17 = c_Nat_OSuc(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_odd__plus__odd,axiom,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__plus__odd) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( X23 != X22
=> ( ~ c_Orderings_Oord__class_Oless(X3,X23,X22)
=> c_Orderings_Oord__class_Oless(X3,X22,X23) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_not__one__le__zero,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X20] : c_Nat_OSuc(X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_neg__one__odd__power,axiom,
! [X23,X3] :
( class_Int_Onumber__ring(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__odd__power) ).
fof(fact_neg__one__even__odd__power,axiom,
! [X23,X3] :
( class_Int_Onumber__ring(X3)
=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__even__odd__power) ).
fof(fact_linorder__neqE__nat,axiom,
! [X22,X23] :
( X23 != X22
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_Suc__not__Zero,axiom,
! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).
fof(fact_nat_Osimps_I3_J,axiom,
! [X47] : c_Nat_OSuc(X47) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).
fof(fact_Suc__neq__Zero,axiom,
! [X19] : c_Nat_OSuc(X19) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_Zero__not__Suc,axiom,
! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X48] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X19] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X20] : c_Nat_OSuc(X20) != X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X20] : X20 != c_Nat_OSuc(X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_less__nat__zero__code,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_not__less0,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_rel__simps_I38_J,axiom,
! [X4] :
( c_Int_OPls = c_Int_OBit0(X4)
<=> c_Int_OPls = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(fact_rel__simps_I44_J,axiom,
! [X5] :
( c_Int_OBit0(X5) = c_Int_OPls
<=> X5 = c_Int_OPls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(fact_less__irrefl__nat,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_rel__simps_I45_J,axiom,
! [X7] : c_Int_OBit0(X7) != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [X6] : c_Int_OMin != c_Int_OBit0(X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_odd__pos,axiom,
! [X20] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__pos) ).
fof(fact_nonzero__number__of__Min,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(fact_not__iszero__1,axiom,
! [X3] :
( class_Rings_Osemiring__1(X3)
=> ~ c_Int_Oiszero(X3,c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(fact_pos2,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos2) ).
fof(fact_numeral__3__eq__3,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X21,X2,X22,X23,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)),c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X22,X21))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_nat__le__add__iff1,axiom,
! [X17,X18,X68,X66,X65] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X17,X18,X68,X66,X65] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [X17,X18,X68,X65,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X17,X18,X68,X65,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_le__add__iff1,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42),X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
<=> c_Orderings_Oord__class_Oless__eq(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41))
<=> c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_zdiv__zadd1__eq,axiom,
! [X33,X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),X33) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X21,X33)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X33),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).
fof(fact_numeral__2__eq__2,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X20,X19,X52,X53,X51] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X53)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X52),X19),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X20,X19,X52,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X53),X52),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_inf__period_I3_J,axiom,
! [X57,X72,X41,X3] :
( ( class_Rings_Ocomm__ring(X3)
& class_Rings_Odvd(X3) )
=> ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
=> ! [X56,X59] :
( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
<=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X57,X72,X41,X3] :
( ( class_Rings_Ocomm__ring(X3)
& class_Rings_Odvd(X3) )
=> ( c_Rings_Odvd__class_Odvd(X3,X41,X72)
=> ! [X56,X59] :
( c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,X56,X57))
<=> c_Rings_Odvd__class_Odvd(X3,X41,c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X56,c_Groups_Otimes__class_Otimes(X3,X59,X72)),X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X73,X74,X39,X54,X35,X21] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X73,X74,X39,X54,X35,X21] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_zdvd__period,axiom,
! [X42,X57,X15,X41,X25] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X41)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X57))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X42,X41)),X57)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__period) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(fact_unique__quotient__lemma,axiom,
! [X54,X35,X73,X74,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X21)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,X35) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X54,X35,X73,X74,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X74),X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X35),X54))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X73)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,X74) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [X35,X21,X54,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [X35,X54,X21,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_convex__bound__le,axiom,
! [X9,X52,X22,X2,X23,X3] :
( class_Rings_Olinordered__semiring__1(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X23,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X22,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
=> ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X9,X52,X22,X2,X23,X3] :
( class_Rings_Olinordered__semiring__1__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X23,X2)
=> ( c_Orderings_Oord__class_Oless(X3,X22,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X52)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X9)
=> ( c_Groups_Oplus__class_Oplus(X3,X52,X9) = c_Groups_Oone__class_Oone(X3)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X52,X23),c_Groups_Otimes__class_Otimes(X3,X9,X22)),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [X35,X54,X21,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X54)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).
fof(fact_zmult2__lemma__aux3,axiom,
! [X35,X21,X54,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X35,X33)),X54)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_unity__coeff__ex,axiom,
! [X4,X55,X3] :
( ( class_Rings_Odvd(X3)
& class_Rings_Osemiring__0(X3) )
=> ( ? [X56] : hBOOL(hAPP(X55,c_Groups_Otimes__class_Otimes(X3,X4,X56)))
<=> ? [X56] :
( c_Rings_Odvd__class_Odvd(X3,X4,c_Groups_Oplus__class_Oplus(X3,X56,c_Groups_Ozero__class_Ozero(X3)))
& hBOOL(hAPP(X55,X56)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X17,X18,X68,X66,X65] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,X66)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X66,X65),X68),X18) = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X17,X18,X68,X65,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X66,X68),X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X65,X68),X17)
<=> X18 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66),X68),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_mult__diff__mult,axiom,
! [X21,X2,X22,X23,X3] :
( class_Rings_Oring(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X2,X21)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X21)),c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X2),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X3)
| X14 != c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)),c_Groups_Ozero__class_Ozero(X3))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
& X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_eq__add__iff1,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oring(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
<=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),X67),X42) = X41 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X41,X24,X42,X67,X25,X3] :
( class_Rings_Oring(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X67),X42) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X24,X67),X41)
<=> X42 = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X24,X25),X67),X41) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_combine__common__factor,axiom,
! [X33,X21,X45,X2,X3] :
( class_Rings_Osemiring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X45),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X21,X45),X33)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X45),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_crossproduct__noteq,axiom,
! [X41,X42,X24,X25,X3] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
=> ( ( X25 != X24
& X42 != X41 )
<=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X41)) != c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X25,X41),c_Groups_Otimes__class_Otimes(X3,X24,X42)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X46,X15,X14,X16,X3] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X14),c_Groups_Otimes__class_Otimes(X3,X15,X46)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X16,X46),c_Groups_Otimes__class_Otimes(X3,X15,X14))
<=> ( X16 = X15
| X14 = X46 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_left__add__mult__distrib,axiom,
! [X7,X51,X52,X53] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X52),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X52),X7)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X52),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_q__neg__lemma,axiom,
! [X73,X74,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X73)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X74,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X73,X74,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X39,X74),X73))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X73,X39)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X74) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_mod__diff__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Oring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__eq) ).
fof(fact_mod__add__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_mod__mult__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_power__Suc__less,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_nat__diff__split,axiom,
! [X24,X25,X55] :
( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
=> hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X69] :
( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
=> hBOOL(hAPP(X55,X69)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_mod__diff__cong,axiom,
! [X39,X21,X43,X33,X2,X3] :
( class_Divides_Oring__div(X3)
=> ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
=> ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X43,X39),X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__cong) ).
fof(fact_mod__add__cong,axiom,
! [X39,X21,X43,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
=> ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X43,X39),X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X39,X21,X43,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Divides_Odiv__class_Omod(X3,X2,X33) = c_Divides_Odiv__class_Omod(X3,X43,X33)
=> ( c_Divides_Odiv__class_Omod(X3,X21,X33) = c_Divides_Odiv__class_Omod(X3,X39,X33)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X43,X39),X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_odd__less__0,axiom,
! [X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46),X46),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X26,X27,X28,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X26,X27,X28,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,c_Groups_Otimes__class_Otimes(X3,X27,X26))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_mult__mono_H,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X33,X34)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_le__diff__iff,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_zdvd__reduce,axiom,
! [X18,X17,X5] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18)))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X5,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_div__add,axiom,
! [X22,X23,X10,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X10,X23)
=> ( c_Rings_Odvd__class_Odvd(X3,X10,X22)
=> c_Divides_Odiv__class_Odiv(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X10) = c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Odiv(X3,X23,X10),c_Divides_Odiv__class_Odiv(X3,X22,X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__add) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__ring(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_power__less__power__Suc,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X21,X33,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X21,X2,X33,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X21,X33,X2,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X21,X33,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X21,X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X21,X2,X33,X3] :
( class_Rings_Olinordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X21,X2,X33,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless__eq(X3,X24,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_power__increasing__iff,axiom,
! [X14,X15,X24,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X20,X19,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X14,X15,X24,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X24)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X24,X15),c_Power_Opower__class_Opower(X3,X24,X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X20,X19,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_left__diff__distrib__number__of,axiom,
! [X9,X21,X2,X30] :
( ( class_Int_Onumber(X30)
& class_Rings_Oring(X30) )
=> c_Groups_Otimes__class_Otimes(X30,c_Groups_Ominus__class_Ominus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).
fof(fact_left__distrib__number__of,axiom,
! [X9,X21,X2,X30] :
( ( class_Int_Onumber(X30)
& class_Rings_Osemiring(X30) )
=> c_Groups_Otimes__class_Otimes(X30,c_Groups_Oplus__class_Oplus(X30,X2,X21),c_Int_Onumber__class_Onumber__of(X30,X9)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,X2,c_Int_Onumber__class_Onumber__of(X30,X9)),c_Groups_Otimes__class_Otimes(X30,X21,c_Int_Onumber__class_Onumber__of(X30,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_right__diff__distrib__number__of,axiom,
! [X33,X21,X9,X30] :
( ( class_Int_Onumber(X30)
& class_Rings_Oring(X30) )
=> c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Ominus__class_Ominus(X30,X21,X33)) = c_Groups_Ominus__class_Ominus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [X33,X21,X9,X30] :
( ( class_Int_Onumber(X30)
& class_Rings_Osemiring(X30) )
=> c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),c_Groups_Oplus__class_Oplus(X30,X21,X33)) = c_Groups_Oplus__class_Oplus(X30,c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X21),c_Groups_Otimes__class_Otimes(X30,c_Int_Onumber__class_Onumber__of(X30,X9),X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X14,X15,X46] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X14,X15,X46] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X46,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_mult__le__cancel2,axiom,
! [X17,X5,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_power__dvd__imp__le,axiom,
! [X20,X19,X53] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X53)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).
fof(fact_mult__le__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_dvd__mult__cancel,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_real__mult__less__iff1,axiom,
! [X14,X15,X46] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X46)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X46),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X46))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X20,X19,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X53)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X19),c_Power_Opower__class_Opower(tc_Nat_Onat,X53,X20))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_power__decreasing,axiom,
! [X2,X62,X20,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X2,X62,X20,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X62),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
& c_Orderings_Oord__class_Oless(X3,X25,X24) )
| ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X24,X42,X25,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
<=> ( ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X42)
& c_Orderings_Oord__class_Oless(X3,X25,X24) )
| ( c_Orderings_Oord__class_Oless(X3,X42,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless(X3,X24,X25) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_power__strict__mono,axiom,
! [X20,X21,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X26,X27,X28,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),c_Groups_Otimes__class_Otimes(X3,X28,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X21,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X21,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_zmod__simps_I2_J,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__diff__left__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Oring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).
fof(fact_mod__add__left__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X33),X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__diff__right__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Oring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Ominus__class_Ominus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_mod__mult__right__eq,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Omod(X3,X21,X33)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_add__number__of__diff1,axiom,
! [X33,X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X33)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).
fof(fact_add__number__of__left,axiom,
! [X10,X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).
fof(fact_mult__number__of__left,axiom,
! [X10,X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X8),X10)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_realpow__minus__mult,axiom,
! [X23,X20,X3] :
( class_Groups_Omonoid__mult(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X23) = c_Power_Opower__class_Opower(X3,X23,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X34,X33,X21,X2,X54,X3] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
=> ( X54 != c_Groups_Ozero__class_Ozero(X3)
=> ( ( X2 = X21
& X33 != X34 )
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X54,X33)) != c_Groups_Oplus__class_Oplus(X3,X21,c_Groups_Otimes__class_Otimes(X3,X54,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_div__power,axiom,
! [X20,X23,X22,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X22,X23)
=> c_Power_Opower__class_Opower(X3,c_Divides_Odiv__class_Odiv(X3,X23,X22),X20) = c_Divides_Odiv__class_Odiv(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__power) ).
fof(fact_zdiv__mono2,axiom,
! [X21,X39,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2) ).
fof(fact_zdiv__mono2__neg,axiom,
! [X21,X39,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X39,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X39),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).
fof(fact_zdiff__zmod__left,axiom,
! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).
fof(fact_zpower__zmod,axiom,
! [X22,X19,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X19),X22),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_zdiff__zmod__right,axiom,
! [X19,X22,X23] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X19)),X19) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X23,X22),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X33,X21,X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X21),X33) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21,X33)),X33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_power__le__dvd,axiom,
! [X19,X21,X20,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X20),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__dvd) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [X24,X25,X42,X3] :
( class_Rings_Oidom(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X42,X25),c_Groups_Otimes__class_Otimes(X3,X42,X24))
<=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [X24,X42,X25,X3] :
( class_Rings_Oidom(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X25,X42),c_Groups_Otimes__class_Otimes(X3,X24,X42))
<=> ( X42 = c_Groups_Ozero__class_Ozero(X3)
| c_Rings_Odvd__class_Odvd(X3,X25,X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_le__diff__conv2,axiom,
! [X66,X65,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X65)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_power__gt1__lemma,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_add__le__cancel__right,axiom,
! [X24,X42,X25,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
<=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__right,axiom,
! [X21,X33,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__left,axiom,
! [X24,X25,X42,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless__eq(X3,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__le__imp__le__left,axiom,
! [X21,X2,X33,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [X21,X33,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33))
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X24,X42,X25,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X42),c_Groups_Oplus__class_Oplus(X3,X24,X42))
<=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X21,X2,X33,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21))
=> c_Orderings_Oord__class_Oless(X3,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X24,X25,X42,X3] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X42,X25),c_Groups_Oplus__class_Oplus(X3,X42,X24))
<=> c_Orderings_Oord__class_Oless(X3,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_self__quotient__aux2,axiom,
! [X35,X54,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X20,X19,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X7),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_self__quotient__aux1,axiom,
! [X35,X54,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X35))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X2)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X35) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_dvd__diffD,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diffD1) ).
fof(fact_zdvd__mult__cancel,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X19),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X20))
=> ( X7 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__mono,axiom,
! [X57,X18,X5] :
( X5 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X18,X57)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X18),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X57)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__mono) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [X17,X18,X5] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_pow__divides__pow__int,axiom,
! [X21,X20,X2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X20),c_Power_Opower__class_Opower(tc_Int_Oint,X21,X20))
=> ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).
fof(fact_pow__divides__eq__int,axiom,
! [X24,X25,X17] :
( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X25,X17),c_Power_Opower__class_Opower(tc_Int_Oint,X24,X17))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).
fof(fact_pow__divides__eq__nat,axiom,
! [X24,X25,X17] :
( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X25,X17),c_Power_Opower__class_Opower(tc_Nat_Onat,X24,X17))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X25,X24) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(fact_pow__divides__pow__nat,axiom,
! [X21,X20,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X20),c_Power_Opower__class_Opower(tc_Nat_Onat,X21,X20))
=> ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X23,X3] :
( class_Rings_Oring__1(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Oone__class_Oone(X3)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,c_Groups_Oone__class_Oone(X3)),c_Groups_Ominus__class_Ominus(X3,X23,c_Groups_Oone__class_Oone(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_mult__less__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X17,X5,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X21,X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Power_Opower__class_Opower(X3,X2,X20) = c_Power_Opower__class_Opower(X3,X21,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> X2 = X21 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__mono,axiom,
! [X20,X21,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Oordered__comm__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Oordered__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Olinordered__comm__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__right__mono__neg,axiom,
! [X33,X2,X21,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X33,X2,X21,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X33,X2,X21,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X2)
=> ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X33,X2,X21,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X2)
=> ( c_Orderings_Oord__class_Oless(X3,X33,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_mult__right__le__one__le,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X23) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X23)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X22)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X22,c_Groups_Oone__class_Oone(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X22,X23),X23) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_power__increasing,axiom,
! [X2,X62,X20,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X62)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X2,X62,X20,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X62)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X2,X62)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_le__add__diff,axiom,
! [X19,X20,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_mult__dvd__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> ( c_Rings_Odvd__class_Odvd(X3,X33,X34)
=> c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X33,X34)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X33,X34)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X34,X33,X21,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> ( c_Orderings_Oord__class_Oless(X3,X33,X34)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X34)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_realpow__num__eq__if,axiom,
! [X19,X20,X3] :
( class_Power_Opower(X3)
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Oone__class_Oone(X3) )
& ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,X19,X20) = c_Groups_Otimes__class_Otimes(X3,X19,c_Power_Opower__class_Opower(X3,X19,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_dvd__power__le,axiom,
! [X19,X20,X22,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X19)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__le) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X14,X15,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X15,X15),c_Groups_Otimes__class_Otimes(X3,X14,X14)) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
& X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_mod__mult__mult2,axiom,
! [X21,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) = c_Groups_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X21,X19,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),c_Groups_Otimes__class_Otimes(X3,X21,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mod__mult__mult1,axiom,
! [X21,X2,X33,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X33,X2),c_Groups_Otimes__class_Otimes(X3,X33,X21)) = c_Groups_Otimes__class_Otimes(X3,X33,c_Divides_Odiv__class_Omod(X3,X2,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_power__mult__distrib,axiom,
! [X20,X21,X2,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X20) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),c_Power_Opower__class_Opower(X3,X21,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X35,X22,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),X35) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X35),c_Power_Opower__class_Opower(X3,X22,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_mult__left_Odiff,axiom,
! [X44,X22,X23,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X23,X22),X44) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_mult_Odiff__left,axiom,
! [X21,X43,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ominus__class_Ominus(X3,X2,X43),X21) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X44,X22,X23,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X23,X22),X44) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X44),c_Groups_Otimes__class_Otimes(X3,X22,X44)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X21,X43,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X43),X21) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X43,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X33),c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_mult__right_Odiff,axiom,
! [X22,X23,X40,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Ominus__class_Ominus(X3,X23,X22)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_mult_Odiff__right,axiom,
! [X39,X21,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ominus__class_Ominus(X3,X21,X39)) = c_Groups_Ominus__class_Ominus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Oadd,axiom,
! [X22,X23,X40,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X40,c_Groups_Oplus__class_Oplus(X3,X23,X22)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X40,X23),c_Groups_Otimes__class_Otimes(X3,X40,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X39,X21,X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X39)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Otimes__class_Otimes(X3,X2,X39)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X10,X22,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Oplus__class_Oplus(X3,X22,X10)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X22),c_Groups_Otimes__class_Otimes(X3,X23,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mod__mult__self2,axiom,
! [X33,X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X21,X33,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Otimes__class_Otimes(X3,X33,X21)),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X35,X38,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X23,X38),c_Power_Opower__class_Opower(X3,X23,X35)) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X38,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X20,X19,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_zdiv__mono1,axiom,
! [X21,X43,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1) ).
fof(fact_real__mult__less__mono2,axiom,
! [X22,X23,X10] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X22)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X23),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_zmult__zless__mono2,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X7)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X53),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X7,X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_zdiv__mono1__neg,axiom,
! [X21,X43,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X43)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X43,X21),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).
fof(fact_mult__eq__if,axiom,
! [X20,X19] :
( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_power__eq__if,axiom,
! [X38,X19] :
( ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(tc_Nat_Onat,X38,X19) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,c_Power_Opower__class_Opower(tc_Nat_Onat,X38,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_add__le__mono,axiom,
! [X6,X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_mult__le__mono,axiom,
! [X6,X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X10,X70,X8,X71] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X71,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X70,X10)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X71,X70),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X33,X21,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X33,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X33),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X6,X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X6,X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X6)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X2,X21,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X21,X2))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
! [X24,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X24,X25)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X14,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_real__add__mult__distrib,axiom,
! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X8),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12),X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X8,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X8),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_mod__mult__distrib,axiom,
! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X7) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X13,X12)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X12,X13,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X13),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_mod__mult__distrib2,axiom,
! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X20,X19,X7] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X19),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_mod__mult__self3,axiom,
! [X19,X20,X7] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X20),X19),X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self3) ).
fof(fact_le__diff__conv,axiom,
! [X66,X5,X65] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5),X66)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X65,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X5,X65,X66] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X66,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X5))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X66,X5),X65) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_dvd__mod__imp__dvd,axiom,
! [X20,X19,X7,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20))
=> ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
=> c_Rings_Odvd__class_Odvd(X3,X7,X19) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).
fof(fact_dvd__mod__iff,axiom,
! [X18,X17,X5,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,X17)
=> ( c_Rings_Odvd__class_Odvd(X3,X5,c_Divides_Odiv__class_Omod(X3,X18,X17))
<=> c_Rings_Odvd__class_Odvd(X3,X5,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).
fof(fact_zdiv__zmult2__eq,axiom,
! [X21,X2,X33] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X33)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).
fof(fact_add__diff__assoc2,axiom,
! [X53,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X53,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7),X53) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X53,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X53,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X53,X51,X7] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X51)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
! [X25,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).
fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
! [X25,X24] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X25,X24))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).
fof(fact_zero__less__power__nat__eq__number__of,axiom,
! [X16,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq__number__of) ).
fof(fact_pos__imp__zdiv__pos__iff,axiom,
! [X66,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X66) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [X24,X25,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
& c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X24,X25,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X25,X24))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X24) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,X24,c_Groups_Ozero__class_Ozero(X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_numeral__1__eq__Suc__0,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).
fof(fact_zdvd__zmod__imp__zdvd,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod__imp__zdvd) ).
fof(fact_zdvd__zdiffD,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X19,X20))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X20)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X7,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__cancel__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__cancel__semiring(X3)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
& c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) ) )
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__cancel__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__cancel__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__neg__pos,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),c_Groups_Ozero__class_Ozero(X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__cancel__semiring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_split__mult__pos__le,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21) )
| ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
& c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3)) ) )
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_less__1__mult,axiom,
! [X20,X19,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X19)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X20)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Otimes__class_Otimes(X3,X19,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_add__pos__nonneg,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_mult__pos__pos,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__semiring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X21,X2,X3] :
( class_Rings_Oordered__ring(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__neg__neg,axiom,
! [X21,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3))
=> ( c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Ozero__class_Ozero(X3))
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_add__gr__0,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_le__cube,axiom,
! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_add__right__mono,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X21)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_dvd__power__same,axiom,
! [X20,X22,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
=> c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_add__strict__right__mono,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X21)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X33,X2),c_Groups_Oplus__class_Oplus(X3,X33,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_one__less__power,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_le__imp__power__dvd,axiom,
! [X2,X20,X19,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Rings_Odvd__class_Odvd(X3,c_Power_Opower__class_Opower(X3,X2,X19),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).
fof(fact_zmod__eq__dvd__iff,axiom,
! [X14,X17,X15] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X17) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X14,X17)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X17,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__dvd__iff) ).
fof(fact_add__increasing,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
=> c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X2,X21,X33,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X33)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X2)
=> c_Orderings_Oord__class_Oless__eq(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X21,X33)
=> c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X33)
=> c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> ( c_Orderings_Oord__class_Oless(X3,X21,X33)
=> c_Orderings_Oord__class_Oless(X3,X21,c_Groups_Oplus__class_Oplus(X3,X2,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X19,X20)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19)
=> X19 = X20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_zero__le__power__iff,axiom,
! [X17,X25,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X25,X17))
<=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__iff) ).
fof(fact_real__add__left__mono,axiom,
! [X10,X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X23),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X10,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_zadd__left__mono,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X53),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X6,X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X6,X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_mult__le__mono1,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X53,X7),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X51,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X53),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X7,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X53,X51)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X53,X7),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X51,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X19,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X2,X19),X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X2,X19,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X19,c_Groups_Otimes__class_Otimes(X3,X2,X19)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3)),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_dvd__mod,axiom,
! [X20,X19,X7,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X7,X19)
=> ( c_Rings_Odvd__class_Odvd(X3,X7,X20)
=> c_Rings_Odvd__class_Odvd(X3,X7,c_Divides_Odiv__class_Omod(X3,X19,X20)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mod) ).
fof(fact_dvd__diff,axiom,
! [X10,X22,X23,X3] :
( class_Rings_Ocomm__ring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X23,X22)
=> ( c_Rings_Odvd__class_Odvd(X3,X23,X10)
=> c_Rings_Odvd__class_Odvd(X3,X23,c_Groups_Ominus__class_Ominus(X3,X22,X10)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_dvd__mult__cancel2,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X18),X18)
<=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).
fof(fact_dvd__mult__cancel1,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17),X18)
<=> X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_div__nonpos__pos__le0,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).
fof(fact_div__nonneg__neg__le0,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_real__mult__order,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X23)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X22)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_eq__diff__iff,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X17)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X5) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X5)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_int__div__less__self,axiom,
! [X7,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X7)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X23,X7),X23) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__div__less__self) ).
fof(fact_diff__less,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,X25,X25))
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless__eq(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X25,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,X25,X25),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless(X3,X25,c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X27,X28,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X28) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oab__semigroup__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X33) = c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X21,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_power__commutes,axiom,
! [X20,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X2,X20),X2) = c_Groups_Otimes__class_Otimes(X3,X2,c_Power_Opower__class_Opower(X3,X2,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Oab__semigroup__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33) = c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X27,X28,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X28),X27) = c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X28,X27)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X34,X33,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X33),X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X26,X27,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Otimes__class_Otimes(X3,X29,X27),X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X34,X33,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oplus__class_Oplus(X3,X33,X34)) = c_Groups_Oplus__class_Oplus(X3,X33,c_Groups_Oplus__class_Oplus(X3,X2,X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X26,X27,X29,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X29,c_Groups_Otimes__class_Otimes(X3,X27,X26)) = c_Groups_Otimes__class_Otimes(X3,X27,c_Groups_Otimes__class_Otimes(X3,X29,X26)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_nat__numeral__1__eq__1,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).
fof(fact_one__is__num__one,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(fact_Numeral1__eq1__nat,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(fact_power__mult,axiom,
! [X20,X19,X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)) = c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X2,X19),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X35,X38,X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,c_Power_Opower__class_Opower(X3,X23,X38),X35) = c_Power_Opower__class_Opower(X3,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X38,X35)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X24,X25,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X24,X25,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X25,X24)
<=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ominus__class_Ominus(X3,X25,X24),c_Groups_Ozero__class_Ozero(X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_zdvd__zmod,axiom,
! [X20,X19,X75] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X19)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,X20)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,X75,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__zmod) ).
fof(fact_dvd__diff__nat,axiom,
! [X20,X19,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X19)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X41,X42,X24,X25,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X25,X24)
<=> c_Orderings_Oord__class_Oless__eq(X3,X42,X41) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X41,X42,X24,X25,X3] :
( class_Groups_Oordered__ab__group__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
=> ( c_Orderings_Oord__class_Oless(X3,X25,X24)
<=> c_Orderings_Oord__class_Oless(X3,X42,X41) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_dvd__mult__left,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
=> c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvd__mult__right,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X33)
=> c_Rings_Odvd__class_Odvd(X3,X21,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_diff__cancel,axiom,
! [X20,X19,X7] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X19),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X20,X7,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X7),X51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X7,X51,X53] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,X51),X7) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X11,X12,X13] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,X12),X11) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X13,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X7,X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zpower__zpower,axiom,
! [X10,X22,X23] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X22),X10) = c_Power_Opower__class_Opower(tc_Int_Oint,X23,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X22,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_real__mult__assoc,axiom,
! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X13,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X12,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_zmult__assoc,axiom,
! [X11,X12,X13] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,X12),X11) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X13,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X12,X11)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X7,X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20),X7) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X10,X22,X23] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X10)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X46,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46)
| X16 = X46 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X17,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
<=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X17,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X17))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_add1__zle__eq,axiom,
! [X46,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)),X46)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X46,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X46,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X46,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_mod__mod__cancel,axiom,
! [X2,X21,X33,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X33,X21)
=> c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X33) = c_Divides_Odiv__class_Omod(X3,X2,X33) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).
fof(fact_real__le__eq__diff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_less__bin__lemma,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5,X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zero__less__diff,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X20,X19,X6,X7] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X7,X6)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__leD1,axiom,
! [X20,X7,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X20,X7,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_dvd__reduce,axiom,
! [X17,X5] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X5,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__reduce) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X14,X15,X3] :
( class_Groups_Oordered__comm__monoid__add(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X14)
=> ( c_Groups_Oplus__class_Oplus(X3,X15,X14) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X3)
& X14 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
! [X14,X15,X3] :
( ( class_Divides_Osemiring__div(X3)
& class_Int_Onumber(X3) )
=> ( c_Rings_Odvd__class_Odvd(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Divides_Odiv__class_Omod(X3,c_Int_Onumber__class_Onumber__of(X3,X14),c_Int_Onumber__class_Onumber__of(X3,X15)) = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).
fof(fact_le__mod__geq,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__mod__geq) ).
fof(fact_less__nat__number__of,axiom,
! [X60,X61] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X60) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X61,X60) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_power__inject__exp,axiom,
! [X17,X18,X25,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X25)
=> ( c_Power_Opower__class_Opower(X3,X25,X18) = c_Power_Opower__class_Opower(X3,X25,X17)
<=> X18 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_one__le__power,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [X20,X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_odd__nonzero,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_zdvd__iff__zmod__eq__0__number__of,axiom,
! [X14,X15] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14))
<=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X15)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
fof(fact_dvd__power,axiom,
! [X23,X20,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
| X23 = c_Groups_Oone__class_Oone(X3) )
=> c_Rings_Odvd__class_Odvd(X3,X23,c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__power) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X17,X18,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
<=> X18 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_dvd__mult__div__cancel,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Divides_Odiv__class_Odiv(X3,X21,X2)) = X21 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).
fof(fact_dvd__mult2,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__mult,axiom,
! [X21,X33,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X33)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X33)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__mult) ).
fof(fact_le__imp__0__less,axiom,
! [X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_neg__mod__conj,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__sign) ).
fof(fact_pos__mod__conj,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__sign,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X20,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X19,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X19,X19) = c_Groups_Otimes__class_Otimes(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3)),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X10,X8] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oone__class_Oone(tc_Int_Oint)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [X7,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X7),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_mod__le__divisor,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
fof(fact_pos__mod__bound,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_mod__less__divisor,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
fof(fact_neg__mod__bound,axiom,
! [X2,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X20,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X20)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X53)) = X53 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_less__imp__diff__less,axiom,
! [X20,X7,X51] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X51,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X51,X20),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_trans__le__add1,axiom,
! [X19,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_trans__le__add2,axiom,
! [X19,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_trans__less__add1,axiom,
! [X19,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [X19,X51,X53] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,X51)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X53,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X51)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_even__power__nat,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X14))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__power__nat) ).
fof(fact_le__number__of,axiom,
! [X14,X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).
fof(fact_less__number__of,axiom,
! [X14,X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).
fof(fact_dvd__trans,axiom,
! [X33,X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> ( c_Rings_Odvd__class_Odvd(X3,X21,X33)
=> c_Rings_Odvd__class_Odvd(X3,X2,X33) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_add__number__of__eq,axiom,
! [X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_arith__simps_I32_J,axiom,
! [X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) = c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_number__of__diff,axiom,
! [X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X9,X8)) = c_Groups_Ominus__class_Ominus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).
fof(fact_number__of__add,axiom,
! [X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)) = c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_number__of__mult,axiom,
! [X8,X9,X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)) = c_Groups_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X3,X9),c_Int_Onumber__class_Onumber__of(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).
fof(fact_dvd__pos__nat,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).
fof(fact_zdiv__eq__0__iff,axiom,
! [X5,X66] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X66,X5) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X66)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X66,X5) )
| ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X66) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(fact_div__pos__pos__trivial,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).
fof(fact_div__neg__neg__trivial,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X21)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [X21,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X2)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21) = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_zdvd__imp__le,axiom,
! [X20,X10] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X10,X20)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_dvd__imp__le,axiom,
! [X20,X7] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X7,X20)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X5,X65,X66] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X66,X65)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X65,X66) = X5
<=> X65 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X66) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_mod__mod__trivial,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mod__add__self1,axiom,
! [X2,X21,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X21,X2),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = c_Divides_Odiv__class_Omod(X3,X2,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_real__le__trans,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X51)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X51,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_zle__trans,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X51)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X51,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X53,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X7,X51,X53] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X51)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X51,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X53,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_dvd_Oorder__trans,axiom,
! [X10,X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_zmod__minus1,axiom,
! [X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X21) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1) ).
fof(fact_even__add,axiom,
! [X17,X18] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
<=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__add) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [X8,X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [X8,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_even__product,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X15,X14))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__product) ).
fof(fact_even__product__nat,axiom,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__product__nat) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_less__number__of__int__code,axiom,
! [X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_le__special_I1_J,axiom,
! [X14,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).
fof(fact_less__special_I1_J,axiom,
! [X14,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(X3,X14))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).
fof(fact_le__special_I3_J,axiom,
! [X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_less__special_I3_J,axiom,
! [X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Rings_Olinordered__idom(X3) )
=> ( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X15),c_Groups_Ozero__class_Ozero(X3))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_zero__le__even__power,axiom,
! [X23,X20,X3] :
( ( class_Groups_Omonoid__mult(X3)
& class_Rings_Olinordered__ring(X3) )
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X23,X20)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power) ).
fof(fact_zero__less__two,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oplus__class_Oplus(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Oone__class_Oone(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_even__power,axiom,
! [X17,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X15,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__power) ).
fof(fact_nat__less__cases,axiom,
! [X55,X17,X18] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
=> hBOOL(hAPP(hAPP(X55,X17),X18)) )
=> ( ( X18 = X17
=> hBOOL(hAPP(hAPP(X55,X17),X18)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
=> hBOOL(hAPP(hAPP(X55,X17),X18)) )
=> hBOOL(hAPP(hAPP(X55,X17),X18)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X41,X42,X24,X25,X3] :
( class_Groups_Oab__group__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ominus__class_Ominus(X3,X42,X41)
=> ( X25 = X24
<=> X42 = X41 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_less__add__one,axiom,
! [X2,X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Oone__class_Oone(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_power__eq__0__iff__number__of,axiom,
! [X16,X25,X3] :
( ( class_Power_Opower(X3)
& class_Rings_Omult__zero(X3)
& class_Rings_Ono__zero__divisors(X3)
& class_Rings_Ozero__neq__one(X3) )
=> ( c_Power_Opower__class_Opower(X3,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
& c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff__number__of) ).
fof(fact_add__right__imp__eq,axiom,
! [X33,X2,X21,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X21,X2) = c_Groups_Oplus__class_Oplus(X3,X33,X2)
=> X21 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X42,X25,X24,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X24,X25) = c_Groups_Oplus__class_Oplus(X3,X42,X25)
<=> X24 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Ocancel__ab__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
=> X21 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X33,X21,X2,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X2,X21) = c_Groups_Oplus__class_Oplus(X3,X2,X33)
=> X21 = X33 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X42,X24,X25,X3] :
( class_Groups_Ocancel__semigroup__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X25,X24) = c_Groups_Oplus__class_Oplus(X3,X25,X42)
<=> X24 = X42 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_diffs0__imp__equal,axiom,
! [X20,X19] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_less__0__number__of,axiom,
! [X61] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X61) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(fact_zero__le__square,axiom,
! [X2,X3] :
( class_Rings_Olinordered__ring(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Otimes__class_Otimes(X3,X2,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_real__mult__right__cancel,axiom,
! [X24,X25,X42] :
( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X25,X42) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X24,X42)
<=> X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_mult__cancel2,axiom,
! [X17,X5,X18] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X5) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X5)
<=> ( X18 = X17
| X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__left__cancel,axiom,
! [X24,X25,X42] :
( X42 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X25) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X42,X24)
<=> X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X17,X18,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
<=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X18 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X17,X18,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X18) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X17)
<=> ( X18 = X17
| X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mod__div__trivial,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Odiv(X3,c_Divides_Odiv__class_Omod(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__div__trivial) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X2,X21,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X21,X2),X21) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Otimes__class_Otimes(X3,X2,X21),X21) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_real__le__antisym,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10)
=> X10 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_zle__antisym,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10)
=> X10 = X8 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19)
=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_dvd_Oantisym,axiom,
! [X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23)
=> X23 = X22 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_dvd__antisym,axiom,
! [X20,X19] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X19,X20)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19)
=> X19 = X20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [X15,X14] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Oeq__iff,axiom,
! [X14,X15] :
( X15 = X14
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).
fof(fact_add__diff__cancel,axiom,
! [X21,X2,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ominus__class_Ominus(X3,c_Groups_Oplus__class_Oplus(X3,X2,X21),X21) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X21,X2,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ominus__class_Ominus(X3,X2,X21),X21) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_dvd__triv__left,axiom,
! [X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X2,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__triv__right,axiom,
! [X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Otimes__class_Otimes(X3,X21,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_nat__add__right__cancel,axiom,
! [X17,X5,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X5)
<=> X18 = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X17,X18,X5] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X17)
<=> X18 = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X41,X18] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X41,X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_mod__eq__0__iff,axiom,
! [X41,X18] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X18,X41) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ? [X76] : X18 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
fof(fact_le__iff__add,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
<=> ? [X59] : X17 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_zmod__zdiv__trivial,axiom,
! [X21,X2] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X21),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(fact_diff__add__0,axiom,
! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(fact_diff__add__inverse,axiom,
! [X19,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),X20) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X20,X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20),X20) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_even__plus__even,axiom,
! [X22,X23] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__plus__even) ).
fof(fact_mod__less__eq__dividend,axiom,
! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(fact_diff__le__self,axiom,
! [X20,X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X19,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__square,axiom,
! [X19] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X19)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_dvd__eq__mod__eq__0,axiom,
! [X24,X25,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X25,X24)
<=> c_Divides_Odiv__class_Omod(X3,X24,X25) = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).
fof(fact_dvd__imp__mod__0,axiom,
! [X21,X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,X2,X21)
=> c_Divides_Odiv__class_Omod(X3,X21,X2) = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).
fof(fact_dvdI,axiom,
! [X7,X21,X2,X3] :
( class_Rings_Odvd(X3)
=> ( X2 = c_Groups_Otimes__class_Otimes(X3,X21,X7)
=> c_Rings_Odvd__class_Odvd(X3,X21,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvdI) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X46] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X46)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X46) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_diff__is__0__eq,axiom,
! [X17,X18] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_real__less__def,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
& X15 != X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_less__eq__real__def,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
| X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_zless__le,axiom,
! [X16,X46] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X46,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X46,X16)
& X46 != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_le__neq__implies__less,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> ( X19 != X20
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
| X18 = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
& X18 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_mod__less,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X20,X19] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
| X19 = X20 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__imp__le__nat,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_even__times__anything,axiom,
! [X22,X23] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__times__anything) ).
fof(fact_anything__times__even,axiom,
! [X23,X22] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_anything__times__even) ).
fof(fact_power__eq__0__iff,axiom,
! [X17,X25,X3] :
( ( class_Power_Opower(X3)
& class_Rings_Omult__zero(X3)
& class_Rings_Ono__zero__divisors(X3)
& class_Rings_Ozero__neq__one(X3) )
=> ( c_Power_Opower__class_Opower(X3,X25,X17) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
& X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_power__0__left__number__of,axiom,
! [X8,X3] :
( ( class_Power_Opower(X3)
& class_Rings_Osemiring__0(X3) )
=> ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Oone__class_Oone(X3) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X8)) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X33,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,X33) = c_Groups_Oplus__class_Oplus(X3,X33,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X21,X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Otimes__class_Otimes(X3,X21,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_divisors__zero,axiom,
! [X21,X2,X3] :
( class_Rings_Ono__zero__divisors(X3)
=> ( c_Groups_Otimes__class_Otimes(X3,X2,X21) = c_Groups_Ozero__class_Ozero(X3)
=> ( X2 = c_Groups_Ozero__class_Ozero(X3)
| X21 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X21,X2,X3] :
( class_Rings_Ono__zero__divisors(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> ( X21 != c_Groups_Ozero__class_Ozero(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,X21) != c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_mult__eq__0__iff,axiom,
! [X24,X25,X3] :
( class_Rings_Oring__no__zero__divisors(X3)
=> ( c_Groups_Otimes__class_Otimes(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
<=> ( X25 = c_Groups_Ozero__class_Ozero(X3)
| X24 = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_neg__one__even__power,axiom,
! [X23,X3] :
( class_Int_Onumber__ring(X3)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__even__power) ).
fof(fact_zless__linear,axiom,
! [X22,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X23,X22)
| X23 = X22
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X17,X18] :
( X18 != X17
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_dvd__0__left,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> ( c_Rings_Odvd__class_Odvd(X3,c_Groups_Ozero__class_Ozero(X3),X2)
=> X2 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__left) ).
fof(fact_real__le__linear,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X10,X8)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_zle__linear,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X10,X8)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zadd__commute,axiom,
! [X8,X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X20,X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_real__mult__commute,axiom,
! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X8) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X8,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_zmult__commute,axiom,
! [X8,X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,X8) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X20,X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Groups_Oplus__class_Oplus(X3,X25,X25) = c_Groups_Ozero__class_Ozero(X3)
<=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_field__power__not__zero,axiom,
! [X20,X2,X3] :
( class_Rings_Oring__1__no__zero__divisors(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Power_Opower__class_Opower(X3,X2,X20) != c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_double__zero__sym,axiom,
! [X25,X3] :
( class_Groups_Olinordered__ab__group__add(X3)
=> ( c_Groups_Ozero__class_Ozero(X3) = c_Groups_Oplus__class_Oplus(X3,X25,X25)
<=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_zmult__eq__1__iff,axiom,
! [X17,X18] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X18,X17) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( X18 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X17 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| ( X18 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& X17 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [X20,X19] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X19,X20) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( X19 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X19 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
fof(fact_right__minus__eq,axiom,
! [X24,X25,X3] :
( class_Groups_Ogroup__add(X3)
=> ( c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3)
<=> X25 = X24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X24,X25,X3] :
( class_Groups_Oab__group__add(X3)
=> ( X25 = X24
<=> c_Groups_Ominus__class_Ominus(X3,X25,X24) = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_add__0__iff,axiom,
! [X25,X24,X3] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3)
=> ( X24 = c_Groups_Oplus__class_Oplus(X3,X24,X25)
<=> X25 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_eq__number__of__0,axiom,
! [X61] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [X61] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_mult__is__0,axiom,
! [X17,X18] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_neq0__conv,axiom,
! [X17] :
( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X20,X19] :
( X19 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,X20)
=> ( X20 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_nat__dvd__1__iff__1,axiom,
! [X18] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_le__0__eq,axiom,
! [X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X17,X18] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_add__is__0,axiom,
! [X17,X18] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X17,X18] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X18,X17)
<=> ( X18 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X17 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_gr__implies__not0,axiom,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_add__eq__self__zero,axiom,
! [X20,X19] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X20) = X19
=> X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_less__not__refl3,axiom,
! [X63,X64] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X64,X63)
=> X64 != X63 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X19,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
=> X19 != X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_bin__less__0__simps_I1_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(fact_add__numeral__0,axiom,
! [X2,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__numeral__0__right,axiom,
! [X2,X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_power__0__left,axiom,
! [X20,X3] :
( ( class_Power_Opower(X3)
& class_Rings_Osemiring__0(X3) )
=> ( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Oone__class_Oone(X3) )
& ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X3,c_Groups_Ozero__class_Ozero(X3),X20) = c_Groups_Ozero__class_Ozero(X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_rel__simps_I20_J,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
fof(fact_rel__simps_I7_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).
fof(fact_rel__simps_I3_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
fof(fact_rel__simps_I2_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).
fof(fact_zmod__minus1__right,axiom,
! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_zero__le__one,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Groups_Oone__class_Oone(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_mod__0,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_power__one,axiom,
! [X20,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,c_Groups_Oone__class_Oone(X3),X20) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult__left_Ozero,axiom,
! [X22,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X22) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_mult_Ozero__left,axiom,
! [X21,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X21) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult__zero__left,axiom,
! [X2,X3] :
( class_Rings_Omult__zero(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Ozero__class_Ozero(X3),X2) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mod__by__1,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Oone__class_Oone(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_mult__right_Ozero,axiom,
! [X23,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X23,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_mult_Ozero__right,axiom,
! [X2,X3] :
( class_RealVector_Oreal__normed__algebra(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult__zero__right,axiom,
! [X2,X3] :
( class_Rings_Omult__zero(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_div__self,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> ( X2 != c_Groups_Ozero__class_Ozero(X3)
=> c_Divides_Odiv__class_Odiv(X3,X2,X2) = c_Groups_Oone__class_Oone(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__self) ).
fof(fact_power__0,axiom,
! [X2,X3] :
( class_Power_Opower(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_add__0,axiom,
! [X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X2,X3] :
( class_Groups_Omonoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,c_Groups_Ozero__class_Ozero(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_mult__1,axiom,
! [X2,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,c_Groups_Oone__class_Oone(X3),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_div__by__1,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Odiv(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(fact_mod__by__0,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_diff__0__right,axiom,
! [X2,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ominus__class_Ominus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X2,X3] :
( class_Groups_Ocomm__monoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X2,X3] :
( class_Groups_Omonoid__add(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Oplus__class_Oplus(X3,X2,c_Groups_Ozero__class_Ozero(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X2,X3] :
( class_Groups_Ocomm__monoid__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Groups_Otimes__class_Otimes(X3,X2,c_Groups_Oone__class_Oone(X3)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_one__dvd,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,c_Groups_Oone__class_Oone(X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__0__right,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X2,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_power__one__right,axiom,
! [X2,X3] :
( class_Groups_Omonoid__mult(X3)
=> c_Power_Opower__class_Opower(X3,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X23,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Power_Opower__class_Opower(X3,X23,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_mod__self,axiom,
! [X2,X3] :
( class_Divides_Osemiring__div(X3)
=> c_Divides_Odiv__class_Omod(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_diff__self,axiom,
! [X2,X3] :
( class_Groups_Ogroup__add(X3)
=> c_Groups_Ominus__class_Ominus(X3,X2,X2) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_dvd__refl,axiom,
! [X2,X3] :
( class_Rings_Ocomm__semiring__1(X3)
=> c_Rings_Odvd__class_Odvd(X3,X2,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_One__nat__def,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(fact_eq__number__of,axiom,
! [X14,X15,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Int_Oring__char__0(X3) )
=> ( c_Int_Onumber__class_Onumber__of(X3,X15) = c_Int_Onumber__class_Onumber__of(X3,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(fact_gr0I,axiom,
! [X20] :
( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_zdiv__self,axiom,
! [X2] :
( X2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(fact_zmod__zero,axiom,
! [X21] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_diff__0__eq__0,axiom,
! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_mult__0,axiom,
! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_DIVISION__BY__ZERO,axiom,
! [X2] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(fact_mult__0__right,axiom,
! [X19] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zadd__0,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_real__mult__1,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zmult__1,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X19] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X20] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_eq__imp__le,axiom,
! [X20,X19] :
( X19 = X20
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_dvd_Oeq__refl,axiom,
! [X22,X23] :
( X23 = X22
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_zmod__self,axiom,
! [X2] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_diff__self__eq__0,axiom,
! [X19] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_real__le__refl,axiom,
! [X8] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_zle__refl,axiom,
! [X8] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_dvd_Oorder__refl,axiom,
! [X23] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_add__Pls,axiom,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(fact_diff__bin__simps_I1_J,axiom,
! [X7] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X7,c_Int_OPls) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(fact_add__Pls__right,axiom,
! [X7] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X7,c_Int_OPls) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_mult__Pls,axiom,
! [X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X8) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(fact_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(fact_iszero__Numeral0,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
fof(fact_iszero__def,axiom,
! [X46,X3] :
( class_Rings_Osemiring__1(X3)
=> ( c_Int_Oiszero(X3,X46)
<=> X46 = c_Groups_Ozero__class_Ozero(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).
fof(fact_iszero__0,axiom,
! [X3] :
( class_Rings_Osemiring__1(X3)
=> c_Int_Oiszero(X3,c_Groups_Ozero__class_Ozero(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(fact_odd__one__int,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__one__int) ).
fof(fact_odd__1__nat,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__1__nat) ).
fof(fact_number__of__Pls,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X3] :
( class_Int_Onumber__ring(X3)
=> c_Groups_Ozero__class_Ozero(X3) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_one__neq__zero,axiom,
! [X3] :
( class_Rings_Ozero__neq__one(X3)
=> c_Groups_Oone__class_Oone(X3) != c_Groups_Ozero__class_Ozero(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_zero__neq__one,axiom,
! [X3] :
( class_Rings_Ozero__neq__one(X3)
=> c_Groups_Ozero__class_Ozero(X3) != c_Groups_Oone__class_Oone(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_number__of__is__id,axiom,
! [X7] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X7) = X7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(conj_1,conjecture,
v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_number__of2,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_bin__less__0__simps_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(fact_rel__simps_I24_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).
fof(fact_rel__simps_I23_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
fof(fact_rel__simps_I19_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).
fof(fact_rel__simps_I6_J,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
fof(fact_eq__number__of__Pls__Min,axiom,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(fact_even__zero__int,axiom,
c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__zero__int) ).
fof(fact_even__zero__nat,axiom,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__zero__nat) ).
fof(fact_nat__number__of__Pls,axiom,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).
fof(fact_zero__is__num__zero,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(fact_semiring__norm_I113_J,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(fact_e,axiom,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_assms_I2_J,axiom,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I2_J) ).
fof(fact_n,axiom,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n) ).
fof(arity_Int__Oint__Divides_Oring__div,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
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/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(arity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).
fof(arity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(arity_Nat__Onat__Int_Onumber,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(arity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(arity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(fact_rel__simps_I37_J,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
fof(fact_rel__simps_I40_J,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(i_0_1157,plain,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Power_Opower__class_Opower(X3,X23,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3,X22,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(i_0_1158,plain,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
<=> ? [X31] : X15 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X31),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(fof_simplification,[status(thm)],[fact_odd__equiv__def]) ).
fof(i_0_1159,plain,
! [X17] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
<=> ? [X1] : X17 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) ),
inference(fof_simplification,[status(thm)],[fact_odd__Suc__mult__two__ex]) ).
fof(i_0_1160,plain,
! [X2,X3] :
( class_Rings_Olinordered__idom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).
fof(i_0_1161,plain,
! [X9,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X9)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X8))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).
fof(i_0_1162,plain,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X31] : X15 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31)) ),
inference(fof_simplification,[status(thm)],[fact_odd__nat__equiv__def2]) ).
fof(i_0_1163,plain,
! [X8,X3] :
( ( class_Int_Onumber__ring(X3)
& class_Int_Oring__char__0(X3) )
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(X8))) ),
inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).
fof(i_0_1164,plain,
! [X3] :
( class_Int_Onumber__ring(X3)
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OBit1(c_Int_OPls))) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).
fof(i_0_1165,plain,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(fof_simplification,[status(thm)],[fact_odd__nat__equiv__def]) ).
fof(i_0_1166,plain,
! [X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X23,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(fof_simplification,[status(thm)],[fact_odd__nat__mod__two__eq__one]) ).
fof(i_0_1167,plain,
! [X5,X17,X55] :
( epred1_3(X55,X17,X5)
<=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X55,X17)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5)
=> ! [X77,X58] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X58)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X58,X5)
& X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X55,X58)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X77,X58] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X58)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X58,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& X17 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X55,X58)) ) ) ) ),
introduced(definition) ).
fof(i_0_1168,plain,
! [X20,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> X19 = c_Nat_OSuc(X20) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_1169,plain,
! [X17,X18] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X17),X18) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_1170,plain,
! [X17,X18] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1171,plain,
! [X18,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> X17 = X18 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1172,plain,
! [X19,X20] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Nat_OSuc(X19))
=> X19 = X20 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1173,plain,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,c_Nat_OSuc(X20))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> X19 = X20 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1174,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X20),X20),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_1175,plain,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X15))
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15) ),
inference(fof_simplification,[status(thm)],[fact_even__Suc]) ).
fof(i_0_1176,plain,
! [X3566,X3567,X3568] :
( ~ class_Int_Onumber__ring(X3568)
| c_Power_Opower__class_Opower(X3568,c_Groups_Ominus__class_Ominus(X3568,X3567,X3566),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X3568,c_Groups_Oplus__class_Oplus(X3568,c_Power_Opower__class_Opower(X3568,X3567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3568,X3566,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3568,c_Groups_Otimes__class_Otimes(X3568,c_Int_Onumber__class_Onumber__of(X3568,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3567),X3566)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).
fof(i_0_1177,plain,
! [X3292] : c_Int_OBit0(X3292) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3292,X3292),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(i_0_1178,plain,
! [X4319] : c_Int_OBit1(X4319) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4319),X4319),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(i_0_1179,plain,
! [X3187,X3188,X3189] :
( ~ class_Int_Onumber__ring(X3189)
| c_Power_Opower__class_Opower(X3189,c_Groups_Oplus__class_Oplus(X3189,X3188,X3187),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3189,c_Groups_Oplus__class_Oplus(X3189,c_Power_Opower__class_Opower(X3189,X3188,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3189,X3187,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X3189,c_Groups_Otimes__class_Otimes(X3189,c_Int_Onumber__class_Onumber__of(X3189,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3188),X3187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).
fof(i_0_1180,plain,
! [X3557,X3558] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3558,X3557),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3558,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3557,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3558),X3557)),
inference(variable_rename,[status(thm)],[fact_real__sum__squared__expand]) ).
fof(i_0_1181,plain,
! [X3561,X3562,X3563] :
( ~ class_Rings_Olinordered__idom(X3563)
| ~ c_Orderings_Oord__class_Oless__eq(X3563,c_Groups_Ozero__class_Ozero(X3563),c_Power_Opower__class_Opower(X3563,X3562,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3561))))
| c_Orderings_Oord__class_Oless__eq(X3563,c_Groups_Ozero__class_Ozero(X3563),X3562) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).
fof(i_0_1182,plain,
! [X4667] : c_Nat_OSuc(X4667) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4667,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1183,plain,
! [X3061,X3062,X3063] :
( ( ~ c_Orderings_Oord__class_Oless(X3063,c_Groups_Ozero__class_Ozero(X3063),c_Groups_Oplus__class_Oplus(X3063,c_Power_Opower__class_Opower(X3063,X3062,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3063,X3061,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X3062 != c_Groups_Ozero__class_Ozero(X3063)
| X3061 != c_Groups_Ozero__class_Ozero(X3063)
| ~ class_Rings_Olinordered__idom(X3063) )
& ( X3062 = c_Groups_Ozero__class_Ozero(X3063)
| c_Orderings_Oord__class_Oless(X3063,c_Groups_Ozero__class_Ozero(X3063),c_Groups_Oplus__class_Oplus(X3063,c_Power_Opower__class_Opower(X3063,X3062,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3063,X3061,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X3063) )
& ( X3061 = c_Groups_Ozero__class_Ozero(X3063)
| c_Orderings_Oord__class_Oless(X3063,c_Groups_Ozero__class_Ozero(X3063),c_Groups_Oplus__class_Oplus(X3063,c_Power_Opower__class_Opower(X3063,X3062,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3063,X3061,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X3063) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).
fof(i_0_1184,plain,
! [X4583,X4584,X4585] :
( ( X4584 = c_Groups_Ozero__class_Ozero(X4585)
| ~ c_Orderings_Oord__class_Oless__eq(X4585,c_Groups_Oplus__class_Oplus(X4585,c_Power_Opower__class_Opower(X4585,X4584,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4585,X4583,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4585))
| ~ class_Rings_Olinordered__idom(X4585) )
& ( X4583 = c_Groups_Ozero__class_Ozero(X4585)
| ~ c_Orderings_Oord__class_Oless__eq(X4585,c_Groups_Oplus__class_Oplus(X4585,c_Power_Opower__class_Opower(X4585,X4584,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4585,X4583,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4585))
| ~ class_Rings_Olinordered__idom(X4585) )
& ( X4584 != c_Groups_Ozero__class_Ozero(X4585)
| X4583 != c_Groups_Ozero__class_Ozero(X4585)
| c_Orderings_Oord__class_Oless__eq(X4585,c_Groups_Oplus__class_Oplus(X4585,c_Power_Opower__class_Opower(X4585,X4584,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4585,X4583,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X4585))
| ~ class_Rings_Olinordered__idom(X4585) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).
fof(i_0_1185,plain,
! [X3058,X3059,X3060] :
( ~ class_Rings_Olinordered__idom(X3060)
| ~ c_Orderings_Oord__class_Oless(X3060,c_Groups_Oplus__class_Oplus(X3060,c_Power_Opower__class_Opower(X3060,X3059,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3060,X3058,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3060)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1157])]) ).
fof(i_0_1186,plain,
! [X3231] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3231,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3231),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_four__x__squared]) ).
fof(i_0_1187,plain,
! [X4745,X4746] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4746,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4745)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4746)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4745,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4746)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zmod__mult__2])]) ).
fof(i_0_1188,plain,
! [X4962,X4963] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4963)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4962)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4963)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4962,X4963))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).
fof(i_0_1189,plain,
! [X3072,X3073,X3074] :
( ~ class_Rings_Olinordered__idom(X3074)
| ~ c_Orderings_Oord__class_Oless(X3074,X3073,c_Groups_Ozero__class_Ozero(X3074))
| c_Orderings_Oord__class_Oless(X3074,c_Power_Opower__class_Opower(X3074,X3073,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3072))),c_Groups_Ozero__class_Ozero(X3074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).
fof(i_0_1190,plain,
! [X4580,X4581,X4582] :
( ~ class_Rings_Olinordered__idom(X4582)
| c_Orderings_Oord__class_Oless__eq(X4582,c_Groups_Ozero__class_Ozero(X4582),c_Groups_Oplus__class_Oplus(X4582,c_Power_Opower__class_Opower(X4582,X4581,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4582,X4580,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__ge__zero])]) ).
fof(i_0_1191,plain,
! [X4589,X4590,X4591] :
( ~ class_Rings_Olinordered__idom(X4591)
| ~ c_Orderings_Oord__class_Oless__eq(X4591,c_Power_Opower__class_Opower(X4591,X4590,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4589)),c_Groups_Ozero__class_Ozero(X4591))
| X4590 = c_Groups_Ozero__class_Ozero(X4591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power__le__0__imp__0])]) ).
fof(i_0_1192,plain,
! [X4571,X4572,X4573] :
( ~ class_Rings_Olinordered__semidom(X4573)
| ~ c_Orderings_Oord__class_Oless__eq(X4573,c_Power_Opower__class_Opower(X4573,X4572,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4573,X4571,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X4573,c_Groups_Ozero__class_Ozero(X4573),X4571)
| c_Orderings_Oord__class_Oless__eq(X4573,X4572,X4571) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).
fof(i_0_1193,plain,
! [X4577,X4578,X4579] :
( ~ class_Rings_Olinordered__semidom(X4579)
| ~ c_Orderings_Oord__class_Oless(X4579,c_Power_Opower__class_Opower(X4579,X4578,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X4579,X4577,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X4579,c_Groups_Ozero__class_Ozero(X4579),X4577)
| c_Orderings_Oord__class_Oless(X4579,X4578,X4577) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).
fof(i_0_1194,plain,
! [X3180,X3181,X3182] :
( ( X3181 = c_Groups_Ozero__class_Ozero(X3182)
| c_Groups_Oplus__class_Oplus(X3182,c_Power_Opower__class_Opower(X3182,X3181,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3182,X3180,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X3182)
| ~ class_Rings_Olinordered__idom(X3182) )
& ( X3180 = c_Groups_Ozero__class_Ozero(X3182)
| c_Groups_Oplus__class_Oplus(X3182,c_Power_Opower__class_Opower(X3182,X3181,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3182,X3180,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X3182)
| ~ class_Rings_Olinordered__idom(X3182) )
& ( X3181 != c_Groups_Ozero__class_Ozero(X3182)
| X3180 != c_Groups_Ozero__class_Ozero(X3182)
| c_Groups_Oplus__class_Oplus(X3182,c_Power_Opower__class_Opower(X3182,X3181,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3182,X3180,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X3182)
| ~ class_Rings_Olinordered__idom(X3182) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).
fof(i_0_1195,plain,
! [X3559,X3560] :
( ( X3560 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3560,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3559,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3559 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3560,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3559,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3560 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3559 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3560,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3559,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__sum__zero__iff])])]) ).
fof(i_0_1196,plain,
! [X3190,X3191,X3192] :
( ~ class_Groups_Omonoid__mult(X3192)
| c_Power_Opower__class_Opower(X3192,X3191,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3190))) = c_Groups_Otimes__class_Otimes(X3192,X3191,c_Power_Opower__class_Opower(X3192,c_Power_Opower__class_Opower(X3192,X3191,X3190),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__odd__eq])]) ).
fof(i_0_1197,plain,
! [X4964,X4965] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4965,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4964)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4965)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4964,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4965) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).
fof(i_0_1198,plain,
! [X4966,X4967] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4967)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4966)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4967)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4966,X4967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).
fof(i_0_1199,plain,
! [X3193,X3194,X3195] :
( ~ class_Rings_Ocomm__semiring__1(X3195)
| c_Power_Opower__class_Opower(X3195,X3194,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3193))) = c_Groups_Otimes__class_Otimes(X3195,X3194,c_Groups_Otimes__class_Otimes(X3195,c_Power_Opower__class_Opower(X3195,X3194,X3193),c_Power_Opower__class_Opower(X3195,X3194,X3193))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).
fof(i_0_1200,plain,
! [X3564,X3565] :
( ~ class_Int_Onumber__ring(X3565)
| c_Power_Opower__class_Opower(X3565,c_Int_Onumber__class_Onumber__of(X3565,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3564))) = c_Int_Onumber__class_Onumber__of(X3565,c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).
fof(i_0_1201,plain,
! [X4586,X4587,X4588] :
( ~ class_Rings_Olinordered__idom(X4588)
| c_Orderings_Oord__class_Oless__eq(X4588,c_Groups_Ozero__class_Ozero(X4588),c_Power_Opower__class_Opower(X4588,X4587,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4586))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).
fof(i_0_1202,plain,
! [X4574,X4575,X4576] :
( ~ class_Rings_Olinordered__semidom(X4576)
| c_Power_Opower__class_Opower(X4576,X4575,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X4576,X4574,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(X4576,c_Groups_Ozero__class_Ozero(X4576),X4575)
| ~ c_Orderings_Oord__class_Oless__eq(X4576,c_Groups_Ozero__class_Ozero(X4576),X4574)
| X4575 = X4574 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).
fof(i_0_1203,plain,
! [X3185,X3186] :
( ( ~ c_Orderings_Oord__class_Oless(X3186,c_Groups_Ozero__class_Ozero(X3186),c_Power_Opower__class_Opower(X3186,X3185,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X3185 != c_Groups_Ozero__class_Ozero(X3186)
| ~ class_Rings_Olinordered__idom(X3186) )
& ( X3185 = c_Groups_Ozero__class_Ozero(X3186)
| c_Orderings_Oord__class_Oless(X3186,c_Groups_Ozero__class_Ozero(X3186),c_Power_Opower__class_Opower(X3186,X3185,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X3186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).
fof(i_0_1204,plain,
! [X3569,X3571,X3572] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3569)
| X3569 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk12_1(X3569)),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( X3571 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3572),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3571) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1158])])])])]) ).
fof(i_0_1205,plain,
! [X2687,X2689,X2690] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2687)
| X2687 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk3_1(X2687))) )
& ( X2689 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2690))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2689) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1159])])])])]) ).
fof(i_0_1206,plain,
! [X3183,X3184] :
( ~ class_Rings_Olinordered__idom(X3184)
| ~ c_Orderings_Oord__class_Oless(X3184,c_Power_Opower__class_Opower(X3184,X3183,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1160])]) ).
fof(i_0_1207,plain,
! [X4959] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4959,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4959,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4959,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4959,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq__one__mod__two])]) ).
fof(i_0_1208,plain,
! [X3227,X3228,X3229] :
( ~ class_Groups_Omonoid__mult(X3229)
| c_Power_Opower__class_Opower(X3229,X3228,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3227)) = c_Power_Opower__class_Opower(X3229,c_Power_Opower__class_Opower(X3229,X3228,X3227),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__eq])]) ).
fof(i_0_1209,plain,
! [X4743,X4744] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4744))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X4743)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4744))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4743),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4744))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4744))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X4743)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4744))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4743),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4744))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1161])]) ).
fof(i_0_1210,plain,
! [X2691,X2692,X2693] :
( ~ class_Rings_Ocomm__semiring__1(X2693)
| c_Power_Opower__class_Opower(X2693,X2692,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2691)) = c_Groups_Otimes__class_Otimes(X2693,c_Power_Opower__class_Opower(X2693,X2692,X2691),c_Power_Opower__class_Opower(X2693,X2692,X2691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).
fof(i_0_1211,plain,
! [X4504,X4505] :
( ~ class_Int_Onumber__ring(X4505)
| c_Power_Opower__class_Opower(X4505,c_Int_Onumber__class_Onumber__of(X4505,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4504)) = c_Groups_Oone__class_Oone(X4505) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).
fof(i_0_1212,plain,
! [X4569,X4570] :
( ~ class_Rings_Olinordered__idom(X4570)
| c_Orderings_Oord__class_Oless__eq(X4570,c_Groups_Ozero__class_Ozero(X4570),c_Power_Opower__class_Opower(X4570,X4569,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power2])]) ).
fof(i_0_1213,plain,
! [X4691] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X4691)),
inference(variable_rename,[status(thm)],[fact_two__realpow__ge__one]) ).
fof(i_0_1214,plain,
! [X3057] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X3057))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X3057),
inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(i_0_1215,plain,
! [X3214,X3215] :
( ~ class_Groups_Omonoid__mult(X3215)
| c_Power_Opower__class_Opower(X3215,X3214,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3215,c_Groups_Otimes__class_Otimes(X3215,X3214,X3214),X3214) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).
fof(i_0_1216,plain,
! [X4431] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4431)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4431,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| X4431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4431 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__pos__lt__two__imp__zero__or__one])]) ).
fof(i_0_1217,plain,
! [X3488] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3488,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| X3488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3488 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__2__cases])]) ).
fof(i_0_1218,plain,
! [X3217,X3218] :
( ( c_Power_Opower__class_Opower(X3218,X3217,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X3218)
| X3217 = c_Groups_Ozero__class_Ozero(X3218)
| ~ class_Rings_Oring__1__no__zero__divisors(X3218) )
& ( X3217 != c_Groups_Ozero__class_Ozero(X3218)
| c_Power_Opower__class_Opower(X3218,X3217,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3218)
| ~ class_Rings_Oring__1__no__zero__divisors(X3218) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).
fof(i_0_1219,plain,
! [X4960] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4960)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4960,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4960,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4960) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__def])]) ).
fof(i_0_1220,plain,
! [X2696,X2698,X2699] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2696)
| X2696 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk4_1(X2696)) )
& ( X2698 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2699)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2698) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__equiv__def])])])])]) ).
fof(i_0_1221,plain,
! [X2602,X2604,X2605] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2602)
| X2602 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk2_1(X2602)) )
& ( X2604 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2605)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2604) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__mult__two__ex])])])])]) ).
fof(i_0_1222,plain,
! [X3487] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3487)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3487) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3487)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3487) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__even__iff__2__dvd])]) ).
fof(i_0_1223,plain,
! [X2708] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2708)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2708) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2708)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2708) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__even__iff__2__dvd])]) ).
fof(i_0_1224,hypothesis,
! [X5069] :
( v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X5069)
| v_thesis____ ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])]) ).
fof(i_0_1225,plain,
! [X4934,X4935] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4935)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4934))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4935),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4934))),
inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).
fof(i_0_1226,plain,
! [X3082] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3082) = c_Nat_OSuc(c_Nat_OSuc(X3082)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(i_0_1227,plain,
! [X3081] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3081,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X3081)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(i_0_1228,plain,
! [X2694,X2695] :
( ~ class_Groups_Omonoid__mult(X2695)
| ~ class_Int_Onumber(X2695)
| c_Power_Opower__class_Opower(X2695,c_Int_Onumber__class_Onumber__of(X2695,X2694),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X2695,c_Int_Onumber__class_Onumber__of(X2695,X2694),c_Int_Onumber__class_Onumber__of(X2695,X2694)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).
fof(i_0_1229,plain,
! [X3225,X3226] :
( ~ class_Int_Onumber__ring(X3226)
| c_Groups_Otimes__class_Otimes(X3226,c_Int_Onumber__class_Onumber__of(X3226,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3225) = c_Groups_Oplus__class_Oplus(X3226,X3225,X3225) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).
fof(i_0_1230,plain,
! [X3223,X3224] :
( ~ class_Int_Onumber__ring(X3224)
| c_Groups_Otimes__class_Otimes(X3224,X3223,c_Int_Onumber__class_Onumber__of(X3224,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3224,X3223,X3223) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(i_0_1231,plain,
! [X3219,X3220] :
( ~ class_Groups_Omonoid__mult(X3220)
| c_Power_Opower__class_Opower(X3220,X3219,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X3220,X3219,X3219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).
fof(i_0_1232,plain,
! [X3221,X3222] :
( ~ class_Rings_Ocomm__semiring__1(X3222)
| c_Groups_Otimes__class_Otimes(X3222,X3221,X3221) = c_Power_Opower__class_Opower(X3222,X3221,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J])]) ).
fof(i_0_1233,plain,
! [X2705] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2705) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2705,X2705),
inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).
fof(i_0_1234,plain,
! [X2706] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2706,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2706,X2706),
inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).
fof(i_0_1235,plain,
! [X4565] :
( ~ class_Rings_Osemiring__1(X4565)
| c_Power_Opower__class_Opower(X4565,c_Groups_Oone__class_Oone(X4565),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4565) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).
fof(i_0_1236,plain,
! [X3216] :
( ~ class_Rings_Osemiring__1(X3216)
| c_Power_Opower__class_Opower(X3216,c_Groups_Ozero__class_Ozero(X3216),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X3216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).
fof(i_0_1237,plain,
! [X3230] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X3230),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X3230,
inference(variable_rename,[status(thm)],[fact_csqrt]) ).
fof(i_0_1238,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk1_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact__096EX_Am_O_An_A_061_A2_A_K_Am_096])]) ).
fof(i_0_1239,plain,
! [X4530,X4531,X4532] :
( ~ class_Rings_Ocomm__ring__1(X4532)
| c_Groups_Ominus__class_Ominus(X4532,c_Power_Opower__class_Opower(X4532,X4531,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X4532,X4530,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X4532,c_Groups_Ominus__class_Ominus(X4532,X4531,X4530),c_Groups_Oplus__class_Oplus(X4532,X4531,X4530)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__two__diff])]) ).
fof(i_0_1240,plain,
! [X4543,X4544] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X4544)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4543),X4544) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4543,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4544,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__eq__diff__pred])]) ).
fof(i_0_1241,plain,
! [X4556] :
( ~ class_Int_Onumber__ring(X4556)
| c_Groups_Oplus__class_Oplus(X4556,c_Groups_Oone__class_Oone(X4556),c_Groups_Oone__class_Oone(X4556)) = c_Int_Onumber__class_Onumber__of(X4556,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__add__one__is__two])]) ).
fof(i_0_1242,plain,
! [X3201,X3203,X3204] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3201)
| X3201 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk5_1(X3201))) )
& ( X3203 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3204))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3203) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1162])])])])]) ).
fof(i_0_1243,plain,
! [X4452,X4453,X4454,X4455] :
( ~ class_Rings_Olinordered__semidom(X4455)
| ~ c_Orderings_Oord__class_Oless__eq(X4455,c_Power_Opower__class_Opower(X4455,X4454,c_Nat_OSuc(X4453)),c_Power_Opower__class_Opower(X4455,X4452,c_Nat_OSuc(X4453)))
| ~ c_Orderings_Oord__class_Oless__eq(X4455,c_Groups_Ozero__class_Ozero(X4455),X4452)
| c_Orderings_Oord__class_Oless__eq(X4455,X4454,X4452) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
fof(i_0_1244,plain,
! [X3956,X3957] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3957),c_Int_OBit1(X3956))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3957,X3956) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3957,X3956)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3957),c_Int_OBit1(X3956)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).
fof(i_0_1245,plain,
! [X3954,X3955] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3955),c_Int_OBit1(X3954))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3955,X3954) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3955,X3954)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3955),c_Int_OBit1(X3954)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).
fof(i_0_1246,plain,
! [X3011,X3012] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3012),c_Int_OBit1(X3011))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3012,X3011) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3012,X3011)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3012),c_Int_OBit1(X3011)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).
fof(i_0_1247,plain,
! [X3009,X3010] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3010),c_Int_OBit1(X3009))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3010,X3009) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3010,X3009)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3010),c_Int_OBit1(X3009)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).
fof(i_0_1248,plain,
! [X4308,X4309,X4310] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X4310),X4309),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X4310),X4308))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4309,X4308) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4309,X4308)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X4310),X4309),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X4310),X4308)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_1249,plain,
! [X3432,X3433,X3434] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3434),X3433),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3434),X3432))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3433,X3432) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3433,X3432)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3434),X3433),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3434),X3432)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1250,plain,
! [X3209,X3210] :
( ~ class_Int_Onumber__ring(X3210)
| ~ class_Int_Oring__char__0(X3210)
| ~ c_Int_Oiszero(X3210,c_Int_Onumber__class_Onumber__of(X3210,c_Int_OBit1(X3209))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1163])]) ).
fof(i_0_1251,plain,
! [X2707] :
( ~ class_Int_Onumber__ring(X2707)
| ~ c_Int_Oiszero(X2707,c_Int_Onumber__class_Onumber__of(X2707,c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1164])]) ).
fof(i_0_1252,plain,
! [X4190,X4191] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X4191),c_Int_OBit1(X4190)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4191,X4190)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).
fof(i_0_1253,plain,
! [X4188,X4189] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X4189),c_Int_OBit0(X4188)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4189,X4188)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).
fof(i_0_1254,plain,
! [X3380,X3381] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X3381),c_Int_OBit0(X3380)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3381,X3380)),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(i_0_1255,plain,
! [X3382,X3383] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X3383),c_Int_OBit1(X3382)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3383,X3382)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(i_0_1256,plain,
! [X3438,X3439] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X3439),X3438) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3439,X3438)),X3438),
inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).
fof(i_0_1257,plain,
! [X4968,X4969,X4970] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4970,X4969),X4968)),X4969) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4968),X4969),
inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).
fof(i_0_1258,plain,
! [X22,X23,X3] :
( class_Rings_Olinordered__ring(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X23,X23),c_Groups_Otimes__class_Otimes(X3,X22,X22)),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1259,plain,
! [X4555] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X4555)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4555)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X4555)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4555)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).
fof(i_0_1260,plain,
! [X4563,X4564] :
( ~ class_Int_Onumber__ring(X4564)
| c_Groups_Oplus__class_Oplus(X4564,c_Int_Onumber__class_Onumber__of(X4564,X4563),c_Groups_Oone__class_Oone(X4564)) = c_Int_Onumber__class_Onumber__of(X4564,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4563,c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).
fof(i_0_1261,plain,
! [X4561,X4562] :
( ~ class_Int_Onumber__ring(X4562)
| c_Groups_Oplus__class_Oplus(X4562,c_Groups_Oone__class_Oone(X4562),c_Int_Onumber__class_Onumber__of(X4562,X4561)) = c_Int_Onumber__class_Onumber__of(X4562,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4561)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(i_0_1262,plain,
! [X3741] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X3741)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X3741)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).
fof(i_0_1263,plain,
! [X4720,X4721,X4722,X4723] :
( ~ class_Groups_Omonoid__mult(X4723)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4722,X4721)
| c_Power_Opower__class_Opower(X4723,X4720,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4721),X4722)) = c_Groups_Otimes__class_Otimes(X4723,c_Power_Opower__class_Opower(X4723,X4720,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4721,X4722)),X4720) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff])]) ).
fof(i_0_1264,plain,
! [X4499,X4500] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4500),c_Int_OBit0(X4499))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4500,X4499) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4500,X4499)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4500),c_Int_OBit0(X4499)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).
fof(i_0_1265,plain,
! [X4497,X4498] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4498),c_Int_OBit0(X4497))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4498,X4497) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4498,X4497)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4498),c_Int_OBit0(X4497)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).
fof(i_0_1266,plain,
! [X3172,X3173] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3173),c_Int_OBit0(X3172))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3173,X3172) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3173,X3172)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3173),c_Int_OBit0(X3172)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).
fof(i_0_1267,plain,
! [X3170,X3171] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3171),c_Int_OBit0(X3170))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3171,X3170) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3171,X3170)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3171),c_Int_OBit0(X3170)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).
fof(i_0_1268,plain,
! [X4291,X4292] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4292),c_Int_OBit1(X4291))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4292,X4291) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4292,X4291)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4292),c_Int_OBit1(X4291)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).
fof(i_0_1269,plain,
! [X4289,X4290] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4290),c_Int_OBit1(X4289))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4290,X4289) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4290,X4289)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4290),c_Int_OBit1(X4289)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).
fof(i_0_1270,plain,
! [X4495,X4496] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4496),c_Int_OBit1(X4495))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4496,X4495) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4496,X4495)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4496),c_Int_OBit1(X4495)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).
fof(i_0_1271,plain,
! [X4493,X4494] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4494),c_Int_OBit1(X4493))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4494,X4493) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4494,X4493)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X4494),c_Int_OBit1(X4493)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).
fof(i_0_1272,plain,
! [X4489,X4490] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4490)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4490,X4489)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4489)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4490,X4489)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4490)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4489)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4490,X4489)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_1273,plain,
! [X3446,X3447] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3447)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3446)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3446,X3447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1274,plain,
! [X5016] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5016)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5016,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5016,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5016) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1165])]) ).
fof(i_0_1275,plain,
! [X3747,X3748,X3749] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3749,X3748)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3748,X3749)),X3747) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3748),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3749,X3747)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).
fof(i_0_1276,plain,
! [X3744,X3745,X3746] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3746,X3745)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3744,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3745,X3746))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3744,X3746),c_Nat_OSuc(X3745)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).
fof(i_0_1277,plain,
! [X4456,X4457,X4458,X4459] :
( ~ class_Rings_Olinordered__semidom(X4459)
| c_Power_Opower__class_Opower(X4459,X4458,c_Nat_OSuc(X4457)) != c_Power_Opower__class_Opower(X4459,X4456,c_Nat_OSuc(X4457))
| ~ c_Orderings_Oord__class_Oless__eq(X4459,c_Groups_Ozero__class_Ozero(X4459),X4458)
| ~ c_Orderings_Oord__class_Oless__eq(X4459,c_Groups_Ozero__class_Ozero(X4459),X4456)
| X4458 = X4456 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
fof(i_0_1278,plain,
! [X2561,X2562] :
( ~ class_Int_Onumber__ring(X2562)
| c_Groups_Otimes__class_Otimes(X2562,c_Int_Onumber__class_Onumber__of(X2562,c_Int_OBit1(c_Int_OPls)),X2561) = X2561 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).
fof(i_0_1279,plain,
! [X2559,X2560] :
( ~ class_Int_Onumber__ring(X2560)
| c_Groups_Otimes__class_Otimes(X2560,X2559,c_Int_Onumber__class_Onumber__of(X2560,c_Int_OBit1(c_Int_OPls))) = X2559 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).
fof(i_0_1280,plain,
! [X3444,X3445] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3445)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3444)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3445,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3445,X3444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1281,plain,
! [X3442,X3443] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3443)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3442)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3443,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3442,X3443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1282,plain,
! [X3384] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3384,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X3384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3384 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one])]) ).
fof(i_0_1283,plain,
! [X3706,X3707] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3707,c_Int_Onumber__class_Onumber__of(X3707,X3706),c_Groups_Oone__class_Oone(X3707))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3706,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X3707)
| ~ class_Rings_Olinordered__idom(X3707) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3706,c_Int_OBit1(c_Int_OPls))
| c_Orderings_Oord__class_Oless__eq(X3707,c_Int_Onumber__class_Onumber__of(X3707,X3706),c_Groups_Oone__class_Oone(X3707))
| ~ class_Int_Onumber__ring(X3707)
| ~ class_Rings_Olinordered__idom(X3707) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).
fof(i_0_1284,plain,
! [X4559,X4560] :
( ( ~ c_Orderings_Oord__class_Oless(X4560,c_Int_Onumber__class_Onumber__of(X4560,X4559),c_Groups_Oone__class_Oone(X4560))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4559,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X4560)
| ~ class_Rings_Olinordered__idom(X4560) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4559,c_Int_OBit1(c_Int_OPls))
| c_Orderings_Oord__class_Oless(X4560,c_Int_Onumber__class_Onumber__of(X4560,X4559),c_Groups_Oone__class_Oone(X4560))
| ~ class_Int_Onumber__ring(X4560)
| ~ class_Rings_Olinordered__idom(X4560) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).
fof(i_0_1285,plain,
! [X3708,X3709] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3709,c_Groups_Oone__class_Oone(X3709),c_Int_Onumber__class_Onumber__of(X3709,X3708))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X3708)
| ~ class_Int_Onumber__ring(X3709)
| ~ class_Rings_Olinordered__idom(X3709) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X3708)
| c_Orderings_Oord__class_Oless__eq(X3709,c_Groups_Oone__class_Oone(X3709),c_Int_Onumber__class_Onumber__of(X3709,X3708))
| ~ class_Int_Onumber__ring(X3709)
| ~ class_Rings_Olinordered__idom(X3709) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).
fof(i_0_1286,plain,
! [X4557,X4558] :
( ( ~ c_Orderings_Oord__class_Oless(X4558,c_Groups_Oone__class_Oone(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4557))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4557)
| ~ class_Int_Onumber__ring(X4558)
| ~ class_Rings_Olinordered__idom(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4557)
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Oone__class_Oone(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4557))
| ~ class_Int_Onumber__ring(X4558)
| ~ class_Rings_Olinordered__idom(X4558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).
fof(i_0_1287,plain,
! [X24,X25,X55] :
( hBOOL(hAPP(X55,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X25,X24)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X25,X24)
& ~ hBOOL(hAPP(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X69] :
( X25 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X69)
& ~ hBOOL(hAPP(X55,X69)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1288,plain,
! [X3168] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3168),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3168,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3168,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3168),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J])]) ).
fof(i_0_1289,plain,
! [X22,X78,X79,X80] :
( X80 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X79,X78),X22)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X79) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X79)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X79,X22)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X79 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X80,X79) = X22 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(i_0_1290,plain,
! [X3910,X3911,X3912] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3912),X3911),c_Nat_OSuc(X3910)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3912,X3911),X3910),
inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).
fof(i_0_1291,plain,
! [X3725] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X3725))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X3725) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X3725)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X3725)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).
fof(i_0_1292,plain,
! [X4288] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4288))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4288) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4288)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4288)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).
fof(i_0_1293,plain,
! [X4491] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4491))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4491) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4491)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X4491)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).
fof(i_0_1294,plain,
! [X4266] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X4266))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X4266) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X4266)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X4266)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).
fof(i_0_1295,plain,
! [X3726] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3726),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3726,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3726,c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3726),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).
fof(i_0_1296,plain,
! [X4265] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4265),c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4265,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4265,c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X4265),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).
fof(i_0_1297,plain,
! [X4492] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4492),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4492,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4492,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X4492),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).
fof(i_0_1298,plain,
! [X3169] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3169),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3169,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3169,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3169),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).
fof(i_0_1299,plain,
! [X5017] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5017)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5017,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5017,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5017) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__nat__equiv__def])]) ).
fof(i_0_1300,plain,
! [X3205,X3207,X3208] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3205)
| X3205 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk6_1(X3205)) )
& ( X3207 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X3208)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3207) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__nat__equiv__def2])])])])]) ).
fof(i_0_1301,plain,
! [X3743] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X3743)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X3743)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).
fof(i_0_1302,plain,
! [X3742] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X3742)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X3742)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).
fof(i_0_1303,plain,
! [X4463,X4464] :
( ~ class_Int_Onumber__ring(X4464)
| c_Int_Onumber__class_Onumber__of(X4464,c_Int_OBit1(X4463)) = c_Groups_Oplus__class_Oplus(X4464,c_Groups_Oplus__class_Oplus(X4464,c_Groups_Oone__class_Oone(X4464),c_Int_Onumber__class_Onumber__of(X4464,X4463)),c_Int_Onumber__class_Onumber__of(X4464,X4463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).
fof(i_0_1304,plain,
! [X4540,X4541,X4542] :
( ~ class_Rings_Olinordered__semidom(X4542)
| ~ c_Orderings_Oord__class_Oless(X4542,c_Groups_Ozero__class_Ozero(X4542),X4541)
| ~ c_Orderings_Oord__class_Oless(X4542,X4541,c_Groups_Oone__class_Oone(X4542))
| c_Orderings_Oord__class_Oless(X4542,c_Power_Opower__class_Opower(X4542,X4541,c_Nat_OSuc(X4540)),c_Groups_Oone__class_Oone(X4542)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1305,plain,
! [X3842,X3843,X3844] :
( ~ class_Rings_Olinordered__semidom(X3844)
| ~ c_Orderings_Oord__class_Oless__eq(X3844,c_Groups_Ozero__class_Ozero(X3844),X3843)
| ~ c_Orderings_Oord__class_Oless__eq(X3844,X3843,c_Groups_Oone__class_Oone(X3844))
| c_Orderings_Oord__class_Oless__eq(X3844,c_Power_Opower__class_Opower(X3844,X3843,c_Nat_OSuc(X3842)),X3843) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])]) ).
fof(i_0_1306,plain,
! [X7,X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32),X7)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)),X7) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(i_0_1307,plain,
! [X4272,X4273] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4273)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X4273,X4272)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_1308,plain,
! [X4996,X4997] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4997),X4996) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4997,X4996)),X4996),
inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).
fof(i_0_1309,plain,
! [X3852,X3853] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X3853),c_Int_OBit0(X3852)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3853,X3852)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).
fof(i_0_1310,plain,
! [X3290,X3291] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X3291),c_Int_OBit0(X3290)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3291,X3290)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(i_0_1311,plain,
! [X2594,X2595] :
( ( c_Int_OBit1(X2595) != c_Int_OBit1(X2594)
| X2595 = X2594 )
& ( X2595 != X2594
| c_Int_OBit1(X2595) = c_Int_OBit1(X2594) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).
fof(i_0_1312,plain,
! [X3017,X3018,X3019] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3019),X3018) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3019),X3017)
| X3018 = X3017 )
& ( X3018 != X3017
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3019),X3018) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3019),X3017) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1313,plain,
! [X4465,X4466,X4467] :
( ~ class_Rings_Olinordered__semidom(X4467)
| ~ c_Orderings_Oord__class_Oless(X4467,c_Groups_Oone__class_Oone(X4467),X4466)
| c_Orderings_Oord__class_Oless(X4467,c_Groups_Oone__class_Oone(X4467),c_Power_Opower__class_Opower(X4467,X4466,c_Nat_OSuc(X4465))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1314,plain,
! [X4998,X4999] :
( ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4999,X4998)) != X4998
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4999),X4998) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4999,X4998)) = X4998
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X4999),X4998) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4999,X4998)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).
fof(i_0_1315,plain,
! [X3965,X3966] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3966),c_Nat_OSuc(X3965))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3966,X3965) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3966,X3965)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3966),c_Nat_OSuc(X3965)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_1316,plain,
! [X3321,X3322] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3322),c_Nat_OSuc(X3321))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3322,X3321) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3322,X3321)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3322),c_Nat_OSuc(X3321)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1317,plain,
! [X3304,X3305] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3305),c_Nat_OSuc(X3304))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3305,X3304) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1318,plain,
! [X4211] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4211)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4211,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X4211 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).
fof(i_0_1319,plain,
! [X5014] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5014)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5014,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1166])]) ).
fof(i_0_1320,plain,
! [X4212,X4213] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4213)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4213,c_Nat_OSuc(X4212)),X4213) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).
fof(i_0_1321,plain,
! [X3989,X3990] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3990),c_Int_OBit0(X3989))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3990,X3989) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3990,X3989)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3990),c_Int_OBit0(X3989)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).
fof(i_0_1322,plain,
! [X3987,X3988] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3988),c_Int_OBit0(X3987))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3988,X3987) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3988,X3987)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3988),c_Int_OBit0(X3987)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).
fof(i_0_1323,plain,
! [X3015,X3016] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3016),c_Int_OBit0(X3015))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3016,X3015) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3016,X3015)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3016),c_Int_OBit0(X3015)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).
fof(i_0_1324,plain,
! [X3013,X3014] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3014),c_Int_OBit0(X3013))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3014,X3013) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3014,X3013)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3014),c_Int_OBit0(X3013)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).
fof(i_0_1325,plain,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& X15 != c_Groups_Ozero__class_Ozero(X3) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__power__eq__number__of]) ).
fof(i_0_1326,plain,
! [X3212,X3213] :
( ( ~ c_Int_Oiszero(X3213,c_Int_Onumber__class_Onumber__of(X3213,c_Int_OBit0(X3212)))
| c_Int_Oiszero(X3213,c_Int_Onumber__class_Onumber__of(X3213,X3212))
| ~ class_Int_Onumber__ring(X3213)
| ~ class_Int_Oring__char__0(X3213) )
& ( ~ c_Int_Oiszero(X3213,c_Int_Onumber__class_Onumber__of(X3213,X3212))
| c_Int_Oiszero(X3213,c_Int_Onumber__class_Onumber__of(X3213,c_Int_OBit0(X3212)))
| ~ class_Int_Onumber__ring(X3213)
| ~ class_Int_Oring__char__0(X3213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).
fof(i_0_1327,plain,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__power__eq__number__of]) ).
fof(i_0_1328,plain,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__le__zero__eq__number__of]) ).
fof(i_0_1329,plain,
! [X4673,X4674] :
( ( X4674 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4674,X4673) = X4673 )
& ( X4674 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4674,X4673) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4674,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4673)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).
fof(i_0_1330,axiom,
! [X5,X17,X55] :
( hBOOL(hAPP(X55,c_Divides_Odiv__class_Omod(tc_Int_Oint,X17,X5)))
<=> epred1_3(X55,X17,X5) ),
inference(apply_def,[status(thm)],[fact_split__zmod,c_0_1167]) ).
fof(i_0_1331,plain,
! [X5015] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X5015)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5015,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__nat__mod__two__eq__zero])]) ).
fof(i_0_1332,plain,
! [X2585,X2586] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X2586),X2585) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2586,X2585)),
inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).
fof(i_0_1333,plain,
! [X4192] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4192)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X4192)),
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).
fof(i_0_1334,plain,
! [X3733,X3734] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3734,X3733)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3733),X3734) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3733,X3734)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).
fof(i_0_1335,plain,
! [X16,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X3))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__less__zero__eq__number__of]) ).
fof(i_0_1336,plain,
! [X3199,X3200] :
( ~ class_Int_Onumber__ring(X3200)
| c_Int_Onumber__class_Onumber__of(X3200,c_Int_OBit0(X3199)) = c_Groups_Oplus__class_Oplus(X3200,c_Groups_Oplus__class_Oplus(X3200,c_Groups_Ozero__class_Ozero(X3200),c_Int_Onumber__class_Onumber__of(X3200,X3199)),c_Int_Onumber__class_Onumber__of(X3200,X3199)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).
fof(i_0_1337,plain,
! [X22,X23,X20,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X23,X22)
=> c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X23,X20),c_Power_Opower__class_Opower(X3,X22,X20)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__mono__odd]) ).
fof(i_0_1338,plain,
! [X3410,X3411] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3411,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3411,X3410))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1339,plain,
! [X3408,X3409] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3409,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3408,X3409))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1340,plain,
! [X3969,X3970] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3970,c_Nat_OSuc(X3969))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3970,X3969)
| X3970 = c_Nat_OSuc(X3969) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1168])]) ).
fof(i_0_1341,plain,
! [X3963,X3964] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3964,c_Nat_OSuc(X3963))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3964,X3963)
| X3964 = c_Nat_OSuc(X3963) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3964,X3963)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3964,c_Nat_OSuc(X3963)) )
& ( X3964 != c_Nat_OSuc(X3963)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3964,c_Nat_OSuc(X3963)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_1342,plain,
! [X10,X22,X23] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(i_0_1343,plain,
! [X3260,X3261] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3261,X3260)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3261),c_Nat_OSuc(X3260)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1344,plain,
! [X16,X61,X3] :
( ( class_Int_Onumber(X3)
& class_Orderings_Olinorder(X3) )
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X61),c_Int_Onumber__class_Onumber__of(X3,X16))
<=> ~ c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X16),c_Int_Onumber__class_Onumber__of(X3,X61)) ) ),
inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(i_0_1345,plain,
! [X4686] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4686))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4686) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4686),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).
fof(i_0_1346,plain,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> ( X17 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& X15 != c_Groups_Ozero__class_Ozero(X3) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__power__eq]) ).
fof(i_0_1347,plain,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__power__eq]) ).
fof(i_0_1348,plain,
! [X15,X17,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X15,X17))
<=> c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Ozero__class_Ozero(X3),X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__odd__power]) ).
fof(i_0_1349,plain,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
<=> ( X17 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless__eq(X3,X15,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& X15 = c_Groups_Ozero__class_Ozero(X3) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__le__zero__eq]) ).
fof(i_0_1350,plain,
! [X3385,X3386,X3388,X3389,X3390] :
( ( X3386 = c_Nat_OSuc(esk9_2(X3385,X3386))
| X3386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,c_Nat_OSuc(X3385)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X3385,X3386),X3385)
| X3386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3386,c_Nat_OSuc(X3385)) )
& ( X3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,c_Nat_OSuc(X3388)) )
& ( X3389 != c_Nat_OSuc(X3390)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3390,X3388)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,c_Nat_OSuc(X3388)) ) ),
inference(distribute,[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)],[fact_less__Suc__eq__0__disj])])])])])]) ).
fof(i_0_1351,plain,
! [X3983,X3984] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3983,c_Nat_OSuc(X3984))
| X3983 = X3984
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3984,X3983) )
& ( X3983 != X3984
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3983,c_Nat_OSuc(X3984))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3984,X3983) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_1352,plain,
! [X3961,X3962] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3962,X3961)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3961),X3962) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3961),X3962)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3962,X3961) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1169])]) ).
fof(i_0_1353,plain,
! [X3325,X3326] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3326,X3325)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3325,c_Nat_OSuc(X3326)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3325,c_Nat_OSuc(X3326))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3326,X3325) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1170])]) ).
fof(i_0_1354,plain,
! [X4469] :
( ~ class_Int_Onumber__ring(X4469)
| c_Int_Onumber__class_Onumber__of(X4469,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X4469) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).
fof(i_0_1355,plain,
! [X4468] :
( ~ class_Int_Onumber__ring(X4468)
| c_Groups_Oone__class_Oone(X4468) = c_Int_Onumber__class_Onumber__of(X4468,c_Int_OBit1(c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).
fof(i_0_1356,plain,
! [X2565,X2566] : c_Int_OBit0(X2566) != c_Int_OBit1(X2565),
inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(i_0_1357,plain,
! [X2567,X2568] : c_Int_OBit1(X2568) != c_Int_OBit0(X2567),
inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(i_0_1358,plain,
! [X4545,X4546] :
( ~ class_Int_Onumber__ring(X4546)
| c_Groups_Otimes__class_Otimes(X4546,c_Groups_Oplus__class_Oplus(X4546,c_Groups_Oone__class_Oone(X4546),c_Groups_Oone__class_Oone(X4546)),c_Int_Onumber__class_Onumber__of(X4546,X4545)) = c_Int_Onumber__class_Onumber__of(X4546,c_Int_OBit0(X4545)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).
fof(i_0_1359,plain,
! [X3246,X3247,X3248] :
( ~ class_Groups_Omonoid__mult(X3248)
| c_Power_Opower__class_Opower(X3248,X3247,c_Nat_OSuc(X3246)) = c_Groups_Otimes__class_Otimes(X3248,c_Power_Opower__class_Opower(X3248,X3247,X3246),X3247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1360,plain,
! [X3243,X3244,X3245] :
( ~ class_Power_Opower(X3245)
| c_Power_Opower__class_Opower(X3245,X3244,c_Nat_OSuc(X3243)) = c_Groups_Otimes__class_Otimes(X3245,X3244,c_Power_Opower__class_Opower(X3245,X3244,X3243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1361,plain,
! [X2760,X2761,X2762] :
( ~ class_Rings_Ocomm__semiring__1(X2762)
| c_Power_Opower__class_Opower(X2762,X2761,c_Nat_OSuc(X2760)) = c_Groups_Otimes__class_Otimes(X2762,X2761,c_Power_Opower__class_Opower(X2762,X2761,X2760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1362,plain,
! [X2754,X2755,X2756] :
( ~ class_Rings_Ocomm__semiring__1(X2756)
| c_Groups_Otimes__class_Otimes(X2756,c_Power_Opower__class_Opower(X2756,X2755,X2754),X2755) = c_Power_Opower__class_Opower(X2756,X2755,c_Nat_OSuc(X2754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1363,plain,
! [X2757,X2758,X2759] :
( ~ class_Rings_Ocomm__semiring__1(X2759)
| c_Groups_Otimes__class_Otimes(X2759,X2758,c_Power_Opower__class_Opower(X2759,X2758,X2757)) = c_Power_Opower__class_Opower(X2759,X2758,c_Nat_OSuc(X2757)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1364,plain,
! [X17,X15,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X15,X17),c_Groups_Ozero__class_Ozero(X3))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
& c_Orderings_Oord__class_Oless(X3,X15,c_Groups_Ozero__class_Ozero(X3)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__less__zero__eq]) ).
fof(i_0_1365,plain,
! [X3310,X3311,X3312] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3312,X3311)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3311,X3310)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3312),X3310) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1366,plain,
! [X2871] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2871,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X2871 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2871 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2871,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).
fof(i_0_1367,plain,
! [X3908,X3909] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3909),c_Nat_OSuc(X3908)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3909,X3908),
inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).
fof(i_0_1368,plain,
! [X2784,X2785] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X2785),X2784) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2785,c_Nat_OSuc(X2784)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1369,plain,
! [X4606,X4607] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4607,c_Nat_OSuc(X4606)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4607,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4606),
inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).
fof(i_0_1370,plain,
! [X2782,X2783] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X2783),X2782) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2783,X2782)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1371,plain,
! [X2775,X2776] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2776,c_Nat_OSuc(X2775)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2776,X2775)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1372,plain,
! [X2884,X2885] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2885),X2884) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2884,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2885,X2884)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1373,plain,
! [X2882,X2883] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2883,c_Nat_OSuc(X2882)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2883,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2883,X2882)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1374,plain,
! [X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X32)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).
fof(i_0_1375,plain,
! [X3323,X3324] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3324,c_Nat_OSuc(X3323))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3324,X3323)
| X3324 = X3323 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3324,X3323)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3324,c_Nat_OSuc(X3323)) )
& ( X3324 != X3323
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3324,c_Nat_OSuc(X3323)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1376,plain,
! [X3319,X3320] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3320,c_Nat_OSuc(X3319))
| X3320 = X3319
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3320,X3319) )
& ( X3320 != X3319
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3320,c_Nat_OSuc(X3319))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3320,X3319) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1171])])]) ).
fof(i_0_1377,plain,
! [X3317,X3318] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3318,X3317)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3318,c_Nat_OSuc(X3317))
| X3317 = X3318 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1172])]) ).
fof(i_0_1378,plain,
! [X3308,X3309] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3309,c_Nat_OSuc(X3308))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3309,X3308)
| X3309 = X3308 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1173])]) ).
fof(i_0_1379,plain,
! [X3971,X3972] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3972),X3971)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3972,X3971) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_1380,plain,
! [X3985,X3986] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3986),X3985)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3986,X3985) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_1381,plain,
! [X3977,X3978] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3978),X3977)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3978,X3977) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3978,X3977)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3978),X3977) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_1382,plain,
! [X3973,X3974] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3974,X3973)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3974),X3973) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3974),X3973)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3974,X3973) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_1383,plain,
! [X3306,X3307] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3307),X3306)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3307,X3306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1384,plain,
! [X3975,X3976] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3976,c_Nat_OSuc(X3975))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3976,X3975) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3976,X3975)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3976,c_Nat_OSuc(X3975)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_1385,plain,
! [X3174] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3174),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3174,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3174,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3174),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J])]) ).
fof(i_0_1386,plain,
! [X3402,X3403,X3405,X3406,X3407] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3403,X3402)
| X3402 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3403,esk11_2(X3402,X3403))) )
& ( X3405 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3406,X3407))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3406,X3405) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add])])])])]) ).
fof(i_0_1387,plain,
! [X10,X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X22) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(i_0_1388,plain,
! [X10,X22,X23] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X10)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X10,X23) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(i_0_1389,plain,
! [X3313,X3314] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3314,X3313)
| c_Nat_OSuc(X3314) = X3313
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3314),X3313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1390,plain,
! [X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(fof_simplification,[status(thm)],[fact_even__num__iff]) ).
fof(i_0_1391,plain,
! [X3166,X3167] :
( ( X3167 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3167,X3166) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3166 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3167,X3166) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3167 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3166 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3167,X3166) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff])])]) ).
fof(i_0_1392,plain,
! [X20,X7,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X7),X20)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X20)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X20) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1393,plain,
! [X2875,X2876] :
( ( X2876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2876 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) )
& ( X2875 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2876 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) )
& ( X2876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) )
& ( X2875 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) )
& ( X2876 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2875 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) )
& ( X2876 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2875 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2876,X2875) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1394,plain,
! [X2877,X2878] :
( ( X2878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2878 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2877 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2878 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2877 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2877 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2877 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2878 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2877 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2878 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2877 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2878,X2877) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__1])])]) ).
fof(i_0_1395,plain,
! [X4293] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4293))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4293) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4293)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X4293)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).
fof(i_0_1396,plain,
! [X3750] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X3750))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X3750) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X3750)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X3750)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).
fof(i_0_1397,plain,
! [X4267] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X4267))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X4267) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X4267)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X4267)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).
fof(i_0_1398,plain,
! [X3175] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3175))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3175) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3175)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3175)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).
fof(i_0_1399,plain,
! [X3724] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3724),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3724,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3724,c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3724),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).
fof(i_0_1400,plain,
! [X3751] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3751),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3751,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3751,c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3751),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).
fof(i_0_1401,plain,
! [X4294] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4294),c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4294,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4294,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X4294),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).
fof(i_0_1402,plain,
! [X3176] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3176),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3176,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3176,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3176),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).
fof(i_0_1403,plain,
! [X2,X3] :
( class_Rings_Olinordered__ring(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Otimes__class_Otimes(X3,X2,X2),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1404,plain,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X14))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
inference(fof_simplification,[status(thm)],[fact_even__difference__nat]) ).
fof(i_0_1405,plain,
! [X3391] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3391,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3391,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc0])]) ).
fof(i_0_1406,plain,
! [X32,X9] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X32)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X32)) ) ),
inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).
fof(i_0_1407,plain,
! [X3913,X3914] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3914,X3913),c_Nat_OSuc(X3914)),
inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).
fof(i_0_1408,plain,
! [X20,X19] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = X19 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ) ),
inference(fof_simplification,[status(thm)],[fact_mod__if]) ).
fof(i_0_1409,plain,
! [X20,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X20) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20),X20) ),
inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).
fof(i_0_1410,plain,
! [X60,X61] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X61),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X60))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X60)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,c_Int_OPls) ) ),
inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).
fof(i_0_1411,plain,
! [X3863] :
( ( c_Int_OMin != c_Int_OBit1(X3863)
| c_Int_OMin = X3863 )
& ( c_Int_OMin != X3863
| c_Int_OMin = c_Int_OBit1(X3863) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).
fof(i_0_1412,plain,
! [X3864] :
( ( c_Int_OBit1(X3864) != c_Int_OMin
| X3864 = c_Int_OMin )
& ( X3864 != c_Int_OMin
| c_Int_OBit1(X3864) = c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).
fof(i_0_1413,plain,
! [X15] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1414,plain,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X19,X20)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X20,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_zdvd__not__zless]) ).
fof(i_0_1415,plain,
! [X20,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X20,X19) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(i_0_1416,plain,
! [X3960] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3960),X3960),
inference(variable_rename,[status(thm)],[i_0_1174]) ).
fof(i_0_1417,plain,
! [X2570] : c_Int_OBit1(X2570) != c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(i_0_1418,plain,
! [X2569] : c_Int_OPls != c_Int_OBit1(X2569),
inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(i_0_1419,plain,
! [X4671] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4671)
| c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4671,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X4671 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).
fof(i_0_1420,plain,
! [X4672] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4672)
| X4672 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4672,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred_H])]) ).
fof(i_0_1421,plain,
! [X3981,X3982] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3982,X3981)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3982),X3981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_1422,plain,
! [X3967,X3968] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3968,X3967)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3968,c_Nat_OSuc(X3967)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_1423,plain,
! [X3979,X3980] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3980,X3979)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3980,c_Nat_OSuc(X3979)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_1424,plain,
! [X3315,X3316] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3316,X3315)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3316,c_Nat_OSuc(X3315)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_1425,plain,
! [X51,X53] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X53,X51),X53),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1426,plain,
! [X53,X51] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X51,X53),X53),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1427,plain,
! [X3538,X3539] :
( ( c_Power_Opower__class_Opower(tc_Nat_Onat,X3539,X3538) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3538 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3539 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3538 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X3539,X3538) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3539 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,X3539,X3538) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).
fof(i_0_1428,plain,
! [X3540] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3540) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1429,plain,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_odd__plus__even]) ).
fof(i_0_1430,plain,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
inference(fof_simplification,[status(thm)],[fact_even__difference]) ).
fof(i_0_1431,plain,
! [X22,X23] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_even__plus__odd]) ).
fof(i_0_1432,plain,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X14) ) ) ),
inference(fof_simplification,[status(thm)],[fact_even__sum]) ).
fof(i_0_1433,plain,
! [X17,X18] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X17))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_odd__add]) ).
fof(i_0_1434,plain,
! [X14,X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14))
<=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
& ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X14) ) ) ),
inference(fof_simplification,[status(thm)],[fact_even__sum__nat]) ).
fof(i_0_1435,plain,
! [X3032] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X3032))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3032) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3032)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X3032)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1175])]) ).
fof(i_0_1436,plain,
! [X20,X19] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X20)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X20)) = X19 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1437,plain,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X23,X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_odd__times__odd]) ).
fof(i_0_1438,plain,
! [X20,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X23,X20)) ),
inference(fof_simplification,[status(thm)],[fact_odd__pow]) ).
fof(i_0_1439,plain,
! [X3249,X3250] :
( ~ class_Power_Opower(X3250)
| ~ class_Rings_Osemiring__0(X3250)
| c_Power_Opower__class_Opower(X3250,c_Groups_Ozero__class_Ozero(X3250),c_Nat_OSuc(X3249)) = c_Groups_Ozero__class_Ozero(X3250) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_1440,plain,
! [X2828,X2829] :
( c_Nat_OSuc(X2829) != c_Nat_OSuc(X2828)
| X2829 = X2828 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1441,plain,
! [X2786,X2787] :
( ( c_Nat_OSuc(X2787) != c_Nat_OSuc(X2786)
| X2787 = X2786 )
& ( X2787 != X2786
| c_Nat_OSuc(X2787) = c_Nat_OSuc(X2786) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1442,plain,
! [X5000] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5000,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mod__1]) ).
fof(i_0_1443,plain,
! [X21,X2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
=> ( X2 != X21
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(i_0_1444,plain,
! [X22,X23] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X23,X22)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X22,X23) )
| X23 = X22 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(i_0_1445,plain,
! [X21,X2] :
( X2 != X21
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X21)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X21,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(i_0_1446,plain,
! [X14,X15] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& X15 != X14 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).
fof(i_0_1447,plain,
! [X14,X15] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
<=> ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X15,X14)
& ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X14,X15) )
| X15 = X14 ) ),
inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).
fof(i_0_1448,plain,
! [X2712] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2712),
inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).
fof(i_0_1449,plain,
! [X2596,X2597] :
( ( c_Int_OBit0(X2597) != c_Int_OBit0(X2596)
| X2597 = X2596 )
& ( X2597 != X2596
| c_Int_OBit0(X2597) = c_Int_OBit0(X2596) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).
fof(i_0_1450,plain,
! [X4605] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X4605),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4605,
inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).
fof(i_0_1451,plain,
! [X3263] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X3263)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1452,plain,
! [X3262] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3262,c_Nat_OSuc(X3262)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1453,plain,
! [X3392,X3394,X3395] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3392)
| X3392 = c_Nat_OSuc(esk10_1(X3392)) )
& ( X3394 != c_Nat_OSuc(X3395)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3394) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc])])])])]) ).
fof(i_0_1454,plain,
! [X22,X23] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X23)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X22)
=> c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X22)) ) ),
inference(fof_simplification,[status(thm)],[fact_odd__plus__odd]) ).
fof(i_0_1455,plain,
! [X22,X23,X3] :
( class_Rings_Olinordered__idom(X3)
=> ( X23 != X22
=> ( ~ c_Orderings_Oord__class_Oless(X3,X23,X22)
=> c_Orderings_Oord__class_Oless(X3,X22,X23) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1456,plain,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless__eq(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1457,plain,
! [X3] :
( class_Rings_Olinordered__semidom(X3)
=> ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),c_Groups_Ozero__class_Ozero(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1458,plain,
! [X4668] : c_Nat_OSuc(X4668) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4668),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1459,plain,
! [X23,X3] :
( class_Int_Onumber__ring(X3)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ),
inference(fof_simplification,[status(thm)],[fact_neg__one__odd__power]) ).
fof(i_0_1460,plain,
! [X23,X3] :
( class_Int_Onumber__ring(X3)
=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Groups_Oone__class_Oone(X3) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X23)
=> c_Power_Opower__class_Opower(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin),X23) = c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin) ) ) ),
inference(fof_simplification,[status(thm)],[fact_neg__one__even__odd__power]) ).
fof(i_0_1461,plain,
! [X22,X23] :
( X23 != X22
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X22)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X23) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1462,plain,
! [X2993] : c_Nat_OSuc(X2993) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1463,plain,
! [X2992] : c_Nat_OSuc(X2992) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1464,plain,
! [X2990] : c_Nat_OSuc(X2990) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1465,plain,
! [X2995] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2995),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1466,plain,
! [X2994] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2994),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1467,plain,
! [X2991] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2991),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1468,plain,
! [X2768] : c_Nat_OSuc(X2768) != X2768,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1469,plain,
! [X2767] : X2767 != c_Nat_OSuc(X2767),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1470,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1471,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1472,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1473,plain,
! [X2563] :
( ( c_Int_OPls != c_Int_OBit0(X2563)
| c_Int_OPls = X2563 )
& ( c_Int_OPls != X2563
| c_Int_OPls = c_Int_OBit0(X2563) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).
fof(i_0_1474,plain,
! [X2564] :
( ( c_Int_OBit0(X2564) != c_Int_OPls
| X2564 = c_Int_OPls )
& ( X2564 != c_Int_OPls
| c_Int_OBit0(X2564) = c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).
fof(i_0_1475,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1476,plain,
! [X20] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X20),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1477,plain,
! [X3878] : c_Int_OBit0(X3878) != c_Int_OMin,
inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(i_0_1478,plain,
! [X3877] : c_Int_OMin != c_Int_OBit0(X3877),
inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(i_0_1479,plain,
! [X20] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20) ),
inference(fof_simplification,[status(thm)],[fact_odd__pos]) ).
fof(i_0_1480,plain,
! [X3] :
( class_Int_Onumber__ring(X3)
=> ~ c_Int_Oiszero(X3,c_Int_Onumber__class_Onumber__of(X3,c_Int_OMin)) ),
inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).
fof(i_0_1481,plain,
! [X3] :
( class_Rings_Osemiring__1(X3)
=> ~ c_Int_Oiszero(X3,c_Groups_Oone__class_Oone(X3)) ),
inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).
cnf(i_0_1482,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1176]) ).
cnf(i_0_1483,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1177]) ).
cnf(i_0_1484,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1178]) ).
cnf(i_0_1485,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1179]) ).
cnf(i_0_1486,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_1180]) ).
cnf(i_0_1487,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))) ),
inference(split_conjunct,[status(thm)],[i_0_1181]) ).
cnf(i_0_1488,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_1182]) ).
cnf(i_0_1489,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1183]) ).
cnf(i_0_1490,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1184]) ).
cnf(i_0_1491,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1184]) ).
cnf(i_0_1492,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1185]) ).
cnf(i_0_1493,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[i_0_1186]) ).
cnf(i_0_1494,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1187]) ).
cnf(i_0_1495,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1188]) ).
cnf(i_0_1496,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1189]) ).
cnf(i_0_1497,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1184]) ).
cnf(i_0_1498,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1183]) ).
cnf(i_0_1499,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1183]) ).
cnf(i_0_1500,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1190]) ).
cnf(i_0_1501,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1191]) ).
cnf(i_0_1502,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1192]) ).
cnf(i_0_1503,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1193]) ).
cnf(i_0_1504,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1194]) ).
cnf(i_0_1505,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1194]) ).
cnf(i_0_1506,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1195]) ).
cnf(i_0_1507,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1195]) ).
cnf(i_0_1508,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1196]) ).
cnf(i_0_1509,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1197]) ).
cnf(i_0_1510,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1198]) ).
cnf(i_0_1511,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1199]) ).
cnf(i_0_1512,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1200]) ).
cnf(i_0_1513,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1201]) ).
cnf(i_0_1514,plain,
( c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1194]) ).
cnf(i_0_1515,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1195]) ).
cnf(i_0_1516,plain,
( X2 = X3
| ~ class_Rings_Olinordered__semidom(X1)
| c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1202]) ).
cnf(i_0_1517,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1203]) ).
cnf(i_0_1518,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1204]) ).
cnf(i_0_1519,plain,
( X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1205]) ).
cnf(i_0_1520,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1206]) ).
cnf(i_0_1521,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1207]) ).
cnf(i_0_1522,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1208]) ).
cnf(i_0_1523,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1209]) ).
cnf(i_0_1524,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1209]) ).
cnf(i_0_1525,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1210]) ).
cnf(i_0_1526,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1211]) ).
cnf(i_0_1527,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1204]) ).
cnf(i_0_1528,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk3_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1205]) ).
cnf(i_0_1529,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1203]) ).
cnf(i_0_1530,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1212]) ).
cnf(i_0_1531,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
inference(split_conjunct,[status(thm)],[i_0_1213]) ).
cnf(i_0_1532,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1207]) ).
cnf(i_0_1533,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X1))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))),X1),
inference(split_conjunct,[status(thm)],[i_0_1214]) ).
cnf(i_0_1534,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1215]) ).
cnf(i_0_1535,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J]) ).
cnf(i_0_1536,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(split_conjunct,[status(thm)],[i_0_1216]) ).
cnf(i_0_1537,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(split_conjunct,[status(thm)],[i_0_1217]) ).
cnf(i_0_1538,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1218]) ).
cnf(i_0_1539,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_1219]) ).
cnf(i_0_1540,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1220]) ).
cnf(i_0_1541,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1221]) ).
cnf(i_0_1542,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1222]) ).
cnf(i_0_1543,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1223]) ).
cnf(i_0_1544,hypothesis,
( v_thesis____
| v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1224]) ).
cnf(i_0_1545,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X2))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),
inference(split_conjunct,[status(thm)],[i_0_1225]) ).
cnf(i_0_1546,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Nat_OSuc(c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1226]) ).
cnf(i_0_1547,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1227]) ).
cnf(i_0_1548,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Groups_Omonoid__mult(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1228]) ).
cnf(i_0_1549,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1229]) ).
cnf(i_0_1550,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1230]) ).
cnf(i_0_1551,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
cnf(i_0_1552,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1232]) ).
cnf(i_0_1553,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1233]) ).
cnf(i_0_1554,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1234]) ).
cnf(i_0_1555,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk4_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1220]) ).
cnf(i_0_1556,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk2_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1221]) ).
cnf(i_0_1557,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1219]) ).
cnf(i_0_1558,plain,
( c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1218]) ).
cnf(i_0_1559,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1222]) ).
cnf(i_0_1560,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1223]) ).
cnf(i_0_1561,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1235]) ).
cnf(i_0_1562,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1236]) ).
cnf(i_0_1563,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1,
inference(split_conjunct,[status(thm)],[i_0_1237]) ).
cnf(i_0_1564,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J]) ).
cnf(i_0_1565,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[fact_pos2]) ).
cnf(i_0_1566,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk1_0),
inference(split_conjunct,[status(thm)],[i_0_1238]) ).
cnf(i_0_1567,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(split_conjunct,[status(thm)],[fact_numeral__3__eq__3]) ).
fof(i_0_1568,plain,
! [X4093,X4094,X4095,X4096,X4097] :
( ~ class_RealVector_Oreal__normed__algebra(X4097)
| c_Groups_Ominus__class_Ominus(X4097,c_Groups_Otimes__class_Otimes(X4097,X4096,X4095),c_Groups_Otimes__class_Otimes(X4097,X4094,X4093)) = c_Groups_Oplus__class_Oplus(X4097,c_Groups_Oplus__class_Oplus(X4097,c_Groups_Otimes__class_Otimes(X4097,c_Groups_Ominus__class_Ominus(X4097,X4096,X4094),c_Groups_Ominus__class_Ominus(X4097,X4095,X4093)),c_Groups_Otimes__class_Otimes(X4097,c_Groups_Ominus__class_Ominus(X4097,X4096,X4094),X4093)),c_Groups_Otimes__class_Otimes(X4097,X4094,c_Groups_Ominus__class_Ominus(X4097,X4095,X4093))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1569,plain,
! [X3752,X3753,X3754,X3755,X3756] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3755,X3754),X3753),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3756,X3754),X3752))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3755,X3756),X3754),X3753),X3752)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3756,X3755) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3755,X3756),X3754),X3753),X3752)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3755,X3754),X3753),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3756,X3754),X3752))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3756,X3755) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1570,plain,
! [X3782,X3783,X3784,X3785,X3786] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3785,X3784),X3783),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3786,X3784),X3782))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3785,X3786),X3784),X3783),X3782)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3786,X3785) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3785,X3786),X3784),X3783),X3782)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3785,X3784),X3783),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3786,X3784),X3782))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3786,X3785) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_1571,plain,
! [X3767,X3768,X3769,X3770,X3771] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3771,X3769),X3768),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3770,X3769),X3767))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3768,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3770,X3771),X3769),X3767))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3771,X3770) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3768,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3770,X3771),X3769),X3767))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3771,X3769),X3768),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3770,X3769),X3767))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3771,X3770) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1572,plain,
! [X3787,X3788,X3789,X3790,X3791] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3791,X3789),X3788),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3790,X3789),X3787))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3788,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3790,X3791),X3789),X3787))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3791,X3790) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3788,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3790,X3791),X3789),X3787))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3791,X3789),X3788),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3790,X3789),X3787))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3791,X3790) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_1573,plain,
! [X3716,X3717,X3718,X3719,X3720,X3721] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3721,c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,X3720,X3719),X3718),c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,X3717,X3719),X3716))
| c_Orderings_Oord__class_Oless__eq(X3721,c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,c_Groups_Ominus__class_Ominus(X3721,X3720,X3717),X3719),X3718),X3716)
| ~ class_Rings_Oordered__ring(X3721) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3721,c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,c_Groups_Ominus__class_Ominus(X3721,X3720,X3717),X3719),X3718),X3716)
| c_Orderings_Oord__class_Oless__eq(X3721,c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,X3720,X3719),X3718),c_Groups_Oplus__class_Oplus(X3721,c_Groups_Otimes__class_Otimes(X3721,X3717,X3719),X3716))
| ~ class_Rings_Oordered__ring(X3721) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1574,plain,
! [X4324,X4325,X4326,X4327,X4328,X4329] :
( ( ~ c_Orderings_Oord__class_Oless(X4329,c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,X4328,X4327),X4326),c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,X4325,X4327),X4324))
| c_Orderings_Oord__class_Oless(X4329,c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,c_Groups_Ominus__class_Ominus(X4329,X4328,X4325),X4327),X4326),X4324)
| ~ class_Rings_Oordered__ring(X4329) )
& ( ~ c_Orderings_Oord__class_Oless(X4329,c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,c_Groups_Ominus__class_Ominus(X4329,X4328,X4325),X4327),X4326),X4324)
| c_Orderings_Oord__class_Oless(X4329,c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,X4328,X4327),X4326),c_Groups_Oplus__class_Oplus(X4329,c_Groups_Otimes__class_Otimes(X4329,X4325,X4327),X4324))
| ~ class_Rings_Oordered__ring(X4329) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1575,plain,
! [X3710,X3711,X3712,X3713,X3714,X3715] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3715,c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,X3714,X3713),X3712),c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,X3711,X3713),X3710))
| c_Orderings_Oord__class_Oless__eq(X3715,X3712,c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,c_Groups_Ominus__class_Ominus(X3715,X3711,X3714),X3713),X3710))
| ~ class_Rings_Oordered__ring(X3715) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3715,X3712,c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,c_Groups_Ominus__class_Ominus(X3715,X3711,X3714),X3713),X3710))
| c_Orderings_Oord__class_Oless__eq(X3715,c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,X3714,X3713),X3712),c_Groups_Oplus__class_Oplus(X3715,c_Groups_Otimes__class_Otimes(X3715,X3711,X3713),X3710))
| ~ class_Rings_Oordered__ring(X3715) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1576,plain,
! [X4330,X4331,X4332,X4333,X4334,X4335] :
( ( ~ c_Orderings_Oord__class_Oless(X4335,c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,X4334,X4333),X4332),c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,X4331,X4333),X4330))
| c_Orderings_Oord__class_Oless(X4335,X4332,c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,c_Groups_Ominus__class_Ominus(X4335,X4331,X4334),X4333),X4330))
| ~ class_Rings_Oordered__ring(X4335) )
& ( ~ c_Orderings_Oord__class_Oless(X4335,X4332,c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,c_Groups_Ominus__class_Ominus(X4335,X4331,X4334),X4333),X4330))
| c_Orderings_Oord__class_Oless(X4335,c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,X4334,X4333),X4332),c_Groups_Oplus__class_Oplus(X4335,c_Groups_Otimes__class_Otimes(X4335,X4331,X4333),X4330))
| ~ class_Rings_Oordered__ring(X4335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
cnf(i_0_1577,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(X1,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1239]) ).
fof(i_0_1578,plain,
! [X4975,X4976,X4977] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4977,X4976),X4975) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4977,X4975),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4976,X4975)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4977,X4975),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4976,X4975)),X4975)),
inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).
cnf(i_0_1579,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1240]) ).
cnf(i_0_1580,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(split_conjunct,[status(thm)],[fact_numeral__2__eq__2]) ).
cnf(i_0_1581,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
fof(i_0_1582,plain,
! [X3757,X3758,X3759,X3760,X3761] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3761,X3760)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3760,X3759),X3758),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3761,X3759),X3757)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3760,X3761),X3759),X3758),X3757) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1583,plain,
! [X3772,X3773,X3774,X3775,X3776] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3776,X3775)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3776,X3774),X3773),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3775,X3774),X3772)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3773,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3775,X3776),X3774),X3772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1584,plain,
! [X4342,X4343,X4344,X4345,X4346,X4347] :
( ( ~ c_Rings_Odvd__class_Odvd(X4345,X4344,c_Groups_Oplus__class_Oplus(X4345,X4346,X4342))
| c_Rings_Odvd__class_Odvd(X4345,X4344,c_Groups_Oplus__class_Oplus(X4345,c_Groups_Ominus__class_Ominus(X4345,X4346,c_Groups_Otimes__class_Otimes(X4345,X4347,X4343)),X4342))
| ~ c_Rings_Odvd__class_Odvd(X4345,X4344,X4343)
| ~ class_Rings_Ocomm__ring(X4345)
| ~ class_Rings_Odvd(X4345) )
& ( ~ c_Rings_Odvd__class_Odvd(X4345,X4344,c_Groups_Oplus__class_Oplus(X4345,c_Groups_Ominus__class_Ominus(X4345,X4346,c_Groups_Otimes__class_Otimes(X4345,X4347,X4343)),X4342))
| c_Rings_Odvd__class_Odvd(X4345,X4344,c_Groups_Oplus__class_Oplus(X4345,X4346,X4342))
| ~ c_Rings_Odvd__class_Odvd(X4345,X4344,X4343)
| ~ class_Rings_Ocomm__ring(X4345)
| ~ class_Rings_Odvd(X4345) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).
fof(i_0_1585,plain,
! [X4336,X4337,X4338,X4339,X4340,X4341] :
( ( ~ c_Rings_Odvd__class_Odvd(X4339,X4338,c_Groups_Oplus__class_Oplus(X4339,X4340,X4336))
| c_Rings_Odvd__class_Odvd(X4339,X4338,c_Groups_Oplus__class_Oplus(X4339,c_Groups_Ominus__class_Ominus(X4339,X4340,c_Groups_Otimes__class_Otimes(X4339,X4341,X4337)),X4336))
| ~ c_Rings_Odvd__class_Odvd(X4339,X4338,X4337)
| ~ class_Rings_Ocomm__ring(X4339)
| ~ class_Rings_Odvd(X4339) )
& ( ~ c_Rings_Odvd__class_Odvd(X4339,X4338,c_Groups_Oplus__class_Oplus(X4339,c_Groups_Ominus__class_Ominus(X4339,X4340,c_Groups_Otimes__class_Otimes(X4339,X4341,X4337)),X4336))
| c_Rings_Odvd__class_Odvd(X4339,X4338,c_Groups_Oplus__class_Oplus(X4339,X4340,X4336))
| ~ c_Rings_Odvd__class_Odvd(X4339,X4338,X4337)
| ~ class_Rings_Ocomm__ring(X4339)
| ~ class_Rings_Odvd(X4339) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).
fof(i_0_1586,plain,
! [X4698,X4699,X4700,X4701,X4702,X4703] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4703,X4702),X4701) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4700,X4699),X4698)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4700,X4699),X4698),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4701,X4703)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4698)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4700)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4700,X4703)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4699,X4702) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1587,plain,
! [X4709,X4710,X4711,X4712,X4713,X4714] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4714,X4713),X4712) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4711,X4710),X4709)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4711,X4710),X4709))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4709,X4711)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4712)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4711)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4711,X4714)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4713,X4710) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1588,plain,
! [X3273,X3274,X3275,X3276,X3277] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3275,X3274))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3275,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3273,X3276)),X3274))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,X3276) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3275,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3273,X3276)),X3274))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3275,X3274))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3277,X3276) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__period])])]) ).
cnf(i_0_1589,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
cnf(i_0_1590,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
fof(i_0_1591,plain,
! [X4715,X4716,X4717,X4718,X4719] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4719,X4718),X4717),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4719,X4716),X4715))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4717)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4717,X4719)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4715,X4719)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4718,X4716) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1592,plain,
! [X4704,X4705,X4706,X4707,X4708] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4708,X4707),X4706),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4708,X4705),X4704))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4704,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4708,X4704)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4708,X4706)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4705,X4707) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
cnf(i_0_1593,plain,
( X1 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1242]) ).
cnf(i_0_1594,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Power_Opower__class_Opower(X1,X4,c_Nat_OSuc(X3)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1243]) ).
cnf(i_0_1595,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1244]) ).
cnf(i_0_1596,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1245]) ).
cnf(i_0_1597,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1246]) ).
cnf(i_0_1598,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1247]) ).
cnf(i_0_1599,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
cnf(i_0_1600,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1249]) ).
fof(i_0_1601,plain,
! [X4943,X4944,X4945,X4946] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4945)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4945,X4944)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4944,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4943,X4946)),X4945),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4944,X4946)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).
fof(i_0_1602,plain,
! [X4947,X4948,X4949,X4950] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4950)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4949,X4948)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4948,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4949,X4950),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4949,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4947,X4950)),X4948)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).
cnf(i_0_1603,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1250]) ).
fof(i_0_1604,plain,
! [X5070,X5071,X5072,X5073,X5074,X5075,X5076,X5077,X5078,X5079] :
( ( X5070 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X5072,X5071))
| ~ epred1_3(X5072,X5071,X5070) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5070)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5074)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5074,X5070)
| X5071 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5070,X5073),X5074)
| hBOOL(hAPP(X5072,X5074))
| ~ epred1_3(X5072,X5071,X5070) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5070,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5070,X5076)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5076,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5071 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5070,X5075),X5076)
| hBOOL(hAPP(X5072,X5076))
| ~ epred1_3(X5072,X5071,X5070) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| X5077 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X5077,X5078,X5079),X5077)
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk18_3(X5077,X5078,X5079)),esk19_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5077,esk21_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X5077,X5078,X5079),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( X5078 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5077,esk20_3(X5077,X5078,X5079)),esk21_3(X5077,X5078,X5079))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) )
& ( ~ hBOOL(hAPP(X5079,esk21_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,esk19_3(X5077,X5078,X5079)))
| ~ hBOOL(hAPP(X5079,X5078))
| epred1_3(X5079,X5078,X5077) ) ),
inference(distribute,[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)],[i_0_1167])])])])])]) ).
cnf(i_0_1605,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) ),
inference(split_conjunct,[status(thm)],[i_0_1251]) ).
fof(i_0_1606,plain,
! [X4056,X4057,X4058,X4059,X4060,X4061] :
( ~ class_Rings_Olinordered__semiring__1(X4061)
| ~ c_Orderings_Oord__class_Oless__eq(X4061,X4060,X4059)
| ~ c_Orderings_Oord__class_Oless__eq(X4061,X4058,X4059)
| ~ c_Orderings_Oord__class_Oless__eq(X4061,c_Groups_Ozero__class_Ozero(X4061),X4057)
| ~ c_Orderings_Oord__class_Oless__eq(X4061,c_Groups_Ozero__class_Ozero(X4061),X4056)
| c_Groups_Oplus__class_Oplus(X4061,X4057,X4056) != c_Groups_Oone__class_Oone(X4061)
| c_Orderings_Oord__class_Oless__eq(X4061,c_Groups_Oplus__class_Oplus(X4061,c_Groups_Otimes__class_Otimes(X4061,X4057,X4060),c_Groups_Otimes__class_Otimes(X4061,X4056,X4058)),X4059) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1607,plain,
! [X4072,X4073,X4074,X4075,X4076,X4077] :
( ~ class_Rings_Olinordered__semiring__1__strict(X4077)
| ~ c_Orderings_Oord__class_Oless(X4077,X4076,X4075)
| ~ c_Orderings_Oord__class_Oless(X4077,X4074,X4075)
| ~ c_Orderings_Oord__class_Oless__eq(X4077,c_Groups_Ozero__class_Ozero(X4077),X4073)
| ~ c_Orderings_Oord__class_Oless__eq(X4077,c_Groups_Ozero__class_Ozero(X4077),X4072)
| c_Groups_Oplus__class_Oplus(X4077,X4073,X4072) != c_Groups_Oone__class_Oone(X4077)
| c_Orderings_Oord__class_Oless(X4077,c_Groups_Oplus__class_Oplus(X4077,c_Groups_Otimes__class_Otimes(X4077,X4073,X4076),c_Groups_Otimes__class_Otimes(X4077,X4072,X4074)),X4075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1608,plain,
! [X4951,X4952,X4953,X4954] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4954)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4953,X4952)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4952,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4953,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4951,X4954)),X4952),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux2])]) ).
fof(i_0_1609,plain,
! [X4939,X4940,X4941,X4942] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4942)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4941)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4941,X4940)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4940,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4939,X4942)),X4941)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).
fof(i_0_1610,plain,
! [X3232,X3233,X3234,X3235,X3237] :
( ( c_Rings_Odvd__class_Odvd(X3234,X3232,c_Groups_Oplus__class_Oplus(X3234,esk7_3(X3232,X3233,X3234),c_Groups_Ozero__class_Ozero(X3234)))
| ~ hBOOL(hAPP(X3233,c_Groups_Otimes__class_Otimes(X3234,X3232,X3235)))
| ~ class_Rings_Odvd(X3234)
| ~ class_Rings_Osemiring__0(X3234) )
& ( hBOOL(hAPP(X3233,esk7_3(X3232,X3233,X3234)))
| ~ hBOOL(hAPP(X3233,c_Groups_Otimes__class_Otimes(X3234,X3232,X3235)))
| ~ class_Rings_Odvd(X3234)
| ~ class_Rings_Osemiring__0(X3234) )
& ( ~ c_Rings_Odvd__class_Odvd(X3234,X3232,c_Groups_Oplus__class_Oplus(X3234,X3237,c_Groups_Ozero__class_Ozero(X3234)))
| ~ hBOOL(hAPP(X3233,X3237))
| hBOOL(hAPP(X3233,c_Groups_Otimes__class_Otimes(X3234,X3232,esk8_3(X3232,X3233,X3234))))
| ~ class_Rings_Odvd(X3234)
| ~ class_Rings_Osemiring__0(X3234) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).
fof(i_0_1611,plain,
! [X3762,X3763,X3764,X3765,X3766] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3765,X3764),X3763) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3766,X3764),X3762)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3765,X3766),X3764),X3763) = X3762
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3766,X3765) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3765,X3766),X3764),X3763) != X3762
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3765,X3764),X3763) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3766,X3764),X3762)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3766,X3765) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1612,plain,
! [X3777,X3778,X3779,X3780,X3781] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3781,X3779),X3778) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3780,X3779),X3777)
| X3778 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3780,X3781),X3779),X3777)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3781,X3780) )
& ( X3778 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3780,X3781),X3779),X3777)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3781,X3779),X3778) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3780,X3779),X3777)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3781,X3780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1613,plain,
! [X4047,X4048,X4049,X4050,X4051] :
( ~ class_Rings_Oring(X4051)
| c_Groups_Ominus__class_Ominus(X4051,c_Groups_Otimes__class_Otimes(X4051,X4050,X4049),c_Groups_Otimes__class_Otimes(X4051,X4048,X4047)) = c_Groups_Oplus__class_Oplus(X4051,c_Groups_Otimes__class_Otimes(X4051,X4050,c_Groups_Ominus__class_Ominus(X4051,X4049,X4047)),c_Groups_Otimes__class_Otimes(X4051,c_Groups_Ominus__class_Ominus(X4051,X4050,X4048),X4047)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
cnf(i_0_1614,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1252]) ).
fof(i_0_1615,plain,
! [X2888,X2889,X2890] :
( ( ~ c_Orderings_Oord__class_Oless(X2890,c_Groups_Ozero__class_Ozero(X2890),c_Groups_Oplus__class_Oplus(X2890,c_Groups_Otimes__class_Otimes(X2890,X2889,X2889),c_Groups_Otimes__class_Otimes(X2890,X2888,X2888)))
| X2889 != c_Groups_Ozero__class_Ozero(X2890)
| X2888 != c_Groups_Ozero__class_Ozero(X2890)
| ~ class_Rings_Olinordered__ring__strict(X2890) )
& ( X2889 = c_Groups_Ozero__class_Ozero(X2890)
| c_Orderings_Oord__class_Oless(X2890,c_Groups_Ozero__class_Ozero(X2890),c_Groups_Oplus__class_Oplus(X2890,c_Groups_Otimes__class_Otimes(X2890,X2889,X2889),c_Groups_Otimes__class_Otimes(X2890,X2888,X2888)))
| ~ class_Rings_Olinordered__ring__strict(X2890) )
& ( X2888 = c_Groups_Ozero__class_Ozero(X2890)
| c_Orderings_Oord__class_Oless(X2890,c_Groups_Ozero__class_Ozero(X2890),c_Groups_Oplus__class_Oplus(X2890,c_Groups_Otimes__class_Otimes(X2890,X2889,X2889),c_Groups_Otimes__class_Otimes(X2890,X2888,X2888)))
| ~ class_Rings_Olinordered__ring__strict(X2890) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
cnf(i_0_1616,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1253]) ).
cnf(i_0_1617,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1254]) ).
cnf(i_0_1618,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1255]) ).
cnf(i_0_1619,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_1256]) ).
cnf(i_0_1620,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1257]) ).
fof(i_0_1621,plain,
! [X4424,X4425,X4426] :
( ( X4425 = c_Groups_Ozero__class_Ozero(X4426)
| ~ c_Orderings_Oord__class_Oless__eq(X4426,c_Groups_Oplus__class_Oplus(X4426,c_Groups_Otimes__class_Otimes(X4426,X4425,X4425),c_Groups_Otimes__class_Otimes(X4426,X4424,X4424)),c_Groups_Ozero__class_Ozero(X4426))
| ~ class_Rings_Olinordered__ring__strict(X4426) )
& ( X4424 = c_Groups_Ozero__class_Ozero(X4426)
| ~ c_Orderings_Oord__class_Oless__eq(X4426,c_Groups_Oplus__class_Oplus(X4426,c_Groups_Otimes__class_Otimes(X4426,X4425,X4425),c_Groups_Otimes__class_Otimes(X4426,X4424,X4424)),c_Groups_Ozero__class_Ozero(X4426))
| ~ class_Rings_Olinordered__ring__strict(X4426) )
& ( X4425 != c_Groups_Ozero__class_Ozero(X4426)
| X4424 != c_Groups_Ozero__class_Ozero(X4426)
| c_Orderings_Oord__class_Oless__eq(X4426,c_Groups_Oplus__class_Oplus(X4426,c_Groups_Otimes__class_Otimes(X4426,X4425,X4425),c_Groups_Otimes__class_Otimes(X4426,X4424,X4424)),c_Groups_Ozero__class_Ozero(X4426))
| ~ class_Rings_Olinordered__ring__strict(X4426) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1622,plain,
! [X2891,X2892,X2893] :
( ~ class_Rings_Olinordered__ring(X2893)
| ~ c_Orderings_Oord__class_Oless(X2893,c_Groups_Oplus__class_Oplus(X2893,c_Groups_Otimes__class_Otimes(X2893,X2892,X2892),c_Groups_Otimes__class_Otimes(X2893,X2891,X2891)),c_Groups_Ozero__class_Ozero(X2893)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1258])]) ).
fof(i_0_1623,plain,
! [X4081,X4082,X4083,X4084,X4085,X4086] :
( ( c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,X4085,X4084),X4083) != c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,X4082,X4084),X4081)
| c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,c_Groups_Ominus__class_Ominus(X4086,X4085,X4082),X4084),X4083) = X4081
| ~ class_Rings_Oring(X4086) )
& ( c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,c_Groups_Ominus__class_Ominus(X4086,X4085,X4082),X4084),X4083) != X4081
| c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,X4085,X4084),X4083) = c_Groups_Oplus__class_Oplus(X4086,c_Groups_Otimes__class_Otimes(X4086,X4082,X4084),X4081)
| ~ class_Rings_Oring(X4086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1624,plain,
! [X4087,X4088,X4089,X4090,X4091,X4092] :
( ( c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,X4091,X4090),X4089) != c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,X4088,X4090),X4087)
| X4089 = c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,c_Groups_Ominus__class_Ominus(X4092,X4088,X4091),X4090),X4087)
| ~ class_Rings_Oring(X4092) )
& ( X4089 != c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,c_Groups_Ominus__class_Ominus(X4092,X4088,X4091),X4090),X4087)
| c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,X4091,X4090),X4089) = c_Groups_Oplus__class_Oplus(X4092,c_Groups_Otimes__class_Otimes(X4092,X4088,X4090),X4087)
| ~ class_Rings_Oring(X4092) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
cnf(i_0_1625,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk5_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1242]) ).
fof(i_0_1626,plain,
! [X2980,X2981,X2982,X2983,X2984] :
( ~ class_Rings_Osemiring(X2984)
| c_Groups_Oplus__class_Oplus(X2984,c_Groups_Otimes__class_Otimes(X2984,X2983,X2982),c_Groups_Oplus__class_Oplus(X2984,c_Groups_Otimes__class_Otimes(X2984,X2981,X2982),X2980)) = c_Groups_Oplus__class_Oplus(X2984,c_Groups_Otimes__class_Otimes(X2984,c_Groups_Oplus__class_Oplus(X2984,X2983,X2981),X2982),X2980) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1627,plain,
! [X2955,X2956,X2957,X2958,X2959] :
( ( X2958 = X2957
| X2956 = X2955
| c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2956),c_Groups_Otimes__class_Otimes(X2959,X2957,X2955)) != c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2955),c_Groups_Otimes__class_Otimes(X2959,X2957,X2956))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2959) )
& ( X2958 != X2957
| c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2956),c_Groups_Otimes__class_Otimes(X2959,X2957,X2955)) = c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2955),c_Groups_Otimes__class_Otimes(X2959,X2957,X2956))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2959) )
& ( X2956 != X2955
| c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2956),c_Groups_Otimes__class_Otimes(X2959,X2957,X2955)) = c_Groups_Oplus__class_Oplus(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2955),c_Groups_Otimes__class_Otimes(X2959,X2957,X2956))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2959) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1628,plain,
! [X2985,X2986,X2987,X2988,X2989] :
( ( c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2987),c_Groups_Otimes__class_Otimes(X2989,X2986,X2985)) != c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2985),c_Groups_Otimes__class_Otimes(X2989,X2986,X2987))
| X2988 = X2986
| X2987 = X2985
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2989) )
& ( X2988 != X2986
| c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2987),c_Groups_Otimes__class_Otimes(X2989,X2986,X2985)) = c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2985),c_Groups_Otimes__class_Otimes(X2989,X2986,X2987))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2989) )
& ( X2987 != X2985
| c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2987),c_Groups_Otimes__class_Otimes(X2989,X2986,X2985)) = c_Groups_Oplus__class_Oplus(X2989,c_Groups_Otimes__class_Otimes(X2989,X2988,X2985),c_Groups_Otimes__class_Otimes(X2989,X2986,X2987))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2989) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_1629,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1259]) ).
cnf(i_0_1630,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1260]) ).
cnf(i_0_1631,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1261]) ).
cnf(i_0_1632,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(split_conjunct,[status(thm)],[i_0_1262]) ).
cnf(i_0_1633,plain,
( c_Power_Opower__class_Opower(X1,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X3),X2)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)),X4)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1263]) ).
fof(i_0_1634,plain,
! [X3026,X3027,X3028,X3029] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3029,X3028),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3027,X3028),X3026)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3029,X3027),X3028),X3026),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1635,plain,
! [X4601,X4602,X4603] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4603,X4602),X4601),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4601)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4603)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4602,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__neg__lemma])]) ).
cnf(i_0_1636,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1264]) ).
cnf(i_0_1637,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1265]) ).
cnf(i_0_1638,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1266]) ).
cnf(i_0_1639,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1267]) ).
cnf(i_0_1640,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1268]) ).
cnf(i_0_1641,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1642,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1270]) ).
cnf(i_0_1643,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1271]) ).
fof(i_0_1644,plain,
! [X4598,X4599,X4600] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4600,X4599),X4598))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4598,X4600)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4600)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4599) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
cnf(i_0_1645,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1646,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1273]) ).
cnf(i_0_1647,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1244]) ).
cnf(i_0_1648,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1245]) ).
cnf(i_0_1649,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1246]) ).
cnf(i_0_1650,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1247]) ).
cnf(i_0_1651,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1248]) ).
cnf(i_0_1652,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1249]) ).
fof(i_0_1653,plain,
! [X4825,X4826,X4827,X4828] :
( ~ class_Divides_Oring__div(X4828)
| c_Divides_Odiv__class_Omod(X4828,c_Groups_Ominus__class_Ominus(X4828,X4827,X4826),X4825) = c_Divides_Odiv__class_Omod(X4828,c_Groups_Ominus__class_Ominus(X4828,c_Divides_Odiv__class_Omod(X4828,X4827,X4825),c_Divides_Odiv__class_Omod(X4828,X4826,X4825)),X4825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).
fof(i_0_1654,plain,
! [X4773,X4774,X4775,X4776] :
( ~ class_Divides_Osemiring__div(X4776)
| c_Divides_Odiv__class_Omod(X4776,c_Groups_Oplus__class_Oplus(X4776,X4775,X4774),X4773) = c_Divides_Odiv__class_Omod(X4776,c_Groups_Oplus__class_Oplus(X4776,c_Divides_Odiv__class_Omod(X4776,X4775,X4773),c_Divides_Odiv__class_Omod(X4776,X4774,X4773)),X4773) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_1655,plain,
! [X4880,X4881,X4882,X4883] :
( ~ class_Divides_Osemiring__div(X4883)
| c_Divides_Odiv__class_Omod(X4883,c_Groups_Otimes__class_Otimes(X4883,X4882,X4881),X4880) = c_Divides_Odiv__class_Omod(X4883,c_Groups_Otimes__class_Otimes(X4883,c_Divides_Odiv__class_Omod(X4883,X4882,X4880),c_Divides_Odiv__class_Omod(X4883,X4881,X4880)),X4880) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
cnf(i_0_1656,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1657,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
cnf(i_0_1658,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1276]) ).
cnf(i_0_1659,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) != c_Power_Opower__class_Opower(X1,X4,c_Nat_OSuc(X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1277]) ).
cnf(i_0_1660,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1278]) ).
cnf(i_0_1661,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1279]) ).
cnf(i_0_1662,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1280]) ).
cnf(i_0_1663,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1281]) ).
cnf(i_0_1664,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1282]) ).
fof(i_0_1665,plain,
! [X4533,X4534,X4535] :
( ~ class_Rings_Olinordered__semidom(X4535)
| ~ c_Orderings_Oord__class_Oless(X4535,c_Groups_Ozero__class_Ozero(X4535),X4534)
| ~ c_Orderings_Oord__class_Oless(X4535,X4534,c_Groups_Oone__class_Oone(X4535))
| c_Orderings_Oord__class_Oless(X4535,c_Groups_Otimes__class_Otimes(X4535,X4534,c_Power_Opower__class_Opower(X4535,X4534,X4533)),c_Power_Opower__class_Opower(X4535,X4534,X4533)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
cnf(i_0_1666,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
cnf(i_0_1667,plain,
( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1668,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1285]) ).
cnf(i_0_1669,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1286]) ).
fof(i_0_1670,plain,
! [X4241,X4242,X4243,X4244,X4245,X4246,X4247] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4242,X4241)
| hBOOL(hAPP(X4243,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4243,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4242,X4241))) )
& ( X4242 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4241,X4244)
| hBOOL(hAPP(X4243,X4244))
| ~ hBOOL(hAPP(X4243,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4242,X4241))) )
& ( X4246 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4245,esk15_3(X4245,X4246,X4247))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4246,X4245)
| hBOOL(hAPP(X4247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4246,X4245))) )
& ( ~ hBOOL(hAPP(X4247,esk15_3(X4245,X4246,X4247)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4246,X4245)
| hBOOL(hAPP(X4247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4246,X4245))) )
& ( X4246 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4245,esk15_3(X4245,X4246,X4247))
| ~ hBOOL(hAPP(X4247,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4246,X4245))) )
& ( ~ hBOOL(hAPP(X4247,esk15_3(X4245,X4246,X4247)))
| ~ hBOOL(hAPP(X4247,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4247,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4246,X4245))) ) ),
inference(distribute,[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)],[fact_nat__diff__split])])])])])]) ).
fof(i_0_1671,plain,
! [X4233,X4234,X4235,X4236,X4237,X4238,X4239] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4234,X4233)
| hBOOL(hAPP(X4235,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X4235,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4234,X4233))) )
& ( X4234 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4233,X4236)
| hBOOL(hAPP(X4235,X4236))
| ~ hBOOL(hAPP(X4235,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4234,X4233))) )
& ( X4238 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4237,esk14_3(X4237,X4238,X4239))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4238,X4237)
| hBOOL(hAPP(X4239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4237))) )
& ( ~ hBOOL(hAPP(X4239,esk14_3(X4237,X4238,X4239)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4238,X4237)
| hBOOL(hAPP(X4239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4237))) )
& ( X4238 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4237,esk14_3(X4237,X4238,X4239))
| ~ hBOOL(hAPP(X4239,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4237))) )
& ( ~ hBOOL(hAPP(X4239,esk14_3(X4237,X4238,X4239)))
| ~ hBOOL(hAPP(X4239,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X4239,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4238,X4237))) ) ),
inference(distribute,[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)],[i_0_1287])])])])])]) ).
fof(i_0_1672,plain,
! [X4813,X4814,X4815,X4816,X4817,X4818] :
( ~ class_Divides_Oring__div(X4818)
| c_Divides_Odiv__class_Omod(X4818,X4817,X4816) != c_Divides_Odiv__class_Omod(X4818,X4815,X4816)
| c_Divides_Odiv__class_Omod(X4818,X4814,X4816) != c_Divides_Odiv__class_Omod(X4818,X4813,X4816)
| c_Divides_Odiv__class_Omod(X4818,c_Groups_Ominus__class_Ominus(X4818,X4817,X4814),X4816) = c_Divides_Odiv__class_Omod(X4818,c_Groups_Ominus__class_Ominus(X4818,X4815,X4813),X4816) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).
fof(i_0_1673,plain,
! [X4785,X4786,X4787,X4788,X4789,X4790] :
( ~ class_Divides_Osemiring__div(X4790)
| c_Divides_Odiv__class_Omod(X4790,X4789,X4788) != c_Divides_Odiv__class_Omod(X4790,X4787,X4788)
| c_Divides_Odiv__class_Omod(X4790,X4786,X4788) != c_Divides_Odiv__class_Omod(X4790,X4785,X4788)
| c_Divides_Odiv__class_Omod(X4790,c_Groups_Oplus__class_Oplus(X4790,X4789,X4786),X4788) = c_Divides_Odiv__class_Omod(X4790,c_Groups_Oplus__class_Oplus(X4790,X4787,X4785),X4788) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_1674,plain,
! [X4896,X4897,X4898,X4899,X4900,X4901] :
( ~ class_Divides_Osemiring__div(X4901)
| c_Divides_Odiv__class_Omod(X4901,X4900,X4899) != c_Divides_Odiv__class_Omod(X4901,X4898,X4899)
| c_Divides_Odiv__class_Omod(X4901,X4897,X4899) != c_Divides_Odiv__class_Omod(X4901,X4896,X4899)
| c_Divides_Odiv__class_Omod(X4901,c_Groups_Otimes__class_Otimes(X4901,X4900,X4897),X4899) = c_Divides_Odiv__class_Omod(X4901,c_Groups_Otimes__class_Otimes(X4901,X4898,X4896),X4899) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_1675,plain,
! [X4501] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4501),X4501),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4501,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4501,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4501),X4501),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__less__0])]) ).
cnf(i_0_1676,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
fof(i_0_1677,plain,
! [X4955,X4956,X4957,X4958] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4957)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4957)
| X4957 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4958,X4957) = X4955
| X4958 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4957,X4956),X4955) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4957,X4955)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4955,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4957)
| X4957 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4958,X4957) = X4955
| X4958 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4957,X4956),X4955) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4957)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4955,X4957)
| X4957 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4958,X4957) = X4955
| X4958 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4957,X4956),X4955) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4957,X4955)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4955,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4955)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4955,X4957)
| X4957 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4958,X4957) = X4955
| X4958 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4957,X4956),X4955) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1289])])]) ).
fof(i_0_1678,plain,
! [X2658,X2659,X2660,X2661,X2662] :
( ~ class_Rings_Ocomm__semiring__1(X2662)
| c_Groups_Otimes__class_Otimes(X2662,c_Groups_Otimes__class_Otimes(X2662,X2661,X2660),c_Groups_Otimes__class_Otimes(X2662,X2659,X2658)) = c_Groups_Otimes__class_Otimes(X2662,X2659,c_Groups_Otimes__class_Otimes(X2662,c_Groups_Otimes__class_Otimes(X2662,X2661,X2660),X2658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1679,plain,
! [X2663,X2664,X2665,X2666,X2667] :
( ~ class_Rings_Ocomm__semiring__1(X2667)
| c_Groups_Otimes__class_Otimes(X2667,c_Groups_Otimes__class_Otimes(X2667,X2666,X2665),c_Groups_Otimes__class_Otimes(X2667,X2664,X2663)) = c_Groups_Otimes__class_Otimes(X2667,X2666,c_Groups_Otimes__class_Otimes(X2667,X2665,c_Groups_Otimes__class_Otimes(X2667,X2664,X2663))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
cnf(i_0_1680,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),X2),c_Nat_OSuc(X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1290]) ).
cnf(i_0_1681,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1291]) ).
cnf(i_0_1682,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1292]) ).
cnf(i_0_1683,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1293]) ).
cnf(i_0_1684,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1294]) ).
cnf(i_0_1685,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
cnf(i_0_1686,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
cnf(i_0_1687,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
cnf(i_0_1688,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1298]) ).
fof(i_0_1689,plain,
! [X4119,X4120,X4121,X4122,X4123] :
( ~ class_Rings_Oordered__semiring(X4123)
| ~ c_Orderings_Oord__class_Oless__eq(X4123,X4122,X4121)
| ~ c_Orderings_Oord__class_Oless__eq(X4123,X4120,X4119)
| ~ c_Orderings_Oord__class_Oless__eq(X4123,c_Groups_Ozero__class_Ozero(X4123),X4122)
| ~ c_Orderings_Oord__class_Oless__eq(X4123,c_Groups_Ozero__class_Ozero(X4123),X4120)
| c_Orderings_Oord__class_Oless__eq(X4123,c_Groups_Otimes__class_Otimes(X4123,X4122,X4120),c_Groups_Otimes__class_Otimes(X4123,X4121,X4119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1690,plain,
! [X4114,X4115,X4116,X4117,X4118] :
( ~ class_Rings_Oordered__semiring(X4118)
| ~ c_Orderings_Oord__class_Oless__eq(X4118,X4117,X4116)
| ~ c_Orderings_Oord__class_Oless__eq(X4118,X4115,X4114)
| ~ c_Orderings_Oord__class_Oless__eq(X4118,c_Groups_Ozero__class_Ozero(X4118),X4116)
| ~ c_Orderings_Oord__class_Oless__eq(X4118,c_Groups_Ozero__class_Ozero(X4118),X4115)
| c_Orderings_Oord__class_Oless__eq(X4118,c_Groups_Otimes__class_Otimes(X4118,X4117,X4115),c_Groups_Otimes__class_Otimes(X4118,X4116,X4114)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1691,plain,
! [X4381,X4382,X4383,X4384,X4385] :
( ~ class_Rings_Olinordered__semiring__strict(X4385)
| ~ c_Orderings_Oord__class_Oless(X4385,X4384,X4383)
| ~ c_Orderings_Oord__class_Oless__eq(X4385,X4382,X4381)
| ~ c_Orderings_Oord__class_Oless__eq(X4385,c_Groups_Ozero__class_Ozero(X4385),X4384)
| ~ c_Orderings_Oord__class_Oless(X4385,c_Groups_Ozero__class_Ozero(X4385),X4382)
| c_Orderings_Oord__class_Oless(X4385,c_Groups_Otimes__class_Otimes(X4385,X4384,X4382),c_Groups_Otimes__class_Otimes(X4385,X4383,X4381)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1692,plain,
! [X4376,X4377,X4378,X4379,X4380] :
( ~ class_Rings_Olinordered__semiring__strict(X4380)
| ~ c_Orderings_Oord__class_Oless__eq(X4380,X4379,X4378)
| ~ c_Orderings_Oord__class_Oless(X4380,X4377,X4376)
| ~ c_Orderings_Oord__class_Oless(X4380,c_Groups_Ozero__class_Ozero(X4380),X4379)
| ~ c_Orderings_Oord__class_Oless__eq(X4380,c_Groups_Ozero__class_Ozero(X4380),X4377)
| c_Orderings_Oord__class_Oless(X4380,c_Groups_Otimes__class_Otimes(X4380,X4379,X4377),c_Groups_Otimes__class_Otimes(X4380,X4378,X4376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1693,plain,
! [X4386,X4387,X4388,X4389,X4390] :
( ~ class_Rings_Olinordered__semiring__strict(X4390)
| ~ c_Orderings_Oord__class_Oless(X4390,X4389,X4388)
| ~ c_Orderings_Oord__class_Oless(X4390,X4387,X4386)
| ~ c_Orderings_Oord__class_Oless__eq(X4390,c_Groups_Ozero__class_Ozero(X4390),X4389)
| ~ c_Orderings_Oord__class_Oless__eq(X4390,c_Groups_Ozero__class_Ozero(X4390),X4387)
| c_Orderings_Oord__class_Oless(X4390,c_Groups_Otimes__class_Otimes(X4390,X4389,X4387),c_Groups_Otimes__class_Otimes(X4390,X4388,X4386)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1694,plain,
! [X4391,X4392,X4393,X4394,X4395] :
( ~ class_Rings_Olinordered__semiring__strict(X4395)
| ~ c_Orderings_Oord__class_Oless(X4395,X4394,X4393)
| ~ c_Orderings_Oord__class_Oless(X4395,X4392,X4391)
| ~ c_Orderings_Oord__class_Oless(X4395,c_Groups_Ozero__class_Ozero(X4395),X4393)
| ~ c_Orderings_Oord__class_Oless__eq(X4395,c_Groups_Ozero__class_Ozero(X4395),X4392)
| c_Orderings_Oord__class_Oless(X4395,c_Groups_Otimes__class_Otimes(X4395,X4394,X4392),c_Groups_Otimes__class_Otimes(X4395,X4393,X4391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
cnf(i_0_1695,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1299]) ).
cnf(i_0_1696,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1300]) ).
fof(i_0_1697,plain,
! [X4653,X4654,X4655] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4654,X4655),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4653,X4655))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4654,X4653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4655,X4653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4655,X4654) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4654,X4653)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4654,X4655),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4653,X4655))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4655,X4653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4655,X4654) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1698,plain,
! [X3638,X3639,X3640] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3639,X3640),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3638,X3640))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3640,X3638)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3640,X3639) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3639,X3640),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3638,X3640))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3640,X3638)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3640,X3639) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
cnf(i_0_1699,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(split_conjunct,[status(thm)],[i_0_1301]) ).
fof(i_0_1700,plain,
! [X3278,X3279,X3280] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3280,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3279,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3280,X3278)))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3280,X3279) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3280,X3279)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3280,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3279,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3280,X3278))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__reduce])]) ).
cnf(i_0_1701,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(split_conjunct,[status(thm)],[i_0_1302]) ).
fof(i_0_1702,plain,
! [X5062,X5063,X5064,X5065] :
( ~ class_Divides_Osemiring__div(X5065)
| ~ c_Rings_Odvd__class_Odvd(X5065,X5064,X5063)
| ~ c_Rings_Odvd__class_Odvd(X5065,X5064,X5062)
| c_Divides_Odiv__class_Odiv(X5065,c_Groups_Oplus__class_Oplus(X5065,X5063,X5062),X5064) = c_Groups_Oplus__class_Oplus(X5065,c_Divides_Odiv__class_Odiv(X5065,X5063,X5064),c_Divides_Odiv__class_Odiv(X5065,X5062,X5064)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).
fof(i_0_1703,plain,
! [X4427,X4428,X4429] :
( ~ class_Rings_Olinordered__ring(X4429)
| c_Orderings_Oord__class_Oless__eq(X4429,c_Groups_Ozero__class_Ozero(X4429),c_Groups_Oplus__class_Oplus(X4429,c_Groups_Otimes__class_Otimes(X4429,X4428,X4428),c_Groups_Otimes__class_Otimes(X4429,X4427,X4427))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
cnf(i_0_1704,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1705,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1272]) ).
cnf(i_0_1706,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1303]) ).
cnf(i_0_1707,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1304]) ).
fof(i_0_1708,plain,
! [X4443,X4444,X4445] :
( ~ class_Rings_Olinordered__semidom(X4445)
| ~ c_Orderings_Oord__class_Oless(X4445,c_Groups_Oone__class_Oone(X4445),X4444)
| c_Orderings_Oord__class_Oless(X4445,c_Power_Opower__class_Opower(X4445,X4444,X4443),c_Groups_Otimes__class_Otimes(X4445,X4444,c_Power_Opower__class_Opower(X4445,X4444,X4443))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
cnf(i_0_1709,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1305]) ).
fof(i_0_1710,plain,
! [X4356,X4357,X4358,X4359] :
( ~ class_Rings_Olinordered__semiring__strict(X4359)
| ~ c_Orderings_Oord__class_Oless__eq(X4359,c_Groups_Otimes__class_Otimes(X4359,X4358,X4357),c_Groups_Otimes__class_Otimes(X4359,X4356,X4357))
| ~ c_Orderings_Oord__class_Oless(X4359,c_Groups_Ozero__class_Ozero(X4359),X4357)
| c_Orderings_Oord__class_Oless__eq(X4359,X4358,X4356) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1711,plain,
! [X4352,X4353,X4354,X4355] :
( ~ class_Rings_Olinordered__semiring__strict(X4355)
| ~ c_Orderings_Oord__class_Oless__eq(X4355,c_Groups_Otimes__class_Otimes(X4355,X4354,X4353),c_Groups_Otimes__class_Otimes(X4355,X4354,X4352))
| ~ c_Orderings_Oord__class_Oless(X4355,c_Groups_Ozero__class_Ozero(X4355),X4354)
| c_Orderings_Oord__class_Oless__eq(X4355,X4353,X4352) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1712,plain,
! [X4400,X4401,X4402,X4403] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4403,c_Groups_Otimes__class_Otimes(X4403,X4402,X4401),c_Groups_Otimes__class_Otimes(X4403,X4402,X4400))
| c_Orderings_Oord__class_Oless__eq(X4403,X4401,X4400)
| ~ c_Orderings_Oord__class_Oless(X4403,c_Groups_Ozero__class_Ozero(X4403),X4402)
| ~ class_Rings_Olinordered__ring__strict(X4403) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4403,X4401,X4400)
| c_Orderings_Oord__class_Oless__eq(X4403,c_Groups_Otimes__class_Otimes(X4403,X4402,X4401),c_Groups_Otimes__class_Otimes(X4403,X4402,X4400))
| ~ c_Orderings_Oord__class_Oless(X4403,c_Groups_Ozero__class_Ozero(X4403),X4402)
| ~ class_Rings_Olinordered__ring__strict(X4403) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1713,plain,
! [X4372,X4373,X4374,X4375] :
( ~ class_Rings_Olinordered__semiring(X4375)
| ~ c_Orderings_Oord__class_Oless(X4375,c_Groups_Otimes__class_Otimes(X4375,X4374,X4373),c_Groups_Otimes__class_Otimes(X4375,X4372,X4373))
| ~ c_Orderings_Oord__class_Oless__eq(X4375,c_Groups_Ozero__class_Ozero(X4375),X4373)
| c_Orderings_Oord__class_Oless(X4375,X4374,X4372) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1714,plain,
! [X4368,X4369,X4370,X4371] :
( ~ class_Rings_Olinordered__semiring__strict(X4371)
| ~ c_Orderings_Oord__class_Oless(X4371,c_Groups_Otimes__class_Otimes(X4371,X4370,X4369),c_Groups_Otimes__class_Otimes(X4371,X4368,X4369))
| ~ c_Orderings_Oord__class_Oless__eq(X4371,c_Groups_Ozero__class_Ozero(X4371),X4369)
| c_Orderings_Oord__class_Oless(X4371,X4370,X4368) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1715,plain,
! [X4432,X4433,X4434,X4435] :
( ~ class_Rings_Olinordered__semidom(X4435)
| ~ c_Orderings_Oord__class_Oless(X4435,c_Power_Opower__class_Opower(X4435,X4434,X4433),c_Power_Opower__class_Opower(X4435,X4432,X4433))
| ~ c_Orderings_Oord__class_Oless__eq(X4435,c_Groups_Ozero__class_Ozero(X4435),X4432)
| c_Orderings_Oord__class_Oless(X4435,X4434,X4432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1716,plain,
! [X4364,X4365,X4366,X4367] :
( ~ class_Rings_Olinordered__semiring(X4367)
| ~ c_Orderings_Oord__class_Oless(X4367,c_Groups_Otimes__class_Otimes(X4367,X4366,X4365),c_Groups_Otimes__class_Otimes(X4367,X4366,X4364))
| ~ c_Orderings_Oord__class_Oless__eq(X4367,c_Groups_Ozero__class_Ozero(X4367),X4366)
| c_Orderings_Oord__class_Oless(X4367,X4365,X4364) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1717,plain,
! [X4360,X4361,X4362,X4363] :
( ~ class_Rings_Olinordered__semiring__strict(X4363)
| ~ c_Orderings_Oord__class_Oless(X4363,c_Groups_Otimes__class_Otimes(X4363,X4362,X4361),c_Groups_Otimes__class_Otimes(X4363,X4362,X4360))
| ~ c_Orderings_Oord__class_Oless__eq(X4363,c_Groups_Ozero__class_Ozero(X4363),X4362)
| c_Orderings_Oord__class_Oless(X4363,X4361,X4360) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1718,plain,
! [X3145,X3146,X3147,X3148] :
( ( ~ c_Orderings_Oord__class_Oless(X3148,c_Groups_Otimes__class_Otimes(X3148,X3147,X3146),c_Groups_Otimes__class_Otimes(X3148,X3147,X3145))
| c_Orderings_Oord__class_Oless(X3148,X3146,X3145)
| ~ c_Orderings_Oord__class_Oless(X3148,c_Groups_Ozero__class_Ozero(X3148),X3147)
| ~ class_Rings_Olinordered__ring__strict(X3148) )
& ( ~ c_Orderings_Oord__class_Oless(X3148,X3146,X3145)
| c_Orderings_Oord__class_Oless(X3148,c_Groups_Otimes__class_Otimes(X3148,X3147,X3146),c_Groups_Otimes__class_Otimes(X3148,X3147,X3145))
| ~ c_Orderings_Oord__class_Oless(X3148,c_Groups_Ozero__class_Ozero(X3148),X3147)
| ~ class_Rings_Olinordered__ring__strict(X3148) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1719,plain,
! [X4396,X4397,X4398,X4399] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4399,c_Groups_Otimes__class_Otimes(X4399,X4398,X4397),c_Groups_Otimes__class_Otimes(X4399,X4398,X4396))
| c_Orderings_Oord__class_Oless__eq(X4399,X4396,X4397)
| ~ c_Orderings_Oord__class_Oless(X4399,X4398,c_Groups_Ozero__class_Ozero(X4399))
| ~ class_Rings_Olinordered__ring__strict(X4399) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4399,X4396,X4397)
| c_Orderings_Oord__class_Oless__eq(X4399,c_Groups_Otimes__class_Otimes(X4399,X4398,X4397),c_Groups_Otimes__class_Otimes(X4399,X4398,X4396))
| ~ c_Orderings_Oord__class_Oless(X4399,X4398,c_Groups_Ozero__class_Ozero(X4399))
| ~ class_Rings_Olinordered__ring__strict(X4399) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1720,plain,
! [X3126,X3127,X3128,X3129] :
( ( ~ c_Orderings_Oord__class_Oless(X3129,c_Groups_Otimes__class_Otimes(X3129,X3128,X3127),c_Groups_Otimes__class_Otimes(X3129,X3128,X3126))
| c_Orderings_Oord__class_Oless(X3129,X3126,X3127)
| ~ c_Orderings_Oord__class_Oless(X3129,X3128,c_Groups_Ozero__class_Ozero(X3129))
| ~ class_Rings_Olinordered__ring__strict(X3129) )
& ( ~ c_Orderings_Oord__class_Oless(X3129,X3126,X3127)
| c_Orderings_Oord__class_Oless(X3129,c_Groups_Otimes__class_Otimes(X3129,X3128,X3127),c_Groups_Otimes__class_Otimes(X3129,X3128,X3126))
| ~ c_Orderings_Oord__class_Oless(X3129,X3128,c_Groups_Ozero__class_Ozero(X3129))
| ~ class_Rings_Olinordered__ring__strict(X3129) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1721,plain,
! [X3600,X3601,X3602,X3603] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3603,c_Power_Opower__class_Opower(X3603,X3602,X3601),c_Power_Opower__class_Opower(X3603,X3602,X3600))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3601,X3600)
| ~ c_Orderings_Oord__class_Oless(X3603,c_Groups_Oone__class_Oone(X3603),X3602)
| ~ class_Rings_Olinordered__semidom(X3603) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3601,X3600)
| c_Orderings_Oord__class_Oless__eq(X3603,c_Power_Opower__class_Opower(X3603,X3602,X3601),c_Power_Opower__class_Opower(X3603,X3602,X3600))
| ~ c_Orderings_Oord__class_Oless(X3603,c_Groups_Oone__class_Oone(X3603),X3602)
| ~ class_Rings_Olinordered__semidom(X3603) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1722,plain,
! [X3596,X3597,X3598,X3599] :
( ~ class_Rings_Olinordered__semidom(X3599)
| ~ c_Orderings_Oord__class_Oless(X3599,c_Groups_Oone__class_Oone(X3599),X3598)
| ~ c_Orderings_Oord__class_Oless__eq(X3599,c_Power_Opower__class_Opower(X3599,X3598,X3597),c_Power_Opower__class_Opower(X3599,X3598,X3596))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3597,X3596) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1723,plain,
! [X4257,X4258,X4259,X4260] :
( ( ~ c_Orderings_Oord__class_Oless(X4260,c_Power_Opower__class_Opower(X4260,X4259,X4258),c_Power_Opower__class_Opower(X4260,X4259,X4257))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4258,X4257)
| ~ c_Orderings_Oord__class_Oless(X4260,c_Groups_Oone__class_Oone(X4260),X4259)
| ~ class_Rings_Olinordered__semidom(X4260) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4258,X4257)
| c_Orderings_Oord__class_Oless(X4260,c_Power_Opower__class_Opower(X4260,X4259,X4258),c_Power_Opower__class_Opower(X4260,X4259,X4257))
| ~ c_Orderings_Oord__class_Oless(X4260,c_Groups_Oone__class_Oone(X4260),X4259)
| ~ class_Rings_Olinordered__semidom(X4260) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1724,plain,
! [X4253,X4254,X4255,X4256] :
( ~ class_Rings_Olinordered__semidom(X4256)
| ~ c_Orderings_Oord__class_Oless(X4256,c_Groups_Oone__class_Oone(X4256),X4255)
| ~ c_Orderings_Oord__class_Oless(X4256,c_Power_Opower__class_Opower(X4256,X4255,X4254),c_Power_Opower__class_Opower(X4256,X4255,X4253))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4254,X4253) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1725,plain,
! [X4102,X4103,X4104,X4105] :
( ~ class_Int_Onumber(X4105)
| ~ class_Rings_Oring(X4105)
| c_Groups_Otimes__class_Otimes(X4105,c_Groups_Ominus__class_Ominus(X4105,X4104,X4103),c_Int_Onumber__class_Onumber__of(X4105,X4102)) = c_Groups_Ominus__class_Ominus(X4105,c_Groups_Otimes__class_Otimes(X4105,X4104,c_Int_Onumber__class_Onumber__of(X4105,X4102)),c_Groups_Otimes__class_Otimes(X4105,X4103,c_Int_Onumber__class_Onumber__of(X4105,X4102))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).
fof(i_0_1726,plain,
! [X3096,X3097,X3098,X3099] :
( ~ class_Int_Onumber(X3099)
| ~ class_Rings_Osemiring(X3099)
| c_Groups_Otimes__class_Otimes(X3099,c_Groups_Oplus__class_Oplus(X3099,X3098,X3097),c_Int_Onumber__class_Onumber__of(X3099,X3096)) = c_Groups_Oplus__class_Oplus(X3099,c_Groups_Otimes__class_Otimes(X3099,X3098,c_Int_Onumber__class_Onumber__of(X3099,X3096)),c_Groups_Otimes__class_Otimes(X3099,X3097,c_Int_Onumber__class_Onumber__of(X3099,X3096))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).
fof(i_0_1727,plain,
! [X4098,X4099,X4100,X4101] :
( ~ class_Int_Onumber(X4101)
| ~ class_Rings_Oring(X4101)
| c_Groups_Otimes__class_Otimes(X4101,c_Int_Onumber__class_Onumber__of(X4101,X4100),c_Groups_Ominus__class_Ominus(X4101,X4099,X4098)) = c_Groups_Ominus__class_Ominus(X4101,c_Groups_Otimes__class_Otimes(X4101,c_Int_Onumber__class_Onumber__of(X4101,X4100),X4099),c_Groups_Otimes__class_Otimes(X4101,c_Int_Onumber__class_Onumber__of(X4101,X4100),X4098)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).
fof(i_0_1728,plain,
! [X3092,X3093,X3094,X3095] :
( ~ class_Int_Onumber(X3095)
| ~ class_Rings_Osemiring(X3095)
| c_Groups_Otimes__class_Otimes(X3095,c_Int_Onumber__class_Onumber__of(X3095,X3094),c_Groups_Oplus__class_Oplus(X3095,X3093,X3092)) = c_Groups_Oplus__class_Oplus(X3095,c_Groups_Otimes__class_Otimes(X3095,c_Int_Onumber__class_Onumber__of(X3095,X3094),X3093),c_Groups_Otimes__class_Otimes(X3095,c_Int_Onumber__class_Onumber__of(X3095,X3094),X3092)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).
cnf(i_0_1729,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1264]) ).
cnf(i_0_1730,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1265]) ).
cnf(i_0_1731,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1266]) ).
cnf(i_0_1732,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1267]) ).
cnf(i_0_1733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1268]) ).
cnf(i_0_1734,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1269]) ).
cnf(i_0_1735,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1270]) ).
cnf(i_0_1736,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit1(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1271]) ).
fof(i_0_1737,plain,
! [X2700,X2701,X2702] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2702,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2702),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2701),X2700)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2702,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2702),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2701),X2700)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2702,X2701)),X2700) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])]) ).
fof(i_0_1738,plain,
! [X3574,X3575,X3576] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3575,X3576),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3574,X3576))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3575,X3574)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3576) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3575,X3574)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3575,X3576),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3574,X3576))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3576) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1739,plain,
! [X3577,X3578,X3579] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3579,X3578),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3579,X3577))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3578,X3577)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3579) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3578,X3577)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3579,X3578),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3579,X3577))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3579) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1740,plain,
! [X4300,X4301,X4302] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4302,X4301),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4300,X4301))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4301)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4302,X4300) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4301)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4302,X4301),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4300,X4301)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4302,X4300)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4302,X4301),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4300,X4301)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1741,plain,
! [X4680,X4681,X4682] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X4682,X4681),c_Power_Opower__class_Opower(tc_Nat_Onat,X4682,X4680))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4682)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4681,X4680) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).
fof(i_0_1742,plain,
! [X4303,X4304,X4305] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4304),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4303))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4305)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4304,X4303) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4305)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4304),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4303)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4304,X4303)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4304),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4305,X4303)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1743,plain,
! [X4297,X4298,X4299] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4299,X4298),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4299,X4297))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4298,X4297)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4299) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4298,X4297)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4299,X4298),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4299,X4297))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4299) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1744,plain,
! [X3451,X3452,X3453] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3453,X3452),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3453,X3451))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3453)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3452,X3451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).
fof(i_0_1745,plain,
! [X3448,X3449,X3450] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3450,X3449),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3450,X3448))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3449,X3448)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3450) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3449,X3448)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3450,X3449),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3450,X3448))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3450) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).
fof(i_0_1746,plain,
! [X4525,X4526,X4527] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4526,X4527),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4525,X4527))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4526,X4525)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4527) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4526,X4525)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4526,X4527),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4525,X4527))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4527) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1747,plain,
! [X3281,X3282,X3283] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3283)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3283,X3282),c_Power_Opower__class_Opower(tc_Nat_Onat,X3283,X3281))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3282,X3281) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1748,plain,
! [X3423,X3424,X3425] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3425,X3424),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3425,X3423))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3424,X3423)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3425) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3424,X3423)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3425,X3424),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3425,X3423))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3425) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1749,plain,
! [X3580,X3581,X3582,X3583] :
( ~ class_Rings_Olinordered__semidom(X3583)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3582,X3581)
| ~ c_Orderings_Oord__class_Oless__eq(X3583,c_Groups_Ozero__class_Ozero(X3583),X3580)
| ~ c_Orderings_Oord__class_Oless__eq(X3583,X3580,c_Groups_Oone__class_Oone(X3583))
| c_Orderings_Oord__class_Oless__eq(X3583,c_Power_Opower__class_Opower(X3583,X3580,X3581),c_Power_Opower__class_Opower(X3583,X3580,X3582)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1750,plain,
! [X4436,X4437,X4438,X4439] :
( ~ class_Rings_Olinordered__semidom(X4439)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4438,X4437)
| ~ c_Orderings_Oord__class_Oless(X4439,c_Groups_Ozero__class_Ozero(X4439),X4436)
| ~ c_Orderings_Oord__class_Oless(X4439,X4436,c_Groups_Oone__class_Oone(X4439))
| c_Orderings_Oord__class_Oless(X4439,c_Power_Opower__class_Opower(X4439,X4436,X4437),c_Power_Opower__class_Opower(X4439,X4436,X4438)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1751,plain,
! [X3149,X3150,X3151,X3152] :
( ( c_Orderings_Oord__class_Oless(X3152,X3151,c_Groups_Ozero__class_Ozero(X3152))
| c_Orderings_Oord__class_Oless(X3152,c_Groups_Ozero__class_Ozero(X3152),X3151)
| ~ c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) )
& ( c_Orderings_Oord__class_Oless(X3152,X3149,X3150)
| c_Orderings_Oord__class_Oless(X3152,c_Groups_Ozero__class_Ozero(X3152),X3151)
| ~ c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) )
& ( c_Orderings_Oord__class_Oless(X3152,X3151,c_Groups_Ozero__class_Ozero(X3152))
| c_Orderings_Oord__class_Oless(X3152,X3150,X3149)
| ~ c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) )
& ( c_Orderings_Oord__class_Oless(X3152,X3149,X3150)
| c_Orderings_Oord__class_Oless(X3152,X3150,X3149)
| ~ c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) )
& ( ~ c_Orderings_Oord__class_Oless(X3152,c_Groups_Ozero__class_Ozero(X3152),X3151)
| ~ c_Orderings_Oord__class_Oless(X3152,X3150,X3149)
| c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) )
& ( ~ c_Orderings_Oord__class_Oless(X3152,X3151,c_Groups_Ozero__class_Ozero(X3152))
| ~ c_Orderings_Oord__class_Oless(X3152,X3149,X3150)
| c_Orderings_Oord__class_Oless(X3152,c_Groups_Otimes__class_Otimes(X3152,X3151,X3150),c_Groups_Otimes__class_Otimes(X3152,X3151,X3149))
| ~ class_Rings_Olinordered__ring__strict(X3152) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1752,plain,
! [X3153,X3154,X3155,X3156] :
( ( c_Orderings_Oord__class_Oless(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| ~ c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless(X3156,X3153,X3155)
| c_Orderings_Oord__class_Oless(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| ~ c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless(X3156,X3155,X3153)
| ~ c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless(X3156,X3153,X3155)
| c_Orderings_Oord__class_Oless(X3156,X3155,X3153)
| ~ c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( ~ c_Orderings_Oord__class_Oless(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| ~ c_Orderings_Oord__class_Oless(X3156,X3155,X3153)
| c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( ~ c_Orderings_Oord__class_Oless(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| ~ c_Orderings_Oord__class_Oless(X3156,X3153,X3155)
| c_Orderings_Oord__class_Oless(X3156,c_Groups_Otimes__class_Otimes(X3156,X3155,X3154),c_Groups_Otimes__class_Otimes(X3156,X3153,X3154))
| ~ class_Rings_Olinordered__ring__strict(X3156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1753,plain,
! [X4536,X4537,X4538,X4539] :
( ~ class_Rings_Olinordered__semidom(X4539)
| ~ c_Orderings_Oord__class_Oless(X4539,X4538,X4537)
| ~ c_Orderings_Oord__class_Oless__eq(X4539,c_Groups_Ozero__class_Ozero(X4539),X4538)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4536)
| c_Orderings_Oord__class_Oless(X4539,c_Power_Opower__class_Opower(X4539,X4538,X4536),c_Power_Opower__class_Opower(X4539,X4537,X4536)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1754,plain,
! [X2738,X2739,X2740,X2741,X2742] :
( ~ class_Rings_Ocomm__semiring__1(X2742)
| c_Groups_Oplus__class_Oplus(X2742,c_Groups_Oplus__class_Oplus(X2742,X2741,X2740),c_Groups_Oplus__class_Oplus(X2742,X2739,X2738)) = c_Groups_Oplus__class_Oplus(X2742,c_Groups_Oplus__class_Oplus(X2742,X2741,X2739),c_Groups_Oplus__class_Oplus(X2742,X2740,X2738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1755,plain,
! [X2653,X2654,X2655,X2656,X2657] :
( ~ class_Rings_Ocomm__semiring__1(X2657)
| c_Groups_Otimes__class_Otimes(X2657,c_Groups_Otimes__class_Otimes(X2657,X2656,X2655),c_Groups_Otimes__class_Otimes(X2657,X2654,X2653)) = c_Groups_Otimes__class_Otimes(X2657,c_Groups_Otimes__class_Otimes(X2657,X2656,X2654),c_Groups_Otimes__class_Otimes(X2657,X2655,X2653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1756,plain,
! [X4781,X4782,X4783,X4784] :
( ~ class_Divides_Osemiring__div(X4784)
| c_Divides_Odiv__class_Omod(X4784,c_Groups_Oplus__class_Oplus(X4784,c_Divides_Odiv__class_Omod(X4784,X4783,X4782),X4781),X4782) = c_Divides_Odiv__class_Omod(X4784,c_Groups_Oplus__class_Oplus(X4784,X4783,X4781),X4782) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_1757,plain,
! [X4892,X4893,X4894,X4895] :
( ~ class_Divides_Osemiring__div(X4895)
| c_Divides_Odiv__class_Omod(X4895,c_Groups_Otimes__class_Otimes(X4895,c_Divides_Odiv__class_Omod(X4895,X4894,X4893),X4892),X4893) = c_Divides_Odiv__class_Omod(X4895,c_Groups_Otimes__class_Otimes(X4895,X4894,X4892),X4893) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_1758,plain,
! [X4777,X4778,X4779,X4780] :
( ~ class_Divides_Osemiring__div(X4780)
| c_Divides_Odiv__class_Omod(X4780,c_Groups_Oplus__class_Oplus(X4780,X4779,c_Divides_Odiv__class_Omod(X4780,X4778,X4777)),X4777) = c_Divides_Odiv__class_Omod(X4780,c_Groups_Oplus__class_Oplus(X4780,X4779,X4778),X4777) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_1759,plain,
! [X4829,X4830,X4831,X4832] :
( ~ class_Divides_Oring__div(X4832)
| c_Divides_Odiv__class_Omod(X4832,c_Groups_Ominus__class_Ominus(X4832,X4831,X4830),X4829) = c_Divides_Odiv__class_Omod(X4832,c_Groups_Ominus__class_Ominus(X4832,c_Divides_Odiv__class_Omod(X4832,X4831,X4829),X4830),X4829) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).
fof(i_0_1760,plain,
! [X4769,X4770,X4771,X4772] :
( ~ class_Divides_Osemiring__div(X4772)
| c_Divides_Odiv__class_Omod(X4772,c_Groups_Oplus__class_Oplus(X4772,X4771,X4770),X4769) = c_Divides_Odiv__class_Omod(X4772,c_Groups_Oplus__class_Oplus(X4772,c_Divides_Odiv__class_Omod(X4772,X4771,X4769),X4770),X4769) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_1761,plain,
! [X4876,X4877,X4878,X4879] :
( ~ class_Divides_Osemiring__div(X4879)
| c_Divides_Odiv__class_Omod(X4879,c_Groups_Otimes__class_Otimes(X4879,X4878,X4877),X4876) = c_Divides_Odiv__class_Omod(X4879,c_Groups_Otimes__class_Otimes(X4879,c_Divides_Odiv__class_Omod(X4879,X4878,X4876),X4877),X4876) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_1762,plain,
! [X4833,X4834,X4835,X4836] :
( ~ class_Divides_Oring__div(X4836)
| c_Divides_Odiv__class_Omod(X4836,c_Groups_Ominus__class_Ominus(X4836,X4835,X4834),X4833) = c_Divides_Odiv__class_Omod(X4836,c_Groups_Ominus__class_Ominus(X4836,X4835,c_Divides_Odiv__class_Omod(X4836,X4834,X4833)),X4833) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).
fof(i_0_1763,plain,
! [X4765,X4766,X4767,X4768] :
( ~ class_Divides_Osemiring__div(X4768)
| c_Divides_Odiv__class_Omod(X4768,c_Groups_Oplus__class_Oplus(X4768,X4767,X4766),X4765) = c_Divides_Odiv__class_Omod(X4768,c_Groups_Oplus__class_Oplus(X4768,X4767,c_Divides_Odiv__class_Omod(X4768,X4766,X4765)),X4765) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_1764,plain,
! [X4872,X4873,X4874,X4875] :
( ~ class_Divides_Osemiring__div(X4875)
| c_Divides_Odiv__class_Omod(X4875,c_Groups_Otimes__class_Otimes(X4875,X4874,X4873),X4872) = c_Divides_Odiv__class_Omod(X4875,c_Groups_Otimes__class_Otimes(X4875,X4874,c_Divides_Odiv__class_Omod(X4875,X4873,X4872)),X4872) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
cnf(i_0_1765,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1307]) ).
fof(i_0_1766,plain,
! [X4348,X4349,X4350,X4351] :
( ~ class_Int_Onumber__ring(X4351)
| c_Groups_Oplus__class_Oplus(X4351,c_Int_Onumber__class_Onumber__of(X4351,X4350),c_Groups_Ominus__class_Ominus(X4351,c_Int_Onumber__class_Onumber__of(X4351,X4349),X4348)) = c_Groups_Ominus__class_Ominus(X4351,c_Int_Onumber__class_Onumber__of(X4351,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4350,X4349)),X4348) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).
fof(i_0_1767,plain,
! [X2861,X2862,X2863,X2864] :
( ~ class_Int_Onumber__ring(X2864)
| c_Groups_Oplus__class_Oplus(X2864,c_Int_Onumber__class_Onumber__of(X2864,X2863),c_Groups_Oplus__class_Oplus(X2864,c_Int_Onumber__class_Onumber__of(X2864,X2862),X2861)) = c_Groups_Oplus__class_Oplus(X2864,c_Int_Onumber__class_Onumber__of(X2864,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2863,X2862)),X2861) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).
fof(i_0_1768,plain,
! [X2598,X2599,X2600,X2601] :
( ~ class_Int_Onumber__ring(X2601)
| c_Groups_Otimes__class_Otimes(X2601,c_Int_Onumber__class_Onumber__of(X2601,X2600),c_Groups_Otimes__class_Otimes(X2601,c_Int_Onumber__class_Onumber__of(X2601,X2599),X2598)) = c_Groups_Otimes__class_Otimes(X2601,c_Int_Onumber__class_Onumber__of(X2601,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2600,X2599)),X2598) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).
cnf(i_0_1769,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)),X2),
inference(split_conjunct,[status(thm)],[i_0_1308]) ).
fof(i_0_1770,plain,
! [X4683,X4684,X4685] :
( ~ class_Groups_Omonoid__mult(X4685)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4684)
| c_Groups_Otimes__class_Otimes(X4685,c_Power_Opower__class_Opower(X4685,X4683,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4684,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4683) = c_Power_Opower__class_Opower(X4685,X4683,X4684) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
fof(i_0_1771,plain,
! [X3086,X3087,X3088,X3089,X3090,X3091] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3091)
| X3090 = c_Groups_Ozero__class_Ozero(X3091)
| X3089 != X3088
| X3087 = X3086
| c_Groups_Oplus__class_Oplus(X3091,X3089,c_Groups_Otimes__class_Otimes(X3091,X3090,X3087)) != c_Groups_Oplus__class_Oplus(X3091,X3088,c_Groups_Otimes__class_Otimes(X3091,X3090,X3086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1772,plain,
! [X5058,X5059,X5060,X5061] :
( ~ class_Divides_Osemiring__div(X5061)
| ~ c_Rings_Odvd__class_Odvd(X5061,X5060,X5059)
| c_Power_Opower__class_Opower(X5061,c_Divides_Odiv__class_Odiv(X5061,X5059,X5060),X5058) = c_Divides_Odiv__class_Odiv(X5061,c_Power_Opower__class_Opower(X5061,X5059,X5058),c_Power_Opower__class_Opower(X5061,X5060,X5058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).
fof(i_0_1773,plain,
! [X5042,X5043,X5044] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5044)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5043)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5043,X5042)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5044,X5042),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5044,X5043)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).
fof(i_0_1774,plain,
! [X5031,X5032,X5033] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5033,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5032)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5032,X5031)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5033,X5032),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5033,X5031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).
cnf(i_0_1775,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1309]) ).
cnf(i_0_1776,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1310]) ).
fof(i_0_1777,plain,
! [X4819,X4820,X4821] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4821,X4820),X4819),X4820) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4821,X4819),X4820),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).
fof(i_0_1778,plain,
! [X4753,X4754,X4755] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4755,X4754),X4753),X4754) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4755,X4753),X4754),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_1779,plain,
! [X4822,X4823,X4824] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4824,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4823,X4822)),X4822) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4824,X4823),X4822),
inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).
fof(i_0_1780,plain,
! [X4866,X4867,X4868] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4868,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4867,X4866)),X4866) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4868,X4867),X4866),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_1781,plain,
! [X4869,X4870,X4871] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4871,X4870),X4869) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4871,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4870,X4869)),X4869),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
cnf(i_0_1782,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1285]) ).
cnf(i_0_1783,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1286]) ).
cnf(i_0_1784,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1283]) ).
cnf(i_0_1785,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1284]) ).
cnf(i_0_1786,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1311]) ).
cnf(i_0_1787,plain,
( X2 = X3
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1312]) ).
fof(i_0_1788,plain,
! [X4274,X4275,X4276,X4277,X4278] :
( ~ class_Rings_Ocomm__semiring__1(X4278)
| ~ c_Rings_Odvd__class_Odvd(X4278,c_Power_Opower__class_Opower(X4278,X4277,X4276),X4275)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4274,X4276)
| c_Rings_Odvd__class_Odvd(X4278,c_Power_Opower__class_Opower(X4278,X4277,X4274),X4275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__dvd])]) ).
cnf(i_0_1789,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1313]) ).
fof(i_0_1790,plain,
! [X3064,X3065,X3066,X3067] :
( ( ~ c_Rings_Odvd__class_Odvd(X3067,c_Groups_Otimes__class_Otimes(X3067,X3066,X3065),c_Groups_Otimes__class_Otimes(X3067,X3066,X3064))
| X3066 = c_Groups_Ozero__class_Ozero(X3067)
| c_Rings_Odvd__class_Odvd(X3067,X3065,X3064)
| ~ class_Rings_Oidom(X3067) )
& ( X3066 != c_Groups_Ozero__class_Ozero(X3067)
| c_Rings_Odvd__class_Odvd(X3067,c_Groups_Otimes__class_Otimes(X3067,X3066,X3065),c_Groups_Otimes__class_Otimes(X3067,X3066,X3064))
| ~ class_Rings_Oidom(X3067) )
& ( ~ c_Rings_Odvd__class_Odvd(X3067,X3065,X3064)
| c_Rings_Odvd__class_Odvd(X3067,c_Groups_Otimes__class_Otimes(X3067,X3066,X3065),c_Groups_Otimes__class_Otimes(X3067,X3066,X3064))
| ~ class_Rings_Oidom(X3067) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).
fof(i_0_1791,plain,
! [X3068,X3069,X3070,X3071] :
( ( ~ c_Rings_Odvd__class_Odvd(X3071,c_Groups_Otimes__class_Otimes(X3071,X3070,X3069),c_Groups_Otimes__class_Otimes(X3071,X3068,X3069))
| X3069 = c_Groups_Ozero__class_Ozero(X3071)
| c_Rings_Odvd__class_Odvd(X3071,X3070,X3068)
| ~ class_Rings_Oidom(X3071) )
& ( X3069 != c_Groups_Ozero__class_Ozero(X3071)
| c_Rings_Odvd__class_Odvd(X3071,c_Groups_Otimes__class_Otimes(X3071,X3070,X3069),c_Groups_Otimes__class_Otimes(X3071,X3068,X3069))
| ~ class_Rings_Oidom(X3071) )
& ( ~ c_Rings_Odvd__class_Odvd(X3071,X3070,X3068)
| c_Rings_Odvd__class_Odvd(X3071,c_Groups_Otimes__class_Otimes(X3071,X3070,X3069),c_Groups_Otimes__class_Otimes(X3071,X3068,X3069))
| ~ class_Rings_Oidom(X3071) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).
fof(i_0_1792,plain,
! [X3687,X3688,X3689] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3687,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3688,X3689))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3687,X3689),X3688)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3689,X3688) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3687,X3689),X3688)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3687,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3688,X3689))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3689,X3688) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1793,plain,
! [X4440,X4441,X4442] :
( ~ class_Rings_Olinordered__semidom(X4442)
| ~ c_Orderings_Oord__class_Oless(X4442,c_Groups_Oone__class_Oone(X4442),X4441)
| c_Orderings_Oord__class_Oless(X4442,c_Groups_Oone__class_Oone(X4442),c_Groups_Otimes__class_Otimes(X4442,X4441,c_Power_Opower__class_Opower(X4442,X4441,X4440))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1794,plain,
! [X3904,X3905,X3906,X3907] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3907,c_Groups_Oplus__class_Oplus(X3907,X3906,X3905),c_Groups_Oplus__class_Oplus(X3907,X3904,X3905))
| c_Orderings_Oord__class_Oless__eq(X3907,X3906,X3904)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3907) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3907,X3906,X3904)
| c_Orderings_Oord__class_Oless__eq(X3907,c_Groups_Oplus__class_Oplus(X3907,X3906,X3905),c_Groups_Oplus__class_Oplus(X3907,X3904,X3905))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3907) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1795,plain,
! [X3883,X3884,X3885,X3886] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3886)
| ~ c_Orderings_Oord__class_Oless__eq(X3886,c_Groups_Oplus__class_Oplus(X3886,X3885,X3884),c_Groups_Oplus__class_Oplus(X3886,X3883,X3884))
| c_Orderings_Oord__class_Oless__eq(X3886,X3885,X3883) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1796,plain,
! [X3900,X3901,X3902,X3903] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3903,c_Groups_Oplus__class_Oplus(X3903,X3902,X3901),c_Groups_Oplus__class_Oplus(X3903,X3902,X3900))
| c_Orderings_Oord__class_Oless__eq(X3903,X3901,X3900)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3903) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3903,X3901,X3900)
| c_Orderings_Oord__class_Oless__eq(X3903,c_Groups_Oplus__class_Oplus(X3903,X3902,X3901),c_Groups_Oplus__class_Oplus(X3903,X3902,X3900))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3903) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_1797,plain,
! [X3879,X3880,X3881,X3882] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3882)
| ~ c_Orderings_Oord__class_Oless__eq(X3882,c_Groups_Oplus__class_Oplus(X3882,X3881,X3880),c_Groups_Oplus__class_Oplus(X3882,X3881,X3879))
| c_Orderings_Oord__class_Oless__eq(X3882,X3880,X3879) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1798,plain,
! [X3520,X3521,X3522,X3523] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3523)
| ~ c_Orderings_Oord__class_Oless(X3523,c_Groups_Oplus__class_Oplus(X3523,X3522,X3521),c_Groups_Oplus__class_Oplus(X3523,X3520,X3521))
| c_Orderings_Oord__class_Oless(X3523,X3522,X3520) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1799,plain,
! [X3499,X3500,X3501,X3502] :
( ( ~ c_Orderings_Oord__class_Oless(X3502,c_Groups_Oplus__class_Oplus(X3502,X3501,X3500),c_Groups_Oplus__class_Oplus(X3502,X3499,X3500))
| c_Orderings_Oord__class_Oless(X3502,X3501,X3499)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3502) )
& ( ~ c_Orderings_Oord__class_Oless(X3502,X3501,X3499)
| c_Orderings_Oord__class_Oless(X3502,c_Groups_Oplus__class_Oplus(X3502,X3501,X3500),c_Groups_Oplus__class_Oplus(X3502,X3499,X3500))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3502) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1800,plain,
! [X3524,X3525,X3526,X3527] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3527)
| ~ c_Orderings_Oord__class_Oless(X3527,c_Groups_Oplus__class_Oplus(X3527,X3526,X3525),c_Groups_Oplus__class_Oplus(X3527,X3526,X3524))
| c_Orderings_Oord__class_Oless(X3527,X3525,X3524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1801,plain,
! [X3503,X3504,X3505,X3506] :
( ( ~ c_Orderings_Oord__class_Oless(X3506,c_Groups_Oplus__class_Oplus(X3506,X3505,X3504),c_Groups_Oplus__class_Oplus(X3506,X3505,X3503))
| c_Orderings_Oord__class_Oless(X3506,X3504,X3503)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3506) )
& ( ~ c_Orderings_Oord__class_Oless(X3506,X3504,X3503)
| c_Orderings_Oord__class_Oless(X3506,c_Groups_Oplus__class_Oplus(X3506,X3505,X3504),c_Groups_Oplus__class_Oplus(X3506,X3505,X3503))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3506) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
cnf(i_0_1802,plain,
( c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) = X2
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
cnf(i_0_1803,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1315]) ).
cnf(i_0_1804,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1316]) ).
cnf(i_0_1805,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1317]) ).
fof(i_0_1806,plain,
! [X4592,X4593,X4594] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4594)
| X4594 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4593,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4594,X4592))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4593)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4592,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).
cnf(i_0_1807,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1318]) ).
fof(i_0_1808,plain,
! [X4650,X4651,X4652] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4652,X4651)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4652,X4650)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4651,X4652),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4650,X4652)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4651,X4650) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1809,plain,
! [X4595,X4596,X4597] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4597)
| X4597 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4596,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4597,X4595))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,X4597)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
cnf(i_0_1810,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1288]) ).
fof(i_0_1811,plain,
! [X3667,X3668,X3669] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3669,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3668,X3667))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3669,X3667)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3667,X3668)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3669,X3668) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD])]) ).
fof(i_0_1812,plain,
! [X3670,X3671,X3672] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3672,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3671,X3670))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3672,X3671)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3670,X3671)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3672,X3670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD1])]) ).
fof(i_0_1813,plain,
! [X3377,X3378,X3379] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3379,X3378),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3379,X3377))
| X3379 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3378,X3377) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel])]) ).
fof(i_0_1814,plain,
! [X3362,X3363,X3364] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3363,X3362)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3364,X3363),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3364,X3362))
| X3364 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3364,X3363),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3364,X3362))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3363,X3362)
| X3364 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__mono])])]) ).
fof(i_0_1815,plain,
! [X3163,X3164,X3165] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3164),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3163))
| X3165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3164,X3163) )
& ( X3165 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3164),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3163)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3164,X3163)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3164),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3165,X3163)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).
fof(i_0_1816,plain,
! [X4730,X4731,X4732] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4732,X4731),c_Power_Opower__class_Opower(tc_Int_Oint,X4730,X4731))
| X4731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4732,X4730) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int])]) ).
fof(i_0_1817,plain,
! [X4727,X4728,X4729] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4728,X4729),c_Power_Opower__class_Opower(tc_Int_Oint,X4727,X4729))
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4728,X4727)
| X4729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4728,X4727)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4728,X4729),c_Power_Opower__class_Opower(tc_Int_Oint,X4727,X4729))
| X4729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int])])]) ).
fof(i_0_1818,plain,
! [X4740,X4741,X4742] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X4741,X4742),c_Power_Opower__class_Opower(tc_Nat_Onat,X4740,X4742))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4741,X4740)
| X4742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4741,X4740)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X4741,X4742),c_Power_Opower__class_Opower(tc_Nat_Onat,X4740,X4742))
| X4742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat])])]) ).
fof(i_0_1819,plain,
! [X4737,X4738,X4739] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X4739,X4738),c_Power_Opower__class_Opower(tc_Nat_Onat,X4737,X4738))
| X4738 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4739,X4737) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat])]) ).
fof(i_0_1820,plain,
! [X3704,X3705] :
( ~ class_Rings_Oring__1(X3705)
| c_Groups_Ominus__class_Ominus(X3705,c_Groups_Otimes__class_Otimes(X3705,X3704,X3704),c_Groups_Oone__class_Oone(X3705)) = c_Groups_Otimes__class_Otimes(X3705,c_Groups_Oplus__class_Oplus(X3705,X3704,c_Groups_Oone__class_Oone(X3705)),c_Groups_Ominus__class_Ominus(X3705,X3704,c_Groups_Oone__class_Oone(X3705))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
cnf(i_0_1821,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1274]) ).
cnf(i_0_1822,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1319]) ).
fof(i_0_1823,plain,
! [X3414,X3415,X3416] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3416)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3415),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3414)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3415,X3414)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3415),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3414)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3416)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3415,X3414)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3415),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3416,X3414)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1824,plain,
! [X3417,X3418,X3419] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3418)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3419,X3418),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3417,X3418)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3419,X3417)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3419,X3418),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3417,X3418)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3418)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3419,X3417)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3419,X3418),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3417,X3418)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
cnf(i_0_1825,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1320]) ).
cnf(i_0_1826,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
cnf(i_0_1827,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
fof(i_0_1828,plain,
! [X4001,X4002,X4003] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4003,X4002),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4003,X4001))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4002,X4001) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4002,X4001)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4003,X4002),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4003,X4001)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
cnf(i_0_1829,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1323]) ).
cnf(i_0_1830,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1324]) ).
fof(i_0_1831,plain,
! [X3349,X3350,X3351] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3349))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3350,X3349) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3350,X3349)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3351,X3349)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1832,plain,
! [X4446,X4447,X4448,X4449] :
( ~ class_Rings_Olinordered__semidom(X4449)
| c_Power_Opower__class_Opower(X4449,X4448,X4447) != c_Power_Opower__class_Opower(X4449,X4446,X4447)
| ~ c_Orderings_Oord__class_Oless__eq(X4449,c_Groups_Ozero__class_Ozero(X4449),X4448)
| ~ c_Orderings_Oord__class_Oless__eq(X4449,c_Groups_Ozero__class_Ozero(X4449),X4446)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4447)
| X4448 = X4446 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1833,plain,
! [X4227,X4228,X4229,X4230] :
( ~ class_Rings_Olinordered__semidom(X4230)
| ~ c_Orderings_Oord__class_Oless__eq(X4230,X4229,X4228)
| ~ c_Orderings_Oord__class_Oless__eq(X4230,c_Groups_Ozero__class_Ozero(X4230),X4229)
| c_Orderings_Oord__class_Oless__eq(X4230,c_Power_Opower__class_Opower(X4230,X4229,X4227),c_Power_Opower__class_Opower(X4230,X4228,X4227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1834,plain,
! [X4140,X4141,X4142,X4143] :
( ~ class_Rings_Oordered__semiring(X4143)
| ~ c_Orderings_Oord__class_Oless__eq(X4143,X4142,X4141)
| ~ c_Orderings_Oord__class_Oless__eq(X4143,c_Groups_Ozero__class_Ozero(X4143),X4140)
| c_Orderings_Oord__class_Oless__eq(X4143,c_Groups_Otimes__class_Otimes(X4143,X4142,X4140),c_Groups_Otimes__class_Otimes(X4143,X4141,X4140)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1835,plain,
! [X4132,X4133,X4134,X4135] :
( ~ class_Rings_Oordered__comm__semiring(X4135)
| ~ c_Orderings_Oord__class_Oless__eq(X4135,X4134,X4133)
| ~ c_Orderings_Oord__class_Oless__eq(X4135,c_Groups_Ozero__class_Ozero(X4135),X4132)
| c_Orderings_Oord__class_Oless__eq(X4135,c_Groups_Otimes__class_Otimes(X4135,X4132,X4134),c_Groups_Otimes__class_Otimes(X4135,X4132,X4133)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1836,plain,
! [X4136,X4137,X4138,X4139] :
( ~ class_Rings_Oordered__semiring(X4139)
| ~ c_Orderings_Oord__class_Oless__eq(X4139,X4138,X4137)
| ~ c_Orderings_Oord__class_Oless__eq(X4139,c_Groups_Ozero__class_Ozero(X4139),X4136)
| c_Orderings_Oord__class_Oless__eq(X4139,c_Groups_Otimes__class_Otimes(X4139,X4136,X4138),c_Groups_Otimes__class_Otimes(X4139,X4136,X4137)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1837,plain,
! [X3116,X3117,X3118,X3119] :
( ~ class_Rings_Olinordered__semiring__strict(X3119)
| ~ c_Orderings_Oord__class_Oless(X3119,X3118,X3117)
| ~ c_Orderings_Oord__class_Oless(X3119,c_Groups_Ozero__class_Ozero(X3119),X3116)
| c_Orderings_Oord__class_Oless(X3119,c_Groups_Otimes__class_Otimes(X3119,X3118,X3116),c_Groups_Otimes__class_Otimes(X3119,X3117,X3116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1838,plain,
! [X3112,X3113,X3114,X3115] :
( ~ class_Rings_Olinordered__semiring__strict(X3115)
| ~ c_Orderings_Oord__class_Oless(X3115,X3114,X3113)
| ~ c_Orderings_Oord__class_Oless(X3115,c_Groups_Ozero__class_Ozero(X3115),X3112)
| c_Orderings_Oord__class_Oless(X3115,c_Groups_Otimes__class_Otimes(X3115,X3112,X3114),c_Groups_Otimes__class_Otimes(X3115,X3112,X3113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1839,plain,
! [X3108,X3109,X3110,X3111] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3111)
| ~ c_Orderings_Oord__class_Oless(X3111,X3110,X3109)
| ~ c_Orderings_Oord__class_Oless(X3111,c_Groups_Ozero__class_Ozero(X3111),X3108)
| c_Orderings_Oord__class_Oless(X3111,c_Groups_Otimes__class_Otimes(X3111,X3108,X3110),c_Groups_Otimes__class_Otimes(X3111,X3108,X3109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1840,plain,
! [X4128,X4129,X4130,X4131] :
( ~ class_Rings_Oordered__ring(X4131)
| ~ c_Orderings_Oord__class_Oless__eq(X4131,X4130,X4129)
| ~ c_Orderings_Oord__class_Oless__eq(X4131,X4128,c_Groups_Ozero__class_Ozero(X4131))
| c_Orderings_Oord__class_Oless__eq(X4131,c_Groups_Otimes__class_Otimes(X4131,X4129,X4128),c_Groups_Otimes__class_Otimes(X4131,X4130,X4128)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1841,plain,
! [X4124,X4125,X4126,X4127] :
( ~ class_Rings_Oordered__ring(X4127)
| ~ c_Orderings_Oord__class_Oless__eq(X4127,X4126,X4125)
| ~ c_Orderings_Oord__class_Oless__eq(X4127,X4124,c_Groups_Ozero__class_Ozero(X4127))
| c_Orderings_Oord__class_Oless__eq(X4127,c_Groups_Otimes__class_Otimes(X4127,X4124,X4125),c_Groups_Otimes__class_Otimes(X4127,X4124,X4126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1842,plain,
! [X3104,X3105,X3106,X3107] :
( ~ class_Rings_Olinordered__ring__strict(X3107)
| ~ c_Orderings_Oord__class_Oless(X3107,X3106,X3105)
| ~ c_Orderings_Oord__class_Oless(X3107,X3104,c_Groups_Ozero__class_Ozero(X3107))
| c_Orderings_Oord__class_Oless(X3107,c_Groups_Otimes__class_Otimes(X3107,X3105,X3104),c_Groups_Otimes__class_Otimes(X3107,X3106,X3104)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1843,plain,
! [X3100,X3101,X3102,X3103] :
( ~ class_Rings_Olinordered__ring__strict(X3103)
| ~ c_Orderings_Oord__class_Oless(X3103,X3102,X3101)
| ~ c_Orderings_Oord__class_Oless(X3103,X3100,c_Groups_Ozero__class_Ozero(X3103))
| c_Orderings_Oord__class_Oless(X3103,c_Groups_Otimes__class_Otimes(X3103,X3100,X3101),c_Groups_Otimes__class_Otimes(X3103,X3100,X3102)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
cnf(i_0_1844,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1295]) ).
cnf(i_0_1845,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1297]) ).
cnf(i_0_1846,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1296]) ).
cnf(i_0_1847,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1298]) ).
cnf(i_0_1848,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1291]) ).
cnf(i_0_1849,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1292]) ).
cnf(i_0_1850,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1294]) ).
cnf(i_0_1851,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1293]) ).
fof(i_0_1852,plain,
! [X3738,X3739,X3740] :
( ~ class_Rings_Olinordered__idom(X3740)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,c_Groups_Ozero__class_Ozero(X3740),X3739)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,c_Groups_Ozero__class_Ozero(X3740),X3738)
| ~ c_Orderings_Oord__class_Oless__eq(X3740,X3738,c_Groups_Oone__class_Oone(X3740))
| c_Orderings_Oord__class_Oless__eq(X3740,c_Groups_Otimes__class_Otimes(X3740,X3739,X3738),X3739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1853,plain,
! [X3735,X3736,X3737] :
( ~ class_Rings_Olinordered__idom(X3737)
| ~ c_Orderings_Oord__class_Oless__eq(X3737,c_Groups_Ozero__class_Ozero(X3737),X3736)
| ~ c_Orderings_Oord__class_Oless__eq(X3737,c_Groups_Ozero__class_Ozero(X3737),X3735)
| ~ c_Orderings_Oord__class_Oless__eq(X3737,X3735,c_Groups_Oone__class_Oone(X3737))
| c_Orderings_Oord__class_Oless__eq(X3737,c_Groups_Otimes__class_Otimes(X3737,X3735,X3736),X3736) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1854,plain,
! [X3589,X3590,X3591,X3592] :
( ~ class_Rings_Olinordered__semidom(X3592)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3591,X3590)
| ~ c_Orderings_Oord__class_Oless__eq(X3592,c_Groups_Oone__class_Oone(X3592),X3589)
| c_Orderings_Oord__class_Oless__eq(X3592,c_Power_Opower__class_Opower(X3592,X3589,X3591),c_Power_Opower__class_Opower(X3592,X3589,X3590)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1855,plain,
! [X4249,X4250,X4251,X4252] :
( ~ class_Rings_Olinordered__semidom(X4252)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4251,X4250)
| ~ c_Orderings_Oord__class_Oless(X4252,c_Groups_Oone__class_Oone(X4252),X4249)
| c_Orderings_Oord__class_Oless(X4252,c_Power_Opower__class_Opower(X4252,X4249,X4251),c_Power_Opower__class_Opower(X4252,X4249,X4250)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1856,plain,
! [X3078,X3079,X3080] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),X3079)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| X3079 != c_Groups_Ozero__class_Ozero(X3080)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),X3079)
| X3079 != c_Groups_Ozero__class_Ozero(X3080)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| X3079 = c_Groups_Ozero__class_Ozero(X3080)
| c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078))
| ~ c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),X3079)
| c_Orderings_Oord__class_Oless(X3080,c_Groups_Ozero__class_Ozero(X3080),c_Power_Opower__class_Opower(X3080,X3079,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3078)))
| ~ class_Rings_Olinordered__idom(X3080) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])])]) ).
fof(i_0_1857,plain,
! [X3695,X3696,X3697] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3697,X3696)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3695,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3696,X3695),X3697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1858,plain,
! [X3887,X3888,X3889,X3890,X3891] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3891)
| ~ c_Orderings_Oord__class_Oless__eq(X3891,X3890,X3889)
| ~ c_Orderings_Oord__class_Oless__eq(X3891,X3888,X3887)
| c_Orderings_Oord__class_Oless__eq(X3891,c_Groups_Oplus__class_Oplus(X3891,X3890,X3888),c_Groups_Oplus__class_Oplus(X3891,X3889,X3887)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1859,plain,
! [X2913,X2914,X2915,X2916,X2917] :
( ~ class_Rings_Ocomm__semiring__1(X2917)
| ~ c_Rings_Odvd__class_Odvd(X2917,X2916,X2915)
| ~ c_Rings_Odvd__class_Odvd(X2917,X2914,X2913)
| c_Rings_Odvd__class_Odvd(X2917,c_Groups_Otimes__class_Otimes(X2917,X2916,X2914),c_Groups_Otimes__class_Otimes(X2917,X2915,X2913)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).
fof(i_0_1860,plain,
! [X4198,X4199,X4200,X4201,X4202] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4202)
| ~ c_Orderings_Oord__class_Oless(X4202,X4201,X4200)
| ~ c_Orderings_Oord__class_Oless__eq(X4202,X4199,X4198)
| c_Orderings_Oord__class_Oless(X4202,c_Groups_Oplus__class_Oplus(X4202,X4201,X4199),c_Groups_Oplus__class_Oplus(X4202,X4200,X4198)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1861,plain,
! [X4193,X4194,X4195,X4196,X4197] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4197)
| ~ c_Orderings_Oord__class_Oless__eq(X4197,X4196,X4195)
| ~ c_Orderings_Oord__class_Oless(X4197,X4194,X4193)
| c_Orderings_Oord__class_Oless(X4197,c_Groups_Oplus__class_Oplus(X4197,X4196,X4194),c_Groups_Oplus__class_Oplus(X4197,X4195,X4193)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1862,plain,
! [X3515,X3516,X3517,X3518,X3519] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3519)
| ~ c_Orderings_Oord__class_Oless(X3519,X3518,X3517)
| ~ c_Orderings_Oord__class_Oless(X3519,X3516,X3515)
| c_Orderings_Oord__class_Oless(X3519,c_Groups_Oplus__class_Oplus(X3519,X3518,X3516),c_Groups_Oplus__class_Oplus(X3519,X3517,X3515)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1863,plain,
! [X4724,X4725,X4726] :
( ( X4725 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4726,X4724,X4725) = c_Groups_Oone__class_Oone(X4726)
| ~ class_Power_Opower(X4726) )
& ( X4725 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4726,X4724,X4725) = c_Groups_Otimes__class_Otimes(X4726,X4724,c_Power_Opower__class_Opower(X4726,X4724,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4725,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X4726) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1864,plain,
! [X4932,X4933] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4933)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4933,X4932),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4933,X4932) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4933,X4932) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).
fof(i_0_1865,plain,
! [X4279,X4280,X4281,X4282,X4283] :
( ~ class_Rings_Ocomm__semiring__1(X4283)
| ~ c_Rings_Odvd__class_Odvd(X4283,X4282,X4281)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4280,X4279)
| c_Rings_Odvd__class_Odvd(X4283,c_Power_Opower__class_Opower(X4283,X4282,X4280),c_Power_Opower__class_Opower(X4283,X4281,X4279)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__le])]) ).
cnf(i_0_1866,plain,
( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1326]) ).
fof(i_0_1867,plain,
! [X3083,X3084,X3085] :
( ( X3084 = c_Groups_Ozero__class_Ozero(X3085)
| c_Groups_Oplus__class_Oplus(X3085,c_Groups_Otimes__class_Otimes(X3085,X3084,X3084),c_Groups_Otimes__class_Otimes(X3085,X3083,X3083)) != c_Groups_Ozero__class_Ozero(X3085)
| ~ class_Rings_Olinordered__ring__strict(X3085) )
& ( X3083 = c_Groups_Ozero__class_Ozero(X3085)
| c_Groups_Oplus__class_Oplus(X3085,c_Groups_Otimes__class_Otimes(X3085,X3084,X3084),c_Groups_Otimes__class_Otimes(X3085,X3083,X3083)) != c_Groups_Ozero__class_Ozero(X3085)
| ~ class_Rings_Olinordered__ring__strict(X3085) )
& ( X3084 != c_Groups_Ozero__class_Ozero(X3085)
| X3083 != c_Groups_Ozero__class_Ozero(X3085)
| c_Groups_Oplus__class_Oplus(X3085,c_Groups_Otimes__class_Otimes(X3085,X3084,X3084),c_Groups_Otimes__class_Otimes(X3085,X3083,X3083)) = c_Groups_Ozero__class_Ozero(X3085)
| ~ class_Rings_Olinordered__ring__strict(X3085) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_1868,plain,
! [X4552,X4553,X4554] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),c_Power_Opower__class_Opower(X4554,X4553,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552)))
| ~ class_Rings_Olinordered__idom(X4554) )
& ( c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),X4553)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),c_Power_Opower__class_Opower(X4554,X4553,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552)))
| ~ class_Rings_Olinordered__idom(X4554) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552))
| c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),c_Power_Opower__class_Opower(X4554,X4553,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552)))
| ~ class_Rings_Olinordered__idom(X4554) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),X4553)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Ozero__class_Ozero(X4554),c_Power_Opower__class_Opower(X4554,X4553,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4552)))
| ~ class_Rings_Olinordered__idom(X4554) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1327])])]) ).
fof(i_0_1869,plain,
! [X4566,X4567,X4568] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( X4567 = c_Groups_Ozero__class_Ozero(X4568)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| c_Orderings_Oord__class_Oless__eq(X4568,X4567,c_Groups_Ozero__class_Ozero(X4568))
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( X4567 = c_Groups_Ozero__class_Ozero(X4568)
| c_Orderings_Oord__class_Oless__eq(X4568,X4567,c_Groups_Ozero__class_Ozero(X4568))
| ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| ~ c_Orderings_Oord__class_Oless__eq(X4568,X4567,c_Groups_Ozero__class_Ozero(X4568))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566))
| X4567 != c_Groups_Ozero__class_Ozero(X4568)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X4568,c_Power_Opower__class_Opower(X4568,X4567,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4566)),c_Groups_Ozero__class_Ozero(X4568))
| ~ class_Rings_Olinordered__idom(X4568) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1328])])]) ).
fof(i_0_1870,plain,
! [X4888,X4889,X4890,X4891] :
( ~ class_Divides_Osemiring__div(X4891)
| c_Divides_Odiv__class_Omod(X4891,c_Groups_Otimes__class_Otimes(X4891,X4890,X4889),c_Groups_Otimes__class_Otimes(X4891,X4888,X4889)) = c_Groups_Otimes__class_Otimes(X4891,c_Divides_Odiv__class_Omod(X4891,X4890,X4888),X4889) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_1871,plain,
! [X2976,X2977,X2978,X2979] :
( ~ class_Rings_Ocomm__semiring__1(X2979)
| c_Groups_Oplus__class_Oplus(X2979,c_Groups_Otimes__class_Otimes(X2979,X2978,X2977),c_Groups_Otimes__class_Otimes(X2979,X2976,X2977)) = c_Groups_Otimes__class_Otimes(X2979,c_Groups_Oplus__class_Oplus(X2979,X2978,X2976),X2977) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1872,plain,
! [X4884,X4885,X4886,X4887] :
( ~ class_Divides_Osemiring__div(X4887)
| c_Divides_Odiv__class_Omod(X4887,c_Groups_Otimes__class_Otimes(X4887,X4886,X4885),c_Groups_Otimes__class_Otimes(X4887,X4886,X4884)) = c_Groups_Otimes__class_Otimes(X4887,X4886,c_Divides_Odiv__class_Omod(X4887,X4885,X4884)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_1873,plain,
! [X3531,X3532,X3533,X3534] :
( ~ class_Groups_Ocomm__monoid__mult(X3534)
| c_Power_Opower__class_Opower(X3534,c_Groups_Otimes__class_Otimes(X3534,X3533,X3532),X3531) = c_Groups_Otimes__class_Otimes(X3534,c_Power_Opower__class_Opower(X3534,X3533,X3531),c_Power_Opower__class_Opower(X3534,X3532,X3531)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1874,plain,
! [X2930,X2931,X2932,X2933] :
( ~ class_Rings_Ocomm__semiring__1(X2933)
| c_Power_Opower__class_Opower(X2933,c_Groups_Otimes__class_Otimes(X2933,X2932,X2931),X2930) = c_Groups_Otimes__class_Otimes(X2933,c_Power_Opower__class_Opower(X2933,X2932,X2930),c_Power_Opower__class_Opower(X2933,X2931,X2930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1875,plain,
! [X3832,X3833,X3834,X3835] :
( ~ class_RealVector_Oreal__normed__algebra(X3835)
| c_Groups_Otimes__class_Otimes(X3835,c_Groups_Ominus__class_Ominus(X3835,X3834,X3833),X3832) = c_Groups_Ominus__class_Ominus(X3835,c_Groups_Otimes__class_Otimes(X3835,X3834,X3832),c_Groups_Otimes__class_Otimes(X3835,X3833,X3832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1876,plain,
! [X3828,X3829,X3830,X3831] :
( ~ class_RealVector_Oreal__normed__algebra(X3831)
| c_Groups_Otimes__class_Otimes(X3831,c_Groups_Ominus__class_Ominus(X3831,X3830,X3829),X3828) = c_Groups_Ominus__class_Ominus(X3831,c_Groups_Otimes__class_Otimes(X3831,X3830,X3828),c_Groups_Otimes__class_Otimes(X3831,X3829,X3828)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1877,plain,
! [X2960,X2961,X2962,X2963] :
( ~ class_Rings_Ocomm__semiring(X2963)
| c_Groups_Otimes__class_Otimes(X2963,c_Groups_Oplus__class_Oplus(X2963,X2962,X2961),X2960) = c_Groups_Oplus__class_Oplus(X2963,c_Groups_Otimes__class_Otimes(X2963,X2962,X2960),c_Groups_Otimes__class_Otimes(X2963,X2961,X2960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1878,plain,
! [X2972,X2973,X2974,X2975] :
( ~ class_RealVector_Oreal__normed__algebra(X2975)
| c_Groups_Otimes__class_Otimes(X2975,c_Groups_Oplus__class_Oplus(X2975,X2974,X2973),X2972) = c_Groups_Oplus__class_Oplus(X2975,c_Groups_Otimes__class_Otimes(X2975,X2974,X2972),c_Groups_Otimes__class_Otimes(X2975,X2973,X2972)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1879,plain,
! [X2968,X2969,X2970,X2971] :
( ~ class_RealVector_Oreal__normed__algebra(X2971)
| c_Groups_Otimes__class_Otimes(X2971,c_Groups_Oplus__class_Oplus(X2971,X2970,X2969),X2968) = c_Groups_Oplus__class_Oplus(X2971,c_Groups_Otimes__class_Otimes(X2971,X2970,X2968),c_Groups_Otimes__class_Otimes(X2971,X2969,X2968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1880,plain,
! [X2964,X2965,X2966,X2967] :
( ~ class_Rings_Ocomm__semiring__1(X2967)
| c_Groups_Otimes__class_Otimes(X2967,c_Groups_Oplus__class_Oplus(X2967,X2966,X2965),X2964) = c_Groups_Oplus__class_Oplus(X2967,c_Groups_Otimes__class_Otimes(X2967,X2966,X2964),c_Groups_Otimes__class_Otimes(X2967,X2965,X2964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1881,plain,
! [X3824,X3825,X3826,X3827] :
( ~ class_RealVector_Oreal__normed__algebra(X3827)
| c_Groups_Otimes__class_Otimes(X3827,X3826,c_Groups_Ominus__class_Ominus(X3827,X3825,X3824)) = c_Groups_Ominus__class_Ominus(X3827,c_Groups_Otimes__class_Otimes(X3827,X3826,X3825),c_Groups_Otimes__class_Otimes(X3827,X3826,X3824)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1882,plain,
! [X3820,X3821,X3822,X3823] :
( ~ class_RealVector_Oreal__normed__algebra(X3823)
| c_Groups_Otimes__class_Otimes(X3823,X3822,c_Groups_Ominus__class_Ominus(X3823,X3821,X3820)) = c_Groups_Ominus__class_Ominus(X3823,c_Groups_Otimes__class_Otimes(X3823,X3822,X3821),c_Groups_Otimes__class_Otimes(X3823,X3822,X3820)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1883,plain,
! [X2951,X2952,X2953,X2954] :
( ~ class_RealVector_Oreal__normed__algebra(X2954)
| c_Groups_Otimes__class_Otimes(X2954,X2953,c_Groups_Oplus__class_Oplus(X2954,X2952,X2951)) = c_Groups_Oplus__class_Oplus(X2954,c_Groups_Otimes__class_Otimes(X2954,X2953,X2952),c_Groups_Otimes__class_Otimes(X2954,X2953,X2951)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1884,plain,
! [X2943,X2944,X2945,X2946] :
( ~ class_RealVector_Oreal__normed__algebra(X2946)
| c_Groups_Otimes__class_Otimes(X2946,X2945,c_Groups_Oplus__class_Oplus(X2946,X2944,X2943)) = c_Groups_Oplus__class_Oplus(X2946,c_Groups_Otimes__class_Otimes(X2946,X2945,X2944),c_Groups_Otimes__class_Otimes(X2946,X2945,X2943)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1885,plain,
! [X2947,X2948,X2949,X2950] :
( ~ class_Rings_Ocomm__semiring__1(X2950)
| c_Groups_Otimes__class_Otimes(X2950,X2949,c_Groups_Oplus__class_Oplus(X2950,X2948,X2947)) = c_Groups_Oplus__class_Oplus(X2950,c_Groups_Otimes__class_Otimes(X2950,X2949,X2948),c_Groups_Otimes__class_Otimes(X2950,X2949,X2947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1886,plain,
! [X4849,X4850,X4851,X4852] :
( ~ class_Divides_Osemiring__div(X4852)
| c_Divides_Odiv__class_Omod(X4852,c_Groups_Oplus__class_Oplus(X4852,X4851,c_Groups_Otimes__class_Otimes(X4852,X4850,X4849)),X4850) = c_Divides_Odiv__class_Omod(X4852,X4851,X4850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_1887,plain,
! [X4853,X4854,X4855,X4856] :
( ~ class_Divides_Osemiring__div(X4856)
| c_Divides_Odiv__class_Omod(X4856,c_Groups_Oplus__class_Oplus(X4856,X4855,c_Groups_Otimes__class_Otimes(X4856,X4854,X4853)),X4853) = c_Divides_Odiv__class_Omod(X4856,X4855,X4853) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
cnf(i_0_1888,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1329]) ).
fof(i_0_1889,plain,
! [X2857,X2858,X2859,X2860] :
( ~ class_Rings_Ocomm__semiring__1(X2860)
| c_Groups_Otimes__class_Otimes(X2860,c_Power_Opower__class_Opower(X2860,X2859,X2858),c_Power_Opower__class_Opower(X2860,X2859,X2857)) = c_Power_Opower__class_Opower(X2860,X2859,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2858,X2857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1890,plain,
! [X3239,X3240,X3241,X3242] :
( ~ class_Groups_Omonoid__mult(X3242)
| c_Power_Opower__class_Opower(X3242,X3241,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3240,X3239)) = c_Groups_Otimes__class_Otimes(X3242,c_Power_Opower__class_Opower(X3242,X3241,X3240),c_Power_Opower__class_Opower(X3242,X3241,X3239)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1891,plain,
! [X5026,X5027,X5028] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5028,X5027)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5026)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5028,X5026),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5027,X5026)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).
fof(i_0_1892,plain,
! [X4520,X4521,X4522] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4522)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4521,X4520)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4522,X4521),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4522,X4520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1893,plain,
! [X3177,X3178,X3179] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3179,X3178)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3177)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3177,X3179),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3177,X3178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1894,plain,
! [X3426,X3427,X3428] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3428,X3427)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3426)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3428,X3426),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3427,X3426)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1895,plain,
! [X3429,X3430,X3431] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3431,X3430)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3429)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3429,X3431),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3429,X3430)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1896,plain,
! [X5023,X5024,X5025] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5025,X5024)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5023,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5024,X5023),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5025,X5023)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).
fof(i_0_1897,plain,
! [X4675,X4676] :
( ( X4676 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4676,X4675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4676,X4675) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4675,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4676,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4675)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1898,plain,
! [X4678,X4679] :
( ( X4679 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X4678,X4679) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X4678,X4679) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4678,c_Power_Opower__class_Opower(tc_Nat_Onat,X4678,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4679,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__if])]) ).
fof(i_0_1899,plain,
! [X4936,X4937,X4938] :
( ( ~ hBOOL(hAPP(X4938,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4937,X4936)))
| epred1_3(X4938,X4937,X4936) )
& ( ~ epred1_3(X4938,X4937,X4936)
| hBOOL(hAPP(X4938,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4937,X4936))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1330])]) ).
fof(i_0_1900,plain,
! [X4013,X4014,X4015,X4016] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4016,X4015)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4014,X4013)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4016,X4014),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4015,X4013)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1901,plain,
! [X4036,X4037,X4038,X4039] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4039,X4038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4037,X4036)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4039,X4037),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4038,X4036)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1902,plain,
! [X4311,X4312,X4313,X4314] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4314,X4313)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4312,X4311)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4314,X4312),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4313,X4311)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1903,plain,
! [X3632,X3633,X3634] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3634,X3633)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3632,X3634)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3634,X3632),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3633,X3632)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1904,plain,
! [X3635,X3636,X3637] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3637,X3636)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3637,X3635)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3635,X3636),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3635,X3637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1905,plain,
! [X3336,X3337,X3338,X3339] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3339,X3338)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3337,X3336)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3339,X3337),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3338,X3336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1906,plain,
! [X3130,X3131,X3132] :
( ~ class_Rings_Olinordered__semiring__strict(X3132)
| ~ c_Orderings_Oord__class_Oless(X3132,c_Groups_Ozero__class_Ozero(X3132),c_Groups_Otimes__class_Otimes(X3132,X3131,X3130))
| ~ c_Orderings_Oord__class_Oless(X3132,c_Groups_Ozero__class_Ozero(X3132),X3130)
| c_Orderings_Oord__class_Oless(X3132,c_Groups_Ozero__class_Ozero(X3132),X3131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1907,plain,
! [X3133,X3134,X3135] :
( ~ class_Rings_Olinordered__semiring__strict(X3135)
| ~ c_Orderings_Oord__class_Oless(X3135,c_Groups_Ozero__class_Ozero(X3135),c_Groups_Otimes__class_Otimes(X3135,X3134,X3133))
| ~ c_Orderings_Oord__class_Oless(X3135,c_Groups_Ozero__class_Ozero(X3135),X3134)
| c_Orderings_Oord__class_Oless(X3135,c_Groups_Ozero__class_Ozero(X3135),X3133) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
cnf(i_0_1908,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk6_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1300]) ).
fof(i_0_1909,plain,
! [X5045,X5046] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5045,X5046)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5046,X5045))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5046) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5045)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5046,X5045))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5046) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5045,X5046)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5045)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5046,X5045))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5046) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).
cnf(i_0_1910,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2)) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1314]) ).
cnf(i_0_1911,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1299]) ).
cnf(i_0_1912,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1331]) ).
fof(i_0_1913,plain,
! [X4528,X4529] :
( ( X4529 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4529,X4529),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4528,X4528)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4528 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4529,X4529),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4528,X4528)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4529 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4528 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4529,X4529),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4528,X4528)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff])])]) ).
fof(i_0_1914,plain,
! [X4517,X4518,X4519] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4519,X4518),X4517) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4519,X4517),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4518,X4517)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(i_0_1915,plain,
! [X3936,X3937,X3938] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3938,X3937),X3936) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3938,X3936),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3937,X3936)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
cnf(i_0_1916,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X1),X2) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1332]) ).
fof(i_0_1917,plain,
! [X3359,X3360,X3361] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3361,X3360),X3359) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3361,X3359),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3360,X3359)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1918,plain,
! [X4993,X4994,X4995] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4995,X4994),X4993) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4995,X4993),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4994,X4993)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).
fof(i_0_1919,plain,
! [X3949,X3950,X3951] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3951,X3950),X3949) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3951,X3949),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3950,X3949)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1920,plain,
! [X3023,X3024,X3025] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3025,X3024),X3023) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3025,X3023),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3024,X3023)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1921,plain,
! [X2879,X2880,X2881] : c_Power_Opower__class_Opower(tc_Int_Oint,X2881,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2880,X2879)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2881,X2880),c_Power_Opower__class_Opower(tc_Int_Oint,X2881,X2879)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1922,plain,
! [X3939,X3940,X3941] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3941,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3940,X3939)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3941,X3940),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3941,X3939)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1923,plain,
! [X3356,X3357,X3358] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3358,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3357,X3356)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3358,X3357),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3358,X3356)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1924,plain,
! [X4990,X4991,X4992] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4992,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4991,X4990)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4992,X4991),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4992,X4990)),
inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).
fof(i_0_1925,plain,
! [X3946,X3947,X3948] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3948,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3947,X3946)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3948,X3947),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3948,X3946)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1926,plain,
! [X3020,X3021,X3022] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3022,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3021,X3020)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3022,X3021),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3022,X3020)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1927,plain,
! [X5009,X5010,X5011] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5011,X5010),X5009),X5010) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5009,X5010),
inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).
cnf(i_0_1928,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1259]) ).
cnf(i_0_1929,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
inference(split_conjunct,[status(thm)],[i_0_1333]) ).
cnf(i_0_1930,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X2),X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1334]) ).
fof(i_0_1931,plain,
! [X3698,X3699,X3700] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3700,X3699),X3698)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3700,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3698,X3699)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3700,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3698,X3699))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3700,X3699),X3698) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1932,plain,
! [X3931,X3932,X3933] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3933,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3932,X3931))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3933,X3931),X3932) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3933,X3931),X3932)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3933,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3932,X3931)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1933,plain,
! [X3054,X3055,X3056] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3054))
| ~ c_Orderings_Oord__class_Oless(X3056,c_Power_Opower__class_Opower(X3056,X3055,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3054)),c_Groups_Ozero__class_Ozero(X3056))
| ~ class_Rings_Olinordered__idom(X3056) )
& ( c_Orderings_Oord__class_Oless(X3056,X3055,c_Groups_Ozero__class_Ozero(X3056))
| ~ c_Orderings_Oord__class_Oless(X3056,c_Power_Opower__class_Opower(X3056,X3055,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3054)),c_Groups_Ozero__class_Ozero(X3056))
| ~ class_Rings_Olinordered__idom(X3056) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3054))
| ~ c_Orderings_Oord__class_Oless(X3056,X3055,c_Groups_Ozero__class_Ozero(X3056))
| c_Orderings_Oord__class_Oless(X3056,c_Power_Opower__class_Opower(X3056,X3055,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3054)),c_Groups_Ozero__class_Ozero(X3056))
| ~ class_Rings_Olinordered__idom(X3056) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1335])])]) ).
fof(i_0_1934,plain,
! [X4803,X4804,X4805,X4806] :
( ~ class_Divides_Osemiring__div(X4806)
| ~ c_Rings_Odvd__class_Odvd(X4806,X4805,c_Divides_Odiv__class_Omod(X4806,X4804,X4803))
| ~ c_Rings_Odvd__class_Odvd(X4806,X4805,X4803)
| c_Rings_Odvd__class_Odvd(X4806,X4805,X4804) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).
fof(i_0_1935,plain,
! [X4791,X4792,X4793,X4794] :
( ( ~ c_Rings_Odvd__class_Odvd(X4794,X4793,c_Divides_Odiv__class_Omod(X4794,X4791,X4792))
| c_Rings_Odvd__class_Odvd(X4794,X4793,X4791)
| ~ c_Rings_Odvd__class_Odvd(X4794,X4793,X4792)
| ~ class_Divides_Osemiring__div(X4794) )
& ( ~ c_Rings_Odvd__class_Odvd(X4794,X4793,X4791)
| c_Rings_Odvd__class_Odvd(X4794,X4793,c_Divides_Odiv__class_Omod(X4794,X4791,X4792))
| ~ c_Rings_Odvd__class_Odvd(X4794,X4793,X4792)
| ~ class_Divides_Osemiring__div(X4794) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).
fof(i_0_1936,plain,
! [X5055,X5056,X5057] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5057)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5056,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5055,X5057)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5056,X5055),X5057) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).
fof(i_0_1937,plain,
! [X3676,X3677,X3678] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3678,X3677)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3677,X3678),X3676) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3677,X3676),X3678) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1938,plain,
! [X3673,X3674,X3675] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3675,X3674)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3674,X3673),X3675) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3674,X3675),X3673) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1939,plain,
! [X3679,X3680,X3681] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3681,X3680)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3679,X3680),X3681) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3679,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3680,X3681)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1940,plain,
! [X3701,X3702,X3703] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3703,X3702)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3701,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3702,X3703)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3701,X3703),X3702) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1941,plain,
! [X3690,X3691,X3692] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3692,X3691)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3690,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3691,X3692)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3690,X3691),X3692) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1942,plain,
! [X5049,X5050] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5049,X5050))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5049)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5050) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5049)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5049,X5050))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5050) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1943,plain,
! [X5036,X5037] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5036,X5037))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5037,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5036,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5036,X5037))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5037,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff])])]) ).
fof(i_0_1944,plain,
! [X3398,X3399] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3399,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3398)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3398) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3399) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3398) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3399,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3398))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3399)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3399,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3398))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq__number__of])])]) ).
fof(i_0_1945,plain,
! [X5047,X5048] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5047,X5048))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5048,X5047)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5048) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5048,X5047)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5047,X5048))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5048) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).
fof(i_0_1946,plain,
! [X4159,X4160,X4161] :
( ( c_Orderings_Oord__class_Oless__eq(X4161,X4160,c_Groups_Ozero__class_Ozero(X4161))
| c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4160)
| ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) )
& ( c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4159)
| c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4160)
| ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) )
& ( c_Orderings_Oord__class_Oless__eq(X4161,X4160,c_Groups_Ozero__class_Ozero(X4161))
| c_Orderings_Oord__class_Oless__eq(X4161,X4159,c_Groups_Ozero__class_Ozero(X4161))
| ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) )
& ( c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4159)
| c_Orderings_Oord__class_Oless__eq(X4161,X4159,c_Groups_Ozero__class_Ozero(X4161))
| ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4160)
| ~ c_Orderings_Oord__class_Oless__eq(X4161,X4159,c_Groups_Ozero__class_Ozero(X4161))
| c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4161,X4160,c_Groups_Ozero__class_Ozero(X4161))
| ~ c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Ozero__class_Ozero(X4161),X4159)
| c_Orderings_Oord__class_Oless__eq(X4161,c_Groups_Otimes__class_Otimes(X4161,X4160,X4159),c_Groups_Ozero__class_Ozero(X4161))
| ~ class_Rings_Olinordered__ring__strict(X4161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1947,plain,
! [X4162,X4163,X4164] :
( ( c_Orderings_Oord__class_Oless__eq(X4164,X4163,c_Groups_Ozero__class_Ozero(X4164))
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4163)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) )
& ( c_Orderings_Oord__class_Oless__eq(X4164,X4162,c_Groups_Ozero__class_Ozero(X4164))
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4163)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) )
& ( c_Orderings_Oord__class_Oless__eq(X4164,X4163,c_Groups_Ozero__class_Ozero(X4164))
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4162)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) )
& ( c_Orderings_Oord__class_Oless__eq(X4164,X4162,c_Groups_Ozero__class_Ozero(X4164))
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4162)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4163)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),X4162)
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4164,X4163,c_Groups_Ozero__class_Ozero(X4164))
| ~ c_Orderings_Oord__class_Oless__eq(X4164,X4162,c_Groups_Ozero__class_Ozero(X4164))
| c_Orderings_Oord__class_Oless__eq(X4164,c_Groups_Ozero__class_Ozero(X4164),c_Groups_Otimes__class_Otimes(X4164,X4163,X4162))
| ~ class_Rings_Olinordered__ring__strict(X4164) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
cnf(i_0_1948,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_numeral__1__eq__Suc__0]) ).
fof(i_0_1949,plain,
! [X4747,X4748,X4749] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4749,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4748,X4747))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4749,X4747)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4749,X4748) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod__imp__zdvd])]) ).
fof(i_0_1950,plain,
! [X3586,X3587,X3588] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3588,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3587,X3586))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3588,X3586)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3588,X3587) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD])]) ).
cnf(i_0_1951,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1336]) ).
fof(i_0_1952,plain,
! [X4315,X4316,X4317,X4318] :
( ~ class_Rings_Olinordered__idom(X4318)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4317)
| ~ c_Orderings_Oord__class_Oless__eq(X4318,X4316,X4315)
| c_Orderings_Oord__class_Oless__eq(X4318,c_Power_Opower__class_Opower(X4318,X4316,X4317),c_Power_Opower__class_Opower(X4318,X4315,X4317)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1337])]) ).
cnf(i_0_1953,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),
inference(split_conjunct,[status(thm)],[i_0_1338]) ).
cnf(i_0_1954,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(split_conjunct,[status(thm)],[i_0_1339]) ).
cnf(i_0_1955,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1340]) ).
cnf(i_0_1956,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1341]) ).
fof(i_0_1957,plain,
! [X4147,X4148,X4149] :
( ~ class_Rings_Oordered__cancel__semiring(X4149)
| ~ c_Orderings_Oord__class_Oless__eq(X4149,X4148,c_Groups_Ozero__class_Ozero(X4149))
| ~ c_Orderings_Oord__class_Oless__eq(X4149,c_Groups_Ozero__class_Ozero(X4149),X4147)
| c_Orderings_Oord__class_Oless__eq(X4149,c_Groups_Otimes__class_Otimes(X4149,X4148,X4147),c_Groups_Ozero__class_Ozero(X4149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1958,plain,
! [X4108,X4109,X4110] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ozero__class_Ozero(X4110),X4109)
| ~ c_Orderings_Oord__class_Oless__eq(X4110,X4108,c_Groups_Ozero__class_Ozero(X4110))
| c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Otimes__class_Otimes(X4110,X4109,X4108),c_Groups_Ozero__class_Ozero(X4110))
| ~ class_Rings_Oordered__cancel__semiring(X4110) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4110,X4109,c_Groups_Ozero__class_Ozero(X4110))
| ~ c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Ozero__class_Ozero(X4110),X4108)
| c_Orderings_Oord__class_Oless__eq(X4110,c_Groups_Otimes__class_Otimes(X4110,X4109,X4108),c_Groups_Ozero__class_Ozero(X4110))
| ~ class_Rings_Oordered__cancel__semiring(X4110) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1959,plain,
! [X4153,X4154,X4155] :
( ~ class_Rings_Oordered__cancel__semiring(X4155)
| ~ c_Orderings_Oord__class_Oless__eq(X4155,c_Groups_Ozero__class_Ozero(X4155),X4154)
| ~ c_Orderings_Oord__class_Oless__eq(X4155,X4153,c_Groups_Ozero__class_Ozero(X4155))
| c_Orderings_Oord__class_Oless__eq(X4155,c_Groups_Otimes__class_Otimes(X4155,X4154,X4153),c_Groups_Ozero__class_Ozero(X4155)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1960,plain,
! [X4150,X4151,X4152] :
( ~ class_Rings_Oordered__cancel__semiring(X4152)
| ~ c_Orderings_Oord__class_Oless__eq(X4152,c_Groups_Ozero__class_Ozero(X4152),X4151)
| ~ c_Orderings_Oord__class_Oless__eq(X4152,X4150,c_Groups_Ozero__class_Ozero(X4152))
| c_Orderings_Oord__class_Oless__eq(X4152,c_Groups_Otimes__class_Otimes(X4152,X4150,X4151),c_Groups_Ozero__class_Ozero(X4152)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1961,plain,
! [X3123,X3124,X3125] :
( ~ class_Rings_Olinordered__semiring__strict(X3125)
| ~ c_Orderings_Oord__class_Oless(X3125,X3124,c_Groups_Ozero__class_Ozero(X3125))
| ~ c_Orderings_Oord__class_Oless(X3125,c_Groups_Ozero__class_Ozero(X3125),X3123)
| c_Orderings_Oord__class_Oless(X3125,c_Groups_Otimes__class_Otimes(X3125,X3124,X3123),c_Groups_Ozero__class_Ozero(X3125)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1962,plain,
! [X3139,X3140,X3141] :
( ~ class_Rings_Olinordered__semiring__strict(X3141)
| ~ c_Orderings_Oord__class_Oless(X3141,c_Groups_Ozero__class_Ozero(X3141),X3140)
| ~ c_Orderings_Oord__class_Oless(X3141,X3139,c_Groups_Ozero__class_Ozero(X3141))
| c_Orderings_Oord__class_Oless(X3141,c_Groups_Otimes__class_Otimes(X3141,X3140,X3139),c_Groups_Ozero__class_Ozero(X3141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1963,plain,
! [X3136,X3137,X3138] :
( ~ class_Rings_Olinordered__semiring__strict(X3138)
| ~ c_Orderings_Oord__class_Oless(X3138,c_Groups_Ozero__class_Ozero(X3138),X3137)
| ~ c_Orderings_Oord__class_Oless(X3138,X3136,c_Groups_Ozero__class_Ozero(X3138))
| c_Orderings_Oord__class_Oless(X3138,c_Groups_Otimes__class_Otimes(X3138,X3136,X3137),c_Groups_Ozero__class_Ozero(X3138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1964,plain,
! [X4185,X4186,X4187] :
( ~ class_Groups_Oordered__comm__monoid__add(X4187)
| ~ c_Orderings_Oord__class_Oless__eq(X4187,X4186,c_Groups_Ozero__class_Ozero(X4187))
| ~ c_Orderings_Oord__class_Oless__eq(X4187,X4185,c_Groups_Ozero__class_Ozero(X4187))
| c_Orderings_Oord__class_Oless__eq(X4187,c_Groups_Oplus__class_Oplus(X4187,X4186,X4185),c_Groups_Ozero__class_Ozero(X4187)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1965,plain,
! [X4418,X4419,X4420] :
( ~ class_Groups_Oordered__comm__monoid__add(X4420)
| ~ c_Orderings_Oord__class_Oless(X4420,X4419,c_Groups_Ozero__class_Ozero(X4420))
| ~ c_Orderings_Oord__class_Oless__eq(X4420,X4418,c_Groups_Ozero__class_Ozero(X4420))
| c_Orderings_Oord__class_Oless(X4420,c_Groups_Oplus__class_Oplus(X4420,X4419,X4418),c_Groups_Ozero__class_Ozero(X4420)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1966,plain,
! [X4421,X4422,X4423] :
( ~ class_Groups_Oordered__comm__monoid__add(X4423)
| ~ c_Orderings_Oord__class_Oless__eq(X4423,X4422,c_Groups_Ozero__class_Ozero(X4423))
| ~ c_Orderings_Oord__class_Oless(X4423,X4421,c_Groups_Ozero__class_Ozero(X4423))
| c_Orderings_Oord__class_Oless(X4423,c_Groups_Oplus__class_Oplus(X4423,X4422,X4421),c_Groups_Ozero__class_Ozero(X4423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1967,plain,
! [X3549,X3550,X3551] :
( ~ class_Groups_Oordered__comm__monoid__add(X3551)
| ~ c_Orderings_Oord__class_Oless(X3551,X3550,c_Groups_Ozero__class_Ozero(X3551))
| ~ c_Orderings_Oord__class_Oless(X3551,X3549,c_Groups_Ozero__class_Ozero(X3551))
| c_Orderings_Oord__class_Oless(X3551,c_Groups_Oplus__class_Oplus(X3551,X3550,X3549),c_Groups_Ozero__class_Ozero(X3551)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1968,plain,
! [X4171,X4172,X4173] :
( ~ class_Groups_Oordered__comm__monoid__add(X4173)
| ~ c_Orderings_Oord__class_Oless__eq(X4173,c_Groups_Ozero__class_Ozero(X4173),X4172)
| ~ c_Orderings_Oord__class_Oless__eq(X4173,c_Groups_Ozero__class_Ozero(X4173),X4171)
| c_Orderings_Oord__class_Oless__eq(X4173,c_Groups_Ozero__class_Ozero(X4173),c_Groups_Oplus__class_Oplus(X4173,X4172,X4171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1969,plain,
! [X4156,X4157,X4158] :
( ~ class_Rings_Oordered__cancel__semiring(X4158)
| ~ c_Orderings_Oord__class_Oless__eq(X4158,c_Groups_Ozero__class_Ozero(X4158),X4157)
| ~ c_Orderings_Oord__class_Oless__eq(X4158,c_Groups_Ozero__class_Ozero(X4158),X4156)
| c_Orderings_Oord__class_Oless__eq(X4158,c_Groups_Ozero__class_Ozero(X4158),c_Groups_Otimes__class_Otimes(X4158,X4157,X4156)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1970,plain,
! [X4111,X4112,X4113] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4113,c_Groups_Ozero__class_Ozero(X4113),X4112)
| ~ c_Orderings_Oord__class_Oless__eq(X4113,c_Groups_Ozero__class_Ozero(X4113),X4111)
| c_Orderings_Oord__class_Oless__eq(X4113,c_Groups_Ozero__class_Ozero(X4113),c_Groups_Otimes__class_Otimes(X4113,X4112,X4111))
| ~ class_Rings_Oordered__ring(X4113) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4113,X4112,c_Groups_Ozero__class_Ozero(X4113))
| ~ c_Orderings_Oord__class_Oless__eq(X4113,X4111,c_Groups_Ozero__class_Ozero(X4113))
| c_Orderings_Oord__class_Oless__eq(X4113,c_Groups_Ozero__class_Ozero(X4113),c_Groups_Otimes__class_Otimes(X4113,X4112,X4111))
| ~ class_Rings_Oordered__ring(X4113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1971,plain,
! [X4203,X4204,X4205] :
( ~ class_Rings_Olinordered__semidom(X4205)
| ~ c_Orderings_Oord__class_Oless(X4205,c_Groups_Oone__class_Oone(X4205),X4204)
| ~ c_Orderings_Oord__class_Oless(X4205,c_Groups_Oone__class_Oone(X4205),X4203)
| c_Orderings_Oord__class_Oless(X4205,c_Groups_Oone__class_Oone(X4205),c_Groups_Otimes__class_Otimes(X4205,X4204,X4203)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1972,plain,
! [X4404,X4405,X4406] :
( ~ class_Groups_Oordered__comm__monoid__add(X4406)
| ~ c_Orderings_Oord__class_Oless(X4406,c_Groups_Ozero__class_Ozero(X4406),X4405)
| ~ c_Orderings_Oord__class_Oless__eq(X4406,c_Groups_Ozero__class_Ozero(X4406),X4404)
| c_Orderings_Oord__class_Oless(X4406,c_Groups_Ozero__class_Ozero(X4406),c_Groups_Oplus__class_Oplus(X4406,X4405,X4404)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1973,plain,
! [X4407,X4408,X4409] :
( ~ class_Groups_Oordered__comm__monoid__add(X4409)
| ~ c_Orderings_Oord__class_Oless__eq(X4409,c_Groups_Ozero__class_Ozero(X4409),X4408)
| ~ c_Orderings_Oord__class_Oless(X4409,c_Groups_Ozero__class_Ozero(X4409),X4407)
| c_Orderings_Oord__class_Oless(X4409,c_Groups_Ozero__class_Ozero(X4409),c_Groups_Oplus__class_Oplus(X4409,X4408,X4407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1974,plain,
! [X3552,X3553,X3554] :
( ~ class_Groups_Oordered__comm__monoid__add(X3554)
| ~ c_Orderings_Oord__class_Oless(X3554,c_Groups_Ozero__class_Ozero(X3554),X3553)
| ~ c_Orderings_Oord__class_Oless(X3554,c_Groups_Ozero__class_Ozero(X3554),X3552)
| c_Orderings_Oord__class_Oless(X3554,c_Groups_Ozero__class_Ozero(X3554),c_Groups_Oplus__class_Oplus(X3554,X3553,X3552)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1975,plain,
! [X3142,X3143,X3144] :
( ~ class_Rings_Olinordered__semiring__strict(X3144)
| ~ c_Orderings_Oord__class_Oless(X3144,c_Groups_Ozero__class_Ozero(X3144),X3143)
| ~ c_Orderings_Oord__class_Oless(X3144,c_Groups_Ozero__class_Ozero(X3144),X3142)
| c_Orderings_Oord__class_Oless(X3144,c_Groups_Ozero__class_Ozero(X3144),c_Groups_Otimes__class_Otimes(X3144,X3143,X3142)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1976,plain,
! [X4144,X4145,X4146] :
( ~ class_Rings_Oordered__ring(X4146)
| ~ c_Orderings_Oord__class_Oless__eq(X4146,X4145,c_Groups_Ozero__class_Ozero(X4146))
| ~ c_Orderings_Oord__class_Oless__eq(X4146,X4144,c_Groups_Ozero__class_Ozero(X4146))
| c_Orderings_Oord__class_Oless__eq(X4146,c_Groups_Ozero__class_Ozero(X4146),c_Groups_Otimes__class_Otimes(X4146,X4145,X4144)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1977,plain,
! [X3120,X3121,X3122] :
( ~ class_Rings_Olinordered__ring__strict(X3122)
| ~ c_Orderings_Oord__class_Oless(X3122,X3121,c_Groups_Ozero__class_Ozero(X3122))
| ~ c_Orderings_Oord__class_Oless(X3122,X3120,c_Groups_Ozero__class_Ozero(X3122))
| c_Orderings_Oord__class_Oless(X3122,c_Groups_Ozero__class_Ozero(X3122),c_Groups_Otimes__class_Otimes(X3122,X3121,X3120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1978,plain,
! [X3400,X3401] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3401)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3400) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3401)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3400)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3401,X3400)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1979,plain,
! [X4029] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4029,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4029,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4029,X4029))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1980,plain,
! [X3896,X3897,X3898,X3899] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3899)
| ~ c_Orderings_Oord__class_Oless__eq(X3899,X3898,X3897)
| c_Orderings_Oord__class_Oless__eq(X3899,c_Groups_Oplus__class_Oplus(X3899,X3898,X3896),c_Groups_Oplus__class_Oplus(X3899,X3897,X3896)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1981,plain,
! [X3892,X3893,X3894,X3895] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3895)
| ~ c_Orderings_Oord__class_Oless__eq(X3895,X3894,X3893)
| c_Orderings_Oord__class_Oless__eq(X3895,c_Groups_Oplus__class_Oplus(X3895,X3892,X3894),c_Groups_Oplus__class_Oplus(X3895,X3892,X3893)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1982,plain,
! [X3541,X3542,X3543,X3544] :
( ~ class_Rings_Ocomm__semiring__1(X3544)
| ~ c_Rings_Odvd__class_Odvd(X3544,X3543,X3542)
| c_Rings_Odvd__class_Odvd(X3544,c_Power_Opower__class_Opower(X3544,X3543,X3541),c_Power_Opower__class_Opower(X3544,X3542,X3541)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_1983,plain,
! [X3507,X3508,X3509,X3510] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3510)
| ~ c_Orderings_Oord__class_Oless(X3510,X3509,X3508)
| c_Orderings_Oord__class_Oless(X3510,c_Groups_Oplus__class_Oplus(X3510,X3509,X3507),c_Groups_Oplus__class_Oplus(X3510,X3508,X3507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1984,plain,
! [X3511,X3512,X3513,X3514] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3514)
| ~ c_Orderings_Oord__class_Oless(X3514,X3513,X3512)
| c_Orderings_Oord__class_Oless(X3514,c_Groups_Oplus__class_Oplus(X3514,X3511,X3513),c_Groups_Oplus__class_Oplus(X3514,X3511,X3512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1985,plain,
! [X4460,X4461,X4462] :
( ~ class_Rings_Olinordered__semidom(X4462)
| ~ c_Orderings_Oord__class_Oless(X4462,c_Groups_Oone__class_Oone(X4462),X4461)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4460)
| c_Orderings_Oord__class_Oless(X4462,c_Groups_Oone__class_Oone(X4462),c_Power_Opower__class_Opower(X4462,X4461,X4460)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1986,plain,
! [X4284,X4285,X4286,X4287] :
( ~ class_Rings_Ocomm__semiring__1(X4287)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4286,X4285)
| c_Rings_Odvd__class_Odvd(X4287,c_Power_Opower__class_Opower(X4287,X4284,X4286),c_Power_Opower__class_Opower(X4287,X4284,X4285)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd])]) ).
fof(i_0_1987,plain,
! [X2850,X2851,X2852] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2852,X2850)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2851,X2850)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2850,X2851)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2852,X2851)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2851,X2852) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2850,X2852)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2851,X2850)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2850,X2851)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2852,X2851)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2851,X2852) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1342])])]) ).
cnf(i_0_1988,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1315]) ).
cnf(i_0_1989,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1316]) ).
cnf(i_0_1990,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1343]) ).
fof(i_0_1991,plain,
! [X4756,X4757,X4758] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4758,X4757) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X4756,X4757)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4757,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4758,X4756)) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4757,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4758,X4756))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4758,X4757) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X4756,X4757) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__dvd__iff])]) ).
fof(i_0_1992,plain,
! [X4177,X4178,X4179,X4180] :
( ~ class_Groups_Oordered__comm__monoid__add(X4180)
| ~ c_Orderings_Oord__class_Oless__eq(X4180,c_Groups_Ozero__class_Ozero(X4180),X4179)
| ~ c_Orderings_Oord__class_Oless__eq(X4180,X4178,X4177)
| c_Orderings_Oord__class_Oless__eq(X4180,X4178,c_Groups_Oplus__class_Oplus(X4180,X4179,X4177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1993,plain,
! [X4181,X4182,X4183,X4184] :
( ~ class_Groups_Oordered__comm__monoid__add(X4184)
| ~ c_Orderings_Oord__class_Oless__eq(X4184,c_Groups_Ozero__class_Ozero(X4184),X4183)
| ~ c_Orderings_Oord__class_Oless__eq(X4184,X4182,X4181)
| c_Orderings_Oord__class_Oless__eq(X4184,X4182,c_Groups_Oplus__class_Oplus(X4184,X4181,X4183)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1994,plain,
! [X4410,X4411,X4412,X4413] :
( ~ class_Groups_Oordered__comm__monoid__add(X4413)
| ~ c_Orderings_Oord__class_Oless(X4413,c_Groups_Ozero__class_Ozero(X4413),X4412)
| ~ c_Orderings_Oord__class_Oless__eq(X4413,X4411,X4410)
| c_Orderings_Oord__class_Oless(X4413,X4411,c_Groups_Oplus__class_Oplus(X4413,X4412,X4410)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1995,plain,
! [X4414,X4415,X4416,X4417] :
( ~ class_Groups_Oordered__comm__monoid__add(X4417)
| ~ c_Orderings_Oord__class_Oless__eq(X4417,c_Groups_Ozero__class_Ozero(X4417),X4416)
| ~ c_Orderings_Oord__class_Oless(X4417,X4415,X4414)
| c_Orderings_Oord__class_Oless(X4417,X4415,c_Groups_Oplus__class_Oplus(X4417,X4416,X4414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1996,plain,
! [X2713,X2714,X2715,X2716] :
( ~ class_Rings_Olinordered__semidom(X2716)
| ~ c_Orderings_Oord__class_Oless(X2716,c_Groups_Ozero__class_Ozero(X2716),X2715)
| ~ c_Orderings_Oord__class_Oless(X2716,X2714,X2713)
| c_Orderings_Oord__class_Oless(X2716,X2714,c_Groups_Oplus__class_Oplus(X2716,X2715,X2713)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1997,plain,
! [X4206,X4207,X4208] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4208,c_Int_Onumber__class_Onumber__of(X4208,X4207),c_Int_Onumber__class_Onumber__of(X4208,X4206))
| ~ c_Orderings_Oord__class_Oless(X4208,c_Int_Onumber__class_Onumber__of(X4208,X4206),c_Int_Onumber__class_Onumber__of(X4208,X4207))
| ~ class_Int_Onumber(X4208)
| ~ class_Orderings_Olinorder(X4208) )
& ( c_Orderings_Oord__class_Oless(X4208,c_Int_Onumber__class_Onumber__of(X4208,X4206),c_Int_Onumber__class_Onumber__of(X4208,X4207))
| c_Orderings_Oord__class_Oless__eq(X4208,c_Int_Onumber__class_Onumber__of(X4208,X4207),c_Int_Onumber__class_Onumber__of(X4208,X4206))
| ~ class_Int_Onumber(X4208)
| ~ class_Orderings_Olinorder(X4208) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1344])])]) ).
cnf(i_0_1998,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1345]) ).
fof(i_0_1999,plain,
! [X3051,X3052,X3053] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| X3051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3052)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| X3051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| X3052 != c_Groups_Ozero__class_Ozero(X3053)
| X3051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3052)
| X3052 != c_Groups_Ozero__class_Ozero(X3053)
| X3051 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( X3051 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| X3052 = c_Groups_Ozero__class_Ozero(X3053)
| c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3051)
| ~ c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),X3052)
| c_Orderings_Oord__class_Oless(X3053,c_Groups_Ozero__class_Ozero(X3053),c_Power_Opower__class_Opower(X3053,X3052,X3051))
| ~ class_Rings_Olinordered__idom(X3053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1346])])]) ).
fof(i_0_2000,plain,
! [X3958,X3959] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3959)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3958)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3959,X3958)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3958,X3959)
| X3959 = X3958 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg])]) ).
fof(i_0_2001,plain,
! [X4484,X4485,X4486] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4484)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4484)
| ~ c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),c_Power_Opower__class_Opower(X4486,X4485,X4484))
| ~ class_Rings_Olinordered__idom(X4486) )
& ( c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),X4485)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4484)
| ~ c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),c_Power_Opower__class_Opower(X4486,X4485,X4484))
| ~ class_Rings_Olinordered__idom(X4486) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4484)
| c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),c_Power_Opower__class_Opower(X4486,X4485,X4484))
| ~ class_Rings_Olinordered__idom(X4486) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4484)
| ~ c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),X4485)
| c_Orderings_Oord__class_Oless__eq(X4486,c_Groups_Ozero__class_Ozero(X4486),c_Power_Opower__class_Opower(X4486,X4485,X4484))
| ~ class_Rings_Olinordered__idom(X4486) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1347])])]) ).
fof(i_0_2002,plain,
! [X4481,X4482,X4483] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4483,c_Groups_Ozero__class_Ozero(X4483),c_Power_Opower__class_Opower(X4483,X4482,X4481))
| c_Orderings_Oord__class_Oless__eq(X4483,c_Groups_Ozero__class_Ozero(X4483),X4482)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4481)
| ~ class_Rings_Olinordered__idom(X4483) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4483,c_Groups_Ozero__class_Ozero(X4483),X4482)
| c_Orderings_Oord__class_Oless__eq(X4483,c_Groups_Ozero__class_Ozero(X4483),c_Power_Opower__class_Opower(X4483,X4482,X4481))
| ~ class_Rings_Olinordered__idom(X4483) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4481)
| c_Orderings_Oord__class_Oless__eq(X4483,c_Groups_Ozero__class_Ozero(X4483),c_Power_Opower__class_Opower(X4483,X4482,X4481))
| ~ class_Rings_Olinordered__idom(X4483) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__iff])])]) ).
fof(i_0_2003,plain,
! [X4475,X4476,X4477] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4477,c_Groups_Ozero__class_Ozero(X4477),c_Power_Opower__class_Opower(X4477,X4475,X4476))
| c_Orderings_Oord__class_Oless__eq(X4477,c_Groups_Ozero__class_Ozero(X4477),X4475)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4476)
| ~ class_Rings_Olinordered__idom(X4477) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4477,c_Groups_Ozero__class_Ozero(X4477),X4475)
| c_Orderings_Oord__class_Oless__eq(X4477,c_Groups_Ozero__class_Ozero(X4477),c_Power_Opower__class_Opower(X4477,X4475,X4476))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4476)
| ~ class_Rings_Olinordered__idom(X4477) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1348])])]) ).
fof(i_0_2004,plain,
! [X4549,X4550,X4551] :
( ( X4549 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( X4550 = c_Groups_Ozero__class_Ozero(X4551)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| c_Orderings_Oord__class_Oless__eq(X4551,X4550,c_Groups_Ozero__class_Ozero(X4551))
| ~ c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( X4550 = c_Groups_Ozero__class_Ozero(X4551)
| c_Orderings_Oord__class_Oless__eq(X4551,X4550,c_Groups_Ozero__class_Ozero(X4551))
| ~ c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4551,X4550,c_Groups_Ozero__class_Ozero(X4551))
| X4549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4549)
| X4550 != c_Groups_Ozero__class_Ozero(X4551)
| X4549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X4551,c_Power_Opower__class_Opower(X4551,X4550,X4549),c_Groups_Ozero__class_Ozero(X4551))
| ~ class_Rings_Olinordered__idom(X4551) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1349])])]) ).
fof(i_0_2005,plain,
! [X3593,X3594,X3595] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3595,X3594)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3593,X3595),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3593,X3594)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
cnf(i_0_2006,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1321]) ).
cnf(i_0_2007,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1322]) ).
fof(i_0_2008,plain,
! [X4040,X4041,X4042] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4042,X4041)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4040,X4042),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4040,X4041)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_2009,plain,
! [X4637,X4638,X4639] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4639,X4638)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4639,X4637),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4638,X4637)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_2010,plain,
! [X4634,X4635,X4636] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4636,X4635)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4634,X4635),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4634,X4636)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_2011,plain,
! [X4010,X4011,X4012] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4012,X4011)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4012,X4010),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4011,X4010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_2012,plain,
! [X4030,X4031,X4032] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4032,X4031)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4032,X4030),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4031,X4030)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_2013,plain,
! [X4033,X4034,X4035] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4035,X4034)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4033,X4035),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4033,X4034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
cnf(i_0_2014,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1323]) ).
cnf(i_0_2015,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OBit0(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1324]) ).
fof(i_0_2016,plain,
! [X3301,X3302,X3303] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3303,X3302)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3303,X3301),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3302,X3301)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_2017,plain,
! [X3340,X3341,X3342] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3342,X3341)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3342,X3340),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3341,X3340)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
cnf(i_0_2018,plain,
( X1 = c_Nat_OSuc(esk9_2(X2,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1350]) ).
cnf(i_0_2019,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1351]) ).
fof(i_0_2020,plain,
! [X4219,X4220,X4221] :
( ~ class_Rings_Ocomm__semiring__1(X4221)
| c_Groups_Oplus__class_Oplus(X4221,c_Groups_Otimes__class_Otimes(X4221,X4220,X4219),X4219) = c_Groups_Otimes__class_Otimes(X4221,c_Groups_Oplus__class_Oplus(X4221,X4220,c_Groups_Oone__class_Oone(X4221)),X4219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_2021,plain,
! [X4216,X4217,X4218] :
( ~ class_Rings_Ocomm__semiring__1(X4218)
| c_Groups_Oplus__class_Oplus(X4218,X4217,c_Groups_Otimes__class_Otimes(X4218,X4216,X4217)) = c_Groups_Otimes__class_Otimes(X4218,c_Groups_Oplus__class_Oplus(X4218,X4216,c_Groups_Oone__class_Oone(X4218)),X4217) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
fof(i_0_2022,plain,
! [X4799,X4800,X4801,X4802] :
( ~ class_Divides_Osemiring__div(X4802)
| ~ c_Rings_Odvd__class_Odvd(X4802,X4801,X4800)
| ~ c_Rings_Odvd__class_Odvd(X4802,X4801,X4799)
| c_Rings_Odvd__class_Odvd(X4802,X4801,c_Divides_Odiv__class_Omod(X4802,X4800,X4799)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).
fof(i_0_2023,plain,
! [X3845,X3846,X3847,X3848] :
( ~ class_Rings_Ocomm__ring__1(X3848)
| ~ c_Rings_Odvd__class_Odvd(X3848,X3847,X3846)
| ~ c_Rings_Odvd__class_Odvd(X3848,X3847,X3845)
| c_Rings_Odvd__class_Odvd(X3848,X3847,c_Groups_Ominus__class_Ominus(X3848,X3846,X3845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_2024,plain,
! [X2750,X2751,X2752,X2753] :
( ~ class_Rings_Ocomm__semiring__1(X2753)
| ~ c_Rings_Odvd__class_Odvd(X2753,X2752,X2751)
| ~ c_Rings_Odvd__class_Odvd(X2753,X2752,X2750)
| c_Rings_Odvd__class_Odvd(X2753,X2752,c_Groups_Oplus__class_Oplus(X2753,X2751,X2750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
cnf(i_0_2025,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1352]) ).
cnf(i_0_2026,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1353]) ).
cnf(i_0_2027,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1354]) ).
cnf(i_0_2028,plain,
( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1355]) ).
cnf(i_0_2029,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X1,X2),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1350]) ).
fof(i_0_2030,plain,
! [X4689,X4690] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4689,X4690),X4690)
| X4689 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4690) )
& ( X4689 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4689,X4690),X4690)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4690) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).
fof(i_0_2031,plain,
! [X4687,X4688] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4688,X4687),X4688)
| X4687 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4688) )
& ( X4687 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4688,X4687),X4688)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4688) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).
cnf(i_0_2032,plain,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
inference(split_conjunct,[status(thm)],[i_0_1356]) ).
cnf(i_0_2033,plain,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
inference(split_conjunct,[status(thm)],[i_0_1357]) ).
fof(i_0_2034,plain,
! [X5034,X5035] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5035,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5034)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5035,X5034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0])]) ).
fof(i_0_2035,plain,
! [X5040,X5041] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5041)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5040,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5041,X5040),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0])]) ).
fof(i_0_2036,plain,
! [X4811,X4812] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4812)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4811)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4812,X4811)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_2037,plain,
! [X4692,X4693] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4693)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4692)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4693,X4692)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_2038,plain,
! [X4694,X4695] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4695)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4694)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4695,X4694)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_2039,plain,
! [X4523,X4524] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4524)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4523)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4524,X4523)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_2040,plain,
! [X3412,X3413] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3413)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3413,X3412)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3412)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3413,X3412)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3413)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3412)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3413,X3412)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
cnf(i_0_2041,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X3))
| X1 != c_Nat_OSuc(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1350]) ).
fof(i_0_2042,plain,
! [X4647,X4648,X4649] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4648,X4649) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4647,X4649)
| X4648 = X4647
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4649,X4647)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4649,X4648) )
& ( X4648 != X4647
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4648,X4649) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4647,X4649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4649,X4647)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4649,X4648) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
cnf(i_0_2043,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1358]) ).
fof(i_0_2044,plain,
! [X5053,X5054] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5054)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X5053)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5054,X5053),X5054) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).
fof(i_0_2045,plain,
! [X3859,X3860] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3860)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3859)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3859,X3860),X3859) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
cnf(i_0_2046,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1359]) ).
cnf(i_0_2047,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1360]) ).
cnf(i_0_2048,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1361]) ).
cnf(i_0_2049,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1362]) ).
cnf(i_0_2050,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Nat_OSuc(X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1363]) ).
fof(i_0_2051,plain,
! [X4167,X4168] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4168,c_Groups_Ozero__class_Ozero(X4168),c_Groups_Oplus__class_Oplus(X4168,X4167,X4167))
| c_Orderings_Oord__class_Oless__eq(X4168,c_Groups_Ozero__class_Ozero(X4168),X4167)
| ~ class_Groups_Olinordered__ab__group__add(X4168) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4168,c_Groups_Ozero__class_Ozero(X4168),X4167)
| c_Orderings_Oord__class_Oless__eq(X4168,c_Groups_Ozero__class_Ozero(X4168),c_Groups_Oplus__class_Oplus(X4168,X4167,X4167))
| ~ class_Groups_Olinordered__ab__group__add(X4168) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add])])]) ).
fof(i_0_2052,plain,
! [X3257,X3258] :
( ( ~ c_Orderings_Oord__class_Oless(X3258,c_Groups_Ozero__class_Ozero(X3258),c_Groups_Oplus__class_Oplus(X3258,X3257,X3257))
| c_Orderings_Oord__class_Oless(X3258,c_Groups_Ozero__class_Ozero(X3258),X3257)
| ~ class_Groups_Olinordered__ab__group__add(X3258) )
& ( ~ c_Orderings_Oord__class_Oless(X3258,c_Groups_Ozero__class_Ozero(X3258),X3257)
| c_Orderings_Oord__class_Oless(X3258,c_Groups_Ozero__class_Ozero(X3258),c_Groups_Oplus__class_Oplus(X3258,X3257,X3257))
| ~ class_Groups_Olinordered__ab__group__add(X3258) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add])])]) ).
fof(i_0_2053,plain,
! [X4169,X4170] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4170,c_Groups_Oplus__class_Oplus(X4170,X4169,X4169),c_Groups_Ozero__class_Ozero(X4170))
| c_Orderings_Oord__class_Oless__eq(X4170,X4169,c_Groups_Ozero__class_Ozero(X4170))
| ~ class_Groups_Olinordered__ab__group__add(X4170) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4170,X4169,c_Groups_Ozero__class_Ozero(X4170))
| c_Orderings_Oord__class_Oless__eq(X4170,c_Groups_Oplus__class_Oplus(X4170,X4169,X4169),c_Groups_Ozero__class_Ozero(X4170))
| ~ class_Groups_Olinordered__ab__group__add(X4170) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
fof(i_0_2054,plain,
! [X3555,X3556] :
( ( ~ c_Orderings_Oord__class_Oless(X3556,c_Groups_Oplus__class_Oplus(X3556,X3555,X3555),c_Groups_Ozero__class_Ozero(X3556))
| c_Orderings_Oord__class_Oless(X3556,X3555,c_Groups_Ozero__class_Ozero(X3556))
| ~ class_Groups_Olinordered__ab__group__add(X3556) )
& ( ~ c_Orderings_Oord__class_Oless(X3556,X3555,c_Groups_Ozero__class_Ozero(X3556))
| c_Orderings_Oord__class_Oless(X3556,c_Groups_Oplus__class_Oplus(X3556,X3555,X3555),c_Groups_Ozero__class_Ozero(X3556))
| ~ class_Groups_Olinordered__ab__group__add(X3556) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero])])]) ).
fof(i_0_2055,plain,
! [X2763,X2764] :
( ( ~ c_Orderings_Oord__class_Oless(X2764,c_Groups_Oplus__class_Oplus(X2764,X2763,X2763),c_Groups_Ozero__class_Ozero(X2764))
| c_Orderings_Oord__class_Oless(X2764,X2763,c_Groups_Ozero__class_Ozero(X2764))
| ~ class_Rings_Olinordered__idom(X2764) )
& ( ~ c_Orderings_Oord__class_Oless(X2764,X2763,c_Groups_Ozero__class_Ozero(X2764))
| c_Orderings_Oord__class_Oless(X2764,c_Groups_Oplus__class_Oplus(X2764,X2763,X2763),c_Groups_Ozero__class_Ozero(X2764))
| ~ class_Rings_Olinordered__idom(X2764) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_2056,plain,
! [X2894,X2895,X2896] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2894)
| ~ c_Orderings_Oord__class_Oless(X2896,c_Power_Opower__class_Opower(X2896,X2895,X2894),c_Groups_Ozero__class_Ozero(X2896))
| ~ class_Rings_Olinordered__idom(X2896) )
& ( c_Orderings_Oord__class_Oless(X2896,X2895,c_Groups_Ozero__class_Ozero(X2896))
| ~ c_Orderings_Oord__class_Oless(X2896,c_Power_Opower__class_Opower(X2896,X2895,X2894),c_Groups_Ozero__class_Ozero(X2896))
| ~ class_Rings_Olinordered__idom(X2896) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2894)
| ~ c_Orderings_Oord__class_Oless(X2896,X2895,c_Groups_Ozero__class_Ozero(X2896))
| c_Orderings_Oord__class_Oless(X2896,c_Power_Opower__class_Opower(X2896,X2895,X2894),c_Groups_Ozero__class_Ozero(X2896))
| ~ class_Rings_Olinordered__idom(X2896) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1364])])]) ).
cnf(i_0_2057,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1365]) ).
fof(i_0_2058,plain,
! [X2734,X2735,X2736,X2737] :
( ~ class_Rings_Ocomm__semiring__1(X2737)
| c_Groups_Oplus__class_Oplus(X2737,c_Groups_Oplus__class_Oplus(X2737,X2736,X2735),X2734) = c_Groups_Oplus__class_Oplus(X2737,c_Groups_Oplus__class_Oplus(X2737,X2736,X2734),X2735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_2059,plain,
! [X2668,X2669,X2670,X2671] :
( ~ class_Rings_Ocomm__semiring__1(X2671)
| c_Groups_Otimes__class_Otimes(X2671,c_Groups_Otimes__class_Otimes(X2671,X2670,X2669),X2668) = c_Groups_Otimes__class_Otimes(X2671,c_Groups_Otimes__class_Otimes(X2671,X2670,X2668),X2669) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_2060,plain,
! [X3460,X3461,X3462,X3463] :
( ~ class_Groups_Oab__semigroup__add(X3463)
| c_Groups_Oplus__class_Oplus(X3463,c_Groups_Oplus__class_Oplus(X3463,X3462,X3461),X3460) = c_Groups_Oplus__class_Oplus(X3463,X3462,c_Groups_Oplus__class_Oplus(X3463,X3461,X3460)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_2061,plain,
! [X2730,X2731,X2732,X2733] :
( ~ class_Rings_Ocomm__semiring__1(X2733)
| c_Groups_Oplus__class_Oplus(X2733,c_Groups_Oplus__class_Oplus(X2733,X2732,X2731),X2730) = c_Groups_Oplus__class_Oplus(X2733,X2732,c_Groups_Oplus__class_Oplus(X2733,X2731,X2730)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_2062,plain,
! [X3535,X3536,X3537] :
( ~ class_Groups_Omonoid__mult(X3537)
| c_Groups_Otimes__class_Otimes(X3537,c_Power_Opower__class_Opower(X3537,X3536,X3535),X3536) = c_Groups_Otimes__class_Otimes(X3537,X3536,c_Power_Opower__class_Opower(X3537,X3536,X3535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_2063,plain,
! [X3456,X3457,X3458,X3459] :
( ~ class_Groups_Oab__semigroup__mult(X3459)
| c_Groups_Otimes__class_Otimes(X3459,c_Groups_Otimes__class_Otimes(X3459,X3458,X3457),X3456) = c_Groups_Otimes__class_Otimes(X3459,X3458,c_Groups_Otimes__class_Otimes(X3459,X3457,X3456)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_2064,plain,
! [X2672,X2673,X2674,X2675] :
( ~ class_Rings_Ocomm__semiring__1(X2675)
| c_Groups_Otimes__class_Otimes(X2675,c_Groups_Otimes__class_Otimes(X2675,X2674,X2673),X2672) = c_Groups_Otimes__class_Otimes(X2675,X2674,c_Groups_Otimes__class_Otimes(X2675,X2673,X2672)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_2065,plain,
! [X2726,X2727,X2728,X2729] :
( ~ class_Rings_Ocomm__semiring__1(X2729)
| c_Groups_Oplus__class_Oplus(X2729,X2728,c_Groups_Oplus__class_Oplus(X2729,X2727,X2726)) = c_Groups_Oplus__class_Oplus(X2729,c_Groups_Oplus__class_Oplus(X2729,X2728,X2727),X2726) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_2066,plain,
! [X2676,X2677,X2678,X2679] :
( ~ class_Rings_Ocomm__semiring__1(X2679)
| c_Groups_Otimes__class_Otimes(X2679,X2678,c_Groups_Otimes__class_Otimes(X2679,X2677,X2676)) = c_Groups_Otimes__class_Otimes(X2679,c_Groups_Otimes__class_Otimes(X2679,X2678,X2677),X2676) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_2067,plain,
! [X2722,X2723,X2724,X2725] :
( ~ class_Rings_Ocomm__semiring__1(X2725)
| c_Groups_Oplus__class_Oplus(X2725,X2724,c_Groups_Oplus__class_Oplus(X2725,X2723,X2722)) = c_Groups_Oplus__class_Oplus(X2725,X2723,c_Groups_Oplus__class_Oplus(X2725,X2724,X2722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_2068,plain,
! [X2680,X2681,X2682,X2683] :
( ~ class_Rings_Ocomm__semiring__1(X2683)
| c_Groups_Otimes__class_Otimes(X2683,X2682,c_Groups_Otimes__class_Otimes(X2683,X2681,X2680)) = c_Groups_Otimes__class_Otimes(X2683,X2681,c_Groups_Otimes__class_Otimes(X2683,X2682,X2680)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
cnf(i_0_2069,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__numeral__1__eq__1]) ).
cnf(i_0_2070,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = 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(i_0_2071,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_Numeral1__eq1__nat]) ).
fof(i_0_2072,plain,
! [X3545,X3546,X3547,X3548] :
( ~ class_Groups_Omonoid__mult(X3548)
| c_Power_Opower__class_Opower(X3548,X3547,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3546,X3545)) = c_Power_Opower__class_Opower(X3548,c_Power_Opower__class_Opower(X3548,X3547,X3546),X3545) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_2073,plain,
! [X2996,X2997,X2998,X2999] :
( ~ class_Rings_Ocomm__semiring__1(X2999)
| c_Power_Opower__class_Opower(X2999,c_Power_Opower__class_Opower(X2999,X2998,X2997),X2996) = c_Power_Opower__class_Opower(X2999,X2998,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2997,X2996)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
cnf(i_0_2074,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1366]) ).
cnf(i_0_2075,plain,
( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)))
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1326]) ).
fof(i_0_2076,plain,
! [X3664,X3665,X3666] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3666,X3665,X3664)
| c_Orderings_Oord__class_Oless__eq(X3666,c_Groups_Ominus__class_Ominus(X3666,X3665,X3664),c_Groups_Ozero__class_Ozero(X3666))
| ~ class_Groups_Oordered__ab__group__add(X3666) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3666,c_Groups_Ominus__class_Ominus(X3666,X3665,X3664),c_Groups_Ozero__class_Ozero(X3666))
| c_Orderings_Oord__class_Oless__eq(X3666,X3665,X3664)
| ~ class_Groups_Oordered__ab__group__add(X3666) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).
fof(i_0_2077,plain,
! [X4078,X4079,X4080] :
( ( ~ c_Orderings_Oord__class_Oless(X4080,X4079,X4078)
| c_Orderings_Oord__class_Oless(X4080,c_Groups_Ominus__class_Ominus(X4080,X4079,X4078),c_Groups_Ozero__class_Ozero(X4080))
| ~ class_Groups_Oordered__ab__group__add(X4080) )
& ( ~ c_Orderings_Oord__class_Oless(X4080,c_Groups_Ominus__class_Ominus(X4080,X4079,X4078),c_Groups_Ozero__class_Ozero(X4080))
| c_Orderings_Oord__class_Oless(X4080,X4079,X4078)
| ~ class_Groups_Oordered__ab__group__add(X4080) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).
cnf(i_0_2078,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(split_conjunct,[status(thm)],[i_0_1367]) ).
cnf(i_0_2079,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)),
inference(split_conjunct,[status(thm)],[i_0_1368]) ).
cnf(i_0_2080,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(split_conjunct,[status(thm)],[i_0_1369]) ).
fof(i_0_2081,plain,
! [X4750,X4751,X4752] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4752,X4751)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4752,X4750)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4752,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4751,X4750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__zmod])]) ).
fof(i_0_2082,plain,
! [X3915,X3916,X3917] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3917,X3916)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3917,X3915)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3917,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3916,X3915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).
cnf(i_0_2083,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1370]) ).
cnf(i_0_2084,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1371]) ).
fof(i_0_2085,plain,
! [X3656,X3657,X3658,X3659,X3660] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3660,X3659,X3658)
| c_Orderings_Oord__class_Oless__eq(X3660,X3657,X3656)
| c_Groups_Ominus__class_Ominus(X3660,X3659,X3658) != c_Groups_Ominus__class_Ominus(X3660,X3657,X3656)
| ~ class_Groups_Oordered__ab__group__add(X3660) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3660,X3657,X3656)
| c_Orderings_Oord__class_Oless__eq(X3660,X3659,X3658)
| c_Groups_Ominus__class_Ominus(X3660,X3659,X3658) != c_Groups_Ominus__class_Ominus(X3660,X3657,X3656)
| ~ class_Groups_Oordered__ab__group__add(X3660) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).
fof(i_0_2086,plain,
! [X3815,X3816,X3817,X3818,X3819] :
( ( ~ c_Orderings_Oord__class_Oless(X3819,X3818,X3817)
| c_Orderings_Oord__class_Oless(X3819,X3816,X3815)
| c_Groups_Ominus__class_Ominus(X3819,X3818,X3817) != c_Groups_Ominus__class_Ominus(X3819,X3816,X3815)
| ~ class_Groups_Oordered__ab__group__add(X3819) )
& ( ~ c_Orderings_Oord__class_Oless(X3819,X3816,X3815)
| c_Orderings_Oord__class_Oless(X3819,X3818,X3817)
| c_Groups_Ominus__class_Ominus(X3819,X3818,X3817) != c_Groups_Ominus__class_Ominus(X3819,X3816,X3815)
| ~ class_Groups_Oordered__ab__group__add(X3819) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
cnf(i_0_2087,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1372]) ).
cnf(i_0_2088,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_1373]) ).
fof(i_0_2089,plain,
! [X3484,X3485] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3485,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3485),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3484)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3484) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3484,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3485),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3484)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3485)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3485,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3484,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3485),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3484)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3485,X3484))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3485,c_Int_OPls) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1374])])]) ).
fof(i_0_2090,plain,
! [X2922,X2923,X2924,X2925] :
( ~ class_Rings_Ocomm__semiring__1(X2925)
| ~ c_Rings_Odvd__class_Odvd(X2925,c_Groups_Otimes__class_Otimes(X2925,X2924,X2923),X2922)
| c_Rings_Odvd__class_Odvd(X2925,X2924,X2922) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).
fof(i_0_2091,plain,
! [X2926,X2927,X2928,X2929] :
( ~ class_Rings_Ocomm__semiring__1(X2929)
| ~ c_Rings_Odvd__class_Odvd(X2929,c_Groups_Otimes__class_Otimes(X2929,X2928,X2927),X2926)
| c_Rings_Odvd__class_Odvd(X2929,X2927,X2926) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_2092,plain,
! [X3925,X3926,X3927] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3927,X3926),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3927,X3925)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3926,X3925),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_2093,plain,
! [X3928,X3929,X3930] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3930,X3929),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3928,X3929)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3930,X3928),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_2094,plain,
! [X4629,X4630,X4631] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4631,X4630),X4629) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4631,X4629),X4630),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_2095,plain,
! [X3922,X3923,X3924] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3924,X3923),X3922) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3924,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3923,X3922)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_2096,plain,
! [X3270,X3271,X3272] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3272,X3271),X3270) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3272,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3271,X3270)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_2097,plain,
! [X2788,X2789,X2790] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2790,X2789),X2788) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2790,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2789,X2788)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_2098,plain,
! [X3000,X3001,X3002] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X3002,X3001),X3000) = c_Power_Opower__class_Opower(tc_Int_Oint,X3002,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3001,X3000)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_2099,plain,
! [X4514,X4515,X4516] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4516,X4515),X4514) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4516,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4515,X4514)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_2100,plain,
! [X2581,X2582,X2583] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2583,X2582),X2581) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2583,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2582,X2581)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_2101,plain,
! [X2625,X2626,X2627] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2627,X2626),X2625) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2627,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2626,X2625)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_2102,plain,
! [X3267,X3268,X3269] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3269,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3268,X3267)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3268,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3269,X3267)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_2103,plain,
! [X2779,X2780,X2781] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2781,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2780,X2779)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2780,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2781,X2779)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_2104,plain,
! [X4321,X4322] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4322,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4321,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4322,X4321)
| X4322 = X4321 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4322,X4321)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4322,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4321,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X4322 != X4321
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4322,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4321,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).
cnf(i_0_2105,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
cnf(i_0_2106,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1376]) ).
cnf(i_0_2107,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1377]) ).
cnf(i_0_2108,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1378]) ).
fof(i_0_2109,plain,
! [X3299,X3300] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3300,X3299))
| X3299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3300) )
& ( X3299 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3300,X3299)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3300)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3300,X3299)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_2110,plain,
! [X3284,X3285] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3285,X3284))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3285)
| X3284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3285)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3285,X3284)) )
& ( X3284 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3285,X3284)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
cnf(i_0_2111,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1379]) ).
fof(i_0_2112,plain,
! [X3801,X3802] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3802,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3801)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3802,X3801) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3802,X3801)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3802,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3801) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
cnf(i_0_2113,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1380]) ).
cnf(i_0_2114,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1381]) ).
cnf(i_0_2115,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1382]) ).
cnf(i_0_2116,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1383]) ).
fof(i_0_2117,plain,
! [X3803,X3804] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3804,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3803,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3804,X3803) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3804,X3803)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3804,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3803,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).
cnf(i_0_2118,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1384]) ).
fof(i_0_2119,plain,
! [X3584,X3585] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3585,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3584,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3585,X3584) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3585,X3584)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3585,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3584,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).
fof(i_0_2120,plain,
! [X4795,X4796,X4797,X4798] :
( ~ class_Divides_Osemiring__div(X4798)
| ~ c_Rings_Odvd__class_Odvd(X4798,X4797,X4796)
| c_Divides_Odiv__class_Omod(X4798,c_Divides_Odiv__class_Omod(X4798,X4795,X4796),X4797) = c_Divides_Odiv__class_Omod(X4798,X4795,X4797) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).
cnf(i_0_2121,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1385]) ).
cnf(i_0_2122,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1386]) ).
fof(i_0_2123,plain,
! [X2825,X2826,X2827] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2827,X2825)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2826,X2825)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2825,X2826)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2827,X2826) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2825,X2827)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2826,X2825)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2825,X2826)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2827,X2826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1387])])]) ).
fof(i_0_2124,plain,
! [X2845,X2846,X2847] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2847,X2845)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2846,X2845)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2847,X2846)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2846,X2847) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2845,X2847)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2846,X2845)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2847,X2846)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2846,X2847) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1388])])]) ).
fof(i_0_2125,plain,
! [X3722,X3723] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3723,X3722)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3723,X3722),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3723,X3722),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3723,X3722) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_2126,plain,
! [X4222,X4223] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4223,X4222)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4223,X4222),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4223,X4222),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4223,X4222) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_2127,plain,
! [X3861,X3862] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3862,X3861))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3861,X3862) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3861,X3862)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3862,X3861)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
cnf(i_0_2128,plain,
( c_Nat_OSuc(X1) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1389]) ).
fof(i_0_2129,plain,
! [X3332,X3333,X3334,X3335] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3335,X3334)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3333,X3334) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3335,X3332)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3333,X3332) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_2130,plain,
! [X4677] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4677)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4677,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4677) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4677,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4677)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4677) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1390])])]) ).
cnf(i_0_2131,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]) ).
fof(i_0_2132,plain,
! [X4023,X4024,X4025] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4025,X4023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4025,X4024),X4023) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4024,X4023)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4025,X4024),X4023) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1392])])]) ).
fof(i_0_2133,plain,
! [X4020,X4021,X4022] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4022,X4021),X4020)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4022,X4020) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_2134,plain,
! [X4017,X4018,X4019] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4019,X4018),X4017)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4018,X4017) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_2135,plain,
! [X3329,X3330,X3331] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3331,X3330),X3329)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3331,X3329) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_2136,plain,
! [X2777,X2778] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2778,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2777,X2778))
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2778,X2777) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2778,X2777)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2778,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2777,X2778)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).
cnf(i_0_2137,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2138,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
cnf(i_0_2139,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk11_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1386]) ).
fof(i_0_2140,plain,
! [X4174,X4175,X4176] :
( ( X4175 = c_Groups_Ozero__class_Ozero(X4176)
| c_Groups_Oplus__class_Oplus(X4176,X4175,X4174) != c_Groups_Ozero__class_Ozero(X4176)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4174)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4175)
| ~ class_Groups_Oordered__comm__monoid__add(X4176) )
& ( X4174 = c_Groups_Ozero__class_Ozero(X4176)
| c_Groups_Oplus__class_Oplus(X4176,X4175,X4174) != c_Groups_Ozero__class_Ozero(X4176)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4174)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4175)
| ~ class_Groups_Oordered__comm__monoid__add(X4176) )
& ( X4175 != c_Groups_Ozero__class_Ozero(X4176)
| X4174 != c_Groups_Ozero__class_Ozero(X4176)
| c_Groups_Oplus__class_Oplus(X4176,X4175,X4174) = c_Groups_Ozero__class_Ozero(X4176)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4174)
| ~ c_Orderings_Oord__class_Oless__eq(X4176,c_Groups_Ozero__class_Ozero(X4176),X4175)
| ~ class_Groups_Oordered__comm__monoid__add(X4176) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
cnf(i_0_2141,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1395]) ).
cnf(i_0_2142,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1396]) ).
cnf(i_0_2143,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1397]) ).
cnf(i_0_2144,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1398]) ).
cnf(i_0_2145,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1399]) ).
cnf(i_0_2146,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1400]) ).
cnf(i_0_2147,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1401]) ).
cnf(i_0_2148,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1402]) ).
fof(i_0_2149,plain,
! [X4912,X4913,X4914] :
( ( ~ c_Rings_Odvd__class_Odvd(X4914,c_Int_Onumber__class_Onumber__of(X4914,X4913),c_Int_Onumber__class_Onumber__of(X4914,X4912))
| c_Divides_Odiv__class_Omod(X4914,c_Int_Onumber__class_Onumber__of(X4914,X4912),c_Int_Onumber__class_Onumber__of(X4914,X4913)) = c_Groups_Ozero__class_Ozero(X4914)
| ~ class_Divides_Osemiring__div(X4914)
| ~ class_Int_Onumber(X4914) )
& ( c_Divides_Odiv__class_Omod(X4914,c_Int_Onumber__class_Onumber__of(X4914,X4912),c_Int_Onumber__class_Onumber__of(X4914,X4913)) != c_Groups_Ozero__class_Ozero(X4914)
| c_Rings_Odvd__class_Odvd(X4914,c_Int_Onumber__class_Onumber__of(X4914,X4913),c_Int_Onumber__class_Onumber__of(X4914,X4912))
| ~ class_Divides_Osemiring__div(X4914)
| ~ class_Int_Onumber(X4914) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of])])]) ).
fof(i_0_2150,plain,
! [X4986,X4987] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4987,X4986)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4986,X4987) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4986,X4987),X4987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).
fof(i_0_2151,plain,
! [X3454,X3455] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3455,X3454)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3454)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3455),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3454)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3455,X3454)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3455),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3454)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3455,X3454)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3455,X3454)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3455),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3454)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3454)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3455,X3454)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3455),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3454)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).
fof(i_0_2152,plain,
! [X4261,X4262,X4263,X4264] :
( ( c_Power_Opower__class_Opower(X4264,X4263,X4262) != c_Power_Opower__class_Opower(X4264,X4263,X4261)
| X4262 = X4261
| ~ c_Orderings_Oord__class_Oless(X4264,c_Groups_Oone__class_Oone(X4264),X4263)
| ~ class_Rings_Olinordered__semidom(X4264) )
& ( X4262 != X4261
| c_Power_Opower__class_Opower(X4264,X4263,X4262) = c_Power_Opower__class_Opower(X4264,X4263,X4261)
| ~ c_Orderings_Oord__class_Oless(X4264,c_Groups_Oone__class_Oone(X4264),X4263)
| ~ class_Rings_Olinordered__semidom(X4264) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_2153,plain,
! [X3157,X3158] :
( ~ class_Rings_Olinordered__ring(X3158)
| ~ c_Orderings_Oord__class_Oless(X3158,c_Groups_Otimes__class_Otimes(X3158,X3157,X3157),c_Groups_Ozero__class_Ozero(X3158)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1403])]) ).
fof(i_0_2154,plain,
! [X3604,X3605,X3606] :
( ~ class_Rings_Olinordered__semidom(X3606)
| ~ c_Orderings_Oord__class_Oless__eq(X3606,c_Groups_Oone__class_Oone(X3606),X3605)
| c_Orderings_Oord__class_Oless__eq(X3606,c_Groups_Oone__class_Oone(X3606),c_Power_Opower__class_Opower(X3606,X3605,X3604)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_2155,plain,
! [X4224,X4225,X4226] :
( ~ class_Rings_Olinordered__semidom(X4226)
| ~ c_Orderings_Oord__class_Oless__eq(X4226,c_Groups_Ozero__class_Ozero(X4226),X4225)
| c_Orderings_Oord__class_Oless__eq(X4226,c_Groups_Ozero__class_Ozero(X4226),c_Power_Opower__class_Opower(X4226,X4225,X4224)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_2156,plain,
! [X3254,X3255,X3256] :
( ~ class_Rings_Olinordered__semidom(X3256)
| ~ c_Orderings_Oord__class_Oless(X3256,c_Groups_Ozero__class_Ozero(X3256),X3255)
| c_Orderings_Oord__class_Oless(X3256,c_Groups_Ozero__class_Ozero(X3256),c_Power_Opower__class_Opower(X3256,X3255,X3254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_2157,plain,
! [X4045,X4046] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4046,X4045)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4046,X4045)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4046,X4045)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4046,X4045)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4046,X4045)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4046)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4045)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4046,X4045)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1404])])]) ).
cnf(i_0_2158,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1405]) ).
fof(i_0_2159,plain,
! [X2703,X2704] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2704,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2704),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2703)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2704,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2704),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2703)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2704,X2703)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])]) ).
cnf(i_0_2160,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1407]) ).
cnf(i_0_2161,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1366]) ).
fof(i_0_2162,plain,
! [X4978,X4979] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4979,X4978)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4979,X4978) = X4979 )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4979,X4978)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4979,X4978) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4979,X4978),X4978) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1408])]) ).
fof(i_0_2163,plain,
! [X4973,X4974] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4974,X4973)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4974,X4973) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4974,X4973),X4973) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1409])]) ).
fof(i_0_2164,plain,
! [X3792,X3793] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3793),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3792))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3793,X3792)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3793,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3793,X3792)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3793),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3792)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3793,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3793),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3792)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1410])])]) ).
fof(i_0_2165,plain,
! [X4320] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4320),X4320) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_2166,plain,
! [X4930,X4931] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4931),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4930))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4930),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4931)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4930),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4931)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4931),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4930)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__iff__zmod__eq__0__number__of])]) ).
cnf(i_0_2167,plain,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1411]) ).
cnf(i_0_2168,plain,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_1412]) ).
fof(i_0_2169,plain,
! [X3264] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3264,X3264))
| X3264 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3264 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3264,X3264)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1413])]) ).
fof(i_0_2170,plain,
! [X4472,X4473,X4474] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4473)
| c_Rings_Odvd__class_Odvd(X4474,X4472,c_Power_Opower__class_Opower(X4474,X4472,X4473))
| ~ class_Rings_Ocomm__semiring__1(X4474) )
& ( X4472 != c_Groups_Oone__class_Oone(X4474)
| c_Rings_Odvd__class_Odvd(X4474,X4472,c_Power_Opower__class_Opower(X4474,X4472,X4473))
| ~ class_Rings_Ocomm__semiring__1(X4474) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).
fof(i_0_2171,plain,
! [X3420,X3421,X3422] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3421) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3420)
| X3421 = X3420
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3422) )
& ( X3421 != X3420
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3421) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3420)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3422) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_2172,plain,
! [X3375,X3376] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3376)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3376,X3375)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X3375,X3376) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1414])]) ).
fof(i_0_2173,plain,
! [X3396,X3397] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3397)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3397,X3396)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3396,X3397) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1415])]) ).
cnf(i_0_2174,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1416]) ).
cnf(i_0_2175,plain,
c_Int_OBit1(X1) != c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_1417]) ).
cnf(i_0_2176,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[i_0_1418]) ).
fof(i_0_2177,plain,
! [X5066,X5067,X5068] :
( ~ class_Divides_Osemiring__div(X5068)
| ~ c_Rings_Odvd__class_Odvd(X5068,X5067,X5066)
| c_Groups_Otimes__class_Otimes(X5068,X5067,c_Divides_Odiv__class_Odiv(X5068,X5066,X5067)) = X5066 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).
cnf(i_0_2178,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1419]) ).
cnf(i_0_2179,plain,
( X1 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1420]) ).
fof(i_0_2180,plain,
! [X2905,X2906,X2907,X2908] :
( ~ class_Rings_Ocomm__semiring__1(X2908)
| ~ c_Rings_Odvd__class_Odvd(X2908,X2907,X2906)
| c_Rings_Odvd__class_Odvd(X2908,X2907,c_Groups_Otimes__class_Otimes(X2908,X2906,X2905)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).
fof(i_0_2181,plain,
! [X2909,X2910,X2911,X2912] :
( ~ class_Rings_Ocomm__semiring__1(X2912)
| ~ c_Rings_Odvd__class_Odvd(X2912,X2911,X2910)
| c_Rings_Odvd__class_Odvd(X2912,X2911,c_Groups_Otimes__class_Otimes(X2912,X2909,X2910)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).
fof(i_0_2182,plain,
! [X4071] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4071)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
cnf(i_0_2183,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1341]) ).
cnf(i_0_2184,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1351]) ).
fof(i_0_2185,plain,
! [X4919,X4920] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4919,X4920),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4920,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4920,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4919,X4920))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4920,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__conj])])]) ).
fof(i_0_2186,plain,
! [X4921,X4922] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4922,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4921,X4922),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])]) ).
cnf(i_0_2187,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1385]) ).
fof(i_0_2188,plain,
! [X4925,X4926] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4925,X4926))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4926) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4925,X4926),X4926)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4926) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).
fof(i_0_2189,plain,
! [X4927,X4928] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4928)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X4927,X4928)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).
fof(i_0_2190,plain,
! [X4696,X4697] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4697)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X4697,X4696)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_2191,plain,
! [X4214,X4215] :
( ~ class_Rings_Ocomm__semiring__1(X4215)
| c_Groups_Oplus__class_Oplus(X4215,X4214,X4214) = c_Groups_Otimes__class_Otimes(X4215,c_Groups_Oplus__class_Oplus(X4215,c_Groups_Oone__class_Oone(X4215),c_Groups_Oone__class_Oone(X4215)),X4214) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_2192,plain,
! [X3799,X3800] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3800,X3799)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3800,c_Groups_Oone__class_Oone(tc_Int_Oint)),X3799) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
cnf(i_0_2193,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1421]) ).
cnf(i_0_2194,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1381]) ).
cnf(i_0_2195,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1382]) ).
cnf(i_0_2196,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1422]) ).
cnf(i_0_2197,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1341]) ).
cnf(i_0_2198,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1423]) ).
cnf(i_0_2199,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1384]) ).
cnf(i_0_2200,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
cnf(i_0_2201,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1424]) ).
fof(i_0_2202,plain,
! [X3354,X3355] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3355,X3354),X3355),
inference(variable_rename,[status(thm)],[i_0_1425]) ).
fof(i_0_2203,plain,
! [X3352,X3353] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3353,X3352),X3352),
inference(variable_rename,[status(thm)],[i_0_1426]) ).
fof(i_0_2204,plain,
! [X4809,X4810] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4810)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4810,X4809),X4810) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).
fof(i_0_2205,plain,
! [X5012,X5013] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5013)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5012,X5013),X5013) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).
fof(i_0_2206,plain,
! [X4904,X4905] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4905)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4904,X4905),X4905) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_2207,plain,
! [X5001,X5002] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5002)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5001,X5002),X5002) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).
fof(i_0_2208,plain,
! [X4902,X4903] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4903,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4903,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4902,X4903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_2209,plain,
! [X3685,X3686] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3686,X3685)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3685,X3686),X3686) = X3685 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_2210,plain,
! [X4640,X4641] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4641,X4640)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4640,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4640,X4641)) = X4641 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_2211,plain,
! [X3693,X3694] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3694,X3693)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3694,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3693,X3694)) = X3693 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_2212,plain,
! [X3627,X3628,X3629] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3629,X3628)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3629,X3627),X3628) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_2213,plain,
! [X4004,X4005,X4006] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4006,X4005)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4006,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4005,X4004)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_2214,plain,
! [X4007,X4008,X4009] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4009,X4008)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4009,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4007,X4008)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_2215,plain,
! [X3346,X3347,X3348] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3348,X3347)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3348,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3347,X3346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_2216,plain,
! [X3343,X3344,X3345] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3345,X3344)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3345,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3343,X3344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
cnf(i_0_2217,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2218,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2219,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
cnf(i_0_2220,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
cnf(i_0_2221,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
fof(i_0_2222,plain,
! [X3436,X3437] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3437)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3437,X3436)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3436)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3437,X3436)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3437)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3436)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3437,X3436)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power__nat])])]) ).
cnf(i_0_2223,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1399]) ).
cnf(i_0_2224,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1401]) ).
cnf(i_0_2225,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_1400]) ).
cnf(i_0_2226,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1402]) ).
cnf(i_0_2227,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1396]) ).
cnf(i_0_2228,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1395]) ).
cnf(i_0_2229,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1397]) ).
cnf(i_0_2230,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1398]) ).
cnf(i_0_2231,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]) ).
cnf(i_0_2232,plain,
( X1 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1391]) ).
fof(i_0_2233,plain,
! [X3646,X3647,X3648] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3648,c_Int_Onumber__class_Onumber__of(X3648,X3647),c_Int_Onumber__class_Onumber__of(X3648,X3646))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3647,X3646)
| ~ class_Int_Onumber__ring(X3648)
| ~ class_Rings_Olinordered__idom(X3648) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3647,X3646)
| c_Orderings_Oord__class_Oless__eq(X3648,c_Int_Onumber__class_Onumber__of(X3648,X3647),c_Int_Onumber__class_Onumber__of(X3648,X3646))
| ~ class_Int_Onumber__ring(X3648)
| ~ class_Rings_Olinordered__idom(X3648) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).
fof(i_0_2234,plain,
! [X2872,X2873,X2874] :
( ( ~ c_Orderings_Oord__class_Oless(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2873),c_Int_Onumber__class_Onumber__of(X2874,X2872))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2873,X2872)
| ~ class_Int_Onumber__ring(X2874)
| ~ class_Rings_Olinordered__idom(X2874) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2873,X2872)
| c_Orderings_Oord__class_Oless(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2873),c_Int_Onumber__class_Onumber__of(X2874,X2872))
| ~ class_Int_Onumber__ring(X2874)
| ~ class_Rings_Olinordered__idom(X2874) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).
fof(i_0_2235,plain,
! [X2746,X2747,X2748,X2749] :
( ~ class_Rings_Ocomm__semiring__1(X2749)
| ~ c_Rings_Odvd__class_Odvd(X2749,X2748,X2747)
| ~ c_Rings_Odvd__class_Odvd(X2749,X2747,X2746)
| c_Rings_Odvd__class_Odvd(X2749,X2748,X2746) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_2236,plain,
! [X2865,X2866,X2867] :
( ~ class_Int_Onumber__ring(X2867)
| c_Groups_Oplus__class_Oplus(X2867,c_Int_Onumber__class_Onumber__of(X2867,X2866),c_Int_Onumber__class_Onumber__of(X2867,X2865)) = c_Int_Onumber__class_Onumber__of(X2867,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2866,X2865)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).
fof(i_0_2237,plain,
! [X2574,X2575,X2576] :
( ~ class_Int_Onumber__ring(X2576)
| c_Groups_Otimes__class_Otimes(X2576,c_Int_Onumber__class_Onumber__of(X2576,X2575),c_Int_Onumber__class_Onumber__of(X2576,X2574)) = c_Int_Onumber__class_Onumber__of(X2576,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2575,X2574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).
fof(i_0_2238,plain,
! [X3661,X3662,X3663] :
( ~ class_Int_Onumber__ring(X3663)
| c_Int_Onumber__class_Onumber__of(X3663,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3662,X3661)) = c_Groups_Ominus__class_Ominus(X3663,c_Int_Onumber__class_Onumber__of(X3663,X3662),c_Int_Onumber__class_Onumber__of(X3663,X3661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).
fof(i_0_2239,plain,
! [X2868,X2869,X2870] :
( ~ class_Int_Onumber__ring(X2870)
| c_Int_Onumber__class_Onumber__of(X2870,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2869,X2868)) = c_Groups_Oplus__class_Oplus(X2870,c_Int_Onumber__class_Onumber__of(X2870,X2869),c_Int_Onumber__class_Onumber__of(X2870,X2868)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
fof(i_0_2240,plain,
! [X2571,X2572,X2573] :
( ~ class_Int_Onumber__ring(X2573)
| c_Int_Onumber__class_Onumber__of(X2573,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2572,X2571)) = c_Groups_Otimes__class_Otimes(X2573,c_Int_Onumber__class_Onumber__of(X2573,X2572),c_Int_Onumber__class_Onumber__of(X2573,X2571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).
fof(i_0_2241,plain,
! [X4735,X4736] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4736)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4735,X4736)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat])]) ).
fof(i_0_2242,plain,
! [X5051,X5052] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5052,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5052)
| X5051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5051,X5052)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5052)
| X5051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5052,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5052,X5051)
| X5051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5051,X5052)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X5052,X5051)
| X5051 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X5051 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5052)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5052,X5051)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5052,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5051,X5052)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5052,X5051) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff])])]) ).
fof(i_0_2243,plain,
! [X5038,X5039] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5039)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5039,X5038)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5039,X5038) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial])]) ).
fof(i_0_2244,plain,
! [X5029,X5030] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5030,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5029,X5030)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5030,X5029) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial])]) ).
cnf(i_0_2245,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_1428]) ).
fof(i_0_2246,plain,
! [X4923,X4924] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4924)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4924,X4923)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4924,X4923) = X4924 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).
fof(i_0_2247,plain,
! [X4917,X4918] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4918,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4917,X4918)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4918,X4917) = X4918 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).
fof(i_0_2248,plain,
! [X4306,X4307] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X4307,X4306)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4306)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4307,X4306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le])]) ).
fof(i_0_2249,plain,
! [X4295,X4296] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4296,X4295)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4295)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4296,X4295) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).
fof(i_0_2250,plain,
! [X3682,X3683,X3684] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3683,X3684) != X3682
| X3683 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3682,X3684)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3684,X3683) )
& ( X3683 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3682,X3684)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3683,X3684) = X3682
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3684,X3683) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_2251,plain,
! [X4863,X4864,X4865] :
( ~ class_Divides_Osemiring__div(X4865)
| c_Divides_Odiv__class_Omod(X4865,c_Divides_Odiv__class_Omod(X4865,X4864,X4863),X4863) = c_Divides_Odiv__class_Omod(X4865,X4864,X4863) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_2252,plain,
! [X4762,X4763,X4764] :
( ~ class_Divides_Osemiring__div(X4764)
| c_Divides_Odiv__class_Omod(X4764,c_Groups_Oplus__class_Oplus(X4764,X4763,X4762),X4763) = c_Divides_Odiv__class_Omod(X4764,X4762,X4763) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_2253,plain,
! [X4759,X4760,X4761] :
( ~ class_Divides_Osemiring__div(X4761)
| c_Divides_Odiv__class_Omod(X4761,c_Groups_Oplus__class_Oplus(X4761,X4760,X4759),X4759) = c_Divides_Odiv__class_Omod(X4761,X4760,X4759) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_2254,plain,
! [X4618,X4619,X4620] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4620,X4619)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4619,X4618)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4620,X4618) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_2255,plain,
! [X4611,X4612,X4613] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4613,X4612)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4612,X4611)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4613,X4611) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_2256,plain,
! [X4642,X4643,X4644] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4644,X4643)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4643,X4642)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4644,X4642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_2257,plain,
! [X2819,X2820,X2821] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2821,X2820)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2820,X2819)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2821,X2819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).
cnf(i_0_2258,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1376]) ).
fof(i_0_2259,plain,
! [X4961] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4961)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X4961) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4961,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).
fof(i_0_2260,plain,
! [X3371,X3372] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3372)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3371)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3372,X3371)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1429])]) ).
fof(i_0_2261,plain,
! [X4054,X4055] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4055)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X4054)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4055,X4054)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1430])])]) ).
fof(i_0_2262,plain,
! [X3369,X3370] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3370)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3369)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3370,X3369)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1431])]) ).
fof(i_0_2263,plain,
! [X3365,X3366] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3366)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3365)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3366,X3365)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1432])])]) ).
fof(i_0_2264,plain,
! [X3037,X3038] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3038)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3037)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3038,X3037)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3037)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3038)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3038,X3037)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3038)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3037)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3038,X3037)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3038)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3037)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3038,X3037)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1433])])]) ).
fof(i_0_2265,plain,
! [X3035,X3036] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3036)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3035)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3036,X3035)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3035)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3036)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3036,X3035)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3036)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3035)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3036,X3035)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3036)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3035)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3036,X3035)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__add])])]) ).
fof(i_0_2266,plain,
! [X3033,X3034] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3034)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3033)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3034,X3033)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1434])])]) ).
cnf(i_0_2267,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1352]) ).
cnf(i_0_2268,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1353]) ).
fof(i_0_2269,plain,
! [X3327,X3328] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3328),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3327)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3328,X3327)),
inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(i_0_2270,plain,
! [X2579,X2580] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2580),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2579)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2580,X2579)),
inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).
cnf(i_0_2271,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1435]) ).
cnf(i_0_2272,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2273,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2274,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
cnf(i_0_2275,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
fof(i_0_2276,plain,
! [X3934,X3935] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3935,X3934)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3934,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3935,X3934)) = X3935 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])]) ).
fof(i_0_2277,plain,
! [X3045,X3046] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3046,X3045))
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3046)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3045) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3046)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3046,X3045)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3045)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3046,X3045)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__product])])]) ).
fof(i_0_2278,plain,
! [X3039,X3040] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3040)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3039)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3040,X3039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1437])]) ).
fof(i_0_2279,plain,
! [X2607,X2608] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2608,X2607))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2608)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2607) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2608)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2608,X2607)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2607)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2608,X2607)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__product__nat])])]) ).
fof(i_0_2280,plain,
! [X4043,X4044] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4044),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4043))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4044,X4043) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4044,X4043)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4044),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X4043)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).
fof(i_0_2281,plain,
! [X3030,X3031] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3031),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3030))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3031,X3030) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3031,X3030)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3031),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3030)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).
cnf(i_0_2282,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
fof(i_0_2283,plain,
! [X4062,X4063] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4063,c_Groups_Ozero__class_Ozero(X4063),c_Int_Onumber__class_Onumber__of(X4063,X4062))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4062)
| ~ class_Int_Onumber__ring(X4063)
| ~ class_Rings_Olinordered__idom(X4063) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X4062)
| c_Orderings_Oord__class_Oless__eq(X4063,c_Groups_Ozero__class_Ozero(X4063),c_Int_Onumber__class_Onumber__of(X4063,X4062))
| ~ class_Int_Onumber__ring(X4063)
| ~ class_Rings_Olinordered__idom(X4063) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).
fof(i_0_2284,plain,
! [X3047,X3048] :
( ( ~ c_Orderings_Oord__class_Oless(X3048,c_Groups_Ozero__class_Ozero(X3048),c_Int_Onumber__class_Onumber__of(X3048,X3047))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3047)
| ~ class_Int_Onumber__ring(X3048)
| ~ class_Rings_Olinordered__idom(X3048) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3047)
| c_Orderings_Oord__class_Oless(X3048,c_Groups_Ozero__class_Ozero(X3048),c_Int_Onumber__class_Onumber__of(X3048,X3047))
| ~ class_Int_Onumber__ring(X3048)
| ~ class_Rings_Olinordered__idom(X3048) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).
fof(i_0_2285,plain,
! [X4064,X4065] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4065,c_Int_Onumber__class_Onumber__of(X4065,X4064),c_Groups_Ozero__class_Ozero(X4065))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4064,c_Int_OPls)
| ~ class_Int_Onumber__ring(X4065)
| ~ class_Rings_Olinordered__idom(X4065) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4064,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(X4065,c_Int_Onumber__class_Onumber__of(X4065,X4064),c_Groups_Ozero__class_Ozero(X4065))
| ~ class_Int_Onumber__ring(X4065)
| ~ class_Rings_Olinordered__idom(X4065) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).
fof(i_0_2286,plain,
! [X3049,X3050] :
( ( ~ c_Orderings_Oord__class_Oless(X3050,c_Int_Onumber__class_Onumber__of(X3050,X3049),c_Groups_Ozero__class_Ozero(X3050))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3049,c_Int_OPls)
| ~ class_Int_Onumber__ring(X3050)
| ~ class_Rings_Olinordered__idom(X3050) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3049,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X3050,c_Int_Onumber__class_Onumber__of(X3050,X3049),c_Groups_Ozero__class_Ozero(X3050))
| ~ class_Int_Onumber__ring(X3050)
| ~ class_Rings_Olinordered__idom(X3050) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
fof(i_0_2287,plain,
! [X4478,X4479,X4480] :
( ~ class_Groups_Omonoid__mult(X4480)
| ~ class_Rings_Olinordered__ring(X4480)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4479)
| c_Orderings_Oord__class_Oless__eq(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Power_Opower__class_Opower(X4480,X4478,X4479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power])]) ).
fof(i_0_2288,plain,
! [X4430] :
( ~ class_Rings_Olinordered__semidom(X4430)
| c_Orderings_Oord__class_Oless(X4430,c_Groups_Ozero__class_Ozero(X4430),c_Groups_Oplus__class_Oplus(X4430,c_Groups_Oone__class_Oone(X4430),c_Groups_Oone__class_Oone(X4430))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_2289,plain,
! [X2886,X2887] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2887)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2887,X2886)) )
& ( X2886 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2887,X2886)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2887)
| X2886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2887,X2886)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power])])]) ).
fof(i_0_2290,plain,
! [X2855,X2856] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2856)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2856,X2855)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1438])]) ).
fof(i_0_2291,plain,
! [X3643,X3644,X3645] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3644,X3645)
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| X3645 = X3644
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,X3644) )
& ( ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| X3645 = X3644
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,X3644) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3644,X3645)
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,X3644) )
& ( ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,X3644) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3644,X3645)
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| X3645 = X3644
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645)) )
& ( ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| X3645 = X3644
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3644,X3645)
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645)) )
& ( ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645))
| ~ hBOOL(hAPP(hAPP(X3643,X3644),X3645)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
cnf(i_0_2292,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1439]) ).
fof(i_0_2293,plain,
! [X3651,X3652,X3653,X3654,X3655] :
( ( X3654 != X3653
| X3652 = X3651
| c_Groups_Ominus__class_Ominus(X3655,X3654,X3653) != c_Groups_Ominus__class_Ominus(X3655,X3652,X3651)
| ~ class_Groups_Oab__group__add(X3655) )
& ( X3652 != X3651
| X3654 = X3653
| c_Groups_Ominus__class_Ominus(X3655,X3654,X3653) != c_Groups_Ominus__class_Ominus(X3655,X3652,X3651)
| ~ class_Groups_Oab__group__add(X3655) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
cnf(i_0_2294,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1393]) ).
cnf(i_0_2295,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_1394]) ).
fof(i_0_2296,plain,
! [X4209,X4210] :
( ~ class_Rings_Olinordered__semidom(X4210)
| c_Orderings_Oord__class_Oless(X4210,X4209,c_Groups_Oplus__class_Oplus(X4210,X4209,c_Groups_Oone__class_Oone(X4210))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_2297,plain,
! [X3196,X3197,X3198] :
( ( X3197 = c_Groups_Ozero__class_Ozero(X3198)
| c_Power_Opower__class_Opower(X3198,X3197,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3196)) != c_Groups_Ozero__class_Ozero(X3198)
| ~ class_Power_Opower(X3198)
| ~ class_Rings_Omult__zero(X3198)
| ~ class_Rings_Ono__zero__divisors(X3198)
| ~ class_Rings_Ozero__neq__one(X3198) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3196) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X3198,X3197,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3196)) != c_Groups_Ozero__class_Ozero(X3198)
| ~ class_Power_Opower(X3198)
| ~ class_Rings_Omult__zero(X3198)
| ~ class_Rings_Ono__zero__divisors(X3198)
| ~ class_Rings_Ozero__neq__one(X3198) )
& ( X3197 != c_Groups_Ozero__class_Ozero(X3198)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3196) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X3198,X3197,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3196)) = c_Groups_Ozero__class_Ozero(X3198)
| ~ class_Power_Opower(X3198)
| ~ class_Rings_Omult__zero(X3198)
| ~ class_Rings_Ono__zero__divisors(X3198)
| ~ class_Rings_Ozero__neq__one(X3198) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of])])]) ).
fof(i_0_2298,plain,
! [X3480,X3481,X3482,X3483] :
( ~ class_Groups_Ocancel__semigroup__add(X3483)
| c_Groups_Oplus__class_Oplus(X3483,X3482,X3481) != c_Groups_Oplus__class_Oplus(X3483,X3480,X3481)
| X3482 = X3480 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_2299,plain,
! [X3468,X3469,X3470,X3471] :
( ( c_Groups_Oplus__class_Oplus(X3471,X3470,X3469) != c_Groups_Oplus__class_Oplus(X3471,X3468,X3469)
| X3470 = X3468
| ~ class_Groups_Ocancel__semigroup__add(X3471) )
& ( X3470 != X3468
| c_Groups_Oplus__class_Oplus(X3471,X3470,X3469) = c_Groups_Oplus__class_Oplus(X3471,X3468,X3469)
| ~ class_Groups_Ocancel__semigroup__add(X3471) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_2300,plain,
! [X3476,X3477,X3478,X3479] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3479)
| c_Groups_Oplus__class_Oplus(X3479,X3478,X3477) != c_Groups_Oplus__class_Oplus(X3479,X3478,X3476)
| X3477 = X3476 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_2301,plain,
! [X3472,X3473,X3474,X3475] :
( ~ class_Groups_Ocancel__semigroup__add(X3475)
| c_Groups_Oplus__class_Oplus(X3475,X3474,X3473) != c_Groups_Oplus__class_Oplus(X3475,X3474,X3472)
| X3473 = X3472 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_2302,plain,
! [X3464,X3465,X3466,X3467] :
( ( c_Groups_Oplus__class_Oplus(X3467,X3466,X3465) != c_Groups_Oplus__class_Oplus(X3467,X3466,X3464)
| X3465 = X3464
| ~ class_Groups_Ocancel__semigroup__add(X3467) )
& ( X3465 != X3464
| c_Groups_Oplus__class_Oplus(X3467,X3466,X3465) = c_Groups_Oplus__class_Oplus(X3467,X3466,X3464)
| ~ class_Groups_Ocancel__semigroup__add(X3467) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_2303,plain,
! [X4502,X4503] :
( ( X4503 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4503,X4502) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4503) )
& ( X4502 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4503,X4502) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4503) )
& ( X4503 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4502 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4503,X4502) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4503) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
cnf(i_0_2304,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1440]) ).
cnf(i_0_2305,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1441]) ).
fof(i_0_2306,plain,
! [X3854,X3855] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3855,X3854) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3854,X3855) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3855 = X3854 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_2307,plain,
! [X3486] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3486))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3486) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3486)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3486)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).
cnf(i_0_2308,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1405]) ).
fof(i_0_2309,plain,
! [X4165,X4166] :
( ~ class_Rings_Olinordered__ring(X4166)
| c_Orderings_Oord__class_Oless__eq(X4166,c_Groups_Ozero__class_Ozero(X4166),c_Groups_Otimes__class_Otimes(X4166,X4165,X4165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_2310,plain,
! [X4506,X4507,X4508] :
( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4507,X4508) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4506,X4508)
| X4507 = X4506
| X4508 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4507 != X4506
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4507,X4508) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4506,X4508)
| X4508 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel])])]) ).
fof(i_0_2311,plain,
! [X2609,X2610,X2611] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2611,X2610) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2609,X2610)
| X2611 = X2609
| X2610 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2611 != X2609
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2611,X2610) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2609,X2610) )
& ( X2610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2611,X2610) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2609,X2610) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_2312,plain,
! [X4509,X4510,X4511] :
( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4511,X4510) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4511,X4509)
| X4510 = X4509
| X4511 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4510 != X4509
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4511,X4510) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4511,X4509)
| X4511 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel])])]) ).
fof(i_0_2313,plain,
! [X2615,X2616,X2617] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2616) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2615)
| X2617 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2616 = X2615 )
& ( X2617 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2616) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2615) )
& ( X2616 != X2615
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2616) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2617,X2615) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2314,plain,
! [X2612,X2613,X2614] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2613) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2612)
| X2613 = X2612
| X2614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2613 != X2612
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2613) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2612) )
& ( X2614 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2613) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2614,X2612) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_2315,plain,
! [X4981,X4982,X4983] :
( ~ class_Divides_Osemiring__div(X4983)
| c_Divides_Odiv__class_Odiv(X4983,c_Divides_Odiv__class_Omod(X4983,X4982,X4981),X4981) = c_Groups_Ozero__class_Ozero(X4983) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).
fof(i_0_2316,plain,
! [X4843,X4844,X4845] :
( ~ class_Divides_Osemiring__div(X4845)
| c_Divides_Odiv__class_Omod(X4845,c_Groups_Otimes__class_Otimes(X4845,X4844,X4843),X4844) = c_Groups_Ozero__class_Ozero(X4845) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_2317,plain,
! [X4846,X4847,X4848] :
( ~ class_Divides_Osemiring__div(X4848)
| c_Divides_Odiv__class_Omod(X4848,c_Groups_Otimes__class_Otimes(X4848,X4847,X4846),X4846) = c_Groups_Ozero__class_Ozero(X4848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
cnf(i_0_2318,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1442]) ).
fof(i_0_2319,plain,
! [X4616,X4617] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4617,X4616)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4616,X4617)
| X4617 = X4616 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_2320,plain,
! [X4614,X4615] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4615,X4614)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4614,X4615)
| X4615 = X4614 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_2321,plain,
! [X4645,X4646] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4646,X4645)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4645,X4646)
| X4646 = X4645 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_2322,plain,
! [X2817,X2818] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2818,X2817)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2817,X2818)
| X2818 = X2817 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).
fof(i_0_2323,plain,
! [X2815,X2816] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2816,X2815)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2815,X2816)
| X2816 = X2815 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).
fof(i_0_2324,plain,
! [X2807,X2808] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2808,X2807)
| X2808 = X2807
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2808,X2807) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2807,X2808)
| X2808 = X2807
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2808,X2807) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1443])])]) ).
fof(i_0_2325,plain,
! [X2805,X2806] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2806,X2805)
| X2806 = X2805
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2806,X2805) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2805,X2806)
| X2806 = X2805
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2806,X2805) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1444])])]) ).
fof(i_0_2326,plain,
! [X2803,X2804] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2803,X2804)
| X2803 = X2804
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2804,X2803) )
& ( X2803 != X2804
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2803,X2804)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2804,X2803) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).
fof(i_0_2327,plain,
! [X2799,X2800] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2800,X2799)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2800,X2799)
| X2800 = X2799 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2799,X2800)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2800,X2799)
| X2800 = X2799 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])])]) ).
fof(i_0_2328,plain,
! [X2791,X2792] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2791,X2792) )
& ( X2792 != X2791
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2791,X2792) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| X2792 = X2791 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2791,X2792)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2792,X2791)
| X2792 = X2791 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])])]) ).
fof(i_0_2329,plain,
! [X2773,X2774] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773)
| X2774 = X2773
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2773,X2774)
| X2774 = X2773
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773) )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2773,X2774)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773) )
& ( X2774 != X2773
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2774,X2773) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])])]) ).
fof(i_0_2330,plain,
! [X2771,X2772] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2772,X2771)
| X2772 != X2771 )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2771,X2772)
| X2772 != X2771 )
& ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2772,X2771)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2771,X2772)
| X2772 = X2771 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).
fof(i_0_2331,plain,
! [X3836,X3837,X3838] :
( ~ class_Groups_Ogroup__add(X3838)
| c_Groups_Ominus__class_Ominus(X3838,c_Groups_Oplus__class_Oplus(X3838,X3837,X3836),X3836) = X3837 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_2332,plain,
! [X3839,X3840,X3841] :
( ~ class_Groups_Ogroup__add(X3841)
| c_Groups_Oplus__class_Oplus(X3841,c_Groups_Ominus__class_Ominus(X3841,X3840,X3839),X3839) = X3840 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
cnf(i_0_2333,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(split_conjunct,[status(thm)],[i_0_1448]) ).
cnf(i_0_2334,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1350]) ).
fof(i_0_2335,plain,
! [X2899,X2900,X2901] :
( ~ class_Rings_Ocomm__semiring__1(X2901)
| c_Rings_Odvd__class_Odvd(X2901,X2900,c_Groups_Otimes__class_Otimes(X2901,X2900,X2899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).
fof(i_0_2336,plain,
! [X2902,X2903,X2904] :
( ~ class_Rings_Ocomm__semiring__1(X2904)
| c_Rings_Odvd__class_Odvd(X2904,X2903,c_Groups_Otimes__class_Otimes(X2904,X2902,X2903)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).
cnf(i_0_2337,plain,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1449]) ).
fof(i_0_2338,plain,
! [X2796,X2797,X2798] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2798,X2797) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2796,X2797)
| X2798 = X2796 )
& ( X2798 != X2796
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2798,X2797) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2796,X2797) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_2339,plain,
! [X2793,X2794,X2795] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2795,X2794) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2795,X2793)
| X2794 = X2793 )
& ( X2794 != X2793
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2795,X2794) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2795,X2793) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_2340,plain,
! [X4906,X4907,X4909,X4910,X4911] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4907,X4906) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4907 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4906,esk16_2(X4906,X4907)) )
& ( X4910 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4909,X4911)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4910,X4909) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__eq__0__iff])])])])]) ).
fof(i_0_2341,plain,
! [X5003,X5004,X5006,X5007,X5008] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5004,X5003) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X5004 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5003,esk17_2(X5003,X5004)) )
& ( X5007 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5006,X5008)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X5007,X5006) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq__0__iff])])])])]) ).
cnf(i_0_2342,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_1450]) ).
cnf(i_0_2343,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
cnf(i_0_2344,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1451]) ).
cnf(i_0_2345,plain,
( c_Int_OBit1(X1) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_1412]) ).
cnf(i_0_2346,plain,
( c_Int_OMin = c_Int_OBit1(X1)
| c_Int_OMin != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1411]) ).
fof(i_0_2347,plain,
! [X3995,X3996,X3998,X3999,X4000] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3996,X3995)
| X3995 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3996,esk13_2(X3995,X3996)) )
& ( X3998 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3999,X4000)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3999,X3998) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__add])])])])]) ).
cnf(i_0_2348,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1452]) ).
fof(i_0_2349,plain,
! [X4984,X4985] : c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4985,X4984),X4984) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).
fof(i_0_2350,plain,
! [X4231,X4232] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4232,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4232,X4231)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
cnf(i_0_2351,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).
fof(i_0_2352,plain,
! [X3920,X3921] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3921,X3920),X3921) = X3920,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_2353,plain,
! [X3918,X3919] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3919,X3918),X3918) = X3919,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_2354,plain,
! [X3367,X3368] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3368)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3367)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3368,X3367)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__plus__even])]) ).
fof(i_0_2355,plain,
! [X4988,X4989] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4989,X4988),X4989),
inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).
fof(i_0_2356,plain,
! [X4625,X4626] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4626,X4625),X4626),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_2357,plain,
! [X3993,X3994] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3994,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3994,X3993)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_2358,plain,
! [X3991,X3992] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3992,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3991,X3992)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_2359,plain,
! [X4028] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4028,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4028,X4028)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_2360,plain,
! [X4857,X4858,X4859] :
( ( ~ c_Rings_Odvd__class_Odvd(X4859,X4858,X4857)
| c_Divides_Odiv__class_Omod(X4859,X4857,X4858) = c_Groups_Ozero__class_Ozero(X4859)
| ~ class_Divides_Osemiring__div(X4859) )
& ( c_Divides_Odiv__class_Omod(X4859,X4857,X4858) != c_Groups_Ozero__class_Ozero(X4859)
| c_Rings_Odvd__class_Odvd(X4859,X4858,X4857)
| ~ class_Divides_Osemiring__div(X4859) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).
fof(i_0_2361,plain,
! [X4860,X4861,X4862] :
( ~ class_Divides_Osemiring__div(X4862)
| ~ c_Rings_Odvd__class_Odvd(X4862,X4861,X4860)
| c_Divides_Odiv__class_Omod(X4862,X4860,X4861) = c_Groups_Ozero__class_Ozero(X4862) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).
cnf(i_0_2362,plain,
( X1 = c_Nat_OSuc(esk10_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1453]) ).
fof(i_0_2363,plain,
! [X2918,X2919,X2920,X2921] :
( ~ class_Rings_Odvd(X2921)
| X2920 != c_Groups_Otimes__class_Otimes(X2921,X2919,X2918)
| c_Rings_Odvd__class_Odvd(X2921,X2919,X2920) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).
cnf(i_0_2364,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1453]) ).
fof(i_0_2365,plain,
! [X3794] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3794)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3794) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3794)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3794) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_2366,plain,
! [X3373,X3374] :
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3374)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3373)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3374,X3373)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1454])]) ).
fof(i_0_2367,plain,
! [X3729,X3730] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3730,X3729) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3730,X3729) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3730,X3729)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3730,X3729) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq])]) ).
fof(i_0_2368,plain,
! [X3609,X3610] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3610,X3609)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3610,X3609) )
& ( X3610 != X3609
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3610,X3609) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3610,X3609)
| X3610 = X3609
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3610,X3609) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2369,plain,
! [X3607,X3608] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3608,X3607)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3608,X3607)
| X3608 = X3607 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3608,X3607)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3608,X3607) )
& ( X3608 != X3607
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3608,X3607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_2370,plain,
! [X4026,X4027] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4027,X4026)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4027,X4026) )
& ( X4027 != X4026
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4027,X4026) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4027,X4026)
| X4027 = X4026
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4027,X4026) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_2371,plain,
! [X3630,X3631] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3631,X3630)
| X3631 = X3630
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3631,X3630) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_2372,plain,
! [X3616,X3617] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3617,X3616)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3617,X3616)
| X3617 = X3616 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3617,X3616)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3617,X3616) )
& ( X3617 != X3616
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3617,X3616) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_2373,plain,
! [X3614,X3615] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3615,X3614)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3615,X3614) )
& ( X3615 != X3614
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3615,X3614) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3615,X3614)
| X3615 = X3614
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3615,X3614) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_2374,plain,
! [X3727,X3728] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3728,X3727)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3728,X3727) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H])]) ).
fof(i_0_2375,plain,
! [X4971,X4972] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4972,X4971)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X4972,X4971) = X4972 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).
fof(i_0_2376,plain,
! [X3641,X3642] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3642,X3641)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3642,X3641) )
& ( X3642 != X3641
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3642,X3641) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2377,plain,
! [X3625,X3626] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3626,X3625)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3626,X3625) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2378,plain,
! [X3043,X3044] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3044)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3044,X3043)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__times__anything])]) ).
fof(i_0_2379,plain,
! [X3041,X3042] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X3042)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3041,X3042)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anything__times__even])]) ).
cnf(i_0_2380,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1435]) ).
fof(i_0_2381,plain,
! [X3251,X3252,X3253] :
( ( X3252 = c_Groups_Ozero__class_Ozero(X3253)
| c_Power_Opower__class_Opower(X3253,X3252,X3251) != c_Groups_Ozero__class_Ozero(X3253)
| ~ class_Power_Opower(X3253)
| ~ class_Rings_Omult__zero(X3253)
| ~ class_Rings_Ono__zero__divisors(X3253)
| ~ class_Rings_Ozero__neq__one(X3253) )
& ( X3251 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X3253,X3252,X3251) != c_Groups_Ozero__class_Ozero(X3253)
| ~ class_Power_Opower(X3253)
| ~ class_Rings_Omult__zero(X3253)
| ~ class_Rings_Ono__zero__divisors(X3253)
| ~ class_Rings_Ozero__neq__one(X3253) )
& ( X3252 != c_Groups_Ozero__class_Ozero(X3253)
| X3251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X3253,X3252,X3251) = c_Groups_Ozero__class_Ozero(X3253)
| ~ class_Power_Opower(X3253)
| ~ class_Rings_Omult__zero(X3253)
| ~ class_Rings_Ono__zero__divisors(X3253)
| ~ class_Rings_Ozero__neq__one(X3253) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2382,plain,
! [X4547,X4548] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4547) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4548,c_Groups_Ozero__class_Ozero(X4548),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4547)) = c_Groups_Oone__class_Oone(X4548)
| ~ class_Power_Opower(X4548)
| ~ class_Rings_Osemiring__0(X4548) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4548,c_Groups_Ozero__class_Ozero(X4548),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4547)) = c_Groups_Ozero__class_Ozero(X4548)
| ~ class_Power_Opower(X4548)
| ~ class_Rings_Osemiring__0(X4548) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of])])]) ).
fof(i_0_2383,plain,
! [X2743,X2744,X2745] :
( ~ class_Rings_Olinordered__idom(X2745)
| X2744 = X2743
| c_Orderings_Oord__class_Oless(X2745,X2744,X2743)
| c_Orderings_Oord__class_Oless(X2745,X2743,X2744) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1455])]) ).
cnf(i_0_2384,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
fof(i_0_2385,plain,
! [X2719,X2720,X2721] :
( ~ class_Rings_Ocomm__semiring__1(X2721)
| c_Groups_Oplus__class_Oplus(X2721,X2720,X2719) = c_Groups_Oplus__class_Oplus(X2721,X2719,X2720) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2386,plain,
! [X2684,X2685,X2686] :
( ~ class_Rings_Ocomm__semiring__1(X2686)
| c_Groups_Otimes__class_Otimes(X2686,X2685,X2684) = c_Groups_Otimes__class_Otimes(X2686,X2684,X2685) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2387,plain,
! [X3731] :
( ~ class_Rings_Olinordered__semidom(X3731)
| ~ c_Orderings_Oord__class_Oless__eq(X3731,c_Groups_Oone__class_Oone(X3731),c_Groups_Ozero__class_Ozero(X3731)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1456])]) ).
fof(i_0_2388,plain,
! [X4107] :
( ~ class_Rings_Olinordered__semidom(X4107)
| ~ c_Orderings_Oord__class_Oless(X4107,c_Groups_Oone__class_Oone(X4107),c_Groups_Ozero__class_Ozero(X4107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1457])]) ).
cnf(i_0_2389,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_1458]) ).
fof(i_0_2390,plain,
! [X2650,X2651,X2652] :
( ~ class_Rings_Ono__zero__divisors(X2652)
| c_Groups_Otimes__class_Otimes(X2652,X2651,X2650) != c_Groups_Ozero__class_Ozero(X2652)
| X2651 = c_Groups_Ozero__class_Ozero(X2652)
| X2650 = c_Groups_Ozero__class_Ozero(X2652) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2391,plain,
! [X2647,X2648,X2649] :
( ~ class_Rings_Ono__zero__divisors(X2649)
| X2648 = c_Groups_Ozero__class_Ozero(X2649)
| X2647 = c_Groups_Ozero__class_Ozero(X2649)
| c_Groups_Otimes__class_Otimes(X2649,X2648,X2647) != c_Groups_Ozero__class_Ozero(X2649) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2392,plain,
! [X2644,X2645,X2646] :
( ( c_Groups_Otimes__class_Otimes(X2646,X2645,X2644) != c_Groups_Ozero__class_Ozero(X2646)
| X2645 = c_Groups_Ozero__class_Ozero(X2646)
| X2644 = c_Groups_Ozero__class_Ozero(X2646)
| ~ class_Rings_Oring__no__zero__divisors(X2646) )
& ( X2645 != c_Groups_Ozero__class_Ozero(X2646)
| c_Groups_Otimes__class_Otimes(X2646,X2645,X2644) = c_Groups_Ozero__class_Ozero(X2646)
| ~ class_Rings_Oring__no__zero__divisors(X2646) )
& ( X2644 != c_Groups_Ozero__class_Ozero(X2646)
| c_Groups_Otimes__class_Otimes(X2646,X2645,X2644) = c_Groups_Ozero__class_Ozero(X2646)
| ~ class_Rings_Oring__no__zero__divisors(X2646) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2393,plain,
! [X4470,X4471] :
( ~ class_Int_Onumber__ring(X4471)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4470)
| c_Power_Opower__class_Opower(X4471,c_Int_Onumber__class_Onumber__of(X4471,c_Int_OMin),X4470) = c_Int_Onumber__class_Onumber__of(X4471,c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])]) ).
fof(i_0_2394,plain,
! [X4069,X4070] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4069)
| c_Power_Opower__class_Opower(X4070,c_Int_Onumber__class_Onumber__of(X4070,c_Int_OMin),X4069) = c_Groups_Oone__class_Oone(X4070)
| ~ class_Int_Onumber__ring(X4070) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4069)
| c_Power_Opower__class_Opower(X4070,c_Int_Onumber__class_Onumber__of(X4070,c_Int_OMin),X4069) = c_Int_Onumber__class_Onumber__of(X4070,c_Int_OMin)
| ~ class_Int_Onumber__ring(X4070) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1460])])]) ).
fof(i_0_2395,plain,
! [X4067,X4068] :
( ~ class_Int_Onumber__ring(X4068)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4067)
| c_Power_Opower__class_Opower(X4068,c_Int_Onumber__class_Onumber__of(X4068,c_Int_OMin),X4067) = c_Groups_Oone__class_Oone(X4068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__one__even__power])]) ).
fof(i_0_2396,plain,
! [X2765,X2766] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2766,X2765)
| X2766 = X2765
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2765,X2766) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2397,plain,
! [X3618,X3619] :
( X3619 = X3618
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3619,X3618)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3618,X3619) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1461])]) ).
fof(i_0_2398,plain,
! [X3612,X3613] :
( ( X3613 = X3612
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3613,X3612)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3612,X3613) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3613,X3612)
| X3613 != X3612 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3612,X3613)
| X3613 != X3612 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2399,plain,
! [X2897,X2898] :
( ~ class_Rings_Ocomm__semiring__1(X2898)
| ~ c_Rings_Odvd__class_Odvd(X2898,c_Groups_Ozero__class_Ozero(X2898),X2897)
| X2897 = c_Groups_Ozero__class_Ozero(X2898) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).
fof(i_0_2400,plain,
! [X4621,X4622] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4622,X4621)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4621,X4622) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2401,plain,
! [X4609,X4610] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4610,X4609)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4609,X4610) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2402,plain,
! [X4627,X4628] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4628,X4627)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4627,X4628) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2403,plain,
! [X3265,X3266] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3266,X3265) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3265,X3266),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2404,plain,
! [X2769,X2770] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2770,X2769) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2769,X2770),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2405,plain,
! [X4512,X4513] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4513,X4512) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4512,X4513),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2406,plain,
! [X2577,X2578] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2578,X2577) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2577,X2578),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2407,plain,
! [X2623,X2624] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2624,X2623) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2623,X2624),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2408,plain,
! [X2934,X2935] :
( ( c_Groups_Oplus__class_Oplus(X2935,X2934,X2934) != c_Groups_Ozero__class_Ozero(X2935)
| X2934 = c_Groups_Ozero__class_Ozero(X2935)
| ~ class_Groups_Olinordered__ab__group__add(X2935) )
& ( X2934 != c_Groups_Ozero__class_Ozero(X2935)
| c_Groups_Oplus__class_Oplus(X2935,X2934,X2934) = c_Groups_Ozero__class_Ozero(X2935)
| ~ class_Groups_Olinordered__ab__group__add(X2935) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2409,plain,
! [X3528,X3529,X3530] :
( ~ class_Rings_Oring__1__no__zero__divisors(X3530)
| X3529 = c_Groups_Ozero__class_Ozero(X3530)
| c_Power_Opower__class_Opower(X3530,X3529,X3528) != c_Groups_Ozero__class_Ozero(X3530) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2410,plain,
! [X3493,X3494] :
( ( c_Groups_Ozero__class_Ozero(X3494) != c_Groups_Oplus__class_Oplus(X3494,X3493,X3493)
| X3493 = c_Groups_Ozero__class_Ozero(X3494)
| ~ class_Groups_Olinordered__ab__group__add(X3494) )
& ( X3493 != c_Groups_Ozero__class_Ozero(X3494)
| c_Groups_Ozero__class_Ozero(X3494) = c_Groups_Oplus__class_Oplus(X3494,X3493,X3493)
| ~ class_Groups_Olinordered__ab__group__add(X3494) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2411,plain,
! [X3797,X3798] :
( ( X3798 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X3798 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X3797 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X3798 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X3798 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X3797 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X3797 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X3797 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X3798 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X3797 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X3798 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X3797 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3798,X3797) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff])])]) ).
fof(i_0_2412,plain,
! [X3795,X3796] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3796,X3795) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X3796 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X3796 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma])]) ).
fof(i_0_2413,plain,
! [X3805,X3806,X3807] :
( ( c_Groups_Ominus__class_Ominus(X3807,X3806,X3805) != c_Groups_Ozero__class_Ozero(X3807)
| X3806 = X3805
| ~ class_Groups_Ogroup__add(X3807) )
& ( X3806 != X3805
| c_Groups_Ominus__class_Ominus(X3807,X3806,X3805) = c_Groups_Ozero__class_Ozero(X3807)
| ~ class_Groups_Ogroup__add(X3807) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2414,plain,
! [X3808,X3809,X3810] :
( ( X3809 != X3808
| c_Groups_Ominus__class_Ominus(X3810,X3809,X3808) = c_Groups_Ozero__class_Ozero(X3810)
| ~ class_Groups_Oab__group__add(X3810) )
& ( c_Groups_Ominus__class_Ominus(X3810,X3809,X3808) != c_Groups_Ozero__class_Ozero(X3810)
| X3809 = X3808
| ~ class_Groups_Oab__group__add(X3810) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).
fof(i_0_2415,plain,
! [X2936,X2937,X2938] :
( ( X2937 != c_Groups_Oplus__class_Oplus(X2938,X2937,X2936)
| X2936 = c_Groups_Ozero__class_Ozero(X2938)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2938) )
& ( X2936 != c_Groups_Ozero__class_Ozero(X2938)
| X2937 = c_Groups_Oplus__class_Oplus(X2938,X2937,X2936)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2938) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2416,plain,
! [X4488] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4488) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4488,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4488,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4488) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__0])]) ).
fof(i_0_2417,plain,
! [X4487] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4487)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4487,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4487,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4487) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).
fof(i_0_2418,plain,
! [X2618,X2619] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2619,X2618) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2618 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2619 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2619,X2618) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2618 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2619,X2618) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__is__0])])]) ).
fof(i_0_2419,plain,
! [X3294] :
( ( X3294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3294) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3294)
| X3294 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2420,plain,
! [X4669,X4670] :
( X4670 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4670,X4669)
| X4669 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10])]) ).
fof(i_0_2421,plain,
! [X4660] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4660,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X4660 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4660 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4660,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1])]) ).
fof(i_0_2422,plain,
! [X3952] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3952,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3952 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3952 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3952,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__0__eq])]) ).
cnf(i_0_2423,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1462]) ).
cnf(i_0_2424,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1463]) ).
cnf(i_0_2425,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1464]) ).
cnf(i_0_2426,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1465]) ).
cnf(i_0_2427,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1466]) ).
cnf(i_0_2428,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1467]) ).
fof(i_0_2429,plain,
! [X4665,X4666] :
( ( X4666 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4666,X4665) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4665 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4666,X4665) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4666 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4665 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4666,X4665) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff])])]) ).
fof(i_0_2430,plain,
! [X3005,X3006] :
( ( X3006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3006,X3005) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3006,X3005) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3006 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3005 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3006,X3005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__is__0])])]) ).
fof(i_0_2431,plain,
! [X4662,X4663] :
( ( X4663 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4663,X4662) )
& ( X4662 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4663,X4662) )
& ( X4663 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4662 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4663,X4662) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2432,plain,
! [X3296,X3297] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3297,X3296)
| X3296 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr__implies__not0])]) ).
cnf(i_0_2433,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1468]) ).
cnf(i_0_2434,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1469]) ).
fof(i_0_2435,plain,
! [X3003,X3004] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3004,X3003) != X3004
| X3003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero])]) ).
fof(i_0_2436,plain,
! [X3295] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3295,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1470]) ).
fof(i_0_2437,plain,
! [X3293] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3293,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1471]) ).
fof(i_0_2438,plain,
! [X3259] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3259,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1472]) ).
fof(i_0_2439,plain,
! [X3623,X3624] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3624,X3623)
| X3624 != X3623 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2440,plain,
! [X3621,X3622] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3622,X3621)
| X3621 != X3622 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2441,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_bin__less__0__simps_I1_J]) ).
fof(i_0_2442,plain,
! [X3161,X3162] :
( ~ class_Int_Onumber__ring(X3162)
| c_Groups_Oplus__class_Oplus(X3162,c_Int_Onumber__class_Onumber__of(X3162,c_Int_OPls),X3161) = X3161 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(i_0_2443,plain,
! [X3159,X3160] :
( ~ class_Int_Onumber__ring(X3160)
| c_Groups_Oplus__class_Oplus(X3160,X3159,c_Int_Onumber__class_Onumber__of(X3160,c_Int_OPls)) = X3159 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
cnf(i_0_2444,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1473]) ).
cnf(i_0_2445,plain,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
fof(i_0_2446,plain,
! [X4450,X4451] :
( ( X4450 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4451,c_Groups_Ozero__class_Ozero(X4451),X4450) = c_Groups_Oone__class_Oone(X4451)
| ~ class_Power_Opower(X4451)
| ~ class_Rings_Osemiring__0(X4451) )
& ( X4450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4451,c_Groups_Ozero__class_Ozero(X4451),X4450) = c_Groups_Ozero__class_Ozero(X4451)
| ~ class_Power_Opower(X4451)
| ~ class_Rings_Osemiring__0(X4451) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2447,plain,
! [X3620] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3620,X3620),
inference(variable_rename,[status(thm)],[i_0_1475]) ).
fof(i_0_2448,plain,
! [X3611] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3611,X3611),
inference(variable_rename,[status(thm)],[i_0_1476]) ).
cnf(i_0_2449,plain,
c_Int_OBit0(X1) != c_Int_OMin,
inference(split_conjunct,[status(thm)],[i_0_1477]) ).
cnf(i_0_2450,plain,
c_Int_OMin != c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_1478]) ).
fof(i_0_2451,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I20_J]) ).
fof(i_0_2452,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I7_J]) ).
fof(i_0_2453,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I3_J]) ).
fof(i_0_2454,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(fof_simplification,[status(thm)],[fact_rel__simps_I2_J]) ).
fof(i_0_2455,plain,
! [X4929] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4929,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__minus1__right]) ).
fof(i_0_2456,plain,
! [X3732] :
( ~ class_Rings_Olinordered__semidom(X3732)
| c_Orderings_Oord__class_Oless__eq(X3732,c_Groups_Ozero__class_Ozero(X3732),c_Groups_Oone__class_Oone(X3732)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2457,plain,
! [X4106] :
( ~ class_Rings_Olinordered__semidom(X4106)
| c_Orderings_Oord__class_Oless(X4106,c_Groups_Ozero__class_Ozero(X4106),c_Groups_Oone__class_Oone(X4106)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2458,plain,
! [X4837,X4838] :
( ~ class_Divides_Osemiring__div(X4838)
| c_Divides_Odiv__class_Omod(X4838,c_Groups_Ozero__class_Ozero(X4838),X4837) = c_Groups_Ozero__class_Ozero(X4838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_2459,plain,
! [X3944,X3945] :
( ~ class_Groups_Omonoid__mult(X3945)
| c_Power_Opower__class_Opower(X3945,c_Groups_Oone__class_Oone(X3945),X3944) = c_Groups_Oone__class_Oone(X3945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2460,plain,
! [X2634,X2635] :
( ~ class_RealVector_Oreal__normed__algebra(X2635)
| c_Groups_Otimes__class_Otimes(X2635,c_Groups_Ozero__class_Ozero(X2635),X2634) = c_Groups_Ozero__class_Ozero(X2635) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2461,plain,
! [X2632,X2633] :
( ~ class_RealVector_Oreal__normed__algebra(X2633)
| c_Groups_Otimes__class_Otimes(X2633,c_Groups_Ozero__class_Ozero(X2633),X2632) = c_Groups_Ozero__class_Ozero(X2633) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2462,plain,
! [X2630,X2631] :
( ~ class_Rings_Ocomm__semiring__1(X2631)
| c_Groups_Otimes__class_Otimes(X2631,c_Groups_Ozero__class_Ozero(X2631),X2630) = c_Groups_Ozero__class_Ozero(X2631) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2463,plain,
! [X2628,X2629] :
( ~ class_Rings_Omult__zero(X2629)
| c_Groups_Otimes__class_Otimes(X2629,c_Groups_Ozero__class_Ozero(X2629),X2628) = c_Groups_Ozero__class_Ozero(X2629) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2464,plain,
! [X4915,X4916] :
( ~ class_Divides_Osemiring__div(X4916)
| c_Divides_Odiv__class_Omod(X4916,X4915,c_Groups_Oone__class_Oone(X4916)) = c_Groups_Ozero__class_Ozero(X4916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_2465,plain,
! [X2642,X2643] :
( ~ class_RealVector_Oreal__normed__algebra(X2643)
| c_Groups_Otimes__class_Otimes(X2643,X2642,c_Groups_Ozero__class_Ozero(X2643)) = c_Groups_Ozero__class_Ozero(X2643) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2466,plain,
! [X2640,X2641] :
( ~ class_RealVector_Oreal__normed__algebra(X2641)
| c_Groups_Otimes__class_Otimes(X2641,X2640,c_Groups_Ozero__class_Ozero(X2641)) = c_Groups_Ozero__class_Ozero(X2641) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2467,plain,
! [X2638,X2639] :
( ~ class_Rings_Ocomm__semiring__1(X2639)
| c_Groups_Otimes__class_Otimes(X2639,X2638,c_Groups_Ozero__class_Ozero(X2639)) = c_Groups_Ozero__class_Ozero(X2639) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2468,plain,
! [X2636,X2637] :
( ~ class_Rings_Omult__zero(X2637)
| c_Groups_Otimes__class_Otimes(X2637,X2636,c_Groups_Ozero__class_Ozero(X2637)) = c_Groups_Ozero__class_Ozero(X2637) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2469,plain,
! [X5021,X5022] :
( ~ class_Divides_Osemiring__div(X5022)
| X5021 = c_Groups_Ozero__class_Ozero(X5022)
| c_Divides_Odiv__class_Odiv(X5022,X5021,X5021) = c_Groups_Oone__class_Oone(X5022) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).
fof(i_0_2470,plain,
! [X3435] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3435)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3435) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1479])]) ).
fof(i_0_2471,plain,
! [X4270,X4271] :
( ~ class_Power_Opower(X4271)
| c_Power_Opower__class_Opower(X4271,X4270,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4271) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2472,plain,
! [X4268,X4269] :
( ~ class_Rings_Ocomm__semiring__1(X4269)
| c_Power_Opower__class_Opower(X4269,X4268,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4269) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2473,plain,
! [X3491,X3492] :
( ~ class_Groups_Ocomm__monoid__add(X3492)
| c_Groups_Oplus__class_Oplus(X3492,c_Groups_Ozero__class_Ozero(X3492),X3491) = X3491 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2474,plain,
! [X3489,X3490] :
( ~ class_Groups_Omonoid__add(X3490)
| c_Groups_Oplus__class_Oplus(X3490,c_Groups_Ozero__class_Ozero(X3490),X3489) = X3489 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2475,plain,
! [X2941,X2942] :
( ~ class_Rings_Ocomm__semiring__1(X2942)
| c_Groups_Oplus__class_Oplus(X2942,c_Groups_Ozero__class_Ozero(X2942),X2941) = X2941 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2476,plain,
! [X3871,X3872] :
( ~ class_Groups_Ocomm__monoid__mult(X3872)
| c_Groups_Otimes__class_Otimes(X3872,c_Groups_Oone__class_Oone(X3872),X3871) = X3871 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2477,plain,
! [X3869,X3870] :
( ~ class_Groups_Omonoid__mult(X3870)
| c_Groups_Otimes__class_Otimes(X3870,c_Groups_Oone__class_Oone(X3870),X3869) = X3869 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2478,plain,
! [X3865,X3866] :
( ~ class_Rings_Ocomm__semiring__1(X3866)
| c_Groups_Otimes__class_Otimes(X3866,c_Groups_Oone__class_Oone(X3866),X3865) = X3865 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2479,plain,
! [X5018,X5019] :
( ~ class_Divides_Osemiring__div(X5019)
| c_Divides_Odiv__class_Odiv(X5019,X5018,c_Groups_Oone__class_Oone(X5019)) = X5018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).
fof(i_0_2480,plain,
! [X4839,X4840] :
( ~ class_Divides_Osemiring__div(X4840)
| c_Divides_Odiv__class_Omod(X4840,X4839,c_Groups_Ozero__class_Ozero(X4840)) = X4839 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_2481,plain,
! [X3813,X3814] :
( ~ class_Groups_Ogroup__add(X3814)
| c_Groups_Ominus__class_Ominus(X3814,X3813,c_Groups_Ozero__class_Ozero(X3814)) = X3813 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2482,plain,
! [X3497,X3498] :
( ~ class_Groups_Ocomm__monoid__add(X3498)
| c_Groups_Oplus__class_Oplus(X3498,X3497,c_Groups_Ozero__class_Ozero(X3498)) = X3497 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2483,plain,
! [X3495,X3496] :
( ~ class_Groups_Omonoid__add(X3496)
| c_Groups_Oplus__class_Oplus(X3496,X3495,c_Groups_Ozero__class_Ozero(X3496)) = X3495 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2484,plain,
! [X2939,X2940] :
( ~ class_Rings_Ocomm__semiring__1(X2940)
| c_Groups_Oplus__class_Oplus(X2940,X2939,c_Groups_Ozero__class_Ozero(X2940)) = X2939 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2485,plain,
! [X3875,X3876] :
( ~ class_Groups_Ocomm__monoid__mult(X3876)
| c_Groups_Otimes__class_Otimes(X3876,X3875,c_Groups_Oone__class_Oone(X3876)) = X3875 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2486,plain,
! [X3873,X3874] :
( ~ class_Groups_Omonoid__mult(X3874)
| c_Groups_Otimes__class_Otimes(X3874,X3873,c_Groups_Oone__class_Oone(X3874)) = X3873 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2487,plain,
! [X3867,X3868] :
( ~ class_Rings_Ocomm__semiring__1(X3868)
| c_Groups_Otimes__class_Otimes(X3868,X3867,c_Groups_Oone__class_Oone(X3868)) = X3867 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2488,plain,
! [X3942,X3943] :
( ~ class_Rings_Ocomm__semiring__1(X3943)
| c_Rings_Odvd__class_Odvd(X3943,c_Groups_Oone__class_Oone(X3943),X3942) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_2489,plain,
! [X2710,X2711] :
( ~ class_Rings_Ocomm__semiring__1(X2711)
| c_Rings_Odvd__class_Odvd(X2711,X2710,c_Groups_Ozero__class_Ozero(X2711)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_2490,plain,
! [X4323] :
( ~ class_Int_Onumber__ring(X4323)
| ~ c_Int_Oiszero(X4323,c_Int_Onumber__class_Onumber__of(X4323,c_Int_OMin)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1480])]) ).
fof(i_0_2491,plain,
! [X4658,X4659] :
( ~ class_Groups_Omonoid__mult(X4659)
| c_Power_Opower__class_Opower(X4659,X4658,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4658 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2492,plain,
! [X4656,X4657] :
( ~ class_Rings_Ocomm__semiring__1(X4657)
| c_Power_Opower__class_Opower(X4657,X4656,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4656 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2493,plain,
! [X4841,X4842] :
( ~ class_Divides_Osemiring__div(X4842)
| c_Divides_Odiv__class_Omod(X4842,X4841,X4841) = c_Groups_Ozero__class_Ozero(X4842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_2494,plain,
! [X3811,X3812] :
( ~ class_Groups_Ogroup__add(X3812)
| c_Groups_Ominus__class_Ominus(X3812,X3811,X3811) = c_Groups_Ozero__class_Ozero(X3812) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2495,plain,
! [X2717,X2718] :
( ~ class_Rings_Ocomm__semiring__1(X2718)
| c_Rings_Odvd__class_Odvd(X2718,X2717,X2717) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
cnf(i_0_2496,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_One__nat__def]) ).
fof(i_0_2497,plain,
! [X2588,X2589,X2590] :
( ( c_Int_Onumber__class_Onumber__of(X2590,X2589) != c_Int_Onumber__class_Onumber__of(X2590,X2588)
| X2589 = X2588
| ~ class_Int_Onumber__ring(X2590)
| ~ class_Int_Oring__char__0(X2590) )
& ( X2589 != X2588
| c_Int_Onumber__class_Onumber__of(X2590,X2589) = c_Int_Onumber__class_Onumber__of(X2590,X2588)
| ~ class_Int_Onumber__ring(X2590)
| ~ class_Int_Oring__char__0(X2590) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).
fof(i_0_2498,plain,
! [X3298] :
( X3298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3298) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2499,plain,
! [X5020] :
( X5020 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X5020,X5020) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).
fof(i_0_2500,plain,
! [X4807] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_2501,plain,
! [X3858] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3858) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2502,plain,
! [X2621] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2503,plain,
! [X4980] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X4980,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
& c_Divides_Odiv__class_Omod(tc_Int_Oint,X4980,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4980 ),
inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).
fof(i_0_2504,plain,
! [X2620] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2620,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0__right]) ).
fof(i_0_2505,plain,
! [X3286] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3286) = X3286,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2506,plain,
! [X3008] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3008) = X3008,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2507,plain,
! [X4604] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4604) = X4604,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2508,plain,
! [X4053] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4053) = X4053,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2509,plain,
! [X4661] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4661) = X4661,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2510,plain,
! [X3857] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3857,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3857,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2511,plain,
! [X3287] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3287,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X3287,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2512,plain,
! [X3007] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3007,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3007,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2513,plain,
! [X4052] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4052,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4052,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2514,plain,
! [X4664] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4664,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4664,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2515,plain,
! [X4632,X4633] :
( X4633 != X4632
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4633,X4632) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2516,plain,
! [X2801,X2802] :
( X2802 != X2801
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2802,X2801) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).
fof(i_0_2517,plain,
! [X3953] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3953),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2518,plain,
! [X3573] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3573),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2519,plain,
! [X4734] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4734),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(i_0_2520,plain,
! [X4733] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X4733,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
cnf(i_0_2521,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
cnf(i_0_2522,plain,
( c_Int_OPls = c_Int_OBit0(X1)
| c_Int_OPls != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1473]) ).
fof(i_0_2523,plain,
! [X4808] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4808,X4808) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_2524,plain,
! [X3856] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3856,X3856) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2525,plain,
! [X4623] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4623,X4623),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2526,plain,
! [X4608] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4608,X4608),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2527,plain,
! [X4624] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4624,X4624),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2528,plain,
! [X2709] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2709,X2709),
inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(i_0_2529,plain,
! [X3289] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X3289) = X3289,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(i_0_2530,plain,
! [X3851] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3851,c_Int_OPls) = X3851,
inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).
fof(i_0_2531,plain,
! [X3288] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3288,c_Int_OPls) = X3288,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(i_0_2532,plain,
! [X2584] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X2584) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
cnf(i_0_2533,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).
fof(i_0_2534,plain,
! [X3211] :
( ~ class_Int_Onumber__ring(X3211)
| c_Int_Oiszero(X3211,c_Int_Onumber__class_Onumber__of(X3211,c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).
fof(i_0_2535,plain,
! [X4066] :
( ~ class_Rings_Osemiring__1(X4066)
| ~ c_Int_Oiszero(X4066,c_Groups_Oone__class_Oone(X4066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1481])]) ).
fof(i_0_2536,plain,
! [X3075,X3076] :
( ( ~ c_Int_Oiszero(X3076,X3075)
| X3075 = c_Groups_Ozero__class_Ozero(X3076)
| ~ class_Rings_Osemiring__1(X3076) )
& ( X3075 != c_Groups_Ozero__class_Ozero(X3076)
| c_Int_Oiszero(X3076,X3075)
| ~ class_Rings_Osemiring__1(X3076) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).
fof(i_0_2537,plain,
! [X3077] :
( ~ class_Rings_Osemiring__1(X3077)
| c_Int_Oiszero(X3077,c_Groups_Ozero__class_Ozero(X3077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).
fof(i_0_2538,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(fof_simplification,[status(thm)],[fact_odd__one__int]) ).
fof(i_0_2539,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_odd__1__nat]) ).
fof(i_0_2540,plain,
! [X2587] :
( ~ class_Int_Onumber__ring(X2587)
| c_Int_Onumber__class_Onumber__of(X2587,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X2587) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).
fof(i_0_2541,plain,
! [X2606] :
( ~ class_Int_Onumber__ring(X2606)
| c_Groups_Ozero__class_Ozero(X2606) = c_Int_Onumber__class_Onumber__of(X2606,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
fof(i_0_2542,plain,
! [X3850] :
( ~ class_Rings_Ozero__neq__one(X3850)
| c_Groups_Oone__class_Oone(X3850) != c_Groups_Ozero__class_Ozero(X3850) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2543,plain,
! [X3849] :
( ~ class_Rings_Ozero__neq__one(X3849)
| c_Groups_Ozero__class_Ozero(X3849) != c_Groups_Oone__class_Oone(X3849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2544,plain,
! [X2622] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2622) = X2622,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
fof(i_0_2545,negated_conjecture,
~ v_thesis____,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_1])]) ).
cnf(i_0_2546,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1482,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2547,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),X3))
| ~ class_Int_Onumber__ring(X1) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1485,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2548,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),X2)),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1486,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2549,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1487,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2550,plain,
( X3 != c_Groups_Ozero__class_Ozero(X1)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1489,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2551,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1490,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2552,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1491,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2553,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1492,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2554,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
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(rw,[status(thm)],[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(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1493,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2555,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1494,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2556,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1495,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2557,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1496,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2558,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1497,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2559,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1498,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2560,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1499,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2561,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1500,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2562,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1501,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2563,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1502,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2564,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1503,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2565,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1504,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2566,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1505,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2567,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1506,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2568,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1507,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2569,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(X1) ),
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(rw,[status(thm)],[i_0_1508,c_0_1483]),c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2570,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1509,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2571,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)),c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1510,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2572,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1511,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2573,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1512,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2574,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1513,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2575,plain,
( c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1514,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2576,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1515,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2577,plain,
( X2 = X3
| c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1516,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2578,plain,
( X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1517,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2579,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1518,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2580,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1519,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2581,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1520,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2582,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1521,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2583,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3)) = c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1522,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2584,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1523,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2585,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1524,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2586,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X3)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1525,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2587,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1526,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2588,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk12_1(X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1527,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2589,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk3_1(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1528,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2590,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1529,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2591,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1530,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2592,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1531,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2593,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1532,c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2594,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1533,c_0_1488]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2595,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1534,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2596,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1535,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2597,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1536,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2598,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1537,c_0_1483]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2599,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1538,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2600,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1539,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2601,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1540,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2602,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1541,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2603,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1542,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2604,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1543,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2605,hypothesis,
( v_thesis____
| v_na____ != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1544,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2606,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1545,c_0_1483]),c_0_1483]),c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2607,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),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(rw,[status(thm)],[i_0_1546,c_0_1483]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2608,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),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(rw,[status(thm)],[i_0_1547,c_0_1483]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2609,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1548,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2610,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X2) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1549,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2611,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1550,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2612,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1551,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2613,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,X2) = c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1552,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2614,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1553,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2615,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1554,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2616,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk4_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1555,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2617,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk2_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1556,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2618,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1557,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2619,plain,
( c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1558,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2620,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1559,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2621,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1560,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2622,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1561,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2623,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Osemiring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1562,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2624,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1563,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2625,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1564,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2626,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1565,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2627,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1566,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2628,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),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(rw,[status(thm)],[i_0_1567,c_0_1488]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2629,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5)),c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Ominus__class_Ominus(X1,X3,X5)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1568]),
[final] ).
cnf(i_0_2630,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2631,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2632,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2633,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1572]),
[final] ).
cnf(i_0_2634,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2635,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5),X6)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2636,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2637,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X5),X2),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X5),X6))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X5),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2638,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1569]),
[final] ).
cnf(i_0_2639,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3),X5)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1570]),
[final] ).
cnf(i_0_2640,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1571]),
[final] ).
cnf(i_0_2641,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1572]),
[final] ).
cnf(i_0_2642,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Power_Opower__class_Opower(X1,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1577,c_0_1488]),c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2643,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2644,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4),X6)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2645,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1575]),
[final] ).
cnf(i_0_2646,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1576]),
[final] ).
cnf(i_0_2647,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3)),c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3)),
inference(split_conjunct,[status(thm)],[i_0_1578]),
[final] ).
cnf(i_0_2648,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1579,c_0_1488]),c_0_1484]),
[final] ).
cnf(i_0_2649,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),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(rw,[status(thm)],[i_0_1580,c_0_1483]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2650,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1581,c_0_1483]),c_0_1488]),c_0_1488]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2651,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1582]),
[final] ).
cnf(i_0_2652,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1583]),
[final] ).
cnf(i_0_2653,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2654,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)),X6))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X5)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2655,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X2)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X5),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X5),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1586]),
[final] ).
cnf(i_0_2656,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X5)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X5),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X5),X6))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1587]),
[final] ).
cnf(i_0_2657,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X4)),X5))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2658,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1589,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2659,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1590,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2660,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1591]),
[final] ).
cnf(i_0_2661,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X5)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1592]),
[final] ).
cnf(i_0_2662,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1593,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2663,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Power_Opower__class_Opower(X1,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1594,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2664,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X5,X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1584]),
[final] ).
cnf(i_0_2665,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X5,X6)),X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X6)
| ~ class_Rings_Ocomm__ring(X1)
| ~ class_Rings_Odvd(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1585]),
[final] ).
cnf(i_0_2666,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1595,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2667,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1596,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2668,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1597,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2669,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1598,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2670,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1599,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2671,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1600,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2672,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1601]),
[final] ).
cnf(i_0_2673,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2674,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X5)),X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1588]),
[final] ).
cnf(i_0_2675,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))) ),
inference(rw,[status(thm)],[i_0_1603,c_0_1484]),
[final] ).
cnf(i_0_2676,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk18_3(X2,X1,X3)),esk19_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2677,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) ),
inference(rw,[status(thm)],[i_0_1605,c_0_1484]),
[final] ).
cnf(i_0_2678,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X2),c_Groups_Otimes__class_Otimes(X1,X6,X4)),X3)
| ~ class_Rings_Olinordered__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1606]),
[final] ).
cnf(i_0_2679,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X2),c_Groups_Otimes__class_Otimes(X1,X6,X4)),X3)
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X6)
| c_Groups_Oplus__class_Oplus(X1,X5,X6) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1607]),
[final] ).
cnf(i_0_2680,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1608]),
[final] ).
cnf(i_0_2681,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X1)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1609]),
[final] ).
cnf(i_0_2682,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk18_3(X2,X1,X3)),esk19_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2683,plain,
( hBOOL(hAPP(X4,c_Groups_Otimes__class_Otimes(X1,X2,esk8_3(X2,X4,X1))))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X4,X3))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2684,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),X4) != X5
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2685,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4),X5)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),X4),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2686,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X5)),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X4),X5))
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1613]),
[final] ).
cnf(i_0_2687,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk19_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2688,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk18_3(X2,X3,X1)),esk19_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2689,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1614,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2690,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1615]),
[final] ).
cnf(i_0_2691,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1616,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2692,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1617,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2693,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1618,c_0_1483]),c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2694,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1619,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2695,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1620,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2696,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2697,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X3),c_Groups_Otimes__class_Otimes(X2,X1,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2698,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2699,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X4),X2),X3) = X5
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1611]),
[final] ).
cnf(i_0_2700,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4,X1),X2),X5)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X2),X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1612]),
[final] ).
cnf(i_0_2701,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X5) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),X6)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4),X5) != X6
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2702,plain,
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X4,X5),X1) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X5),X6)
| X1 != c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,c_Groups_Ominus__class_Ominus(X2,X3,X4),X5),X6)
| ~ class_Rings_Oring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2703,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk19_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2704,plain,
( X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk18_3(X2,X3,X1)),esk19_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2705,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4) = X6
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2706,plain,
( X4 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X5,X2),X3),X6)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),X6)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2707,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk19_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2708,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),esk5_1(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1625,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2709,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3),X5)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1626]),
[final] ).
cnf(i_0_2710,plain,
( X1 = X2
| X3 = X4
| c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X1,X3),c_Groups_Otimes__class_Otimes(X5,X2,X4)) != c_Groups_Oplus__class_Oplus(X5,c_Groups_Otimes__class_Otimes(X5,X1,X4),c_Groups_Otimes__class_Otimes(X5,X2,X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X5) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2711,plain,
( X2 = X4
| X3 = X5
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) != c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2712,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[i_0_1629,c_0_1484]),
[final] ).
cnf(i_0_2713,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1630,c_0_1484]),
[final] ).
cnf(i_0_2714,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1631,c_0_1484]),
[final] ).
cnf(i_0_2715,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1632,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2716,plain,
( c_Power_Opower__class_Opower(X1,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)),X4)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rw,[status(thm)],[i_0_1633,c_0_1488]),
[final] ).
cnf(i_0_2717,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2),X4),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2718,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk19_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2719,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2720,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1636,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2721,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1637,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2722,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1638,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2723,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1639,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2724,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1640,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2725,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1641,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2726,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1642,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2727,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1643,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2728,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1644]),
[final] ).
cnf(i_0_2729,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1645,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2730,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1646,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2731,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,esk7_3(X2,X3,X1),c_Groups_Ozero__class_Ozero(X1)))
| ~ hBOOL(hAPP(X3,c_Groups_Otimes__class_Otimes(X1,X2,X4)))
| ~ class_Rings_Odvd(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2732,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1647,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1648,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2734,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1649,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2735,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1650,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2736,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1651,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2737,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1652,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2738,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1653]),
[final] ).
cnf(i_0_2739,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1654]),
[final] ).
cnf(i_0_2740,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1655]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2742,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2743,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X2,X1,X3),X2)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2744,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2745,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1656,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2746,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1657,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2747,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1658,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2748,plain,
( X2 = X4
| c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Power_Opower__class_Opower(X1,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1659,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2749,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1660,c_0_1484]),
[final] ).
cnf(i_0_2750,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1661,c_0_1484]),
[final] ).
cnf(i_0_2751,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2752,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X2,X1,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2753,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X2,X1,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2754,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2755,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1662,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2756,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1663,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2757,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1664,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2758,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1665]),
[final] ).
cnf(i_0_2759,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_1666,c_0_1484]),
[final] ).
cnf(i_0_2760,plain,
( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Oone__class_Oone(X2))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
inference(rw,[status(thm)],[i_0_1667,c_0_1484]),
[final] ).
cnf(i_0_2761,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1) ),
inference(rw,[status(thm)],[i_0_1668,c_0_1484]),
[final] ).
cnf(i_0_2762,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X1) ),
inference(rw,[status(thm)],[i_0_1669,c_0_1484]),
[final] ).
cnf(i_0_2763,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2764,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2765,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2766,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2767,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X4,X6),X3)
| ~ class_Divides_Oring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2768,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X5),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X4,X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2769,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X5),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X4,X6),X3)
| ~ class_Divides_Osemiring__div(X1)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Divides_Odiv__class_Omod(X1,X4,X3)
| c_Divides_Odiv__class_Omod(X1,X5,X3) != c_Divides_Odiv__class_Omod(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2770,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2771,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rw,[status(thm)],[i_0_1676,c_0_1484]),
[final] ).
cnf(i_0_2772,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2773,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1678]),
[final] ).
cnf(i_0_2774,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X5)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1679]),
[final] ).
cnf(i_0_2775,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk19_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2776,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2777,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X2,X3,X1),X2)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2778,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk19_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2779,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1680,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2780,plain,
( hBOOL(hAPP(X1,esk7_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X1,c_Groups_Otimes__class_Otimes(X3,X2,X4)))
| ~ class_Rings_Odvd(X3)
| ~ class_Rings_Osemiring__0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1610]),
[final] ).
cnf(i_0_2781,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
inference(rw,[status(thm)],[i_0_1681,c_0_1484]),
[final] ).
cnf(i_0_2782,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
inference(rw,[status(thm)],[i_0_1682,c_0_1484]),
[final] ).
cnf(i_0_2783,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
inference(rw,[status(thm)],[i_0_1683,c_0_1484]),
[final] ).
cnf(i_0_2784,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) ),
inference(rw,[status(thm)],[i_0_1684,c_0_1484]),
[final] ).
cnf(i_0_2785,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_1685,c_0_1484]),
[final] ).
cnf(i_0_2786,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_1686,c_0_1484]),
[final] ).
cnf(i_0_2787,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_1687,c_0_1484]),
[final] ).
cnf(i_0_2788,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_1688,c_0_1484]),
[final] ).
cnf(i_0_2789,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2790,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1690]),
[final] ).
cnf(i_0_2791,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1691]),
[final] ).
cnf(i_0_2792,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1692]),
[final] ).
cnf(i_0_2793,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1693]),
[final] ).
cnf(i_0_2794,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1694]),
[final] ).
cnf(i_0_2795,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2796,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2797,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1695,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2798,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1696,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2799,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2800,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2801,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1699,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2802,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_2803,plain,
( hBOOL(hAPP(X5,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X2)
| ~ epred1_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2804,plain,
( hBOOL(hAPP(X5,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X2)
| ~ epred1_3(X5,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2805,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1701,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2806,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1621]),
[final] ).
cnf(i_0_2807,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Groups_Oplus__class_Oplus(X1,X3,X4),X2) = c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),c_Divides_Odiv__class_Odiv(X1,X4,X2))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1702]),
[final] ).
cnf(i_0_2808,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1615]),
[final] ).
cnf(i_0_2809,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X3),c_Groups_Otimes__class_Otimes(X2,X1,X1)))
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1615]),
[final] ).
cnf(i_0_2810,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk19_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2811,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X2,X3,X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2812,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X2,X3,X1),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2813,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk19_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2814,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Otimes__class_Otimes(X1,X3,X3)))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1703]),
[final] ).
cnf(i_0_2815,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1704,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2816,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1705,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2817,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1706,c_0_1484]),
[final] ).
cnf(i_0_2818,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk20_3(X2,X1,X3)),esk21_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2819,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk18_3(X1,X2,X3)),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2820,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[i_0_1707,c_0_1488]),
[final] ).
cnf(i_0_2821,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1708]),
[final] ).
cnf(i_0_2822,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X2)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oone__class_Oone(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[i_0_1709,c_0_1488]),
[final] ).
cnf(i_0_2823,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1710]),
[final] ).
cnf(i_0_2824,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1711]),
[final] ).
cnf(i_0_2825,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_2826,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2827,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_2828,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1715]),
[final] ).
cnf(i_0_2829,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1716]),
[final] ).
cnf(i_0_2830,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1717]),
[final] ).
cnf(i_0_2831,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2832,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2833,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_2834,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_2835,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_2836,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2837,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1724]),
[final] ).
cnf(i_0_2838,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1725]),
[final] ).
cnf(i_0_2839,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Int_Onumber__class_Onumber__of(X1,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1726]),
[final] ).
cnf(i_0_2840,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Oring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1727]),
[final] ).
cnf(i_0_2841,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ class_Int_Onumber(X1)
| ~ class_Rings_Osemiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1728]),
[final] ).
cnf(i_0_2842,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2843,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1729,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2844,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1730,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2845,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1731,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2846,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1732,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2847,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1733,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2848,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1734,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2849,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1735,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2850,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1736,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_2851,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_2852,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_2853,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_2854,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_2855,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1741]),
[final] ).
cnf(i_0_2856,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_2857,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_2858,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1744]),
[final] ).
cnf(i_0_2859,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_2860,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_2861,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1747]),
[final] ).
cnf(i_0_2862,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X1,X4,X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1749]),
[final] ).
cnf(i_0_2864,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X4,X3),c_Power_Opower__class_Opower(X1,X4,X2))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1750]),
[final] ).
cnf(i_0_2865,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2866,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2867,plain,
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X4),c_Groups_Otimes__class_Otimes(X3,X2,X5)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X5),c_Groups_Otimes__class_Otimes(X3,X2,X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1628]),
[final] ).
cnf(i_0_2868,plain,
( c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X4),c_Groups_Otimes__class_Otimes(X3,X2,X5)) = c_Groups_Oplus__class_Oplus(X3,c_Groups_Otimes__class_Otimes(X3,X1,X5),c_Groups_Otimes__class_Otimes(X3,X2,X4))
| X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1627]),
[final] ).
cnf(i_0_2869,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1753]),
[final] ).
cnf(i_0_2870,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2871,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2872,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2873,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2874,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1754]),
[final] ).
cnf(i_0_2875,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X5)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1755]),
[final] ).
cnf(i_0_2876,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_2877,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X4),X3) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1757]),
[final] ).
cnf(i_0_2878,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1758]),
[final] ).
cnf(i_0_2879,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1759]),
[final] ).
cnf(i_0_2880,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1760]),
[final] ).
cnf(i_0_2881,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1761]),
[final] ).
cnf(i_0_2882,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ominus__class_Ominus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Oring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1762]),
[final] ).
cnf(i_0_2883,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1763]),
[final] ).
cnf(i_0_2884,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4)),X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1764]),
[final] ).
cnf(i_0_2885,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2886,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk19_3(X1,X3,X2)))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2887,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1765,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2888,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2889,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2890,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1) = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X3 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X4),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2891,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1766]),
[final] ).
cnf(i_0_2892,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1767]),
[final] ).
cnf(i_0_2893,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X4)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),X4)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1768]),
[final] ).
cnf(i_0_2894,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1769,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2895,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X3) = c_Power_Opower__class_Opower(X1,X3,X2)
| ~ class_Groups_Omonoid__mult(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_2896,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X5 = X6
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X3 != X4
| c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X5)) != c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X6)) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_2897,plain,
( c_Power_Opower__class_Opower(X1,c_Divides_Odiv__class_Odiv(X1,X3,X2),X4) = c_Divides_Odiv__class_Odiv(X1,c_Power_Opower__class_Opower(X1,X3,X4),c_Power_Opower__class_Opower(X1,X2,X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_2898,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1773]),
[final] ).
cnf(i_0_2899,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_2900,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1775,c_0_1483]),c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2901,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1776,c_0_1483]),c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2902,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1777]),
[final] ).
cnf(i_0_2903,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_1778]),
[final] ).
cnf(i_0_2904,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1779]),
[final] ).
cnf(i_0_2905,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_1780]),
[final] ).
cnf(i_0_2906,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)),X3),
inference(split_conjunct,[status(thm)],[i_0_1781]),
[final] ).
cnf(i_0_2907,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1782,c_0_1484]),
[final] ).
cnf(i_0_2908,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) ),
inference(rw,[status(thm)],[i_0_1783,c_0_1484]),
[final] ).
cnf(i_0_2909,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(rw,[status(thm)],[i_0_1784,c_0_1484]),
[final] ).
cnf(i_0_2910,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Oone__class_Oone(X1)) ),
inference(rw,[status(thm)],[i_0_1785,c_0_1484]),
[final] ).
cnf(i_0_2911,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1786,c_0_1484]),c_0_1484]),
[final] ).
cnf(i_0_2912,plain,
( X2 = X3
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1787,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2913,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1697]),
[final] ).
cnf(i_0_2914,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1698]),
[final] ).
cnf(i_0_2915,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X5),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1788]),
[final] ).
cnf(i_0_2916,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk21_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2917,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,esk19_3(X1,X3,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_2918,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2919,plain,
( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2920,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(rw,[status(thm)],[i_0_1789,c_0_1488]),
[final] ).
cnf(i_0_2921,plain,
( hBOOL(hAPP(X4,X3))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2922,plain,
( hBOOL(hAPP(X4,X3))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ hBOOL(hAPP(X4,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2923,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_2924,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_2925,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_2926,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_2927,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_2928,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_2929,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_2930,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_2931,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_2932,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_2933,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_2934,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_2935,plain,
( c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_2936,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1802,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2937,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1803,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2938,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1804,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2939,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1805,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2940,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1806]),
[final] ).
cnf(i_0_2941,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1807,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2942,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1808]),
[final] ).
cnf(i_0_2943,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1809]),
[final] ).
cnf(i_0_2944,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1675]),
[final] ).
cnf(i_0_2945,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rw,[status(thm)],[i_0_1810,c_0_1484]),
[final] ).
cnf(i_0_2946,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_2947,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_2948,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1813]),
[final] ).
cnf(i_0_2949,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X3)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_2950,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_2951,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1816]),
[final] ).
cnf(i_0_2952,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_2953,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_2954,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2),c_Power_Opower__class_Opower(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1819]),
[final] ).
cnf(i_0_2955,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Oone__class_Oone(X1)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1820]),
[final] ).
cnf(i_0_2956,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1821,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2957,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1822,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_2958,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_2959,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_2960,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_1825,c_0_1488]),
[final] ).
cnf(i_0_2961,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1826,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2962,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1827,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2963,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_2964,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1829,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2965,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1830,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_2966,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_2967,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_2968,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_2969,plain,
( X2 = X4
| ~ class_Rings_Olinordered__semidom(X1)
| c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_2970,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1833]),
[final] ).
cnf(i_0_2971,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1834]),
[final] ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Oordered__comm__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1835]),
[final] ).
cnf(i_0_2973,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Oordered__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1836]),
[final] ).
cnf(i_0_2974,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1712]),
[final] ).
cnf(i_0_2975,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2976,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1837]),
[final] ).
cnf(i_0_2977,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2978,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1838]),
[final] ).
cnf(i_0_2979,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1839]),
[final] ).
cnf(i_0_2980,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1718]),
[final] ).
cnf(i_0_2981,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1840]),
[final] ).
cnf(i_0_2982,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1841]),
[final] ).
cnf(i_0_2983,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2984,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1751]),
[final] ).
cnf(i_0_2985,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X4),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1842]),
[final] ).
cnf(i_0_2986,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1752]),
[final] ).
cnf(i_0_2987,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1720]),
[final] ).
cnf(i_0_2988,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1843]),
[final] ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_1844,c_0_1484]),
[final] ).
cnf(i_0_2990,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_1845,c_0_1484]),
[final] ).
cnf(i_0_2991,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_1846,c_0_1484]),
[final] ).
cnf(i_0_2992,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_1847,c_0_1484]),
[final] ).
cnf(i_0_2993,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X1) ),
inference(rw,[status(thm)],[i_0_1848,c_0_1484]),
[final] ).
cnf(i_0_2994,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(rw,[status(thm)],[i_0_1849,c_0_1484]),
[final] ).
cnf(i_0_2995,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(rw,[status(thm)],[i_0_1850,c_0_1484]),
[final] ).
cnf(i_0_2996,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(rw,[status(thm)],[i_0_1851,c_0_1484]),
[final] ).
cnf(i_0_2997,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1852]),
[final] ).
cnf(i_0_2998,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1853]),
[final] ).
cnf(i_0_2999,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk15_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3000,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_3001,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X4,X2),c_Power_Opower__class_Opower(X1,X4,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1854]),
[final] ).
cnf(i_0_3002,plain,
( c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1721]),
[final] ).
cnf(i_0_3003,plain,
( c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X4,X2),c_Power_Opower__class_Opower(X1,X4,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1855]),
[final] ).
cnf(i_0_3004,plain,
( c_Orderings_Oord__class_Oless(X3,c_Power_Opower__class_Opower(X3,X4,X1),c_Power_Opower__class_Opower(X3,X4,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Oone__class_Oone(X3),X4)
| ~ class_Rings_Olinordered__semidom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_3005,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3006,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk15_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3007,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_3008,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1857]),
[final] ).
cnf(i_0_3009,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_3010,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1858]),
[final] ).
cnf(i_0_3011,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1859]),
[final] ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1860]),
[final] ).
cnf(i_0_3013,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1861]),
[final] ).
cnf(i_0_3014,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1862]),
[final] ).
cnf(i_0_3015,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,X3,X1) = c_Groups_Otimes__class_Otimes(X2,X3,c_Power_Opower__class_Opower(X2,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3016,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1864]),
[final] ).
cnf(i_0_3017,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X5))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3018,plain,
( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))) ),
inference(rw,[status(thm)],[i_0_1866,c_0_1483]),
[final] ).
cnf(i_0_3019,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3020,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X3,X3),c_Groups_Otimes__class_Otimes(X2,X1,X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3021,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3022,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3023,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X1,X2,X4),X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1870]),
[final] ).
cnf(i_0_3024,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X4,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1871]),
[final] ).
cnf(i_0_3025,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1872]),
[final] ).
cnf(i_0_3026,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3027,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1874]),
[final] ).
cnf(i_0_3028,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3029,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X4) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1876]),
[final] ).
cnf(i_0_3030,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1877]),
[final] ).
cnf(i_0_3031,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1878]),
[final] ).
cnf(i_0_3032,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1879]),
[final] ).
cnf(i_0_3033,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1880]),
[final] ).
cnf(i_0_3034,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1881]),
[final] ).
cnf(i_0_3035,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4)) = c_Groups_Ominus__class_Ominus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3036,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3037,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3038,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1885]),
[final] ).
cnf(i_0_3039,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1886]),
[final] ).
cnf(i_0_3040,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)),X4) = c_Divides_Odiv__class_Omod(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1887]),
[final] ).
cnf(i_0_3041,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_1888,c_0_1488]),
[final] ).
cnf(i_0_3042,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1889]),
[final] ).
cnf(i_0_3043,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Power_Opower__class_Opower(X1,X2,X4))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1890]),
[final] ).
cnf(i_0_3044,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1738]),
[final] ).
cnf(i_0_3045,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1739]),
[final] ).
cnf(i_0_3046,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1891]),
[final] ).
cnf(i_0_3047,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1743]),
[final] ).
cnf(i_0_3048,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1745]),
[final] ).
cnf(i_0_3049,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1892]),
[final] ).
cnf(i_0_3050,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1746]),
[final] ).
cnf(i_0_3051,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1893]),
[final] ).
cnf(i_0_3052,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1823]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1894]),
[final] ).
cnf(i_0_3054,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1824]),
[final] ).
cnf(i_0_3055,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1895]),
[final] ).
cnf(i_0_3056,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1748]),
[final] ).
cnf(i_0_3057,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1896]),
[final] ).
cnf(i_0_3058,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3059,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3060,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3061,plain,
( epred1_3(X1,X2,X3)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3062,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1900]),
[final] ).
cnf(i_0_3063,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3064,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3065,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1903]),
[final] ).
cnf(i_0_3066,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1904]),
[final] ).
cnf(i_0_3067,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1905]),
[final] ).
cnf(i_0_3068,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3069,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1907]),
[final] ).
cnf(i_0_3070,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3071,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3072,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3073,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3074,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| X2 != c_Groups_Ozero__class_Ozero(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3075,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),esk6_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1908,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3076,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3077,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1910,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3078,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1911,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3079,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1912,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3080,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3081,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3082,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1914]),
[final] ).
cnf(i_0_3083,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1915]),
[final] ).
cnf(i_0_3084,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1916,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3085,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1917]),
[final] ).
cnf(i_0_3086,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X3) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1918]),
[final] ).
cnf(i_0_3087,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1919]),
[final] ).
cnf(i_0_3088,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3089,plain,
c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3090,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3091,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3092,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X3)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3093,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3094,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3095,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3),X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2),
inference(split_conjunct,[status(thm)],[i_0_1927]),
[final] ).
cnf(i_0_3096,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(rw,[status(thm)],[i_0_1928,c_0_1483]),
[final] ).
cnf(i_0_3097,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1929,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3098,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3099,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1930,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3100,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3101,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3102,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3103,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1931]),
[final] ).
cnf(i_0_3104,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1932]),
[final] ).
cnf(i_0_3105,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3106,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1934]),
[final] ).
cnf(i_0_3107,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3108,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1936]),
[final] ).
cnf(i_0_3109,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3110,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1937]),
[final] ).
cnf(i_0_3111,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1938]),
[final] ).
cnf(i_0_3112,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1939]),
[final] ).
cnf(i_0_3113,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1940]),
[final] ).
cnf(i_0_3114,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1941]),
[final] ).
cnf(i_0_3115,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3116,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3117,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3118,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3119,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3120,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3121,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3122,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3123,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3124,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3125,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3126,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3127,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3128,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3129,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1948,c_0_1488]),c_0_1484]),
[final] ).
cnf(i_0_3130,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3131,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1949]),
[final] ).
cnf(i_0_3132,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1950]),
[final] ).
cnf(i_0_3133,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3134,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3135,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3136,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_1951,c_0_1483]),
[final] ).
cnf(i_0_3137,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X3,X2),c_Power_Opower__class_Opower(X1,X4,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1952]),
[final] ).
cnf(i_0_3138,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_1953,c_0_1488]),
[final] ).
cnf(i_0_3139,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_1954,c_0_1488]),
[final] ).
cnf(i_0_3140,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3141,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1955,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3142,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1956,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3143,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3144,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1957]),
[final] ).
cnf(i_0_3145,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3146,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1959]),
[final] ).
cnf(i_0_3147,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1958]),
[final] ).
cnf(i_0_3148,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3149,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3150,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1960]),
[final] ).
cnf(i_0_3151,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1961]),
[final] ).
cnf(i_0_3152,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1962]),
[final] ).
cnf(i_0_3153,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1963]),
[final] ).
cnf(i_0_3154,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1964]),
[final] ).
cnf(i_0_3155,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3156,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1966]),
[final] ).
cnf(i_0_3157,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1967]),
[final] ).
cnf(i_0_3158,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3159,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Oordered__cancel__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3160,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3161,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3162,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1971]),
[final] ).
cnf(i_0_3163,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1972]),
[final] ).
cnf(i_0_3164,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1973]),
[final] ).
cnf(i_0_3165,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1974]),
[final] ).
cnf(i_0_3166,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Olinordered__semiring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1975]),
[final] ).
cnf(i_0_3167,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Oordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1976]),
[final] ).
cnf(i_0_3168,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3169,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__ring__strict(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1947]),
[final] ).
cnf(i_0_3170,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Olinordered__ring__strict(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1977]),
[final] ).
cnf(i_0_3171,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3172,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1))),
inference(split_conjunct,[status(thm)],[i_0_1979]),
[final] ).
cnf(i_0_3173,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1980]),
[final] ).
cnf(i_0_3174,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_3175,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1981]),
[final] ).
cnf(i_0_3176,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_3177,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3178,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3179,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3180,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1983]),
[final] ).
cnf(i_0_3181,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_3182,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1984]),
[final] ).
cnf(i_0_3183,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X4,X2),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_3184,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1985]),
[final] ).
cnf(i_0_3185,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Power_Opower__class_Opower(X1,X4,X2),c_Power_Opower__class_Opower(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1986]),
[final] ).
cnf(i_0_3186,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3187,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1988,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3188,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1989,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3189,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1990,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3190,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3191,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1933]),
[final] ).
cnf(i_0_3192,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3193,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3194,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1992]),
[final] ).
cnf(i_0_3195,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Oplus__class_Oplus(X1,X4,X2))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1993]),
[final] ).
cnf(i_0_3196,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3197,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1995]),
[final] ).
cnf(i_0_3198,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_1996]),
[final] ).
cnf(i_0_3199,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3200,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(rw,[status(thm)],[i_0_1998,c_0_1488]),
[final] ).
cnf(i_0_3201,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3202,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X1),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,X2))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1814]),
[final] ).
cnf(i_0_3203,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X3),c_Power_Opower__class_Opower(tc_Int_Oint,X2,X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1817]),
[final] ).
cnf(i_0_3204,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X3),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X3))
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1818]),
[final] ).
cnf(i_0_3205,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2000]),
[final] ).
cnf(i_0_3206,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3207,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3208,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3209,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3210,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2005]),
[final] ).
cnf(i_0_3211,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2006,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3212,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2007,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3213,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2008]),
[final] ).
cnf(i_0_3214,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3215,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2010]),
[final] ).
cnf(i_0_3216,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2011]),
[final] ).
cnf(i_0_3217,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3218,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3219,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2012]),
[final] ).
cnf(i_0_3220,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3221,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2013]),
[final] ).
cnf(i_0_3222,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3223,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2014,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3224,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2015,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3225,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2016]),
[final] ).
cnf(i_0_3226,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3227,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1831]),
[final] ).
cnf(i_0_3228,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3229,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk9_2(X2,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2018,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3230,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2019,c_0_1488]),
[final] ).
cnf(i_0_3231,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2020]),
[final] ).
cnf(i_0_3232,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oone__class_Oone(X1)),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2021]),
[final] ).
cnf(i_0_3233,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2022]),
[final] ).
cnf(i_0_3234,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Divides_Odiv__class_Omod(X1,X3,X4))
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1935]),
[final] ).
cnf(i_0_3235,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ominus__class_Ominus(X1,X3,X4))
| ~ class_Rings_Ocomm__ring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2023]),
[final] ).
cnf(i_0_3236,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2024]),
[final] ).
cnf(i_0_3237,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2025,c_0_1488]),
[final] ).
cnf(i_0_3238,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2026,c_0_1488]),
[final] ).
cnf(i_0_3239,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_2027,c_0_1484]),
[final] ).
cnf(i_0_3240,plain,
( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_2028,c_0_1484]),
[final] ).
cnf(i_0_3241,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk9_2(X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2029,c_0_1488]),
[final] ).
cnf(i_0_3242,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3243,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3244,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2032,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_3245,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,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)],[i_0_2033,c_0_1483]),c_0_1484]),
[final] ).
cnf(i_0_3246,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2034]),
[final] ).
cnf(i_0_3247,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2035]),
[final] ).
cnf(i_0_3248,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1942]),
[final] ).
cnf(i_0_3249,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3250,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2037]),
[final] ).
cnf(i_0_3251,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2038]),
[final] ).
cnf(i_0_3252,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2039]),
[final] ).
cnf(i_0_3253,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3254,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3255,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X3),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3256,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2041,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3257,plain,
( X1 = X3
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2042]),
[final] ).
cnf(i_0_3258,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[i_0_2043,c_0_1483]),
[final] ).
cnf(i_0_3259,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2044]),
[final] ).
cnf(i_0_3260,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2045]),
[final] ).
cnf(i_0_3261,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(rw,[status(thm)],[i_0_2046,c_0_1488]),
[final] ).
cnf(i_0_3262,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Power_Opower(X1) ),
inference(rw,[status(thm)],[i_0_2047,c_0_1488]),
[final] ).
cnf(i_0_3263,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_2048,c_0_1488]),
[final] ).
cnf(i_0_3264,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_2049,c_0_1488]),
[final] ).
cnf(i_0_3265,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(rw,[status(thm)],[i_0_2050,c_0_1488]),
[final] ).
cnf(i_0_3266,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3267,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3268,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3269,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3270,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3271,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3272,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Power_Opower__class_Opower(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3273,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2057,c_0_1488]),
[final] ).
cnf(i_0_3274,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2058]),
[final] ).
cnf(i_0_3275,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2059]),
[final] ).
cnf(i_0_3276,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2060]),
[final] ).
cnf(i_0_3277,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2061]),
[final] ).
cnf(i_0_3278,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X2,X3),X2) = c_Groups_Otimes__class_Otimes(X1,X2,c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2062]),
[final] ).
cnf(i_0_3279,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3280,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2064]),
[final] ).
cnf(i_0_3281,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2065]),
[final] ).
cnf(i_0_3282,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2066]),
[final] ).
cnf(i_0_3283,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4)) = c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2067]),
[final] ).
cnf(i_0_3284,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4)) = c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2068]),
[final] ).
cnf(i_0_3285,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2069,c_0_1484]),
[final] ).
cnf(i_0_3286,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(rw,[status(thm)],[i_0_2070,c_0_1484]),
[final] ).
cnf(i_0_3287,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(rw,[status(thm)],[i_0_2071,c_0_1484]),
[final] ).
cnf(i_0_3288,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1987]),
[final] ).
cnf(i_0_3289,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4)) = c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2072]),
[final] ).
cnf(i_0_3290,plain,
( c_Power_Opower__class_Opower(X1,c_Power_Opower__class_Opower(X1,X2,X3),X4) = c_Power_Opower__class_Opower(X1,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2073]),
[final] ).
cnf(i_0_3291,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2074,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3292,plain,
( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2)))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) ),
inference(rw,[status(thm)],[i_0_2075,c_0_1483]),
[final] ).
cnf(i_0_3293,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3294,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3295,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2078,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3296,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2079,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3297,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),
inference(rw,[status(thm)],[i_0_2080,c_0_1488]),
[final] ).
cnf(i_0_3298,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2081]),
[final] ).
cnf(i_0_3299,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3300,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3)))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1899]),
[final] ).
cnf(i_0_3301,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3302,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2083,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3303,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2084,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3304,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3305,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3306,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3307,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3308,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ominus__class_Ominus(X1,X4,X5)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3309,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X5)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Groups_Ominus__class_Ominus(X1,X4,X5) != c_Groups_Ominus__class_Ominus(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2086]),
[final] ).
cnf(i_0_3310,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(rw,[status(thm)],[i_0_2087,c_0_1488]),
[final] ).
cnf(i_0_3311,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
inference(rw,[status(thm)],[i_0_2088,c_0_1488]),
[final] ).
cnf(i_0_3312,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3313,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3314,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3315,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1742]),
[final] ).
cnf(i_0_3316,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1740]),
[final] ).
cnf(i_0_3317,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2090]),
[final] ).
cnf(i_0_3318,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3319,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X3),
inference(split_conjunct,[status(thm)],[i_0_2092]),
[final] ).
cnf(i_0_3320,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),
inference(split_conjunct,[status(thm)],[i_0_2093]),
[final] ).
cnf(i_0_3321,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2),
inference(split_conjunct,[status(thm)],[i_0_2094]),
[final] ).
cnf(i_0_3322,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2095]),
[final] ).
cnf(i_0_3323,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2096]),
[final] ).
cnf(i_0_3324,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2097]),
[final] ).
cnf(i_0_3325,plain,
c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2),X3) = c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2098]),
[final] ).
cnf(i_0_3326,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2099]),
[final] ).
cnf(i_0_3327,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2100]),
[final] ).
cnf(i_0_3328,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X3) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
inference(split_conjunct,[status(thm)],[i_0_2101]),
[final] ).
cnf(i_0_3329,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_2102]),
[final] ).
cnf(i_0_3330,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
inference(split_conjunct,[status(thm)],[i_0_2103]),
[final] ).
cnf(i_0_3331,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3332,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2105,c_0_1488]),
[final] ).
cnf(i_0_3333,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2106,c_0_1488]),
[final] ).
cnf(i_0_3334,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2107,c_0_1488]),
[final] ).
cnf(i_0_3335,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2108,c_0_1488]),
[final] ).
cnf(i_0_3336,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3337,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3338,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2111,c_0_1488]),
[final] ).
cnf(i_0_3339,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3340,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2113,c_0_1488]),
[final] ).
cnf(i_0_3341,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2114,c_0_1488]),
[final] ).
cnf(i_0_3342,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2115,c_0_1488]),
[final] ).
cnf(i_0_3343,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) ),
inference(rw,[status(thm)],[i_0_2116,c_0_1488]),
[final] ).
cnf(i_0_3344,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3345,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2118,c_0_1488]),
[final] ).
cnf(i_0_3346,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3347,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),X3)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_1737]),
[final] ).
cnf(i_0_3348,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X4,X3),X2) = c_Divides_Odiv__class_Omod(X1,X4,X2)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2120]),
[final] ).
cnf(i_0_3349,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3350,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3351,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rw,[status(thm)],[i_0_2121,c_0_1483]),
[final] ).
cnf(i_0_3352,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_2122,c_0_1488]),
[final] ).
cnf(i_0_3353,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_3354,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3355,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3356,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3357,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3358,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2128,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3359,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2129]),
[final] ).
cnf(i_0_3360,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X2 != c_Groups_Ozero__class_Ozero(X3)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X1))
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3361,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3362,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2131,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3363,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)),c_Groups_Ozero__class_Ozero(X3))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| X2 != c_Groups_Ozero__class_Ozero(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1869]),
[final] ).
cnf(i_0_3364,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3365,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2132]),
[final] ).
cnf(i_0_3366,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2133]),
[final] ).
cnf(i_0_3367,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2134]),
[final] ).
cnf(i_0_3368,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2135]),
[final] ).
cnf(i_0_3369,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3370,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2137,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3371,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2138,c_0_1488]),c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3372,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk11_2(X2,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2139,c_0_1488]),
[final] ).
cnf(i_0_3373,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3374,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3375,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X3),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3376,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) ),
inference(rw,[status(thm)],[i_0_2141,c_0_1483]),
[final] ).
cnf(i_0_3377,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) ),
inference(rw,[status(thm)],[i_0_2142,c_0_1483]),
[final] ).
cnf(i_0_3378,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) ),
inference(rw,[status(thm)],[i_0_2143,c_0_1483]),
[final] ).
cnf(i_0_3379,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)) ),
inference(rw,[status(thm)],[i_0_2144,c_0_1483]),
[final] ).
cnf(i_0_3380,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_2145,c_0_1483]),
[final] ).
cnf(i_0_3381,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_2146,c_0_1483]),
[final] ).
cnf(i_0_3382,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2147,c_0_1483]),
[final] ).
cnf(i_0_3383,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2148,c_0_1483]),
[final] ).
cnf(i_0_3384,plain,
( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Otimes__class_Otimes(X2,X3,X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1867]),
[final] ).
cnf(i_0_3385,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3386,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3387,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3388,plain,
( c_Divides_Odiv__class_Omod(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Divides_Osemiring__div(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3389,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3390,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X3,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3391,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3392,plain,
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Otimes__class_Otimes(X2,X1,X3),c_Groups_Otimes__class_Otimes(X2,X1,X4))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1790]),
[final] ).
cnf(i_0_3393,plain,
( c_Rings_Odvd__class_Odvd(X2,c_Groups_Otimes__class_Otimes(X2,X3,X1),c_Groups_Otimes__class_Otimes(X2,X4,X1))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1791]),
[final] ).
cnf(i_0_3394,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X3,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3395,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3396,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3397,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2003]),
[final] ).
cnf(i_0_3398,plain,
( X2 = c_Groups_Ozero__class_Ozero(X3)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3399,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk21_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3400,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk19_3(X1,X2,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3401,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1868]),
[final] ).
cnf(i_0_3402,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X3,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3403,plain,
( X3 = X4
| c_Power_Opower__class_Opower(X1,X2,X3) != c_Power_Opower__class_Opower(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2152]),
[final] ).
cnf(i_0_3404,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk21_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3405,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk19_3(X1,X2,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3406,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_1913]),
[final] ).
cnf(i_0_3407,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2123]),
[final] ).
cnf(i_0_3408,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X3,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2124]),
[final] ).
cnf(i_0_3409,plain,
( c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ class_Groups_Oordered__comm__monoid__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3410,plain,
( ~ class_Rings_Olinordered__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2153]),
[final] ).
cnf(i_0_3411,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2053]),
[final] ).
cnf(i_0_3412,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2054]),
[final] ).
cnf(i_0_3413,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2055]),
[final] ).
cnf(i_0_3414,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2154]),
[final] ).
cnf(i_0_3415,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2051]),
[final] ).
cnf(i_0_3416,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3417,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2155]),
[final] ).
cnf(i_0_3418,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2052]),
[final] ).
cnf(i_0_3419,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,X3))
| ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2156]),
[final] ).
cnf(i_0_3420,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3421,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3422,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2158,c_0_1488]),
[final] ).
cnf(i_0_3423,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_3424,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_2160,c_0_1488]),
[final] ).
cnf(i_0_3425,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1815]),
[final] ).
cnf(i_0_3426,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3427,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2161,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3428,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3429,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3430,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2076]),
[final] ).
cnf(i_0_3431,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2077]),
[final] ).
cnf(i_0_3432,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3433,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2165]),
[final] ).
cnf(i_0_3434,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3435,plain,
( c_Int_OMin = X1
| c_Int_OMin != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) ),
inference(rw,[status(thm)],[i_0_2167,c_0_1484]),
[final] ).
cnf(i_0_3436,plain,
( X1 = c_Int_OMin
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Int_OMin ),
inference(rw,[status(thm)],[i_0_2168,c_0_1484]),
[final] ).
cnf(i_0_3437,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3438,plain,
( c_Rings_Odvd__class_Odvd(X2,X3,c_Power_Opower__class_Opower(X2,X3,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3439,plain,
( X2 = X3
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2171]),
[final] ).
cnf(i_0_3440,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3441,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2172]),
[final] ).
cnf(i_0_3442,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2173]),
[final] ).
cnf(i_0_3443,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rw,[status(thm)],[i_0_2174,c_0_1488]),
[final] ).
cnf(i_0_3444,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) != c_Int_OPls,
inference(rw,[status(thm)],[i_0_2175,c_0_1484]),
[final] ).
cnf(i_0_3445,plain,
c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(rw,[status(thm)],[i_0_2176,c_0_1484]),
[final] ).
cnf(i_0_3446,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Divides_Odiv__class_Odiv(X1,X3,X2)) = X3
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2177]),
[final] ).
cnf(i_0_3447,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_2178,c_0_1488]),
[final] ).
cnf(i_0_3448,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_2179,c_0_1488]),
[final] ).
cnf(i_0_3449,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2180]),
[final] ).
cnf(i_0_3450,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3451,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3452,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2183,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3453,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3454,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2031]),
[final] ).
cnf(i_0_3455,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[i_0_2184,c_0_1488]),
[final] ).
cnf(i_0_3456,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3457,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3458,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rw,[status(thm)],[i_0_2187,c_0_1483]),
[final] ).
cnf(i_0_3459,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_3460,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2189]),
[final] ).
cnf(i_0_3461,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_3462,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3463,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1978]),
[final] ).
cnf(i_0_3464,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3465,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3466,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X2) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_3467,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2112]),
[final] ).
cnf(i_0_3468,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3469,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2193,c_0_1488]),
[final] ).
cnf(i_0_3470,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2194,c_0_1488]),
[final] ).
cnf(i_0_3471,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2195,c_0_1488]),
[final] ).
cnf(i_0_3472,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2119]),
[final] ).
cnf(i_0_3473,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2196,c_0_1488]),
[final] ).
cnf(i_0_3474,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2197,c_0_1488]),
[final] ).
cnf(i_0_3475,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2117]),
[final] ).
cnf(i_0_3476,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3477,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2198,c_0_1488]),
[final] ).
cnf(i_0_3478,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2199,c_0_1488]),
[final] ).
cnf(i_0_3479,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2200,c_0_1488]),
[final] ).
cnf(i_0_3480,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2201,c_0_1488]),
[final] ).
cnf(i_0_3481,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2202]),
[final] ).
cnf(i_0_3482,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(split_conjunct,[status(thm)],[i_0_2203]),
[final] ).
cnf(i_0_3483,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2204]),
[final] ).
cnf(i_0_3484,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2205]),
[final] ).
cnf(i_0_3485,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_3486,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3487,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X2,X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2207]),
[final] ).
cnf(i_0_3488,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3489,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2208]),
[final] ).
cnf(i_0_3490,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1856]),
[final] ).
cnf(i_0_3491,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3492,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2125]),
[final] ).
cnf(i_0_3493,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2126]),
[final] ).
cnf(i_0_3494,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2127]),
[final] ).
cnf(i_0_3495,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2209]),
[final] ).
cnf(i_0_3496,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2210]),
[final] ).
cnf(i_0_3497,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1)) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2211]),
[final] ).
cnf(i_0_3498,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2212]),
[final] ).
cnf(i_0_3499,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2213]),
[final] ).
cnf(i_0_3500,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2214]),
[final] ).
cnf(i_0_3501,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2136]),
[final] ).
cnf(i_0_3502,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2215]),
[final] ).
cnf(i_0_3503,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2216]),
[final] ).
cnf(i_0_3504,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2217,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3505,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2218,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3506,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2219,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3507,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2220,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3508,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2221,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3509,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3510,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_2223,c_0_1483]),
[final] ).
cnf(i_0_3511,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2224,c_0_1483]),
[final] ).
cnf(i_0_3512,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OMin) ),
inference(rw,[status(thm)],[i_0_2225,c_0_1483]),
[final] ).
cnf(i_0_3513,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(rw,[status(thm)],[i_0_2226,c_0_1483]),
[final] ).
cnf(i_0_3514,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(rw,[status(thm)],[i_0_2227,c_0_1483]),
[final] ).
cnf(i_0_3515,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1) ),
inference(rw,[status(thm)],[i_0_2228,c_0_1483]),
[final] ).
cnf(i_0_3516,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X1) ),
inference(rw,[status(thm)],[i_0_2229,c_0_1483]),
[final] ).
cnf(i_0_3517,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(rw,[status(thm)],[i_0_2230,c_0_1483]),
[final] ).
cnf(i_0_3518,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2231,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3519,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2232,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3520,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_3521,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3522,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2235]),
[final] ).
cnf(i_0_3523,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2236]),
[final] ).
cnf(i_0_3524,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2237]),
[final] ).
cnf(i_0_3525,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X3)) = c_Groups_Ominus__class_Ominus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2238]),
[final] ).
cnf(i_0_3526,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_3527,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3528,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1944]),
[final] ).
cnf(i_0_3529,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3530,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3531,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3532,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3533,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2244]),
[final] ).
cnf(i_0_3534,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2245,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3535,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber(X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1997]),
[final] ).
cnf(i_0_3536,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3537,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3538,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3539,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3540,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3541,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2130]),
[final] ).
cnf(i_0_3542,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) = X2
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3543,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3544,plain,
( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3545,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X2) = c_Divides_Odiv__class_Omod(X1,X3,X2)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2252]),
[final] ).
cnf(i_0_3546,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = c_Divides_Odiv__class_Omod(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2253]),
[final] ).
cnf(i_0_3547,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2254]),
[final] ).
cnf(i_0_3548,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2255]),
[final] ).
cnf(i_0_3549,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2256]),
[final] ).
cnf(i_0_3550,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X3)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2257]),
[final] ).
cnf(i_0_3551,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_2258,c_0_1488]),
[final] ).
cnf(i_0_3552,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),X1) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_3553,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_3554,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3555,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3556,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_3557,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3558,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3559,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3560,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3561,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3562,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3563,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3564,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3565,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) ),
inference(rw,[status(thm)],[i_0_2267,c_0_1488]),
[final] ).
cnf(i_0_3566,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2268,c_0_1488]),
[final] ).
cnf(i_0_3567,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X2,X3,X1)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3568,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3569,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3570,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2271,c_0_1488]),
[final] ).
cnf(i_0_3571,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2272,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3572,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2273,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3573,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2274,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3574,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2275,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3575,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) = X1 ),
inference(split_conjunct,[status(thm)],[i_0_2276]),
[final] ).
cnf(i_0_3576,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3577,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2278]),
[final] ).
cnf(i_0_3578,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3579,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_3580,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_3581,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3582,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3,c_Power_Opower__class_Opower(X3,X2,X1),c_Groups_Ozero__class_Ozero(X3))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| X2 != c_Groups_Ozero__class_Ozero(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3583,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2282,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3584,plain,
( c_Orderings_Oord__class_Oless__eq(X3,c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2233]),
[final] ).
cnf(i_0_3585,plain,
( c_Orderings_Oord__class_Oless(X3,c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ class_Int_Onumber__ring(X3)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2234]),
[final] ).
cnf(i_0_3586,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3587,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3588,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3589,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3590,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3591,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X3,X2))
| ~ class_Groups_Omonoid__mult(X1)
| ~ class_Rings_Olinordered__ring(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_3592,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3593,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3594,plain,
( X2 = c_Groups_Ozero__class_Ozero(X3)
| c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),c_Power_Opower__class_Opower(X3,X2,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ class_Rings_Olinordered__idom(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3595,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3596,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_3597,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3598,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3599,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2290]),
[final] ).
cnf(i_0_3600,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3601,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2001]),
[final] ).
cnf(i_0_3602,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2002]),
[final] ).
cnf(i_0_3603,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2089]),
[final] ).
cnf(i_0_3604,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(hAPP(X3,X1),X2))
| X2 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3605,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3606,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1) ),
inference(rw,[status(thm)],[i_0_2292,c_0_1488]),
[final] ).
cnf(i_0_3607,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X1,X2) != c_Groups_Ominus__class_Ominus(X5,X3,X4)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3608,plain,
( X3 = X4
| X1 != X2
| c_Groups_Ominus__class_Ominus(X5,X3,X4) != c_Groups_Ominus__class_Ominus(X5,X1,X2)
| ~ class_Groups_Oab__group__add(X5) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3609,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) ),
inference(rw,[status(thm)],[i_0_2294,c_0_1488]),
[final] ).
cnf(i_0_3610,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_2295,c_0_1488]),
[final] ).
cnf(i_0_3611,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2280]),
[final] ).
cnf(i_0_3612,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3613,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2281]),
[final] ).
cnf(i_0_3614,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2159]),
[final] ).
cnf(i_0_3615,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3616,plain,
( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3617,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2283]),
[final] ).
cnf(i_0_3618,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3619,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3620,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3621,plain,
( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X3,X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1999]),
[final] ).
cnf(i_0_3622,plain,
( X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3623,plain,
( X2 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3624,plain,
( X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3625,plain,
( X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3626,plain,
( X3 = X4
| c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[final] ).
cnf(i_0_3627,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3628,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3629,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3630,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2304,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3631,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2305,c_0_1488]),c_0_1488]),
[final] ).
cnf(i_0_3632,plain,
( X1 = X2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3633,plain,
( c_Rings_Odvd__class_Odvd(X2,X1,c_Power_Opower__class_Opower(X2,X1,X3))
| X1 != c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2170]),
[final] ).
cnf(i_0_3634,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3635,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2308,c_0_1488]),
[final] ).
cnf(i_0_3636,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X2))
| ~ class_Rings_Olinordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3637,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3638,plain,
( X1 = X3
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3639,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3640,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = X3
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3641,plain,
( X2 = X3
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3642,plain,
( c_Divides_Odiv__class_Odiv(X1,c_Divides_Odiv__class_Omod(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3643,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_3644,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X3) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3645,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3646,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2318,c_0_1488]),
[final] ).
cnf(i_0_3647,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3648,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3649,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3650,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3651,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3652,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3653,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3654,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3655,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3656,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3657,plain,
( X2 = X1
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3658,plain,
( X1 = X2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3659,plain,
( c_Groups_Ominus__class_Ominus(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3660,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3),X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3661,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),
inference(rw,[status(thm)],[i_0_2333,c_0_1488]),
[final] ).
cnf(i_0_3662,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2334,c_0_1488]),
[final] ).
cnf(i_0_3663,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_3664,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_3665,plain,
( X1 = X2
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_2337,c_0_1483]),c_0_1483]),
[final] ).
cnf(i_0_3666,plain,
( X1 = X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2338]),
[final] ).
cnf(i_0_3667,plain,
( X2 = X3
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2339]),
[final] ).
cnf(i_0_3668,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_3669,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,esk17_2(X2,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3670,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(rw,[status(thm)],[i_0_2342,c_0_1488]),
[final] ).
cnf(i_0_3671,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3672,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| X1 != X2 ),
inference(rw,[status(thm)],[i_0_2343,c_0_1488]),
[final] ).
cnf(i_0_3673,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_2344,c_0_1488]),
[final] ).
cnf(i_0_3674,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2109]),
[final] ).
cnf(i_0_3675,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2110]),
[final] ).
cnf(i_0_3676,plain,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(rw,[status(thm)],[i_0_2345,c_0_1484]),
[final] ).
cnf(i_0_3677,plain,
( c_Int_OMin = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)
| c_Int_OMin != X1 ),
inference(rw,[status(thm)],[i_0_2346,c_0_1484]),
[final] ).
cnf(i_0_3678,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk13_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2347]),
[final] ).
cnf(i_0_3679,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1))
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2169]),
[final] ).
cnf(i_0_3680,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rw,[status(thm)],[i_0_2348,c_0_1488]),
[final] ).
cnf(i_0_3681,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3682,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3683,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2),X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2349]),
[final] ).
cnf(i_0_3684,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2350]),
[final] ).
cnf(i_0_3685,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = c_Int_OMin,
inference(rw,[status(thm)],[i_0_2351,c_0_1484]),
[final] ).
cnf(i_0_3686,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3687,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[i_0_2353]),
[final] ).
cnf(i_0_3688,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3689,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3690,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3691,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3692,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3693,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3694,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3695,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2355]),
[final] ).
cnf(i_0_3696,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_2356]),
[final] ).
cnf(i_0_3697,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3698,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3699,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X1)),
inference(split_conjunct,[status(thm)],[i_0_2359]),
[final] ).
cnf(i_0_3700,plain,
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2303]),
[final] ).
cnf(i_0_3701,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X2)
| c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3702,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2361]),
[final] ).
cnf(i_0_3703,plain,
( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,X2,X3)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3704,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk10_1(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(rw,[status(thm)],[i_0_2362,c_0_1488]),
[final] ).
cnf(i_0_3705,plain,
( c_Rings_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Rings_Odvd(X1)
| X2 != c_Groups_Otimes__class_Otimes(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2363]),
[final] ).
cnf(i_0_3706,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rw,[status(thm)],[i_0_2364,c_0_1488]),
[final] ).
cnf(i_0_3707,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_3708,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_3709,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3710,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2366]),
[final] ).
cnf(i_0_3711,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3712,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2157]),
[final] ).
cnf(i_0_3713,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3714,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3715,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3716,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3717,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3718,plain,
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2340]),
[final] ).
cnf(i_0_3719,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3720,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3721,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3722,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_3723,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3724,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3725,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_3726,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3727,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2374]),
[final] ).
cnf(i_0_3728,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2347]),
[final] ).
cnf(i_0_3729,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3730,plain,
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2375]),
[final] ).
cnf(i_0_3731,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3732,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3733,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_3734,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_3735,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2377]),
[final] ).
cnf(i_0_3736,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3737,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_3738,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3739,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2378]),
[final] ).
cnf(i_0_3740,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2277]),
[final] ).
cnf(i_0_3741,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2379]),
[final] ).
cnf(i_0_3742,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3743,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2279]),
[final] ).
cnf(i_0_3744,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(rw,[status(thm)],[i_0_2380,c_0_1488]),
[final] ).
cnf(i_0_3745,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3)) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3746,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3747,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Power_Opower__class_Opower(X2,X1,X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3748,plain,
( c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Oone__class_Oone(X2)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_3749,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1604]),
[final] ).
cnf(i_0_3750,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2383]),
[final] ).
cnf(i_0_3751,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rw,[status(thm)],[i_0_2384,c_0_1488]),
[final] ).
cnf(i_0_3752,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2382]),
[final] ).
cnf(i_0_3753,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3754,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,X3) = c_Groups_Otimes__class_Otimes(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3755,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2387]),
[final] ).
cnf(i_0_3756,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2388]),
[final] ).
cnf(i_0_3757,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(rw,[status(thm)],[i_0_2389,c_0_1488]),
[final] ).
cnf(i_0_3758,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3759,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3760,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3761,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2390]),
[final] ).
cnf(i_0_3762,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2391]),
[final] ).
cnf(i_0_3763,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3764,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2393]),
[final] ).
cnf(i_0_3765,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X1) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_3766,plain,
( c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2395]),
[final] ).
cnf(i_0_3767,plain,
( c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X1) = c_Groups_Oone__class_Oone(X2)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| ~ class_Int_Onumber__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2394]),
[final] ).
cnf(i_0_3768,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 = X2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2396]),
[final] ).
cnf(i_0_3769,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2397]),
[final] ).
cnf(i_0_3770,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3771,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2399]),
[final] ).
cnf(i_0_3772,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_3773,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2401]),
[final] ).
cnf(i_0_3774,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_3775,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2403]),
[final] ).
cnf(i_0_3776,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2404]),
[final] ).
cnf(i_0_3777,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2405]),
[final] ).
cnf(i_0_3778,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2406]),
[final] ).
cnf(i_0_3779,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2407]),
[final] ).
cnf(i_0_3780,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X2,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2408]),
[final] ).
cnf(i_0_3781,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2409]),
[final] ).
cnf(i_0_3782,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2410]),
[final] ).
cnf(i_0_3783,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3784,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_3785,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X1 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3786,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3787,plain,
( X1 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X1) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3788,plain,
( X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_3789,plain,
( X2 = X3
| c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_3790,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Oplus__class_Oplus(X2,X1,X3)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2415]),
[final] ).
cnf(i_0_3791,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2381]),
[final] ).
cnf(i_0_3792,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_3793,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_3794,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_3795,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_3796,plain,
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3797,plain,
( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2420]),
[final] ).
cnf(i_0_3798,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2421]),
[final] ).
cnf(i_0_3799,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(split_conjunct,[status(thm)],[i_0_2422]),
[final] ).
cnf(i_0_3800,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2423,c_0_1488]),
[final] ).
cnf(i_0_3801,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2424,c_0_1488]),
[final] ).
cnf(i_0_3802,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rw,[status(thm)],[i_0_2425,c_0_1488]),
[final] ).
cnf(i_0_3803,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2426,c_0_1488]),
[final] ).
cnf(i_0_3804,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2427,c_0_1488]),
[final] ).
cnf(i_0_3805,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2428,c_0_1488]),
[final] ).
cnf(i_0_3806,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_3807,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_3808,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3809,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3810,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_3811,plain,
( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_3812,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2432]),
[final] ).
cnf(i_0_3813,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) != X1,
inference(rw,[status(thm)],[i_0_2433,c_0_1488]),
[final] ).
cnf(i_0_3814,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2434,c_0_1488]),
[final] ).
cnf(i_0_3815,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_3816,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2436]),
[final] ).
cnf(i_0_3817,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2437]),
[final] ).
cnf(i_0_3818,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2438]),
[final] ).
cnf(i_0_3819,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3820,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_3821,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2439]),
[final] ).
cnf(i_0_3822,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2440]),
[final] ).
cnf(i_0_3823,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2373]),
[final] ).
cnf(i_0_3824,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3825,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2398]),
[final] ).
cnf(i_0_3826,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2441]),
[final] ).
cnf(i_0_3827,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X2) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2442]),
[final] ).
cnf(i_0_3828,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2443]),
[final] ).
cnf(i_0_3829,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) ),
inference(rw,[status(thm)],[i_0_2444,c_0_1483]),
[final] ).
cnf(i_0_3830,plain,
( X1 = c_Int_OPls
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_2445,c_0_1483]),
[final] ).
cnf(i_0_3831,plain,
( c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_3832,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2447]),
[final] ).
cnf(i_0_3833,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2448]),
[final] ).
cnf(i_0_3834,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OMin,
inference(rw,[status(thm)],[i_0_2449,c_0_1483]),
[final] ).
cnf(i_0_3835,plain,
c_Int_OMin != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(rw,[status(thm)],[i_0_2450,c_0_1483]),
[final] ).
cnf(i_0_3836,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Power_Opower(X2)
| ~ class_Rings_Osemiring__0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_3837,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_3838,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2452]),
[final] ).
cnf(i_0_3839,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2453]),
[final] ).
cnf(i_0_3840,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(split_conjunct,[status(thm)],[i_0_2454]),
[final] ).
cnf(i_0_3841,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(split_conjunct,[status(thm)],[fact_number__of2]),
[final] ).
cnf(i_0_3842,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2416]),
[final] ).
cnf(i_0_3843,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2417]),
[final] ).
cnf(i_0_3844,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3845,plain,
( c_Groups_Oplus__class_Oplus(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2408]),
[final] ).
cnf(i_0_3846,plain,
( c_Groups_Otimes__class_Otimes(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3847,plain,
( c_Groups_Otimes__class_Otimes(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2392]),
[final] ).
cnf(i_0_3848,plain,
( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X1,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2410]),
[final] ).
cnf(i_0_3849,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_3850,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2457]),
[final] ).
cnf(i_0_3851,plain,
( c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2458]),
[final] ).
cnf(i_0_3852,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2459]),
[final] ).
cnf(i_0_3853,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2460]),
[final] ).
cnf(i_0_3854,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2461]),
[final] ).
cnf(i_0_3855,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2462]),
[final] ).
cnf(i_0_3856,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2463]),
[final] ).
cnf(i_0_3857,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Oone__class_Oone(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2464]),
[final] ).
cnf(i_0_3858,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2465]),
[final] ).
cnf(i_0_3859,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2466]),
[final] ).
cnf(i_0_3860,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2467]),
[final] ).
cnf(i_0_3861,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Omult__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2468]),
[final] ).
cnf(i_0_3862,plain,
( c_Power_Opower__class_Opower(X2,X3,X1) = c_Groups_Oone__class_Oone(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Power_Opower(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1863]),
[final] ).
cnf(i_0_3863,plain,
( X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2415]),
[final] ).
cnf(i_0_3864,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Divides_Odiv__class_Odiv(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2469]),
[final] ).
cnf(i_0_3865,plain,
( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Ogroup__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2413]),
[final] ).
cnf(i_0_3866,plain,
( c_Groups_Ominus__class_Ominus(X3,X1,X2) = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Groups_Oab__group__add(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2414]),
[final] ).
cnf(i_0_3867,plain,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2470]),
[final] ).
cnf(i_0_3868,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Power_Opower(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2471]),
[final] ).
cnf(i_0_3869,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2472]),
[final] ).
cnf(i_0_3870,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2473]),
[final] ).
cnf(i_0_3871,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2474]),
[final] ).
cnf(i_0_3872,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2475]),
[final] ).
cnf(i_0_3873,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2476]),
[final] ).
cnf(i_0_3874,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2477]),
[final] ).
cnf(i_0_3875,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oone__class_Oone(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2478]),
[final] ).
cnf(i_0_3876,plain,
( c_Divides_Odiv__class_Odiv(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_3877,plain,
( c_Divides_Odiv__class_Omod(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2480]),
[final] ).
cnf(i_0_3878,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2481]),
[final] ).
cnf(i_0_3879,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2482]),
[final] ).
cnf(i_0_3880,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Groups_Omonoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2483]),
[final] ).
cnf(i_0_3881,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2484]),
[final] ).
cnf(i_0_3882,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2485]),
[final] ).
cnf(i_0_3883,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2486]),
[final] ).
cnf(i_0_3884,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2487]),
[final] ).
cnf(i_0_3885,plain,
( c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2488]),
[final] ).
cnf(i_0_3886,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2489]),
[final] ).
cnf(i_0_3887,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2430]),
[final] ).
cnf(i_0_3888,plain,
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X1 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3889,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2429]),
[final] ).
cnf(i_0_3890,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2431]),
[final] ).
cnf(i_0_3891,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)) ),
inference(split_conjunct,[status(thm)],[i_0_2490]),
[final] ).
cnf(i_0_3892,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_3893,plain,
( c_Power_Opower__class_Opower(X1,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2492]),
[final] ).
cnf(i_0_3894,plain,
( c_Divides_Odiv__class_Omod(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Divides_Osemiring__div(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_3895,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2494]),
[final] ).
cnf(i_0_3896,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2422]),
[final] ).
cnf(i_0_3897,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2421]),
[final] ).
cnf(i_0_3898,plain,
( c_Rings_Odvd__class_Odvd(X1,X2,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2495]),
[final] ).
cnf(i_0_3899,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[i_0_2496,c_0_1488]),
[final] ).
cnf(i_0_3900,plain,
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3901,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1898]),
[final] ).
cnf(i_0_3902,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1897]),
[final] ).
cnf(i_0_3903,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_3904,plain,
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2418]),
[final] ).
cnf(i_0_3905,plain,
( X2 = X3
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Int_Onumber__class_Onumber__of(X1,X3)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_3906,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2498]),
[final] ).
cnf(i_0_3907,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2419]),
[final] ).
cnf(i_0_3908,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = X2
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_1329]),
[final] ).
cnf(i_0_3909,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2499]),
[final] ).
cnf(i_0_3910,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]),
[final] ).
cnf(i_0_3911,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]),
[final] ).
cnf(i_0_3912,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_int__0__less__1]),
[final] ).
cnf(i_0_3913,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2500]),
[final] ).
cnf(i_0_3914,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2501]),
[final] ).
cnf(i_0_3915,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2502]),
[final] ).
cnf(i_0_3916,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_3917,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2504]),
[final] ).
cnf(i_0_3918,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2505]),
[final] ).
cnf(i_0_3919,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2506]),
[final] ).
cnf(i_0_3920,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2507]),
[final] ).
cnf(i_0_3921,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2508]),
[final] ).
cnf(i_0_3922,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2509]),
[final] ).
cnf(i_0_3923,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2503]),
[final] ).
cnf(i_0_3924,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2510]),
[final] ).
cnf(i_0_3925,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2511]),
[final] ).
cnf(i_0_3926,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2512]),
[final] ).
cnf(i_0_3927,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2513]),
[final] ).
cnf(i_0_3928,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2514]),
[final] ).
cnf(i_0_3929,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3930,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2515]),
[final] ).
cnf(i_0_3931,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2376]),
[final] ).
cnf(i_0_3932,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2372]),
[final] ).
cnf(i_0_3933,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2516]),
[final] ).
cnf(i_0_3934,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3935,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3936,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3937,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_2517]),
[final] ).
cnf(i_0_3938,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_2518]),
[final] ).
cnf(i_0_3939,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
inference(split_conjunct,[status(thm)],[i_0_2519]),
[final] ).
cnf(i_0_3940,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2520]),
[final] ).
cnf(i_0_3941,plain,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_2521,c_0_1483]),
[final] ).
cnf(i_0_3942,plain,
( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)
| c_Int_OPls != X1 ),
inference(rw,[status(thm)],[i_0_2522,c_0_1483]),
[final] ).
cnf(i_0_3943,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[i_0_2523]),
[final] ).
cnf(i_0_3944,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_2524]),
[final] ).
cnf(i_0_3945,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_bin__less__0__simps_I2_J]),
[final] ).
cnf(i_0_3946,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2525]),
[final] ).
cnf(i_0_3947,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_3948,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_3949,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2528]),
[final] ).
cnf(i_0_3950,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2529]),
[final] ).
cnf(i_0_3951,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2530]),
[final] ).
cnf(i_0_3952,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2531]),
[final] ).
cnf(i_0_3953,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_2532]),
[final] ).
cnf(i_0_3954,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I24_J]),
[final] ).
cnf(i_0_3955,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I23_J]),
[final] ).
cnf(i_0_3956,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I19_J]),
[final] ).
cnf(i_0_3957,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_rel__simps_I6_J]),
[final] ).
cnf(i_0_3958,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
inference(rw,[status(thm)],[i_0_2533,c_0_1483]),
[final] ).
cnf(i_0_3959,plain,
( c_Int_Oiszero(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2534]),
[final] ).
cnf(i_0_3960,plain,
( ~ class_Rings_Osemiring__1(X1)
| ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2535]),
[final] ).
cnf(i_0_3961,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Int_Oiszero(X1,X2)
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2536]),
[final] ).
cnf(i_0_3962,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
inference(split_conjunct,[status(thm)],[fact_eq__number__of__Pls__Min]),
[final] ).
cnf(i_0_3963,plain,
( c_Int_Oiszero(X2,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Osemiring__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2536]),
[final] ).
cnf(i_0_3964,plain,
( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Osemiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2537]),
[final] ).
cnf(i_0_3965,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[i_0_2538]),
[final] ).
cnf(i_0_3966,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_3967,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2540]),
[final] ).
cnf(i_0_3968,plain,
( c_Groups_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2541]),
[final] ).
cnf(i_0_3969,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2542]),
[final] ).
cnf(i_0_3970,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2543]),
[final] ).
cnf(i_0_3971,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(split_conjunct,[status(thm)],[fact_even__zero__int]),
[final] ).
cnf(i_0_3972,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[fact_even__zero__nat]),
[final] ).
cnf(i_0_3973,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_nat__number__of__Pls]),
[final] ).
cnf(i_0_3974,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_zero__is__num__zero]),
[final] ).
cnf(i_0_3975,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I113_J]),
[final] ).
cnf(i_0_3976,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2544]),
[final] ).
cnf(i_0_3977,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(split_conjunct,[status(thm)],[fact_e]),
[final] ).
cnf(i_0_3978,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]),
[final] ).
cnf(i_0_3979,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_int__0__neq__1]),
[final] ).
cnf(i_0_3980,plain,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_assms_I2_J]),
[final] ).
cnf(i_0_3981,plain,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_n]),
[final] ).
cnf(i_0_3982,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
[final] ).
cnf(i_0_3983,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3984,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_3985,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3986,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3987,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3988,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3989,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3990,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3991,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_3992,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_3993,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_3994,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3995,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3996,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]),
[final] ).
cnf(i_0_3997,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3998,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3999,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4000,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_4001,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_4002,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]),
[final] ).
cnf(i_0_4003,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_4004,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
[final] ).
cnf(i_0_4005,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_4006,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]),
[final] ).
cnf(i_0_4007,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_4008,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_4009,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_4010,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4011,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4012,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]),
[final] ).
cnf(i_0_4013,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_4014,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_4015,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]),
[final] ).
cnf(i_0_4016,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4017,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4018,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_4019,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4020,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4021,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_4022,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_4023,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_4024,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_4025,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]),
[final] ).
cnf(i_0_4026,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]),
[final] ).
cnf(i_0_4027,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]),
[final] ).
cnf(i_0_4028,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]),
[final] ).
cnf(i_0_4029,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_4030,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_4031,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_4032,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_4033,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4034,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4035,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]),
[final] ).
cnf(i_0_4036,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4037,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4038,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4039,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]),
[final] ).
cnf(i_0_4040,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4041,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4042,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4043,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4044,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4045,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]),
[final] ).
cnf(i_0_4046,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4047,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4048,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4049,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]),
[final] ).
cnf(i_0_4050,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4051,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4052,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4053,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4054,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4055,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4056,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4057,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]),
[final] ).
cnf(i_0_4058,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4059,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4060,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4061,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]),
[final] ).
cnf(i_0_4062,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4063,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4064,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4065,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]),
[final] ).
cnf(i_0_4066,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4067,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4068,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4069,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]),
[final] ).
cnf(i_0_4070,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_4071,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_4072,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_4073,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_4074,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4075,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4076,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4077,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4078,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_4079,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_4080,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]),
[final] ).
cnf(i_0_4081,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4082,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4083,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4084,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]),
[final] ).
cnf(i_0_4085,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_4086,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_4087,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_4088,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_4089,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_4090,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_4091,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]),
[final] ).
cnf(i_0_4092,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_4093,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_4094,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]),
[final] ).
cnf(i_0_4095,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4096,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4097,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4098,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4099,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_4100,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_4101,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_4102,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_4103,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_4104,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_4105,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_4106,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4107,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4108,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4109,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4110,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_4111,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_4112,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]),
[final] ).
cnf(i_0_4113,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]),
[final] ).
cnf(i_0_4114,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_4115,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]),
[final] ).
cnf(i_0_4116,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]),
[final] ).
cnf(i_0_4117,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]),
[final] ).
cnf(i_0_4118,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_4119,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_4120,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4121,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4122,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_4123,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]),
[final] ).
cnf(i_0_4124,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4125,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4126,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4127,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4128,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4129,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4130,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4131,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4132,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4133,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4134,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4135,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4136,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]),
[final] ).
cnf(i_0_4137,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_4138,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_4139,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]),
[final] ).
cnf(i_0_4140,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]),
[final] ).
cnf(i_0_4141,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]),
[final] ).
cnf(i_0_4142,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4143,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4144,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4145,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]),
[final] ).
cnf(i_0_4146,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_4147,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_4148,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_4149,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_4150,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]),
[final] ).
cnf(i_0_4151,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]),
[final] ).
cnf(i_0_4152,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
[final] ).
cnf(i_0_4153,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
[final] ).
cnf(i_0_4154,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]),
[final] ).
cnf(i_0_4155,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]),
[final] ).
cnf(i_0_4156,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]),
[final] ).
cnf(i_0_4157,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]),
[final] ).
cnf(i_0_4158,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]),
[final] ).
cnf(i_0_4159,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
[final] ).
cnf(i_0_4160,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]),
[final] ).
cnf(i_0_4161,negated_conjecture,
~ v_thesis____,
inference(split_conjunct,[status(thm)],[i_0_2545]),
[final] ).
cnf(i_0_4162,plain,
c_Int_OPls != c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
[final] ).
cnf(i_0_4163,plain,
c_Int_OMin != c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
[final] ).
cnf(i_0_4164,axiom,
X1 = X1 ).
cnf(i_0_4165,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4166,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4167,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_4168,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_4169,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_4170,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4171,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4172,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4173,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4174,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4175,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4176,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4177,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4178,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4179,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_4180,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_4181,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_4182,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4183,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4184,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4185,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4186,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4187,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4188,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4189,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4190,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4191,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4192,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4193,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4194,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4195,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4196,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4197,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4198,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4199,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4200,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4201,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4202,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4203,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4204,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_4205,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_4206,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4207,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4208,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4209,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4210,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4211,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4212,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4213,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4214,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4215,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4216,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4217,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4218,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4219,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4220,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4221,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4222,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4223,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4224,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4225,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4226,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4227,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4228,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4229,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4230,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4231,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4232,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4233,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4234,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4235,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4236,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4237,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4238,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4239,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4240,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4241,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4242,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4243,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4244,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4245,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4246,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4247,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4248,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4249,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4250,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4251,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4252,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4253,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4254,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4255,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4256,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4257,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4258,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4259,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_4260,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_4261,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4164_001,axiom,
X1 = X1 ).
cnf(i_0_4165_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4166_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4167_004,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_4168_005,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_4169_006,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_4170_007,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4171_008,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4172_009,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4173_010,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4174_011,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4175_012,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4176_013,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4177_014,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4178_015,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4179_016,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_4180_017,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_4181_018,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_4182_019,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4183_020,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4184_021,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4185_022,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4186_023,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X1,X3,X4) = c_Divides_Odiv__class_Odiv(X2,X3,X4) ) ).
cnf(i_0_4187_024,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X1,X4) = c_Divides_Odiv__class_Odiv(X3,X2,X4) ) ).
cnf(i_0_4188_025,axiom,
( X1 != X2
| c_Divides_Odiv__class_Odiv(X3,X4,X1) = c_Divides_Odiv__class_Odiv(X3,X4,X2) ) ).
cnf(i_0_4189_026,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4190_027,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4191_028,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4192_029,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4193_030,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4194_031,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4195_032,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4196_033,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4197_034,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4198_035,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4199_036,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4200_037,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4201_038,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4202_039,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4203_040,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4204_041,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X1,X3)
| c_Int_Oiszero(X2,X3) ) ).
cnf(i_0_4205_042,axiom,
( X1 != X2
| ~ c_Int_Oiszero(X3,X1)
| c_Int_Oiszero(X3,X2) ) ).
cnf(i_0_4206_043,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4207_044,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4208_045,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4209_046,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4210_047,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4211_048,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4212_049,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4213_050,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4214_051,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4215_052,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4216_053,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4217_054,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4218_055,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4219_056,axiom,
( X1 != X2
| ~ class_Divides_Oring__div(X1)
| class_Divides_Oring__div(X2) ) ).
cnf(i_0_4220_057,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4221_058,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4222_059,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4223_060,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4224_061,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4225_062,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4226_063,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4227_064,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4228_065,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4229_066,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4230_067,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4231_068,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4232_069,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4233_070,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4234_071,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4235_072,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4236_073,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4237_074,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4238_075,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4239_076,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4240_077,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4241_078,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4242_079,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4243_080,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4244_081,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4245_082,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4246_083,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4247_084,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4248_085,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4249_086,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4250_087,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4251_088,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4252_089,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4253_090,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4254_091,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4255_092,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4256_093,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4257_094,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4258_095,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4259_096,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_4260_097,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_4261_098,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4262,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(equality_inference,[],[2577]) ).
cnf(i_0_4263,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) ),
inference(equality_inference,[],[2578]) ).
cnf(i_0_4264,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_inference,[],[2579]) ).
cnf(i_0_4265,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[2580]) ).
cnf(i_0_4266,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)),
inference(equality_inference,[],[2601]) ).
cnf(i_0_4267,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1)),
inference(equality_inference,[],[2602]) ).
cnf(i_0_4268,plain,
( ~ class_Rings_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[2619]) ).
cnf(i_0_4269,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_inference,[],[2655]) ).
cnf(i_0_4270,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X1)) ),
inference(equality_inference,[],[2656]) ).
cnf(i_0_4271,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[2662]) ).
cnf(i_0_4272,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4)) ),
inference(equality_inference,[],[2684]) ).
cnf(i_0_4273,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3),X4)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3),X4) ),
inference(equality_inference,[],[2685]) ).
cnf(i_0_4274,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X2),X3) = X3 ),
inference(equality_inference,[],[2699]) ).
cnf(i_0_4275,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X3),X2) ),
inference(equality_inference,[],[2700]) ).
cnf(i_0_4276,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X5,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X5),X3),X4)) ),
inference(equality_inference,[],[2701]) ).
cnf(i_0_4277,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X4,X2),X3),X5)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X5) ),
inference(equality_inference,[],[2702]) ).
cnf(i_0_4278,plain,
( ~ class_Rings_Oring(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X2,X2),X3),X4) = X4 ),
inference(equality_inference,[],[2705]) ).
cnf(i_0_4279,plain,
( ~ class_Rings_Oring(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ominus__class_Ominus(X1,X3,X3),X4),X2) ),
inference(equality_inference,[],[2706]) ).
cnf(i_0_4280,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2711]) ).
cnf(i_0_4281,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(equality_inference,[],[2748]) ).
cnf(i_0_4282,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X1)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),X2),X1) = X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(equality_inference,[],[2772]) ).
cnf(i_0_4283,plain,
c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),
inference(equality_inference,[],[2798]) ).
cnf(i_0_4284,plain,
( ~ epred1_3(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,X4)) ),
inference(equality_inference,[],[2803]) ).
cnf(i_0_4285,plain,
( ~ epred1_3(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,X4)) ),
inference(equality_inference,[],[2804]) ).
cnf(i_0_4286,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X1),X2) = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2842]) ).
cnf(i_0_4287,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
inference(equality_inference,[],[2868]) ).
cnf(i_0_4288,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X3),X2),X1) = X2
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(equality_inference,[],[2890]) ).
cnf(i_0_4289,plain,
X1 = X1,
inference(equality_inference,[],[2911]) ).
cnf(i_0_4290,plain,
X1 = X1,
inference(equality_inference,[],[2912]) ).
cnf(i_0_4291,plain,
( hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2),X3))) ),
inference(equality_inference,[],[2922]) ).
cnf(i_0_4292,plain,
( X1 = X1
| ~ class_Rings_Olinordered__semidom(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
inference(equality_inference,[],[2969]) ).
cnf(i_0_4293,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1))
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3228]) ).
cnf(i_0_4294,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(equality_inference,[],[3256]) ).
cnf(i_0_4295,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(equality_inference,[],[3257]) ).
cnf(i_0_4296,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),
inference(equality_inference,[],[3301]) ).
cnf(i_0_4297,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3352]) ).
cnf(i_0_4298,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3360]) ).
cnf(i_0_4299,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3370]) ).
cnf(i_0_4300,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3371]) ).
cnf(i_0_4301,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2),c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X3)) ),
inference(equality_inference,[],[3392]) ).
cnf(i_0_4302,plain,
( ~ class_Rings_Oidom(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Otimes__class_Otimes(X1,X3,c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3393]) ).
cnf(i_0_4303,plain,
( ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3402]) ).
cnf(i_0_4304,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[3403]) ).
cnf(i_0_4305,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)),
inference(equality_inference,[],[3425]) ).
cnf(i_0_4306,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(equality_inference,[],[3437]) ).
cnf(i_0_4307,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3439]) ).
cnf(i_0_4308,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(equality_inference,[],[3453]) ).
cnf(i_0_4309,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(equality_inference,[],[3454]) ).
cnf(i_0_4310,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3504]) ).
cnf(i_0_4311,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3505]) ).
cnf(i_0_4312,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3506]) ).
cnf(i_0_4313,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(equality_inference,[],[3507]) ).
cnf(i_0_4314,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1) = X2 ),
inference(equality_inference,[],[3542]) ).
cnf(i_0_4315,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X1) ),
inference(equality_inference,[],[3543]) ).
cnf(i_0_4316,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3582]) ).
cnf(i_0_4317,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_inference,[],[3583]) ).
cnf(i_0_4318,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3605]) ).
cnf(i_0_4319,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3609]) ).
cnf(i_0_4320,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3610]) ).
cnf(i_0_4321,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(equality_inference,[],[3621]) ).
cnf(i_0_4322,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3623]) ).
cnf(i_0_4323,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3624]) ).
cnf(i_0_4324,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3626]) ).
cnf(i_0_4325,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2)) ),
inference(equality_inference,[],[3633]) ).
cnf(i_0_4326,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3637]) ).
cnf(i_0_4327,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3638]) ).
cnf(i_0_4328,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3639]) ).
cnf(i_0_4329,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3641]) ).
cnf(i_0_4330,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3662]) ).
cnf(i_0_4331,plain,
X1 = X1,
inference(equality_inference,[],[3665]) ).
cnf(i_0_4332,plain,
X1 = X1,
inference(equality_inference,[],[3666]) ).
cnf(i_0_4333,plain,
X1 = X1,
inference(equality_inference,[],[3667]) ).
cnf(i_0_4334,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_inference,[],[3671]) ).
cnf(i_0_4335,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3672]) ).
cnf(i_0_4336,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3675]) ).
cnf(i_0_4337,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin),c_Int_OMin) = c_Int_OMin,
inference(equality_inference,[],[3676]) ).
cnf(i_0_4338,plain,
c_Int_OMin = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(equality_inference,[],[3677]) ).
cnf(i_0_4339,plain,
( ~ class_Rings_Odvd(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
inference(equality_inference,[],[3705]) ).
cnf(i_0_4340,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_inference,[],[3706]) ).
cnf(i_0_4341,plain,
c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X2),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[3718]) ).
cnf(i_0_4342,plain,
c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3719]) ).
cnf(i_0_4343,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3728]) ).
cnf(i_0_4344,plain,
( ~ epred1_3(X1,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(X1,X2)) ),
inference(equality_inference,[],[3749]) ).
cnf(i_0_4345,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_inference,[],[3751]) ).
cnf(i_0_4346,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
inference(equality_inference,[],[3759]) ).
cnf(i_0_4347,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3760]) ).
cnf(i_0_4348,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Omult__zero(X1)
| ~ class_Rings_Ono__zero__divisors(X1)
| ~ class_Rings_Ozero__neq__one(X1)
| c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3791]) ).
cnf(i_0_4349,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3812]) ).
cnf(i_0_4350,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3819]) ).
cnf(i_0_4351,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3820]) ).
cnf(i_0_4352,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3824]) ).
cnf(i_0_4353,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3825]) ).
cnf(i_0_4354,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3845]) ).
cnf(i_0_4355,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| c_Groups_Otimes__class_Otimes(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3846]) ).
cnf(i_0_4356,plain,
( ~ class_Rings_Oring__no__zero__divisors(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3847]) ).
cnf(i_0_4357,plain,
( ~ class_Groups_Olinordered__ab__group__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3848]) ).
cnf(i_0_4358,plain,
( ~ class_Power_Opower(X1)
| c_Power_Opower__class_Opower(X1,X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3862]) ).
cnf(i_0_4359,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3863]) ).
cnf(i_0_4360,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3865]) ).
cnf(i_0_4361,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3866]) ).
cnf(i_0_4362,plain,
c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(equality_inference,[],[3900]) ).
cnf(i_0_4363,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(equality_inference,[],[3901]) ).
cnf(i_0_4364,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3903]) ).
cnf(i_0_4365,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(equality_inference,[],[3904]) ).
cnf(i_0_4366,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[3905]) ).
cnf(i_0_4367,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(equality_inference,[],[3908]) ).
cnf(i_0_4368,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3929]) ).
cnf(i_0_4369,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3932]) ).
cnf(i_0_4370,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3935]) ).
cnf(i_0_4371,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3936]) ).
cnf(i_0_4372,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
inference(equality_inference,[],[3941]) ).
cnf(i_0_4373,plain,
c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(equality_inference,[],[3942]) ).
cnf(i_0_4374,plain,
( ~ class_Rings_Osemiring__1(X1)
| c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3963]) ).
cnf(i_0_4375,plain,
$false,
inference(scs_inference,[],[i_0_4161,i_0_2627,i_0_2605]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWW196+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n017.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 06:22:57 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 2.30/2.78 % Version : CSE_E---1.7
% 2.30/2.78 % Problem : theBenchmark.p
% 2.30/2.78 % SZS status Theorem for theBenchmark.p
% 2.30/2.78 % SZS output start CNFRefutation
% See solution above
% 2.45/2.91 % Total time : 2.438s
%------------------------------------------------------------------------------