%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW198+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 : n008.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 05:29:29 PM UTC 2026
% Result : Theorem 3.09s 3.80s
% Output : CNFRefutation 3.19s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_1493)
% Comments :
%------------------------------------------------------------------------------
fof(fact_not__sum__power2__lt__zero,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).
fof(fact_odd__Suc__mult__two__ex,axiom,
! [X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = 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))),X23)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).
fof(fact_power2__less__0,axiom,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ~ c_Orderings_Oord__class_Oless(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_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__0) ).
fof(conj_0,conjecture,
? [X23] : v_na____ = 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))),X23)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_zmod__number__of__Bit1,axiom,
! [X22,X9] :
( ( 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,X9))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X22)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9))) = 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,X22),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9))),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,X9))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X22)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9))) = 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,X22),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9))),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)
<=> ? [X24] : 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))),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nat__equiv__def2) ).
fof(fact_le__SucE,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Nat_OSuc(X13))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> X10 = c_Nat_OSuc(X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).
fof(fact_not__less__eq__eq,axiom,
! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_not__less__eq,axiom,
! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__SucE,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X13))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> X10 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).
fof(fact_less__antisym,axiom,
! [X10,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Nat_OSuc(X10))
=> X10 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [X4,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X4))
<=> X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_Suc__n__not__le__n,axiom,
! [X13] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X13),X13),
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_real__sqrt__sum__squares__mult__squared__eq,axiom,
! [X46,X44,X17,X18] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X44,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,X46,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X44,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,X46,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_real__sqrt__sum__squares__mult__squared__eq) ).
fof(fact_Bit0__def,axiom,
! [X8] : c_Int_OBit0(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X8] : c_Int_OBit1(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_real__sqrt__sum__squares__triangle__ineq,axiom,
! [X39,X25,X38,X1] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X38),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_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X39),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_NthRoot_Osqrt(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,X25,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X38,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,X39,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_real__sqrt__sum__squares__triangle__ineq) ).
fof(fact_arctan__half,axiom,
! [X18] : c_Transcendental_Oarctan(X18) = 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))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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_arctan__half) ).
fof(fact_cos__x__y__le__one,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__x__y__le__one) ).
fof(fact_real__sqrt__sum__squares__mult__ge__zero,axiom,
! [X46,X44,X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X44,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,X46,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_real__sqrt__sum__squares__mult__ge__zero) ).
fof(fact_real__sqrt__sum__squares__less,axiom,
! [X17,X56,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X56,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X56,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X56) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__less) ).
fof(fact_lemma__sqrt__hcomplex__capprox,axiom,
! [X17,X18,X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X56,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X17,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X56,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X56) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__sqrt__hcomplex__capprox) ).
fof(fact_real__sqrt__ge__abs1,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_real__sqrt__ge__abs1) ).
fof(fact_real__sqrt__ge__abs2,axiom,
! [X18,X17] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_real__sqrt__ge__abs2) ).
fof(fact_real__sqrt__sum__squares__ge__zero,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_real__sqrt__sum__squares__ge__zero) ).
fof(fact_real__sqrt__sum__squares__ge1,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_real__sqrt__sum__squares__ge1) ).
fof(fact_real__sqrt__sum__squares__ge2,axiom,
! [X18,X17] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,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_real__sqrt__sum__squares__ge2) ).
fof(fact_power2__sum,axiom,
! [X17,X18,X2] :
( class_Int_Onumber__ring(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Oplus__class_Oplus(X2,X18,X17),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X18),X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__sum) ).
fof(fact_real__sum__squared__expand,axiom,
! [X17,X18] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17),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,X18,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,X17,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))),X18),X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__squared__expand) ).
fof(fact_odd__0__le__power__imp__0__le,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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))),X13))))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_Suc__eq__plus1,axiom,
! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,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,X2] :
( class_Rings_Olinordered__idom(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,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,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(X2)
| X14 != c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [X14,X15,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,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X2)
& X14 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
! [X17,X18] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = X17
=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel2) ).
fof(fact_real__sqrt__sum__squares__eq__cancel,axiom,
! [X17,X18] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,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,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) = X18
=> X17 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__sum__squares__eq__cancel) ).
fof(fact_four__x__squared,axiom,
! [X18] : 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,X18,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))),X18),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,
! [X25,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,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))),X25)),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,X25,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1)),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,
! [X25,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> 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))),X25)),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,X25,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).
fof(fact_odd__power__less__zero,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,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))),X13))),c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_sum__power2__ge__zero,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,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,
! [X8,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,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))),X8)),c_Groups_Ozero__class_Ozero(X2))
=> X1 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__power__le__0__imp__0) ).
fof(fact_power2__less__imp__less,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless(X2,X18,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).
fof(fact_power2__le__imp__le,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X18,X17) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).
fof(fact_sum__power2__eq__zero__iff,axiom,
! [X14,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X14,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X2)
& X14 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
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,
! [X13,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,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))),X13))) = c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,c_Power_Opower__class_Opower(X2,X1,X13),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_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [X13,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,X18,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))),X13))) = c_Groups_Otimes__class_Otimes(X2,X18,c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X18,X13),c_Power_Opower__class_Opower(X2,X18,X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_eq__divide__2__times__iff,axiom,
! [X54,X14,X15] :
( X15 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X14,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))),X54))
<=> 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))),X15) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X14,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).
fof(fact_power__m1__odd,axiom,
! [X13,X2] :
( class_Int_Onumber__ring(X2)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,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))),X13))) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__odd) ).
fof(fact_zero__le__even__power_H,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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))),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).
fof(fact_real__sum__of__halves,axiom,
! [X18] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_lemma__real__divide__sqrt__less,axiom,
! [X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X56,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__real__divide__sqrt__less) ).
fof(fact_power2__eq__imp__eq,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> X18 = X17 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).
fof(fact_half__gt__zero__iff,axiom,
! [X70,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber__ring(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X70,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X70) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).
fof(fact_zero__less__power2,axiom,
! [X27,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
<=> X27 != c_Groups_Ozero__class_Ozero(X2) ) ),
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,
! [X13,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,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))),X13)) = c_Power_Opower__class_Opower(X2,c_Power_Opower__class_Opower(X2,X1,X13),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_abs__power2,axiom,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Oabs__class_Oabs(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,X1,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_abs__power2) ).
fof(fact_real__gt__half__sum,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).
fof(fact_real__less__half__sum,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__half__sum) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
! [X13,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,X18,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))),X13)) = c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X18,X13),c_Power_Opower__class_Opower(X2,X18,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
fof(fact_less__one__imp__sqr__less__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__one__imp__sqr__less__one) ).
fof(fact_half__gt__zero,axiom,
! [X57,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber__ring(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X57)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X57,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero) ).
fof(fact_real__sqrt__pow2__gt__zero,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),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_real__sqrt__pow2__gt__zero) ).
fof(fact_half,axiom,
! [X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber__ring(X2) )
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half) ).
fof(fact_power__m1__even,axiom,
! [X13,X2] :
( class_Int_Onumber__ring(X2)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,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))),X13)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__m1__even) ).
fof(fact_zero__le__power2,axiom,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(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))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power2) ).
fof(fact_two__realpow__ge__one,axiom,
! [X13] : 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))),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_two__realpow__ge__one) ).
fof(fact_power2__abs,axiom,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(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,X1,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_power2__abs) ).
fof(fact_real__sqrt__abs,axiom,
! [X18] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(fact_Suc3__eq__add__3,axiom,
! [X13] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X13))) = 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))),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).
fof(fact_power3__eq__cube,axiom,
! [X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power3__eq__cube) ).
fof(fact_int__pos__lt__two__imp__zero__or__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( X18 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X18 = 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_real__sqrt__unique,axiom,
! [X18,X17] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X18
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X17)
=> c_NthRoot_Osqrt(X18) = X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__unique) ).
fof(fact_real__sqrt__pow2__iff,axiom,
! [X15] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X15
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__pow2__iff) ).
fof(fact_less__2__cases,axiom,
! [X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> ( X13 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X13 = 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,
! [X27,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( c_Power_Opower__class_Opower(X2,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_even__mult__two__ex,axiom,
! [X3] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = 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))),X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__mult__two__ex) ).
fof(fact_zmod__number__of__Bit0,axiom,
! [X9,X22] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X22)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9))) = 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,X22),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).
fof(fact_add__2__eq__Suc,axiom,
! [X13] : 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))),X13) = c_Nat_OSuc(c_Nat_OSuc(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).
fof(fact_add__2__eq__Suc_H,axiom,
! [X13] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).
fof(fact_power2__eq__square__number__of,axiom,
! [X9,X31] :
( ( class_Groups_Omonoid__mult(X31)
& class_Int_Onumber(X31) )
=> c_Power_Opower__class_Opower(X31,c_Int_Onumber__class_Onumber__of(X31,X9),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X31,c_Int_Onumber__class_Onumber__of(X31,X9),c_Int_Onumber__class_Onumber__of(X31,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_real__sqrt__pow2,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__pow2) ).
fof(fact_mult__2,axiom,
! [X21,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X21) = c_Groups_Oplus__class_Oplus(X2,X21,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).
fof(fact_mult__2__right,axiom,
! [X21,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,X21,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X2,X21,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_power2__eq__square,axiom,
! [X1,X2] :
( class_Groups_Omonoid__mult(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_Groups_Otimes__class_Otimes(X2,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__eq__square) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X18,X18) = c_Power_Opower__class_Opower(X2,X18,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,
! [X21] : 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))),X21) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2) ).
fof(fact_nat__mult__2__right,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X21,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,X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).
fof(fact_one__power2,axiom,
! [X2] :
( class_Rings_Osemiring__1(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__power2) ).
fof(fact_zero__power2,axiom,
! [X2] :
( class_Rings_Osemiring__1(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__power2) ).
fof(fact_csqrt,axiom,
! [X21] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X21),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_csqrt) ).
fof(fact_one__add__one__is__two,axiom,
! [X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2)) = c_Int_Onumber__class_Onumber__of(X2,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,
! [X25,X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13)),c_Power_Opower__class_Opower(X2,X25,c_Nat_OSuc(X13)))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).
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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X6))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).
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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit1(X6))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).
fof(fact_Suc__mult__less__cancel1,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X3))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [X27,X16,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [X27,X16,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [X16,X26,X27,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [X16,X26,X27,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_divide__less__eq__number__of,axiom,
! [X16,X48,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_divide__le__eq__number__of,axiom,
! [X16,X48,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [X48,X26,X16,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [X48,X26,X16,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_add__Bit1__Bit0,axiom,
! [X7,X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X8),c_Int_OBit0(X7)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).
fof(fact_add__Bit0__Bit1,axiom,
! [X7,X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X8),c_Int_OBit1(X7)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).
fof(fact_mult__Bit1,axiom,
! [X7,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X8),X7) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X7)),X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit1) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X18),c_Groups_Otimes__class_Otimes(X2,X17,X17)),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_number__of1,axiom,
! [X13] :
( 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,X13))
=> ( 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(X13)))
& 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(X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).
fof(fact_add__special_I3_J,axiom,
! [X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Groups_Oone__class_Oone(X2)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,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,
! [X9,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X9)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X6))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).
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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X5),c_Int_OBit0(X6))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X6))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit1(X6))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).
fof(fact_one__less__mult,axiom,
! [X10,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> 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,X10,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [X3,X4] :
( 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,X4,X3))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_divide__less__eq,axiom,
! [X27,X48,X26,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).
fof(fact_divide__le__eq,axiom,
! [X27,X48,X26,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).
fof(fact_less__divide__eq,axiom,
! [X48,X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).
fof(fact_le__divide__eq,axiom,
! [X48,X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).
fof(fact_divide__Numeral1,axiom,
! [X18,X2] :
( ( class_Fields_Ofield(X2)
& class_Int_Onumber__ring(X2) )
=> c_Rings_Oinverse__class_Odivide(X2,X18,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls))) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).
fof(fact_divide__numeral__1,axiom,
! [X1,X2] :
( ( class_Fields_Ofield(X2)
& class_Int_Onumber__ring(X2) )
=> c_Rings_Oinverse__class_Odivide(X2,X1,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).
fof(fact_power__inject__base,axiom,
! [X25,X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13)) = c_Power_Opower__class_Opower(X2,X25,c_Nat_OSuc(X13))
=> ( 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),X25)
=> X1 = X25 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__base) ).
fof(fact_mult__numeral__1,axiom,
! [X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls)),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_mult__numeral__1__right,axiom,
! [X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls))) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(fact_n__less__n__mult__m,axiom,
! [X10,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_n__less__m__mult__n,axiom,
! [X10,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X10)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_nat__lt__two__imp__zero__or__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( X18 = 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_nat__lt__two__imp__zero__or__one) ).
fof(fact_less__special_I4_J,axiom,
! [X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Groups_Oone__class_Oone(X2))
<=> 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_I4_J,axiom,
! [X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Groups_Oone__class_Oone(X2))
<=> 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_I2_J,axiom,
! [X14,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,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_le__special_I2_J,axiom,
! [X14,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,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_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,
! [X17,X74,X75,X76] :
( X76 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X75,X74),X17)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X75) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X17)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X75 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X75) = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).
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_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_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_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_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_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_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_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_even__nat__equiv__def2,axiom,
! [X15] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X24] : X15 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__nat__equiv__def2) ).
fof(fact_number__of__Bit1,axiom,
! [X9,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(X9)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Int_Onumber__class_Onumber__of(X2,X9)),c_Int_Onumber__class_Onumber__of(X2,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_power__Suc__less__one,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13)),c_Groups_Oone__class_Oone(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).
fof(fact_realpow__Suc__le__self,axiom,
! [X13,X57,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X57)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X57,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X57,c_Nat_OSuc(X13)),X57) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).
fof(fact_nat__number__of__mult__left,axiom,
! [X8,X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),X8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),X8)) = 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,X22,X47)),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).
fof(fact_nat__one__le__power,axiom,
! [X13,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X41)
=> 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,X41,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__one__le__power) ).
fof(fact_add__Bit0__Bit0,axiom,
! [X7,X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X8),c_Int_OBit0(X7)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).
fof(fact_rel__simps_I51_J,axiom,
! [X6,X5] :
( c_Int_OBit1(X5) = c_Int_OBit1(X6)
<=> X5 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(fact_Suc__mult__cancel1,axiom,
! [X3,X4,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X4) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X5),X3)
<=> X4 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).
fof(fact_power__gt1,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1) ).
fof(fact_Suc__less__SucD,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X10),c_Nat_OSuc(X13))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_Suc__less__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X4),c_Nat_OSuc(X3))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_Suc__le__mono,axiom,
! [X4,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),c_Nat_OSuc(X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).
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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X6))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).
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,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X5),c_Int_OBit0(X6))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).
fof(fact_zero__less__power__eq__number__of,axiom,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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(X2) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__eq__number__of) ).
fof(fact_zero__le__power__eq__number__of,axiom,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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(X2,c_Groups_Ozero__class_Ozero(X2),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,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X2))
<=> ( 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(X2,X15,c_Groups_Ozero__class_Ozero(X2)) )
| ( 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(X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__zero__eq__number__of) ).
fof(fact_split__zmod,axiom,
! [X5,X3,X63] :
( hBOOL(hAPP(X63,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X5)))
<=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X63,X3)) )
& ( 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)
& X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X63,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))
& X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X63,X58)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(fact_mult__Bit0,axiom,
! [X7,X8] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X8),X7) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).
fof(fact_power__less__zero__eq__number__of,axiom,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X2))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X2,X15,c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__zero__eq__number__of) ).
fof(fact_number__of__Bit0,axiom,
! [X9,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(X9)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X9)),c_Int_Onumber__class_Onumber__of(X2,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).
fof(fact_power__mono__odd,axiom,
! [X17,X18,X13,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X18,X13),c_Power_Opower__class_Opower(X2,X17,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono__odd) ).
fof(fact_less__add__Suc1,axiom,
! [X10,X41] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__add__Suc2,axiom,
! [X10,X41] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_le__Suc__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,c_Nat_OSuc(X3))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
| X4 = c_Nat_OSuc(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__mono,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X10),c_Nat_OSuc(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).
fof(fact_le__number__of__eq__not__less,axiom,
! [X16,X40,X2] :
( ( class_Int_Onumber(X2)
& class_Orderings_Olinorder(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X40),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Int_Onumber__class_Onumber__of(X2,X40)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).
fof(fact_zero__less__power__eq,axiom,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& X15 != c_Groups_Ozero__class_Ozero(X2) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power__eq) ).
fof(fact_zero__le__power__eq,axiom,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__eq) ).
fof(fact_zero__le__odd__power,axiom,
! [X15,X3,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__odd__power) ).
fof(fact_power__le__zero__eq,axiom,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X15,X3),c_Groups_Ozero__class_Ozero(X2))
<=> ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless__eq(X2,X15,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& X15 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__zero__eq) ).
fof(fact_less__Suc__eq__0__disj,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_OSuc(X3))
<=> ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ? [X58] :
( X4 = c_Nat_OSuc(X58)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X58,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).
fof(fact_le__less__Suc__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X4))
<=> X3 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).
fof(fact_numeral__1__eq__1,axiom,
! [X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oone__class_Oone(X2) = c_Int_Onumber__class_Onumber__of(X2,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,
! [X7,X8] : c_Int_OBit0(X8) != c_Int_OBit1(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(fact_rel__simps_I50_J,axiom,
! [X7,X8] : c_Int_OBit1(X8) != c_Int_OBit0(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).
fof(fact_double__number__of__Bit0,axiom,
! [X9,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2)),c_Int_Onumber__class_Onumber__of(X2,X9)) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OBit0(X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_power__Suc2,axiom,
! [X13,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13)) = c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X1,X13),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
! [X32,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,X18,c_Nat_OSuc(X32)) = c_Groups_Otimes__class_Otimes(X2,X18,c_Power_Opower__class_Opower(X2,X18,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).
fof(fact_power__Suc,axiom,
! [X13,X1,X2] :
( class_Power_Opower(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Nat_OSuc(X13)) = c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,X1,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [X32,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X18,X32),X18) = c_Power_Opower__class_Opower(X2,X18,c_Nat_OSuc(X32)) ),
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,
! [X32,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X18,c_Power_Opower__class_Opower(X2,X18,X32)) = c_Power_Opower__class_Opower(X2,X18,c_Nat_OSuc(X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).
fof(fact_power__less__zero__eq,axiom,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X15,X3),c_Groups_Ozero__class_Ozero(X2))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless(X2,X15,c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__zero__eq) ).
fof(fact_less__trans__Suc,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X55,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X41),X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X18] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_add__Suc__shift,axiom,
! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X10),X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Nat_OSuc(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).
fof(fact_add__Suc,axiom,
! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X10),X13) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).
fof(fact_add__Suc__right,axiom,
! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Nat_OSuc(X13)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).
fof(fact_mult__Suc,axiom,
! [X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X10),X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).
fof(fact_mult__Suc__right,axiom,
! [X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Nat_OSuc(X13)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_add__nat__number__of,axiom,
! [X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X47)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).
fof(fact_less__Suc__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_OSuc(X3))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| X4 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__lessD,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X10),X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__le__lessD,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).
fof(fact_Suc__le__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X4),X3)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).
fof(fact_less__eq__Suc__le,axiom,
! [X4,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_Suc__leD,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).
fof(fact_less__Suc__eq__le,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,c_Nat_OSuc(X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
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,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
<=> ? [X42] : X3 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X42)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_Suc__lessI,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> ( c_Nat_OSuc(X10) != X13
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X10),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).
fof(fact_mult__eq__1__iff,axiom,
! [X3,X4] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X3) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X4 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X3 = 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,
! [X13,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X8),X13)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_one__is__add,axiom,
! [X3,X4] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3)
<=> ( ( X4 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X3 = 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,
! [X3,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( X4 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X3 = 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_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_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_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_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_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_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_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_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_less__fun__def,axiom,
! [X66,X67,X2,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X2,X31),X67,X66)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X67,X66)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X66,X67) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_not__square__less__zero,axiom,
! [X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_less__Suc0,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> X3 = 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,
! [X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X47)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).
fof(fact_le__nat__number__of,axiom,
! [X51,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X40),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,c_Int_OPls) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).
fof(fact_rel__simps_I43_J,axiom,
! [X6] :
( c_Int_OMin = c_Int_OBit1(X6)
<=> c_Int_OMin = X6 ),
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_rel__simps_I46_J,axiom,
! [X8] : c_Int_OBit1(X8) != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(fact_rel__simps_I39_J,axiom,
! [X7] : c_Int_OPls != c_Int_OBit1(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(fact_Suc__leI,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X10),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).
fof(fact_less__SucI,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).
fof(fact_le__imp__less__Suc,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).
fof(fact_le__SucI,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Nat_OSuc(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).
fof(fact_not__add__less1,axiom,
! [X55,X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X55),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X41,X55] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X4,X15] :
( c_Power_Opower__class_Opower(tc_Nat_Onat,X15,X4) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X4 = 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,
! [X13] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13) = 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__add,axiom,
! [X3,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ) ),
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_less__le__not__le,axiom,
! [X14,X15,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X2,X14,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_power__0__Suc,axiom,
! [X13,X2] :
( ( class_Power_Opower(X2)
& class_Rings_Osemiring__0(X2) )
=> c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),c_Nat_OSuc(X13)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__Suc) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X1,X25,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ~ c_Orderings_Oord__class_Oless(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_order__less__asym,axiom,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X25,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ~ c_Orderings_Oord__class_Oless(X2,X25,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X2,X14,X15)
| X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_leD,axiom,
! [X18,X17,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> ~ c_Orderings_Oord__class_Oless(X2,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(X2,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_linorder__not__le,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> c_Orderings_Oord__class_Oless(X2,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_nat_Oinject,axiom,
! [X19,X20] :
( c_Nat_OSuc(X20) = c_Nat_OSuc(X19)
<=> X20 = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
fof(fact_Suc__inject,axiom,
! [X17,X18] :
( c_Nat_OSuc(X18) = c_Nat_OSuc(X17)
=> X18 = X17 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(fact_rel__simps_I48_J,axiom,
! [X6,X5] :
( c_Int_OBit0(X5) = c_Int_OBit0(X6)
<=> X5 = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
fof(fact_zero__less__Suc,axiom,
! [X13] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_lessI,axiom,
! [X13] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Nat_OSuc(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(fact_gr0__conv__Suc,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3)
<=> ? [X23] : X3 = c_Nat_OSuc(X23) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_abs__not__less__zero,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_norm__not__less__zero,axiom,
! [X18,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_linorder__cases,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ( X18 != X17
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( X18 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X15,X14,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X14,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X18 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_not__leE,axiom,
! [X18,X17,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> c_Orderings_Oord__class_Oless(X2,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_leI,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_linorder__le__cases,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_not__one__less__zero,axiom,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_not__one__le__zero,axiom,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(fact_neg__one__odd__power,axiom,
! [X18,X2] :
( class_Int_Onumber__ring(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__odd__power) ).
fof(fact_neg__one__even__odd__power,axiom,
! [X18,X2] :
( class_Int_Onumber__ring(X2)
=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Groups_Oone__class_Oone(X2) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__even__odd__power) ).
fof(fact_linorder__neqE__nat,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_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X18,X2] :
( class_Orderings_Opreorder(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,X18,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_Suc__not__Zero,axiom,
! [X10] : c_Nat_OSuc(X10) != 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,
! [X11] : c_Nat_OSuc(X11) != 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,
! [X10] : c_Nat_OSuc(X10) != 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,
! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).
fof(fact_nat_Osimps_I2_J,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(fact_Zero__neq__Suc,axiom,
! [X10] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).
fof(fact_Suc__n__not__n,axiom,
! [X13] : c_Nat_OSuc(X13) != X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(fact_n__not__Suc__n,axiom,
! [X13] : X13 != c_Nat_OSuc(X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_not__less0,axiom,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__nat__zero__code,axiom,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_less__zeroE,axiom,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,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,
! [X6] :
( c_Int_OPls = c_Int_OBit0(X6)
<=> c_Int_OPls = X6 ),
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,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_less__not__refl,axiom,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_rel__simps_I45_J,axiom,
! [X8] : c_Int_OBit0(X8) != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [X7] : c_Int_OMin != c_Int_OBit0(X7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_odd__pos,axiom,
! [X13] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__pos) ).
fof(fact_real__sqrt__two__gt__one,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__one) ).
fof(fact_real__sqrt__two__gt__zero,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__two__gt__zero) ).
fof(fact_real__sqrt__two__ge__zero,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__two__ge__zero) ).
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_le__fun__def,axiom,
! [X66,X67,X2,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X67,X66)
<=> ! [X68] : c_Orderings_Oord__class_Oless__eq(X31,hAPP(X67,X68),hAPP(X66,X68)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_power2__i,axiom,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Complex_Oii,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power2__i) ).
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_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_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_IH,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,v_na____)
=> ( X23 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X72] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,X72,X23)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IH) ).
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_calculation,axiom,
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
=> ? [X72] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,X72,v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X64,X65,X43,X57,X32,X25] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X32),X57) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X43,X65),X64)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X43,X65),X64),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X64)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X65,X32) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X64,X65,X43,X57,X32,X25] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X32),X57) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X43,X65),X64)
=> ( 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,X43,X65),X64))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X65) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
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,
! [X57,X32,X64,X65,X25] :
( 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,X25,X65),X64),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X32),X57))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X64)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X25)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X65,X32) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X57,X32,X64,X65,X25] :
( 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,X25,X65),X64),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X32),X57))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X57)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X64)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X65) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_zmult2__lemma__aux4,axiom,
! [X32,X25,X57,X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X38)),X57),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).
fof(fact_zmult2__lemma__aux1,axiom,
! [X32,X57,X25,X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X57)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,X38),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X38)),X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).
fof(fact_real__sqrt__mult__self__sum__ge__zero,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X18),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17,X17)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
fof(fact_le__real__sqrt__sumsq,axiom,
! [X17,X18] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X18),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X17,X17)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__real__sqrt__sumsq) ).
fof(fact_convex__bound__lt,axiom,
! [X22,X56,X17,X1,X18,X2] :
( class_Rings_Olinordered__semiring__1__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X1)
=> ( c_Orderings_Oord__class_Oless(X2,X17,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X56)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X22)
=> ( c_Groups_Oplus__class_Oplus(X2,X56,X22) = c_Groups_Oone__class_Oone(X2)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X56,X18),c_Groups_Otimes__class_Otimes(X2,X22,X17)),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_convex__bound__le,axiom,
! [X22,X56,X17,X1,X18,X2] :
( class_Rings_Olinordered__semiring__1(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X56)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X22)
=> ( c_Groups_Oplus__class_Oplus(X2,X56,X22) = c_Groups_Oone__class_Oone(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X56,X18),c_Groups_Otimes__class_Otimes(X2,X22,X17)),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_zmult2__lemma__aux2,axiom,
! [X32,X57,X25,X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X57)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X57,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,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X38)),X57),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,
! [X32,X25,X57,X38] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X38)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X25)
=> 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,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X38)),X57)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).
fof(fact_add__frac__eq,axiom,
! [X9,X18,X21,X17,X2] :
( class_Fields_Ofield(X2)
=> ( X17 != c_Groups_Ozero__class_Ozero(X2)
=> ( X21 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Rings_Oinverse__class_Odivide(X2,X9,X21)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X21),c_Groups_Otimes__class_Otimes(X2,X9,X17)),c_Groups_Otimes__class_Otimes(X2,X17,X21)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X14,X15,X2] :
( class_Rings_Olinordered__ring__strict(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,X15,X15),c_Groups_Otimes__class_Otimes(X2,X14,X14)))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X2)
| X14 != c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X14,X15,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X15,X15),c_Groups_Otimes__class_Otimes(X2,X14,X14)),c_Groups_Ozero__class_Ozero(X2))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X2)
& X14 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_combine__common__factor,axiom,
! [X38,X25,X52,X1,X2] :
( class_Rings_Osemiring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X52),c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X25,X52),X38)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X52),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_crossproduct__noteq,axiom,
! [X53,X48,X26,X27,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( ( X27 != X26
& X48 != X53 )
<=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),c_Groups_Otimes__class_Otimes(X2,X26,X53)) != c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X27,X53),c_Groups_Otimes__class_Otimes(X2,X26,X48)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X54,X15,X14,X16,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X16,X14),c_Groups_Otimes__class_Otimes(X2,X15,X54)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X16,X54),c_Groups_Otimes__class_Otimes(X2,X15,X14))
<=> ( X16 = X15
| X14 = X54 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_left__add__mult__distrib,axiom,
! [X8,X55,X56,X41] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X56),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X56),X8)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X55),X56),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_q__neg__lemma,axiom,
! [X64,X65,X43] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X43,X65),X64),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),X64)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X65,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,
! [X64,X65,X43] :
( 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,X43,X65),X64))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X64,X43)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X65) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_mod__add__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),c_Divides_Odiv__class_Omod(X2,X25,X38)),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__eq) ).
fof(fact_mod__mult__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),c_Divides_Odiv__class_Omod(X2,X25,X38)),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__eq) ).
fof(fact_gt__half__sum,axiom,
! [X25,X1,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2))),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).
fof(fact_less__half__sum,axiom,
! [X25,X1,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> c_Orderings_Oord__class_Oless(X2,X1,c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).
fof(fact_divide__strict__left__mono,axiom,
! [X38,X1,X25,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25))
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X38,X1),c_Rings_Oinverse__class_Odivide(X2,X38,X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_divide__left__mono,axiom,
! [X38,X1,X25,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X38,X1),c_Rings_Oinverse__class_Odivide(X2,X38,X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).
fof(fact_divide__strict__left__mono__neg,axiom,
! [X38,X25,X1,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25))
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X38,X1),c_Rings_Oinverse__class_Odivide(X2,X38,X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_divide__left__mono__neg,axiom,
! [X38,X25,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X38,X1),c_Rings_Oinverse__class_Odivide(X2,X38,X25)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X21,X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X9),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X9,X21)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X21))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_power__Suc__less,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,X1,X13)),c_Power_Opower__class_Opower(X2,X1,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_mod__add__cong,axiom,
! [X43,X25,X45,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( c_Divides_Odiv__class_Omod(X2,X1,X38) = c_Divides_Odiv__class_Omod(X2,X45,X38)
=> ( c_Divides_Odiv__class_Omod(X2,X25,X38) = c_Divides_Odiv__class_Omod(X2,X43,X38)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X45,X43),X38) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__cong) ).
fof(fact_mod__mult__cong,axiom,
! [X43,X25,X45,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> ( c_Divides_Odiv__class_Omod(X2,X1,X38) = c_Divides_Odiv__class_Omod(X2,X45,X38)
=> ( c_Divides_Odiv__class_Omod(X2,X25,X38) = c_Divides_Odiv__class_Omod(X2,X43,X38)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X45,X43),X38) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__cong) ).
fof(fact_odd__less__0,axiom,
! [X54] :
( 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),X54),X54),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X60,X17,X57,X18,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),X57)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X17),X60)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X18,X17)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X57,X60)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_norm__mult__less,axiom,
! [X60,X17,X57,X18,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),X57)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X17),X60)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X57,X60)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X33,X34,X35,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),c_Groups_Otimes__class_Otimes(X2,X34,X33)) = c_Groups_Otimes__class_Otimes(X2,X34,c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),X33)) ),
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,
! [X33,X34,X35,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),c_Groups_Otimes__class_Otimes(X2,X34,X33)) = c_Groups_Otimes__class_Otimes(X2,X36,c_Groups_Otimes__class_Otimes(X2,X35,c_Groups_Otimes__class_Otimes(X2,X34,X33))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_frac__less2,axiom,
! [X21,X9,X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X9)
=> ( c_Orderings_Oord__class_Oless(X2,X9,X21)
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X21),c_Rings_Oinverse__class_Odivide(X2,X17,X9)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).
fof(fact_frac__less,axiom,
! [X21,X9,X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X9,X21)
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X21),c_Rings_Oinverse__class_Odivide(X2,X17,X9)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).
fof(fact_mult__strict__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,X39)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,X39)
=> ( 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),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,X39)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,X39)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_frac__le,axiom,
! [X21,X9,X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X9,X21)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X21),c_Rings_Oinverse__class_Odivide(X2,X17,X9)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).
fof(fact_mult__mono_H,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Oordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,X39)
=> ( 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),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Oordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,X39)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X39)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_abs__mult__less,axiom,
! [X39,X25,X38,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oabs__class_Oabs(X2,X1),X38)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oabs__class_Oabs(X2,X25),X39)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)),c_Groups_Otimes__class_Otimes(X2,X38,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__ring(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X18),c_Groups_Otimes__class_Otimes(X2,X17,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_power__less__power__Suc,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,X1,X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X25,X38,X1,X2] :
( class_Rings_Olinordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X25,X38,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X25,X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X25,X1,X38,X2] :
( class_Rings_Olinordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X25,X1,X38,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X48,X27),c_Groups_Otimes__class_Otimes(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless(X2,X27,X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X25,X38,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X25,X1,X38,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X48,X27),c_Groups_Otimes__class_Otimes(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless__eq(X2,X27,X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X48,X27),c_Groups_Otimes__class_Otimes(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless(X2,X26,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X48,X27),c_Groups_Otimes__class_Otimes(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless__eq(X2,X26,X27) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X14,X15,X26,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X26)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X26,X15),c_Power_Opower__class_Opower(X2,X26,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,
! [X13,X10,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X10),c_Power_Opower__class_Opower(X2,X1,X13))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_power__increasing__iff,axiom,
! [X14,X15,X26,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X26)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X26,X15),c_Power_Opower__class_Opower(X2,X26,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,
! [X13,X10,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X10),c_Power_Opower__class_Opower(X2,X1,X13))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_left__distrib__number__of,axiom,
! [X22,X25,X1,X31] :
( ( class_Int_Onumber(X31)
& class_Rings_Osemiring(X31) )
=> c_Groups_Otimes__class_Otimes(X31,c_Groups_Oplus__class_Oplus(X31,X1,X25),c_Int_Onumber__class_Onumber__of(X31,X22)) = c_Groups_Oplus__class_Oplus(X31,c_Groups_Otimes__class_Otimes(X31,X1,c_Int_Onumber__class_Onumber__of(X31,X22)),c_Groups_Otimes__class_Otimes(X31,X25,c_Int_Onumber__class_Onumber__of(X31,X22))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).
fof(fact_right__distrib__number__of,axiom,
! [X38,X25,X22,X31] :
( ( class_Int_Onumber(X31)
& class_Rings_Osemiring(X31) )
=> c_Groups_Otimes__class_Otimes(X31,c_Int_Onumber__class_Onumber__of(X31,X22),c_Groups_Oplus__class_Oplus(X31,X25,X38)) = c_Groups_Oplus__class_Oplus(X31,c_Groups_Otimes__class_Otimes(X31,c_Int_Onumber__class_Onumber__of(X31,X22),X25),c_Groups_Otimes__class_Otimes(X31,c_Int_Onumber__class_Onumber__of(X31,X22),X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).
fof(fact_real__mult__less__iff1,axiom,
! [X14,X15,X54] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X54),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X54))
<=> 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,
! [X13,X10,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X41)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X41,X10),c_Power_Opower__class_Opower(tc_Nat_Onat,X41,X13))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X3,X4,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,X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X14,X15,X54] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X15,X54),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X14,X54))
<=> 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,X54] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X54)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X54,X15),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X54,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,
! [X3,X5,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,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,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__le__cancel1,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3))
<=> ( 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,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X3,X4,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,X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_power__strict__decreasing,axiom,
! [X1,X69,X13,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X69)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X69),c_Power_Opower__class_Opower(X2,X1,X13)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__decreasing,axiom,
! [X1,X69,X13,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X69)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X69),c_Power_Opower__class_Opower(X2,X1,X13)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X48,X27),c_Groups_Otimes__class_Otimes(X2,X48,X26))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
& c_Orderings_Oord__class_Oless(X2,X27,X26) )
| ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless(X2,X26,X27) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X26,X48,X27,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),c_Groups_Otimes__class_Otimes(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
& c_Orderings_Oord__class_Oless(X2,X27,X26) )
| ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless(X2,X26,X27) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_divide__add__eq__iff,axiom,
! [X17,X18,X21,X2] :
( class_Fields_Ofield(X2)
=> ( X21 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X21),X17) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X18,c_Groups_Otimes__class_Otimes(X2,X21,X17)),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [X21,X18,X17,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( X17 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),X21) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X18,c_Groups_Otimes__class_Otimes(X2,X21,X17)),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).
fof(fact_add__divide__eq__iff,axiom,
! [X17,X18,X21,X2] :
( class_Fields_Ofield(X2)
=> ( X21 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oplus__class_Oplus(X2,X18,c_Rings_Oinverse__class_Odivide(X2,X17,X21)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X21,X18),X17),X21) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__num__frac,axiom,
! [X18,X21,X17,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( X17 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oplus__class_Oplus(X2,X21,c_Rings_Oinverse__class_Odivide(X2,X18,X17)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X18,c_Groups_Otimes__class_Otimes(X2,X21,X17)),X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(fact_power__strict__mono,axiom,
! [X13,X25,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( 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),X13)
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_times__divide__times__eq,axiom,
! [X9,X21,X17,X18,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Rings_Oinverse__class_Odivide(X2,X21,X9)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Otimes__class_Otimes(X2,X18,X21),c_Groups_Otimes__class_Otimes(X2,X17,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X39,X38,X25,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Oplus__class_Oplus(X2,X38,X39)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X39)) ),
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,
! [X33,X34,X35,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),c_Groups_Otimes__class_Otimes(X2,X34,X33)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X34),c_Groups_Otimes__class_Otimes(X2,X35,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_zmod__simps_I1_J,axiom,
! [X25,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).
fof(fact_zmod__simps_I4_J,axiom,
! [X25,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).
fof(fact_zmod__simps_I2_J,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Divides_Odiv__class_Omod(X2,X25,X38)),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).
fof(fact_mod__add__left__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).
fof(fact_mod__mult__left__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X2,X1,X38),X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).
fof(fact_mod__add__right__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Divides_Odiv__class_Omod(X2,X25,X38)),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).
fof(fact_mod__mult__right__eq,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) = c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,c_Divides_Odiv__class_Omod(X2,X25,X38)),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).
fof(fact_add__number__of__left,axiom,
! [X21,X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X9),X21)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X9)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).
fof(fact_mult__number__of__left,axiom,
! [X21,X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X9),X21)) = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X9)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X39,X38,X25,X1,X57,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( X57 != c_Groups_Ozero__class_Ozero(X2)
=> ( ( X1 = X25
& X38 != X39 )
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Otimes__class_Otimes(X2,X57,X38)) != c_Groups_Oplus__class_Oplus(X2,X25,c_Groups_Otimes__class_Otimes(X2,X57,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_zpower__zmod,axiom,
! [X17,X10,X18] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X18,X10),X17),X10) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X18,X17),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zmod) ).
fof(fact_zmod__simps_I3_J,axiom,
! [X38,X25,X1] : 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,X25,X38)),X38) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X25),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).
fof(fact_zmod__zmult1__eq,axiom,
! [X38,X25,X1] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X25),X38) = 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,X25,X38)),X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [X27,X26,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [X21,X18,X17,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless(X2,X18,c_Groups_Otimes__class_Otimes(X2,X21,X17))
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_pos__less__divide__eq,axiom,
! [X26,X27,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__divide__le__eq,axiom,
! [X27,X26,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [X21,X18,X17,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,c_Groups_Otimes__class_Otimes(X2,X21,X17))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_pos__le__divide__eq,axiom,
! [X26,X27,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [X27,X26,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_neg__divide__le__eq,axiom,
! [X27,X26,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [X18,X21,X17,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X21,X17),X18)
=> c_Orderings_Oord__class_Oless(X2,X21,c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [X18,X21,X17,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X21,X17),X18)
=> c_Orderings_Oord__class_Oless__eq(X2,X21,c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_neg__less__divide__eq,axiom,
! [X26,X27,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_neg__le__divide__eq,axiom,
! [X26,X27,X48,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_abs__triangle__ineq,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25)),c_Groups_Oplus__class_Oplus(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_norm__triangle__ineq,axiom,
! [X17,X18,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oplus__class_Oplus(X2,X18,X17)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_RealVector_Onorm__class_Onorm(X2,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_norm__mult__ineq,axiom,
! [X17,X18,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_RealVector_Onorm__class_Onorm(X2,X17))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_power__gt1__lemma,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,X1,X13))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_add__less__imp__less__right,axiom,
! [X25,X38,X1,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X38))
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X26,X48,X27,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X27,X48),c_Groups_Oplus__class_Oplus(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless(X2,X27,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X25,X1,X38,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X38,X1),c_Groups_Oplus__class_Oplus(X2,X38,X25))
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X26,X27,X48,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X48,X27),c_Groups_Oplus__class_Oplus(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless(X2,X27,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_add__le__imp__le__right,axiom,
! [X25,X38,X1,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X38))
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X26,X48,X27,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X27,X48),c_Groups_Oplus__class_Oplus(X2,X26,X48))
<=> c_Orderings_Oord__class_Oless__eq(X2,X27,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X25,X1,X38,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X38,X1),c_Groups_Oplus__class_Oplus(X2,X38,X25))
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X26,X27,X48,X2] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X48,X27),c_Groups_Oplus__class_Oplus(X2,X48,X26))
<=> c_Orderings_Oord__class_Oless__eq(X2,X27,X26) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_self__quotient__aux2,axiom,
! [X32,X57,X1] :
( 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,X57,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X32))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X57)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [X32,X57,X1] :
( 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,X57,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,X32))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X57,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X32) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X17,X18,X38,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X38,c_RealVector_Onorm__class_Onorm(X2,X17)))
=> X18 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__less__cancel1,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X4),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3))
<=> ( 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,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X3,X5,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X5),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,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,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_power__mono__even,axiom,
! [X17,X18,X13,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X18),c_Groups_Oabs__class_Oabs(X2,X17))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X18,X13),c_Power_Opower__class_Opower(X2,X17,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono__even) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X3))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X3,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X25,X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Power_Opower__class_Opower(X2,X1,X13) = c_Power_Opower__class_Opower(X2,X25,X13)
=> ( 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),X25)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13)
=> X1 = X25 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_divide__strict__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X38),c_Rings_Oinverse__class_Odivide(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Olinordered__comm__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_divide__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X38),c_Rings_Oinverse__class_Odivide(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).
fof(fact_power__mono,axiom,
! [X13,X25,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Oordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Oordered__comm__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Oordered__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_divide__strict__right__mono__neg,axiom,
! [X38,X1,X25,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X38),c_Rings_Oinverse__class_Odivide(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X38,X1,X25,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X38,X1,X25,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_divide__right__mono__neg,axiom,
! [X38,X25,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X25,X38),c_Rings_Oinverse__class_Odivide(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).
fof(fact_mult__right__mono__neg,axiom,
! [X38,X1,X25,X2] :
( class_Rings_Oordered__ring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X38,X1,X25,X2] :
( class_Rings_Oordered__ring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__right__le__one__le,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17),X18) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,c_Groups_Oone__class_Oone(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X17,X18),X18) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__power__ineq,axiom,
! [X13,X18,X2] :
( class_RealVector_Oreal__normed__algebra__1(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,c_Power_Opower__class_Opower(X2,X18,X13)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_power__strict__increasing,axiom,
! [X1,X69,X13,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X69)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X1,X69)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_power__increasing,axiom,
! [X1,X69,X13,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X69)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X1,X69)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_add__strict__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,X39)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless(X2,X38,X39)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,X39)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__mono,axiom,
! [X39,X38,X25,X1,X2] :
( class_Groups_Oordered__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X38,X39)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X39)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [X17,X18,X38] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X38,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X38,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X17)))
=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_mod__pos__neg__trivial,axiom,
! [X25,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_Oplus__class_Oplus(tc_Int_Oint,X1,X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).
fof(fact_nonzero__power__divide,axiom,
! [X13,X1,X25,X2] :
( class_Fields_Ofield(X2)
=> ( X25 != c_Groups_Ozero__class_Ozero(X2)
=> c_Power_Opower__class_Opower(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25),X13) = c_Rings_Oinverse__class_Odivide(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X14,X15,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X15,X15),c_Groups_Otimes__class_Otimes(X2,X14,X14)) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X2)
& X14 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_mod__mult__mult2,axiom,
! [X25,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) = c_Groups_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Omod(X2,X1,X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X25,X10,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X10),c_Groups_Otimes__class_Otimes(X2,X25,X10)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mod__mult__mult1,axiom,
! [X25,X1,X38,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) = c_Groups_Otimes__class_Otimes(X2,X38,c_Divides_Odiv__class_Omod(X2,X1,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).
fof(fact_divide_Oadd,axiom,
! [X46,X17,X18,X2] :
( class_RealVector_Oreal__normed__field(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X18,X17),X46) = c_Groups_Oplus__class_Oplus(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X46),c_Rings_Oinverse__class_Odivide(X2,X17,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).
fof(fact_add__divide__distrib,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X38),c_Rings_Oinverse__class_Odivide(X2,X25,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).
fof(fact_power__divide,axiom,
! [X13,X25,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Power_Opower__class_Opower(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25),X13) = c_Rings_Oinverse__class_Odivide(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__divide) ).
fof(fact_power__mult__distrib,axiom,
! [X13,X25,X1,X2] :
( class_Groups_Ocomm__monoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X13) = c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X1,X13),c_Power_Opower__class_Opower(X2,X25,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X32,X17,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17),X32) = c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X18,X32),c_Power_Opower__class_Opower(X2,X17,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Ocomm__semiring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X46,X17,X18,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X18,X17),X46) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X46),c_Groups_Otimes__class_Otimes(X2,X17,X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X25,X45,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,X45),X25) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Otimes__class_Otimes(X2,X45,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_mult__right_Oadd,axiom,
! [X17,X18,X44,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,X44,c_Groups_Oplus__class_Oplus(X2,X18,X17)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X44,X18),c_Groups_Otimes__class_Otimes(X2,X44,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X43,X25,X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Oplus__class_Oplus(X2,X25,X43)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Otimes__class_Otimes(X2,X1,X43)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X21,X17,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X18,c_Groups_Oplus__class_Oplus(X2,X17,X21)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17),c_Groups_Otimes__class_Otimes(X2,X18,X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mod__mult__self2,axiom,
! [X38,X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Otimes__class_Otimes(X2,X25,X38)),X25) = c_Divides_Odiv__class_Omod(X2,X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2) ).
fof(fact_mod__mult__self1,axiom,
! [X25,X38,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Otimes__class_Otimes(X2,X38,X25)),X25) = c_Divides_Odiv__class_Omod(X2,X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X32,X37,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X18,X37),c_Power_Opower__class_Opower(X2,X18,X32)) = c_Power_Opower__class_Opower(X2,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X37,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X13,X10,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13)) = c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X1,X10),c_Power_Opower__class_Opower(X2,X1,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_real__mult__less__mono2,axiom,
! [X17,X18,X21] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X21)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21,X18),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_zmult__zless__mono2,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X41,X55)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X41),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X8,X55)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X8)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X41),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X55)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_zadd__zless__mono,axiom,
! [X21,X61,X9,X62] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X62,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X61,X21)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X62,X61),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X21)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_add__less__mono,axiom,
! [X7,X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X7)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X8),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_add__le__mono,axiom,
! [X7,X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X8),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_mult__le__mono,axiom,
! [X7,X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X7)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X7)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X1,X25,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X25,X1))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_abs__eq__mult,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__ring__abs(X2)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
| c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2)) ) )
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
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,
! [X9,X29,X30] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X30,X29),X9) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X30,X9),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X29,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X9,X29,X30] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X29),X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X30,X9),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X29,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X8,X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X21,X17,X18] : c_Power_Opower__class_Opower(tc_Int_Oint,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X18,X17),c_Power_Opower__class_Opower(tc_Int_Oint,X18,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X29,X30,X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X29)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X30),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X29)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X13,X10,X8] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X10),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
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_divide__less__0__iff,axiom,
! [X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X27,X26),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).
fof(fact_divide__le__0__iff,axiom,
! [X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X27,X26),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).
fof(fact_mult__le__0__iff,axiom,
! [X26,X27,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X26),c_Groups_Ozero__class_Ozero(X2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X26) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__less__divide__iff,axiom,
! [X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X27,X26))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X26) )
| ( c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).
fof(fact_zero__le__divide__iff,axiom,
! [X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X27,X26))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X26) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X26,X27,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X27,X26))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X26) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ),
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_divide__neg__pos,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).
fof(fact_divide__pos__neg,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless(X2,X17,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).
fof(fact_mult__neg__pos,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X25,X1),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_divide__nonneg__neg,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless(X2,X17,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).
fof(fact_divide__nonpos__pos,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_split__mult__neg__le,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
& c_Orderings_Oord__class_Oless__eq(X2,X25,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_Groups_Ozero__class_Ozero(X2),X25) ) )
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__cancel__semiring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X25,X1),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_add__neg__neg,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonpos__neg,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__nonpos,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),c_Groups_Ozero__class_Ozero(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_less__1__mult,axiom,
! [X13,X10,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X10)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X13)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Otimes__class_Otimes(X2,X10,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_divide__pos__pos,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).
fof(fact_add__pos__pos,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__nonneg__pos,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__nonneg,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_mult__pos__pos,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__semiring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_divide__nonneg__pos,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(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),X25)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_split__mult__pos__le,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__ring(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),X25) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2)) ) )
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__cancel__semiring(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),X25)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_divide__neg__neg,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X17,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).
fof(fact_mult__neg__neg,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_divide__nonpos__neg,axiom,
! [X17,X18,X2] :
( class_Fields_Olinordered__field(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless(X2,X17,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X25,X1,X2] :
( class_Rings_Oordered__ring(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2))
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X25)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_add__gr__0,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_real__0__le__divide__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X15,X14))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_le__cube,axiom,
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_add__strict__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X38,X1),c_Groups_Oplus__class_Oplus(X2,X38,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact_add__right__mono,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),c_Groups_Oplus__class_Oplus(X2,X25,X38)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__ab__semigroup__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X38,X1),c_Groups_Oplus__class_Oplus(X2,X38,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_one__less__power,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X2,X1,X13)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_add__strict__increasing2,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X38)
=> c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Oplus__class_Oplus(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X38)
=> c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Oplus__class_Oplus(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_pos__add__strict,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X38)
=> c_Orderings_Oord__class_Oless(X2,X25,c_Groups_Oplus__class_Oplus(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__increasing,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X38)
=> c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Oplus__class_Oplus(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X1,X25,X38,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X38)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> c_Orderings_Oord__class_Oless__eq(X2,X25,c_Groups_Oplus__class_Oplus(X2,X1,X38)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_power__one__over,axiom,
! [X13,X1,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X2,X1,X13)) = c_Power_Opower__class_Opower(X2,c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oone__class_Oone(X2),X1),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__over) ).
fof(fact_zero__le__power__iff,axiom,
! [X3,X27,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X27,X3))
<=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__iff) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X41,X55)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X41,X8),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X8),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X21,X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X18),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X21,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_zadd__left__mono,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X41),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_add__le__mono1,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X8),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_mult__le__mono1,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X41,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X55,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X41),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X8,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X10,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X1,X10),X10) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2)),X10) ),
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,
! [X1,X10,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X10,c_Groups_Otimes__class_Otimes(X2,X1,X10)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_abs__add__abs,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25))) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_real__mult__order,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X3))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> 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,X18,X17)) ) ),
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,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> 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,X18,X17)) ) ),
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,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
=> 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,X18,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_mult__divide__mult__cancel__left,axiom,
! [X25,X1,X38,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( X38 != c_Groups_Ozero__class_Ozero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Otimes__class_Otimes(X2,X38,X1),c_Groups_Otimes__class_Otimes(X2,X38,X25)) = c_Rings_Oinverse__class_Odivide(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).
fof(fact_mult__divide__mult__cancel__right,axiom,
! [X25,X1,X38,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( X38 != c_Groups_Ozero__class_Ozero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Otimes__class_Otimes(X2,X1,X38),c_Groups_Otimes__class_Otimes(X2,X25,X38)) = c_Rings_Oinverse__class_Odivide(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X3,X15] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X15),X3))
<=> ( X15 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X27,X27))
<=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,X27,X27))
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X27,X27),c_Groups_Ozero__class_Ozero(X2))
<=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X27,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,X27,X27),c_Groups_Ozero__class_Ozero(X2))
<=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oplus__class_Oplus(X2,X27,X27),c_Groups_Ozero__class_Ozero(X2))
<=> c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),X25) ),
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,
! [X34,X35,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),X34) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X34),X35) ),
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,
! [X38,X25,X1,X2] :
( class_Groups_Oab__semigroup__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,X25,X38)) ),
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,
! [X38,X25,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X38) = c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,X25,X38)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_power__commutes,axiom,
! [X13,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Power_Opower__class_Opower(X2,X1,X13),X1) = c_Groups_Otimes__class_Otimes(X2,X1,c_Power_Opower__class_Opower(X2,X1,X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Oab__semigroup__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) = c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Otimes__class_Otimes(X2,X25,X38)) ),
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,
! [X34,X35,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X35),X34) = c_Groups_Otimes__class_Otimes(X2,X36,c_Groups_Otimes__class_Otimes(X2,X35,X34)) ),
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,
! [X39,X38,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,X38,X39)) = c_Groups_Oplus__class_Oplus(X2,c_Groups_Oplus__class_Oplus(X2,X1,X38),X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_times__divide__eq__right,axiom,
! [X38,X25,X1,X2] :
( class_Rings_Odivision__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Rings_Oinverse__class_Odivide(X2,X25,X38)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X38) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X33,X34,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X36,c_Groups_Otimes__class_Otimes(X2,X34,X33)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Otimes__class_Otimes(X2,X36,X34),X33) ),
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,
! [X39,X38,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oplus__class_Oplus(X2,X38,X39)) = c_Groups_Oplus__class_Oplus(X2,X38,c_Groups_Oplus__class_Oplus(X2,X1,X39)) ),
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,
! [X33,X34,X36,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X36,c_Groups_Otimes__class_Otimes(X2,X34,X33)) = c_Groups_Otimes__class_Otimes(X2,X34,c_Groups_Otimes__class_Otimes(X2,X36,X33)) ),
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,
! [X13,X10,X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)) = c_Power_Opower__class_Opower(X2,c_Power_Opower__class_Opower(X2,X1,X10),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X32,X37,X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,c_Power_Opower__class_Opower(X2,X18,X37),X32) = c_Power_Opower__class_Opower(X2,X18,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X37,X32)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_real__divide__square__eq,axiom,
! [X1,X57] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X57,X1),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X57,X57)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).
fof(fact_zadd__assoc,axiom,
! [X28,X29,X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X29),X28) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X29,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X8,X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zpower__zpower,axiom,
! [X21,X17,X18] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X18,X17),X21) = c_Power_Opower__class_Opower(tc_Int_Oint,X18,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X17,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_real__mult__assoc,axiom,
! [X28,X29,X30] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X30,X29),X28) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X30,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X29,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_zmult__assoc,axiom,
! [X28,X29,X30] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X30,X29),X28) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X30,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X29,X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X8,X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13),X8) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X21,X17,X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,X21)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X17,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X21,X17,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X54,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X54)
| X16 = X54 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X3,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,X3))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X3,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,X3))
<=> ( X3 = 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_add1__zle__eq,axiom,
! [X54,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)),X54)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X54,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X54,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_abs__div__pos,axiom,
! [X18,X17,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X17)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oabs__class_Oabs(X2,X18),X17) = c_Groups_Oabs__class_Oabs(X2,c_Rings_Oinverse__class_Odivide(X2,X18,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div__pos) ).
fof(fact_abs__mult__pos,axiom,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X18)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oabs__class_Oabs(X2,X17),X18) = c_Groups_Oabs__class_Oabs(X2,c_Groups_Otimes__class_Otimes(X2,X17,X18)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_less__add__eq__less,axiom,
! [X13,X10,X7,X8] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X7)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_add__lessD1,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X55),X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_add__leD1,axiom,
! [X13,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X8),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X13,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X8),X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_frac__eq__eq,axiom,
! [X16,X15,X54,X14,X2] :
( class_Fields_Ofield(X2)
=> ( X14 != c_Groups_Ozero__class_Ozero(X2)
=> ( X54 != c_Groups_Ozero__class_Ozero(X2)
=> ( c_Rings_Oinverse__class_Odivide(X2,X15,X14) = c_Rings_Oinverse__class_Odivide(X2,X16,X54)
<=> c_Groups_Otimes__class_Otimes(X2,X15,X54) = c_Groups_Otimes__class_Otimes(X2,X16,X14) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X14,X15,X2] :
( class_Groups_Oordered__comm__monoid__add(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X14)
=> ( c_Groups_Oplus__class_Oplus(X2,X15,X14) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X2)
& X14 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_less__nat__number__of,axiom,
! [X51,X40] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X40),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,X51)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X51) )
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X40,X51) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).
fof(fact_power__inject__exp,axiom,
! [X3,X4,X27,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),X27)
=> ( c_Power_Opower__class_Opower(X2,X27,X4) = c_Power_Opower__class_Opower(X2,X27,X3)
<=> X4 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_zero__less__power,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X1,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_one__le__power,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),X1)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Power_Opower__class_Opower(X2,X1,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X13,X1,X2] :
( 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),c_Power_Opower__class_Opower(X2,X1,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_odd__nonzero,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21),X21) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X3,X4,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,X4) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3)
<=> X4 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_le__imp__0__less,axiom,
! [X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21)
=> 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),X21)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_neg__mod__conj,axiom,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,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,X1,X25),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__conj) ).
fof(fact_neg__mod__sign,axiom,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,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,X1,X25),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,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> ( 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,X25))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25),X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__conj) ).
fof(fact_pos__mod__sign,axiom,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> 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,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__sign) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X13,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> 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,X18,X13)) ),
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,
! [X10,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X10,X10) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2)),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X21,X9] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X9,X21)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Groups_Oone__class_Oone(tc_Int_Oint)),X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_pos__mod__bound,axiom,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25),X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__mod__bound) ).
fof(fact_zmod__le__nonneg__dividend,axiom,
! [X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X10)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X10,X8),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).
fof(fact_neg__mod__bound,axiom,
! [X1,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__mod__bound) ).
fof(fact_power__even__abs__number__of,axiom,
! [X18,X9,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9))
=> c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X18),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9)) = c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__abs__number__of) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [X27,X16,X26,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)) = X27
<=> ( ( c_Int_Onumber__class_Onumber__of(X2,X16) != c_Groups_Ozero__class_Ozero(X2)
=> X26 = c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)) )
& ( c_Int_Onumber__class_Onumber__of(X2,X16) = c_Groups_Ozero__class_Ozero(X2)
=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [X16,X26,X27,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( X27 = c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ( ( c_Int_Onumber__class_Onumber__of(X2,X16) != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)) = X26 )
& ( c_Int_Onumber__class_Onumber__of(X2,X16) = c_Groups_Ozero__class_Ozero(X2)
=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_le__funE,axiom,
! [X15,X66,X67,X2,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X67,X66)
=> c_Orderings_Oord__class_Oless__eq(X31,hAPP(X67,X15),hAPP(X66,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X15,X66,X67,X2,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X67,X66)
=> c_Orderings_Oord__class_Oless__eq(X31,hAPP(X67,X15),hAPP(X66,X15)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_trans__less__add1,axiom,
! [X10,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_trans__less__add2,axiom,
! [X10,X55,X41] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_trans__le__add1,axiom,
! [X10,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_trans__le__add2,axiom,
! [X10,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X55)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_norm__divide,axiom,
! [X25,X1,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_RealVector_Oreal__normed__field(X2) )
=> c_RealVector_Onorm__class_Onorm(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__divide) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [X16,X48,X26,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Rings_Oinverse__class_Odivide(X2,X26,X48) = c_Int_Onumber__class_Onumber__of(X2,X16)
<=> ( ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> X26 = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48) )
& ( X48 = c_Groups_Ozero__class_Ozero(X2)
=> c_Int_Onumber__class_Onumber__of(X2,X16) = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [X48,X26,X16,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Int_Onumber__class_Onumber__of(X2,X16) = c_Rings_Oinverse__class_Odivide(X2,X26,X48)
<=> ( ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48) = X26 )
& ( X48 = c_Groups_Ozero__class_Ozero(X2)
=> c_Int_Onumber__class_Onumber__of(X2,X16) = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_nonzero__abs__divide,axiom,
! [X1,X25,X2] :
( class_Fields_Olinordered__field(X2)
=> ( X25 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).
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_of__real__divide,axiom,
! [X17,X18,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_RealVector_Oreal__field(X2) )
=> c_RealVector_Oof__real(X2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,X17)) = c_Rings_Oinverse__class_Odivide(X2,c_RealVector_Oof__real(X2,X18),c_RealVector_Oof__real(X2,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__divide) ).
fof(fact_of__real_Oadd,axiom,
! [X17,X18,X2] :
( ( class_RealVector_Oreal__algebra__1(X2)
& class_RealVector_Oreal__normed__vector(X2) )
=> c_RealVector_Oof__real(X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17)) = c_Groups_Oplus__class_Oplus(X2,c_RealVector_Oof__real(X2,X18),c_RealVector_Oof__real(X2,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Oadd) ).
fof(fact_nonzero__norm__divide,axiom,
! [X1,X25,X2] :
( class_RealVector_Oreal__normed__field(X2)
=> ( X25 != c_Groups_Ozero__class_Ozero(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X2,X25)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).
fof(fact_less__number__of,axiom,
! [X14,X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Int_Onumber__class_Onumber__of(X2,X14))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X15,X14) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).
fof(fact_le__number__of,axiom,
! [X14,X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Int_Onumber__class_Onumber__of(X2,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_nonzero__of__real__divide,axiom,
! [X18,X17,X2] :
( class_RealVector_Oreal__field(X2)
=> ( X17 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_RealVector_Oof__real(X2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,X17)) = c_Rings_Oinverse__class_Odivide(X2,c_RealVector_Oof__real(X2,X18),c_RealVector_Oof__real(X2,X17)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__of__real__divide) ).
fof(fact_order__less__trans,axiom,
! [X21,X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,X17,X21)
=> c_Orderings_Oord__class_Oless(X2,X18,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X21,X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,X17,X21)
=> c_Orderings_Oord__class_Oless(X2,X18,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__le__trans,axiom,
! [X21,X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X21)
=> c_Orderings_Oord__class_Oless(X2,X18,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_xt1_I10_J,axiom,
! [X21,X18,X17,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X17,X18)
=> ( c_Orderings_Oord__class_Oless(X2,X21,X17)
=> c_Orderings_Oord__class_Oless(X2,X21,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_xt1_I8_J,axiom,
! [X21,X18,X17,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> ( c_Orderings_Oord__class_Oless(X2,X21,X17)
=> c_Orderings_Oord__class_Oless(X2,X21,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I7_J,axiom,
! [X21,X18,X17,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X17,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X21,X17)
=> c_Orderings_Oord__class_Oless(X2,X21,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_order__trans,axiom,
! [X21,X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X21)
=> c_Orderings_Oord__class_Oless__eq(X2,X18,X21) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X21,X18,X17,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X21,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X21,X18) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_abs__divide,axiom,
! [X25,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Rings_Oinverse__class_Odivide(X2,X1,X25)) = c_Rings_Oinverse__class_Odivide(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__divide) ).
fof(fact_abs__mult,axiom,
! [X25,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25)) = c_Groups_Otimes__class_Otimes(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_norm__mult,axiom,
! [X17,X18,X2] :
( class_RealVector_Oreal__normed__div__algebra(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Otimes__class_Otimes(X2,X18,X17)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_RealVector_Onorm__class_Onorm(X2,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_add__number__of__eq,axiom,
! [X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Int_Onumber__class_Onumber__of(X2,X9)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).
fof(fact_arith__simps_I32_J,axiom,
! [X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Int_Onumber__class_Onumber__of(X2,X9)) = c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_of__real__add,axiom,
! [X17,X18,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17)) = c_Groups_Oplus__class_Oplus(X2,c_RealVector_Oof__real(X2,X18),c_RealVector_Oof__real(X2,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__add) ).
fof(fact_of__real__mult,axiom,
! [X17,X18,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X17)) = c_Groups_Otimes__class_Otimes(X2,c_RealVector_Oof__real(X2,X18),c_RealVector_Oof__real(X2,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__mult) ).
fof(fact_number__of__add,axiom,
! [X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X9)) = c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Int_Onumber__class_Onumber__of(X2,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_number__of__mult,axiom,
! [X9,X22,X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X9)) = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X22),c_Int_Onumber__class_Onumber__of(X2,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).
fof(fact_zero__le__power__abs,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X1),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_mod__pos__pos__trivial,axiom,
! [X25,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,X25)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).
fof(fact_mod__neg__neg__trivial,axiom,
! [X25,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,X25,X1)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X25) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).
fof(fact_mod__mod__trivial,axiom,
! [X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X25),X25) = c_Divides_Odiv__class_Omod(X2,X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).
fof(fact_mod__add__self1,axiom,
! [X1,X25,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X25,X1),X25) = c_Divides_Odiv__class_Omod(X2,X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self1) ).
fof(fact_mod__add__self2,axiom,
! [X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Oplus__class_Oplus(X2,X1,X25),X25) = c_Divides_Odiv__class_Omod(X2,X1,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__add__self2) ).
fof(fact_real__le__trans,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X41,X55)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X55,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X41,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_zle__trans,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X41,X55)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X55,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X41,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X8,X55,X41] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X55)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X55,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X41,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_even__add,axiom,
! [X3,X4] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4)
<=> c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__add) ).
fof(fact_plus__numeral__code_I9_J,axiom,
! [X9,X22] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X22),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).
fof(fact_times__numeral__code_I5_J,axiom,
! [X9,X22] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X22),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X18] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
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__number__of__int__code,axiom,
! [X6,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,X6))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).
fof(fact_less__eq__number__of__int__code,axiom,
! [X6,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,X6))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).
fof(fact_power__abs,axiom,
! [X13,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Power_Opower__class_Opower(X2,X1,X13)) = c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X1),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_norm__power,axiom,
! [X13,X18,X2] :
( class_RealVector_Oreal__normed__div__algebra(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Power_Opower__class_Opower(X2,X18,X13)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X13,X18] : 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,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X18),X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_of__real__power,axiom,
! [X13,X18,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,X13)) = c_Power_Opower__class_Opower(X2,c_RealVector_Oof__real(X2,X18),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__power) ).
fof(fact_less__special_I1_J,axiom,
! [X14,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,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_I1_J,axiom,
! [X14,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,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_I3_J,axiom,
! [X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Groups_Ozero__class_Ozero(X2))
<=> 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_le__special_I3_J,axiom,
! [X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X15),c_Groups_Ozero__class_Ozero(X2))
<=> 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_zero__le__even__power,axiom,
! [X18,X13,X2] :
( ( class_Groups_Omonoid__mult(X2)
& class_Rings_Olinordered__ring(X2) )
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X18,X13)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__even__power) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X13,X10] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,X13)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X10) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_zero__less__two,axiom,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oplus__class_Oplus(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Oone__class_Oone(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_complex__of__real__power,axiom,
! [X13,X18] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X18),X13) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(fact_nat__less__cases,axiom,
! [X63,X3,X4] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
=> hBOOL(hAPP(hAPP(X63,X3),X4)) )
=> ( ( X4 = X3
=> hBOOL(hAPP(hAPP(X63,X3),X4)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
=> hBOOL(hAPP(hAPP(X63,X3),X4)) )
=> hBOOL(hAPP(hAPP(X63,X3),X4)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_abs__le__D1,axiom,
! [X25,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X25)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X25) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_abs__power__minus__one,axiom,
! [X13,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> c_Groups_Oabs__class_Oabs(X2,c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X13)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_xt1_I5_J,axiom,
! [X18,X17,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> X18 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X17,X18,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> X18 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X15,X14,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X14,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X14,X15,X2] :
( class_Orderings_Oorder(X2)
=> ( X15 = X14
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
& c_Orderings_Oord__class_Oless__eq(X2,X14,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_less__add__one,axiom,
! [X1,X2] :
( class_Rings_Olinordered__semidom(X2)
=> c_Orderings_Oord__class_Oless(X2,X1,c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Oone__class_Oone(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_power__eq__0__iff__number__of,axiom,
! [X16,X27,X2] :
( ( class_Power_Opower(X2)
& class_Rings_Omult__zero(X2)
& class_Rings_Ono__zero__divisors(X2)
& class_Rings_Ozero__neq__one(X2) )
=> ( c_Power_Opower__class_Opower(X2,X27,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X27 = c_Groups_Ozero__class_Ozero(X2)
& 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,
! [X38,X1,X25,X2] :
( class_Groups_Ocancel__semigroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X25,X1) = c_Groups_Oplus__class_Oplus(X2,X38,X1)
=> X25 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__right__cancel,axiom,
! [X48,X27,X26,X2] :
( class_Groups_Ocancel__semigroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X26,X27) = c_Groups_Oplus__class_Oplus(X2,X48,X27)
<=> X26 = X48 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__imp__eq,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Ocancel__ab__semigroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X25) = c_Groups_Oplus__class_Oplus(X2,X1,X38)
=> X25 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__imp__eq,axiom,
! [X38,X25,X1,X2] :
( class_Groups_Ocancel__semigroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X1,X25) = c_Groups_Oplus__class_Oplus(X2,X1,X38)
=> X25 = X38 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X48,X26,X27,X2] :
( class_Groups_Ocancel__semigroup__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X27,X26) = c_Groups_Oplus__class_Oplus(X2,X27,X48)
<=> X26 = X48 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4)
=> ( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X3) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X4 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X3 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_less__0__number__of,axiom,
! [X40] :
( 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,X40))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).
fof(fact_zero__le__square,axiom,
! [X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Otimes__class_Otimes(X2,X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_real__sqrt__divide,axiom,
! [X17,X18] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X18,X17)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),c_NthRoot_Osqrt(X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__divide) ).
fof(fact_real__sqrt__mult,axiom,
! [X17,X18] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X17)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),c_NthRoot_Osqrt(X17)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__mult) ).
fof(fact_real__mult__right__cancel,axiom,
! [X26,X27,X48] :
( X48 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X27,X48) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X26,X48)
<=> X27 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_mult__cancel2,axiom,
! [X3,X5,X4] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X5) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3,X5)
<=> ( X4 = X3
| 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,
! [X26,X27,X48] :
( X48 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X27) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X48,X26)
<=> X27 = X26 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X3,X4,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X4) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3)
<=> ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X4 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_mult__cancel1,axiom,
! [X3,X4,X5] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X4) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X5,X3)
<=> ( X4 = X3
| X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mod__mult__self1__is__0,axiom,
! [X1,X25,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X25,X1),X25) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).
fof(fact_mod__mult__self2__is__0,axiom,
! [X25,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Otimes__class_Otimes(X2,X1,X25),X25) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).
fof(fact_real__le__antisym,axiom,
! [X9,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X21)
=> X21 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_zle__antisym,axiom,
! [X9,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X9)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X21)
=> X21 = X9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X10)
=> X10 = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_nat__add__right__cancel,axiom,
! [X3,X5,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X5)
<=> X4 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X3,X4,X5] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X4) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X3)
<=> X4 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact_abs__mult__self,axiom,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Oabs__class_Oabs(X2,X1)) = c_Groups_Otimes__class_Otimes(X2,X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_zmod__eq__0__iff,axiom,
! [X53,X4] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4,X53) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> ? [X73] : X4 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X53,X73) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(fact_real__sqrt__power,axiom,
! [X8,X18] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X18,X8)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
<=> ? [X71] : X6 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X71) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_le__iff__add,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
<=> ? [X42] : X3 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X42) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_power__even__abs,axiom,
! [X18,X13,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> c_Power_Opower__class_Opower(X2,c_Groups_Oabs__class_Oabs(X2,X18),X13) = c_Power_Opower__class_Opower(X2,X18,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__even__abs) ).
fof(fact_divide__eq__eq,axiom,
! [X27,X48,X26,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( c_Rings_Oinverse__class_Odivide(X2,X26,X48) = X27
<=> ( ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> X26 = c_Groups_Otimes__class_Otimes(X2,X27,X48) )
& ( X48 = c_Groups_Ozero__class_Ozero(X2)
=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).
fof(fact_eq__divide__eq,axiom,
! [X48,X26,X27,X2] :
( class_Fields_Ofield__inverse__zero(X2)
=> ( X27 = c_Rings_Oinverse__class_Odivide(X2,X26,X48)
<=> ( ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Otimes__class_Otimes(X2,X27,X48) = X26 )
& ( X48 = c_Groups_Ozero__class_Ozero(X2)
=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).
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_le__add1,axiom,
! [X10,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X10,X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__square,axiom,
! [X10] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_real__sqrt__less__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__less__iff) ).
fof(fact_real__sqrt__le__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__le__iff) ).
fof(fact_divide__eq__imp,axiom,
! [X1,X25,X38,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X38 != c_Groups_Ozero__class_Ozero(X2)
=> ( X25 = c_Groups_Otimes__class_Otimes(X2,X1,X38)
=> c_Rings_Oinverse__class_Odivide(X2,X25,X38) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).
fof(fact_nonzero__divide__eq__eq,axiom,
! [X27,X26,X48,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> ( c_Rings_Oinverse__class_Odivide(X2,X26,X48) = X27
<=> X26 = c_Groups_Otimes__class_Otimes(X2,X27,X48) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).
fof(fact_nonzero__eq__divide__eq,axiom,
! [X26,X27,X48,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X48 != c_Groups_Ozero__class_Ozero(X2)
=> ( X27 = c_Rings_Oinverse__class_Odivide(X2,X26,X48)
<=> c_Groups_Otimes__class_Otimes(X2,X27,X48) = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).
fof(fact_eq__divide__imp,axiom,
! [X25,X1,X38,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X38 != c_Groups_Ozero__class_Ozero(X2)
=> ( c_Groups_Otimes__class_Otimes(X2,X1,X38) = X25
=> X1 = c_Rings_Oinverse__class_Odivide(X2,X25,X38) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).
fof(fact_real__sqrt__gt__1__iff,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
fof(fact_real__sqrt__gt__0__iff,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
fof(fact_real__sqrt__ge__1__iff,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
fof(fact_real__sqrt__ge__0__iff,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
fof(fact_real__sqrt__lt__1__iff,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__lt__1__iff) ).
fof(fact_real__sqrt__lt__0__iff,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__lt__0__iff) ).
fof(fact_real__sqrt__le__1__iff,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__le__1__iff) ).
fof(fact_real__sqrt__le__0__iff,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__le__0__iff) ).
fof(fact_zero__less__abs__iff,axiom,
! [X27,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X27))
<=> X27 != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact_real__sqrt__gt__zero,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__gt__zero) ).
fof(fact_real__sqrt__ge__one,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__ge__one) ).
fof(fact_real__sqrt__ge__zero,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__ge__zero) ).
fof(fact_xt1_I11_J,axiom,
! [X1,X25,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> ( X1 != X25
=> c_Orderings_Oord__class_Oless(X2,X25,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X25,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> ( X1 != X25
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X17,X18,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
| X18 = X17 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X25,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X1 != X25
=> ( c_Orderings_Oord__class_Oless__eq(X2,X1,X25)
=> c_Orderings_Oord__class_Oless(X2,X1,X25) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X14,X15,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X2,X15,X14)
| X15 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X14,X15,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
& X15 != X14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X25,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X1 != X25
=> ( c_Orderings_Oord__class_Oless__eq(X2,X25,X1)
=> c_Orderings_Oord__class_Oless(X2,X25,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_arctan__monotone,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X18),c_Transcendental_Oarctan(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__monotone) ).
fof(fact_real__sqrt__less__mono,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),c_NthRoot_Osqrt(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__less__mono) ).
fof(fact_arctan__monotone_H,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X18),c_Transcendental_Oarctan(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).
fof(fact_real__sqrt__le__mono,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X18),c_NthRoot_Osqrt(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__le__mono) ).
fof(fact_abs__le__zero__iff,axiom,
! [X27,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X27),c_Groups_Ozero__class_Ozero(X2))
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_order__less__imp__le,axiom,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X54] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X54)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X54) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X15,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_norm__le__zero__iff,axiom,
! [X15,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X15 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
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,X54] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X54,X16)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X54,X16)
& X54 != X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_le__neq__implies__less,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> ( X10 != X13
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| X4 = X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__less__le,axiom,
! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
& X4 != X3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X13,X10] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
| X10 = X13 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_less__imp__le__nat,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_zabs__less__one__iff,axiom,
! [X54] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X54),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> X54 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X3,X27,X2] :
( ( class_Power_Opower(X2)
& class_Rings_Omult__zero(X2)
& class_Rings_Ono__zero__divisors(X2)
& class_Rings_Ozero__neq__one(X2) )
=> ( c_Power_Opower__class_Opower(X2,X27,X3) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X27 = c_Groups_Ozero__class_Ozero(X2)
& X3 != 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,
! [X9,X2] :
( ( class_Power_Opower(X2)
& class_Rings_Osemiring__0(X2) )
=> ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) = 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,X9)) = c_Groups_Oone__class_Oone(X2) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X9) != 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,X9)) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left__number__of) ).
fof(fact_real__sqrt__abs2,axiom,
! [X18] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X18,X18)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_linorder__neq__iff,axiom,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( X15 != X14
<=> ( c_Orderings_Oord__class_Oless(X2,X15,X14)
| c_Orderings_Oord__class_Oless(X2,X14,X15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
| X18 = X17
| c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_abs__of__pos,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Groups_Oabs__class_Oabs(X2,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_abs__of__nonneg,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1)
=> c_Groups_Oabs__class_Oabs(X2,X1) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_linorder__le__less__linear,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
| c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_linorder__linear,axiom,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
| c_Orderings_Oord__class_Oless__eq(X2,X17,X18) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X38,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,X38) = c_Groups_Oplus__class_Oplus(X2,X38,X1) ),
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,
! [X25,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,X25) = c_Groups_Otimes__class_Otimes(X2,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_mult__eq__0__iff,axiom,
! [X26,X27,X2] :
( class_Rings_Oring__no__zero__divisors(X2)
=> ( c_Groups_Otimes__class_Otimes(X2,X27,X26) = c_Groups_Ozero__class_Ozero(X2)
<=> ( X27 = c_Groups_Ozero__class_Ozero(X2)
| X26 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_no__zero__divisors,axiom,
! [X25,X1,X2] :
( class_Rings_Ono__zero__divisors(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> ( X25 != c_Groups_Ozero__class_Ozero(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,X25) != c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_divisors__zero,axiom,
! [X25,X1,X2] :
( class_Rings_Ono__zero__divisors(X2)
=> ( c_Groups_Otimes__class_Otimes(X2,X1,X25) = c_Groups_Ozero__class_Ozero(X2)
=> ( X1 = c_Groups_Ozero__class_Ozero(X2)
| X25 = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_neg__one__even__power,axiom,
! [X18,X2] :
( class_Int_Onumber__ring(X2)
=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Groups_Oone__class_Oone(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__one__even__power) ).
fof(fact_zless__linear,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X17)
| X18 = X17
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X3,X4] :
( X4 != X3
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_right__inverse__eq,axiom,
! [X27,X26,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X26 != c_Groups_Ozero__class_Ozero(X2)
=> ( c_Rings_Oinverse__class_Odivide(X2,X27,X26) = c_Groups_Oone__class_Oone(X2)
<=> X27 = X26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).
fof(fact_real__le__linear,axiom,
! [X9,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X9)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_zle__linear,axiom,
! [X9,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X9)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_zadd__commute,axiom,
! [X9,X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_real__mult__commute,axiom,
! [X9,X21] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X21,X9) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X9,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_zmult__commute,axiom,
! [X9,X21] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,X9) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X9,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Groups_Oplus__class_Oplus(X2,X27,X27) = c_Groups_Ozero__class_Ozero(X2)
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_field__power__not__zero,axiom,
! [X13,X1,X2] :
( class_Rings_Oring__1__no__zero__divisors(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> c_Power_Opower__class_Opower(X2,X1,X13) != c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_double__zero__sym,axiom,
! [X27,X2] :
( class_Groups_Olinordered__ab__group__add(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = c_Groups_Oplus__class_Oplus(X2,X27,X27)
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
! [X13,X10] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X10,X13) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( X10 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X10 = 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_zmult__eq__1__iff,axiom,
! [X3,X4] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4,X3) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( X4 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X3 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| ( X4 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& X3 = 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_real__sqrt__eq__zero__cancel,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ( c_NthRoot_Osqrt(X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> X18 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__zero__cancel) ).
fof(fact_add__0__iff,axiom,
! [X27,X26,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( X26 = c_Groups_Oplus__class_Oplus(X2,X26,X27)
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_real__sqrt__not__eq__zero,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_NthRoot_Osqrt(X18) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__not__eq__zero) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X17,X18,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> X17 != X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X17,X18,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> X18 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X17,X18,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> X18 != X17 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_eq__number__of__0,axiom,
! [X40] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X40) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).
fof(fact_eq__0__number__of,axiom,
! [X40] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X40)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).
fof(fact_divide__Numeral0,axiom,
! [X18,X2] :
( ( class_Fields_Ofield__inverse__zero(X2)
& class_Int_Onumber__ring(X2) )
=> c_Rings_Oinverse__class_Odivide(X2,X18,c_Int_Onumber__class_Onumber__of(X2,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).
fof(fact_mult__is__0,axiom,
! [X3,X4] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_neq0__conv,axiom,
! [X3] :
( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_abs__ge__zero,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X13,X10] :
( X10 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)
=> ( X13 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X10 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_le__0__eq,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X3 = 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,
! [X3,X4] :
( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X4 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X3 = 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,
! [X3,X4] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X4 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X3 = 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,
! [X3,X4] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4,X3)
<=> ( X4 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X3 = 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,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> X13 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__number__of,axiom,
! [X9,X2] :
( ( class_Int_Onumber__ring(X2)
& class_RealVector_Oreal__normed__algebra__1(X2) )
=> c_RealVector_Onorm__class_Onorm(X2,c_Int_Onumber__class_Onumber__of(X2,X9)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__number__of) ).
fof(fact_norm__ge__zero,axiom,
! [X18,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_add__eq__self__zero,axiom,
! [X13,X10] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13) = X10
=> X13 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_abs__ge__self,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Oabs__class_Oabs(X2,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_less__not__refl3,axiom,
! [X59,X60] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,X59)
=> X60 != X59 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [X10,X13] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X10)
=> X10 != X13 ),
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,
! [X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OPls),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(fact_add__numeral__0__right,axiom,
! [X1,X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Int_Onumber__class_Onumber__of(X2,c_Int_OPls)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(fact_power__0__left,axiom,
! [X13,X2] :
( ( class_Power_Opower(X2)
& class_Rings_Osemiring__0(X2) )
=> ( ( X13 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),X13) = c_Groups_Oone__class_Oone(X2) )
& ( X13 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Power_Opower__class_Opower(X2,c_Groups_Ozero__class_Ozero(X2),X13) = c_Groups_Ozero__class_Ozero(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0__left) ).
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_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_zmod__minus1__right,axiom,
! [X1] : 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(fact_divide__self__if,axiom,
! [X1,X2] :
( class_Rings_Odivision__ring__inverse__zero(X2)
=> ( ( X1 = c_Groups_Ozero__class_Ozero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2) )
& ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Oone__class_Oone(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).
fof(fact_zero__less__one,axiom,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oone__class_Oone(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_zero__le__one,axiom,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oone__class_Oone(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_mod__0,axiom,
! [X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(fact_divide_Ozero,axiom,
! [X17,X2] :
( class_RealVector_Oreal__normed__field(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ozero__class_Ozero(X2),X17) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).
fof(fact_divide__zero__left,axiom,
! [X1,X2] :
( class_Rings_Odivision__ring(X2)
=> c_Rings_Oinverse__class_Odivide(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_power__one,axiom,
! [X13,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,c_Groups_Oone__class_Oone(X2),X13) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_mult_Ozero__left,axiom,
! [X25,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Ozero__class_Ozero(X2),X25) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X17,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Ozero__class_Ozero(X2),X17) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult__zero__left,axiom,
! [X1,X2] :
( class_Rings_Omult__zero(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Ozero__class_Ozero(X2),X1) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mod__by__1,axiom,
! [X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,c_Groups_Oone__class_Oone(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(fact_divide__zero,axiom,
! [X1,X2] :
( class_Rings_Odivision__ring__inverse__zero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).
fof(fact_mult_Ozero__right,axiom,
! [X1,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X18,X2] :
( class_RealVector_Oreal__normed__algebra(X2)
=> c_Groups_Otimes__class_Otimes(X2,X18,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult__zero__right,axiom,
! [X1,X2] :
( class_Rings_Omult__zero(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_divide__self,axiom,
! [X1,X2] :
( class_Rings_Odivision__ring(X2)
=> ( X1 != c_Groups_Ozero__class_Ozero(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Oone__class_Oone(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_power__0,axiom,
! [X1,X2] :
( class_Power_Opower(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_add__0,axiom,
! [X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_add__0__left,axiom,
! [X1,X2] :
( class_Groups_Omonoid__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,c_Groups_Ozero__class_Ozero(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_mult__1,axiom,
! [X1,X2] :
( class_Groups_Ocomm__monoid__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oone__class_Oone(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oone__class_Oone(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__1__left,axiom,
! [X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,c_Groups_Oone__class_Oone(X2),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_mod__by__0,axiom,
! [X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(fact_divide__1,axiom,
! [X1,X2] :
( class_Rings_Odivision__ring(X2)
=> c_Rings_Oinverse__class_Odivide(X2,X1,c_Groups_Oone__class_Oone(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X1,X2] :
( class_Groups_Ocomm__monoid__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_add__0__right,axiom,
! [X1,X2] :
( class_Groups_Omonoid__add(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Oplus__class_Oplus(X2,X1,c_Groups_Ozero__class_Ozero(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X1,X2] :
( class_Groups_Ocomm__monoid__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Oone__class_Oone(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Oone__class_Oone(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_mult__1__right,axiom,
! [X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Groups_Otimes__class_Otimes(X2,X1,c_Groups_Oone__class_Oone(X2)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X18,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> c_Power_Opower__class_Opower(X2,X18,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_power__one__right,axiom,
! [X1,X2] :
( class_Groups_Omonoid__mult(X2)
=> c_Power_Opower__class_Opower(X2,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_mod__self,axiom,
! [X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(fact_order__eq__refl,axiom,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( X18 = X17
=> c_Orderings_Oord__class_Oless__eq(X2,X18,X17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_of__real__number__of__eq,axiom,
! [X9,X2] :
( ( class_Int_Onumber__ring(X2)
& class_RealVector_Oreal__algebra__1(X2) )
=> c_RealVector_Oof__real(X2,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X9)) = c_Int_Onumber__class_Onumber__of(X2,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__number__of__eq) ).
fof(fact_order__refl,axiom,
! [X18,X2] :
( class_Orderings_Opreorder(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X18,X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__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_abs__idempotent,axiom,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Oabs__class_Oabs(X2,X1)) = c_Groups_Oabs__class_Oabs(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_eq__number__of,axiom,
! [X14,X15,X2] :
( ( class_Int_Onumber__ring(X2)
& class_Int_Oring__char__0(X2) )
=> ( c_Int_Onumber__class_Onumber__of(X2,X15) = c_Int_Onumber__class_Onumber__of(X2,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).
fof(fact_gr0I,axiom,
! [X13] :
( X13 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_abs__norm__cancel,axiom,
! [X1,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1)) = c_RealVector_Onorm__class_Onorm(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_norm__of__real,axiom,
! [X57,X2] :
( class_RealVector_Oreal__normed__algebra__1(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_RealVector_Oof__real(X2,X57)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(fact_zmod__zero,axiom,
! [X25] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(fact_mult__0,axiom,
! [X13] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_mult__0__right,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,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,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X13] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_real__mult__1,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zmult__1,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X13] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_zadd__0__right,axiom,
! [X21] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X21] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X21,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X13] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_eq__imp__le,axiom,
! [X13,X10] :
( X10 = X13
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_zmod__self,axiom,
! [X1] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(fact_abs__minus__one,axiom,
! [X2] :
( ( class_Int_Onumber__ring(X2)
& class_Rings_Olinordered__idom(X2) )
=> c_Groups_Oabs__class_Oabs(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__one) ).
fof(fact_of__real__eq__iff,axiom,
! [X14,X15,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> ( c_RealVector_Oof__real(X2,X15) = c_RealVector_Oof__real(X2,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
fof(fact_real__le__refl,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_zle__refl,axiom,
! [X9] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X13] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X13,X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_add__Pls,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(fact_add__Pls__right,axiom,
! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Int_OPls) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_mult__Pls,axiom,
! [X9] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X9) = 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_abs__eq__0,axiom,
! [X27,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Groups_Oabs__class_Oabs(X2,X27) = c_Groups_Ozero__class_Ozero(X2)
<=> X27 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X15,X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> ( c_RealVector_Oof__real(X2,X15) = c_Groups_Ozero__class_Ozero(X2)
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
fof(fact_norm__eq__zero,axiom,
! [X15,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ( c_RealVector_Onorm__class_Onorm(X2,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X78,X79] :
( class_Orderings_Oorder(X79)
=> class_Orderings_Oorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X78,X79] :
( class_Orderings_Oord(X79)
=> class_Orderings_Oord(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X78,X79] :
( class_Orderings_Opreorder(X79)
=> class_Orderings_Opreorder(tc_fun(X78,X79)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_of__real_Ozero,axiom,
! [X2] :
( ( class_RealVector_Oreal__algebra__1(X2)
& class_RealVector_Oreal__normed__vector(X2) )
=> c_RealVector_Oof__real(X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real_Ozero) ).
fof(fact_abs__one,axiom,
! [X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Oone__class_Oone(X2)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_abs__zero,axiom,
! [X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> c_Groups_Oabs__class_Oabs(X2,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_norm__one,axiom,
! [X2] :
( class_RealVector_Oreal__normed__algebra__1(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Oone__class_Oone(X2)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_norm__zero,axiom,
! [X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> c_RealVector_Onorm__class_Onorm(X2,c_Groups_Ozero__class_Ozero(X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_of__real__1,axiom,
! [X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_of__real__0,axiom,
! [X2] :
( class_RealVector_Oreal__algebra__1(X2)
=> c_RealVector_Oof__real(X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__real__0) ).
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_real__norm__def,axiom,
! [X57] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X57) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_number__of__Pls,axiom,
! [X2] :
( class_Int_Onumber__ring(X2)
=> c_Int_Onumber__class_Onumber__of(X2,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(fact_semiring__norm_I112_J,axiom,
! [X2] :
( class_Int_Onumber__ring(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(fact_zero__neq__one,axiom,
! [X2] :
( class_Rings_Ozero__neq__one(X2)
=> c_Groups_Ozero__class_Ozero(X2) != c_Groups_Oone__class_Oone(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X2] :
( class_Rings_Ozero__neq__one(X2)
=> c_Groups_Oone__class_Oone(X2) != c_Groups_Ozero__class_Ozero(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(fact_complex__i__not__number__of,axiom,
! [X9] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).
fof(fact_o,axiom,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o) ).
fof(fact_real__sqrt__eq__iff,axiom,
! [X14,X15] :
( c_NthRoot_Osqrt(X15) = c_NthRoot_Osqrt(X14)
<=> X15 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__iff) ).
fof(fact_real__sqrt__eq__1__iff,axiom,
! [X15] :
( c_NthRoot_Osqrt(X15) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> X15 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
fof(fact_real__sqrt__eq__0__iff,axiom,
! [X15] :
( c_NthRoot_Osqrt(X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__eq__0__iff) ).
fof(fact_number__of__is__id,axiom,
! [X8] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X8) = X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(fact_th0,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_b)),v_b)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th0) ).
fof(fact_i__mult__eq,axiom,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__mult__eq) ).
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_i__squared,axiom,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_i__squared) ).
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_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_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_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_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_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__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_arctan__zero__zero,axiom,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__zero__zero) ).
fof(fact_real__sqrt__one,axiom,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
fof(fact_real__sqrt__zero,axiom,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__zero) ).
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_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(fact_b,axiom,
v_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_b) ).
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_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
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__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
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__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
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__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
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,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__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__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__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__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_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__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,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_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_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__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__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_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__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_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_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__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__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_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_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_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__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__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_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__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__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__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_1175,plain,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Power_Opower__class_Opower(X2,X18,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2,X17,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).
fof(i_0_1176,plain,
! [X3] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
<=> ? [X23] : X3 = 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))),X23)) ),
inference(fof_simplification,[status(thm)],[fact_odd__Suc__mult__two__ex]) ).
fof(i_0_1177,plain,
! [X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> ~ c_Orderings_Oord__class_Oless(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_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).
fof(i_0_1178,negated_conjecture,
~ ? [X23] : v_na____ = 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))),X23)),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(i_0_1179,plain,
! [X22,X9] :
( ( 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,X9))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X22)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9))) = 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,X22),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9))),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,X9))
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X22)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X9))) = 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,X22),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X9))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).
fof(i_0_1180,plain,
! [X15] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
<=> ? [X24] : 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))),X24)) ),
inference(fof_simplification,[status(thm)],[fact_odd__nat__equiv__def2]) ).
fof(i_0_1181,plain,
! [X3,X5,X63] :
( epred1_3(X63,X5,X3)
<=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> hBOOL(hAPP(X63,X3)) )
& ( 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)
& X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X63,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))
& X3 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5,X77),X58) )
=> hBOOL(hAPP(X63,X58)) ) ) ) ),
introduced(definition) ).
fof(i_0_1182,plain,
! [X13,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,c_Nat_OSuc(X13))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> X10 = c_Nat_OSuc(X13) ) ),
inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).
fof(i_0_1183,plain,
! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X3)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3),X4) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).
fof(i_0_1184,plain,
! [X3,X4] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4,X3)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X4)) ),
inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).
fof(i_0_1185,plain,
! [X13,X10] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,c_Nat_OSuc(X13))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X10,X13)
=> X10 = X13 ) ),
inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).
fof(i_0_1186,plain,
! [X10,X13] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Nat_OSuc(X10))
=> X10 = X13 ) ),
inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).
fof(i_0_1187,plain,
! [X4,X3] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(X4))
<=> X3 = X4 ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(i_0_1188,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X13),X13),
inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).
fof(i_0_1189,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_1190,plain,
! [X4119,X4120,X4121,X4122] : c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4122,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,X4121,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X4120,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,X4119,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4122,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,X4121,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X4120,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,X4119,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__mult__squared__eq]) ).
fof(i_0_1191,plain,
! [X3085] : c_Int_OBit0(X3085) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3085,X3085),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(i_0_1192,plain,
! [X4378] : c_Int_OBit1(X4378) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4378),X4378),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(i_0_1193,plain,
! [X4107,X4108,X4109,X4110] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4110,X4109),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_Oplus__class_Oplus(tc_RealDef_Oreal,X4108,X4107),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_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4110,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,X4108,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4109,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,X4107,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__triangle__ineq]) ).
fof(i_0_1194,plain,
! [X4888] : c_Transcendental_Oarctan(X4888) = 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))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4888,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4888,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(variable_rename,[status(thm)],[fact_arctan__half]) ).
fof(i_0_1195,plain,
! [X4599,X4600] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4600,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4600,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,X4599,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_cos__x__y__le__one]) ).
fof(i_0_1196,plain,
! [X3941,X3942,X3943,X3944] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3944,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,X3943,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_Power_Opower__class_Opower(tc_RealDef_Oreal,X3942,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,X3941,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__mult__ge__zero]) ).
fof(i_0_1197,plain,
! [X4536,X4537,X4538] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4538),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4537,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4536),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4537,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4538,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,X4536,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X4537) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__less])]) ).
fof(i_0_1198,plain,
! [X4192,X4193,X4194] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4194)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4193,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4194,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4192,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4194,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4193)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4192)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4193,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,X4192,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X4194) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__sqrt__hcomplex__capprox])]) ).
fof(i_0_1199,plain,
! [X4597,X4598] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4598),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4598,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,X4597,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__ge__abs1]) ).
fof(i_0_1200,plain,
! [X4197,X4198] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4198),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4197,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,X4198,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__ge__abs2]) ).
fof(i_0_1201,plain,
! [X4190,X4191] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4191,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,X4190,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__ge__zero]) ).
fof(i_0_1202,plain,
! [X4113,X4114] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4114,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4114,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,X4113,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__ge1]) ).
fof(i_0_1203,plain,
! [X4111,X4112] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4112,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4111,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,X4112,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__sum__squares__ge2]) ).
fof(i_0_1204,plain,
! [X2815,X2816,X2817] :
( ~ class_Int_Onumber__ring(X2817)
| c_Power_Opower__class_Opower(X2817,c_Groups_Oplus__class_Oplus(X2817,X2816,X2815),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X2817,c_Groups_Oplus__class_Oplus(X2817,c_Power_Opower__class_Opower(X2817,X2816,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X2817,X2815,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Otimes__class_Otimes(X2817,c_Groups_Otimes__class_Otimes(X2817,c_Int_Onumber__class_Onumber__of(X2817,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X2816),X2815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).
fof(i_0_1205,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_1206,plain,
! [X2801,X2802,X2803] :
( ~ class_Rings_Olinordered__idom(X2803)
| ~ c_Orderings_Oord__class_Oless__eq(X2803,c_Groups_Ozero__class_Ozero(X2803),c_Power_Opower__class_Opower(X2803,X2802,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))),X2801))))
| c_Orderings_Oord__class_Oless__eq(X2803,c_Groups_Ozero__class_Ozero(X2803),X2802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).
fof(i_0_1207,plain,
! [X4375] : c_Nat_OSuc(X4375) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4375,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(i_0_1208,plain,
! [X3458,X3459,X3460] :
( ( ~ c_Orderings_Oord__class_Oless(X3460,c_Groups_Ozero__class_Ozero(X3460),c_Groups_Oplus__class_Oplus(X3460,c_Power_Opower__class_Opower(X3460,X3459,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3460,X3458,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| X3459 != c_Groups_Ozero__class_Ozero(X3460)
| X3458 != c_Groups_Ozero__class_Ozero(X3460)
| ~ class_Rings_Olinordered__idom(X3460) )
& ( X3459 = c_Groups_Ozero__class_Ozero(X3460)
| c_Orderings_Oord__class_Oless(X3460,c_Groups_Ozero__class_Ozero(X3460),c_Groups_Oplus__class_Oplus(X3460,c_Power_Opower__class_Opower(X3460,X3459,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3460,X3458,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X3460) )
& ( X3458 = c_Groups_Ozero__class_Ozero(X3460)
| c_Orderings_Oord__class_Oless(X3460,c_Groups_Ozero__class_Ozero(X3460),c_Groups_Oplus__class_Oplus(X3460,c_Power_Opower__class_Opower(X3460,X3459,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3460,X3458,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(X3460) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).
fof(i_0_1209,plain,
! [X3464,X3465,X3466] :
( ( X3465 = c_Groups_Ozero__class_Ozero(X3466)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Oplus__class_Oplus(X3466,c_Power_Opower__class_Opower(X3466,X3465,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3466,X3464,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3466))
| ~ class_Rings_Olinordered__idom(X3466) )
& ( X3464 = c_Groups_Ozero__class_Ozero(X3466)
| ~ c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Oplus__class_Oplus(X3466,c_Power_Opower__class_Opower(X3466,X3465,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3466,X3464,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3466))
| ~ class_Rings_Olinordered__idom(X3466) )
& ( X3465 != c_Groups_Ozero__class_Ozero(X3466)
| X3464 != c_Groups_Ozero__class_Ozero(X3466)
| c_Orderings_Oord__class_Oless__eq(X3466,c_Groups_Oplus__class_Oplus(X3466,c_Power_Opower__class_Opower(X3466,X3465,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3466,X3464,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3466))
| ~ class_Rings_Olinordered__idom(X3466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).
fof(i_0_1210,plain,
! [X3455,X3456,X3457] :
( ~ class_Rings_Olinordered__idom(X3457)
| ~ c_Orderings_Oord__class_Oless(X3457,c_Groups_Oplus__class_Oplus(X3457,c_Power_Opower__class_Opower(X3457,X3456,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3457,X3455,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X3457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1175])]) ).
fof(i_0_1211,plain,
! [X4115,X4116] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4116,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,X4115,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != X4115
| X4116 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel2])]) ).
fof(i_0_1212,plain,
! [X4117,X4118] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4118,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,X4117,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != X4118
| X4117 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__sum__squares__eq__cancel])]) ).
fof(i_0_1213,plain,
! [X2716] : 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,X2716,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))),X2716),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_1214,plain,
! [X5081,X5082] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5082,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))),X5081)),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))),X5082)) = 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,X5081,c_Groups_Oone__class_Oone(tc_Int_Oint)),X5082)),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_1215,plain,
! [X4894,X4895] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4895)
| 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))),X4894)),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))),X4895)) = 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,X4894,X4895))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).
fof(i_0_1216,plain,
! [X2804,X2805,X2806] :
( ~ class_Rings_Olinordered__idom(X2806)
| ~ c_Orderings_Oord__class_Oless(X2806,X2805,c_Groups_Ozero__class_Ozero(X2806))
| c_Orderings_Oord__class_Oless(X2806,c_Power_Opower__class_Opower(X2806,X2805,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))),X2804))),c_Groups_Ozero__class_Ozero(X2806)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).
fof(i_0_1217,plain,
! [X3461,X3462,X3463] :
( ~ class_Rings_Olinordered__idom(X3463)
| c_Orderings_Oord__class_Oless__eq(X3463,c_Groups_Ozero__class_Ozero(X3463),c_Groups_Oplus__class_Oplus(X3463,c_Power_Opower__class_Opower(X3463,X3462,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3463,X3461,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_1218,plain,
! [X2812,X2813,X2814] :
( ~ class_Rings_Olinordered__idom(X2814)
| ~ c_Orderings_Oord__class_Oless__eq(X2814,c_Power_Opower__class_Opower(X2814,X2813,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))),X2812)),c_Groups_Ozero__class_Ozero(X2814))
| X2813 = c_Groups_Ozero__class_Ozero(X2814) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power__le__0__imp__0])]) ).
fof(i_0_1219,plain,
! [X3467,X3468,X3469] :
( ~ class_Rings_Olinordered__semidom(X3469)
| ~ c_Orderings_Oord__class_Oless(X3469,c_Power_Opower__class_Opower(X3469,X3468,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3469,X3467,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X3469,c_Groups_Ozero__class_Ozero(X3469),X3467)
| c_Orderings_Oord__class_Oless(X3469,X3468,X3467) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).
fof(i_0_1220,plain,
! [X3550,X3551,X3552] :
( ~ class_Rings_Olinordered__semidom(X3552)
| ~ c_Orderings_Oord__class_Oless__eq(X3552,c_Power_Opower__class_Opower(X3552,X3551,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3552,X3550,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(X3552,c_Groups_Ozero__class_Ozero(X3552),X3550)
| c_Orderings_Oord__class_Oless__eq(X3552,X3551,X3550) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).
fof(i_0_1221,plain,
! [X3541,X3542,X3543] :
( ( X3542 = c_Groups_Ozero__class_Ozero(X3543)
| c_Groups_Oplus__class_Oplus(X3543,c_Power_Opower__class_Opower(X3543,X3542,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3543,X3541,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X3543)
| ~ class_Rings_Olinordered__idom(X3543) )
& ( X3541 = c_Groups_Ozero__class_Ozero(X3543)
| c_Groups_Oplus__class_Oplus(X3543,c_Power_Opower__class_Opower(X3543,X3542,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3543,X3541,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X3543)
| ~ class_Rings_Olinordered__idom(X3543) )
& ( X3542 != c_Groups_Ozero__class_Ozero(X3543)
| X3541 != c_Groups_Ozero__class_Ozero(X3543)
| c_Groups_Oplus__class_Oplus(X3543,c_Power_Opower__class_Opower(X3543,X3542,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(X3543,X3541,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X3543)
| ~ class_Rings_Olinordered__idom(X3543) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).
fof(i_0_1222,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_1223,plain,
! [X2666,X2667,X2668] :
( ~ class_Groups_Omonoid__mult(X2668)
| c_Power_Opower__class_Opower(X2668,X2667,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))),X2666))) = c_Groups_Otimes__class_Otimes(X2668,X2667,c_Power_Opower__class_Opower(X2668,c_Power_Opower__class_Opower(X2668,X2667,X2666),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_1224,plain,
! [X2707,X2708,X2709] :
( ~ class_Rings_Ocomm__semiring__1(X2709)
| c_Power_Opower__class_Opower(X2709,X2708,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))),X2707))) = c_Groups_Otimes__class_Otimes(X2709,X2708,c_Groups_Otimes__class_Otimes(X2709,c_Power_Opower__class_Opower(X2709,X2708,X2707),c_Power_Opower__class_Opower(X2709,X2708,X2707))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).
fof(i_0_1225,plain,
! [X4620,X4621,X4622] :
( ( X4622 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4621,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))),X4620))
| 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))),X4622) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4621,X4620) )
& ( 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))),X4622) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4621,X4620)
| X4622 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4621,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))),X4620)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__2__times__iff])]) ).
fof(i_0_1226,plain,
! [X2807,X2808] :
( ~ class_Int_Onumber__ring(X2808)
| c_Power_Opower__class_Opower(X2808,c_Int_Onumber__class_Onumber__of(X2808,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))),X2807))) = c_Int_Onumber__class_Onumber__of(X2808,c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).
fof(i_0_1227,plain,
! [X2809,X2810,X2811] :
( ~ class_Rings_Olinordered__idom(X2811)
| c_Orderings_Oord__class_Oless__eq(X2811,c_Groups_Ozero__class_Ozero(X2811),c_Power_Opower__class_Opower(X2811,X2810,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))),X2809))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).
fof(i_0_1228,plain,
! [X4619] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4619,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4619,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X4619,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
fof(i_0_1229,plain,
! [X4595] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4595)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4595,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),X4595) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lemma__real__divide__sqrt__less])]) ).
fof(i_0_1230,plain,
! [X3553,X3554,X3555] :
( ~ class_Rings_Olinordered__semidom(X3555)
| c_Power_Opower__class_Opower(X3555,X3554,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Power_Opower__class_Opower(X3555,X3553,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ c_Orderings_Oord__class_Oless__eq(X3555,c_Groups_Ozero__class_Ozero(X3555),X3554)
| ~ c_Orderings_Oord__class_Oless__eq(X3555,c_Groups_Ozero__class_Ozero(X3555),X3553)
| X3554 = X3553 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).
fof(i_0_1231,plain,
! [X4585,X4586] :
( ( ~ c_Orderings_Oord__class_Oless(X4586,c_Groups_Ozero__class_Ozero(X4586),c_Rings_Oinverse__class_Odivide(X4586,X4585,c_Int_Onumber__class_Onumber__of(X4586,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| c_Orderings_Oord__class_Oless(X4586,c_Groups_Ozero__class_Ozero(X4586),X4585)
| ~ class_Fields_Olinordered__field__inverse__zero(X4586)
| ~ class_Int_Onumber__ring(X4586) )
& ( ~ c_Orderings_Oord__class_Oless(X4586,c_Groups_Ozero__class_Ozero(X4586),X4585)
| c_Orderings_Oord__class_Oless(X4586,c_Groups_Ozero__class_Ozero(X4586),c_Rings_Oinverse__class_Odivide(X4586,X4585,c_Int_Onumber__class_Onumber__of(X4586,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Fields_Olinordered__field__inverse__zero(X4586)
| ~ class_Int_Onumber__ring(X4586) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).
fof(i_0_1232,plain,
! [X3546,X3547] :
( ( ~ c_Orderings_Oord__class_Oless(X3547,c_Groups_Ozero__class_Ozero(X3547),c_Power_Opower__class_Opower(X3547,X3546,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| X3546 != c_Groups_Ozero__class_Ozero(X3547)
| ~ class_Rings_Olinordered__idom(X3547) )
& ( X3546 = c_Groups_Ozero__class_Ozero(X3547)
| c_Orderings_Oord__class_Oless(X3547,c_Groups_Ozero__class_Ozero(X3547),c_Power_Opower__class_Opower(X3547,X3546,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(X3547) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).
fof(i_0_1233,plain,
! [X2644,X2646,X2647] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2644)
| X2644 = 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))),esk1_1(X2644))) )
& ( X2646 != 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))),X2647))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2646) ) ),
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_1176])])])])]) ).
fof(i_0_1234,plain,
! [X3544,X3545] :
( ~ class_Rings_Olinordered__idom(X3545)
| ~ c_Orderings_Oord__class_Oless(X3545,c_Power_Opower__class_Opower(X3545,X3544,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(X3545)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1177])]) ).
fof(i_0_1235,negated_conjecture,
! [X5091] : v_na____ != 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))),X5091)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1178])]) ).
fof(i_0_1236,plain,
! [X5080] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X5080,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,X5080,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,X5080,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,X5080,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_1237,plain,
! [X2698,X2699,X2700] :
( ~ class_Groups_Omonoid__mult(X2700)
| c_Power_Opower__class_Opower(X2700,X2699,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))),X2698)) = c_Power_Opower__class_Opower(X2700,c_Power_Opower__class_Opower(X2700,X2699,X2698),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_1238,plain,
! [X4539,X4540] :
( ~ class_Rings_Olinordered__idom(X4540)
| c_Groups_Oabs__class_Oabs(X4540,c_Power_Opower__class_Opower(X4540,X4539,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Power_Opower__class_Opower(X4540,X4539,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_abs__power2])]) ).
fof(i_0_1239,plain,
! [X5083,X5084] :
( ( ~ 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,X5084))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X5083)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X5084))) = 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,X5083),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5084))),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,X5084))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit1(X5083)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X5084))) = 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,X5083),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5084))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1179])]) ).
fof(i_0_1240,plain,
! [X4592,X4593] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4593,X4592)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4593,X4592),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4592) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__gt__half__sum])]) ).
fof(i_0_1241,plain,
! [X4590,X4591] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4591,X4590)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4591,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4591,X4590),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__half__sum])]) ).
fof(i_0_1242,plain,
! [X2710,X2711,X2712] :
( ~ class_Rings_Ocomm__semiring__1(X2712)
| c_Power_Opower__class_Opower(X2712,X2711,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))),X2710)) = c_Groups_Otimes__class_Otimes(X2712,c_Power_Opower__class_Opower(X2712,X2711,X2710),c_Power_Opower__class_Opower(X2712,X2711,X2710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).
fof(i_0_1243,plain,
! [X4602] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4602),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4602,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__one__imp__sqr__less__one])]) ).
fof(i_0_1244,plain,
! [X4587,X4588] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4588)
| ~ class_Int_Onumber__ring(X4588)
| ~ c_Orderings_Oord__class_Oless(X4588,c_Groups_Ozero__class_Ozero(X4588),X4587)
| c_Orderings_Oord__class_Oless(X4588,c_Groups_Ozero__class_Ozero(X4588),c_Rings_Oinverse__class_Odivide(X4588,X4587,c_Int_Onumber__class_Onumber__of(X4588,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero])]) ).
fof(i_0_1245,plain,
! [X4106] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4106)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4106),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_real__sqrt__pow2__gt__zero])]) ).
fof(i_0_1246,plain,
! [X4601] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4601)
| ~ class_Int_Onumber__ring(X4601)
| c_Orderings_Oord__class_Oless(X4601,c_Groups_Ozero__class_Ozero(X4601),c_Rings_Oinverse__class_Odivide(X4601,c_Groups_Oone__class_Oone(X4601),c_Int_Onumber__class_Onumber__of(X4601,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half])]) ).
fof(i_0_1247,plain,
! [X4195,X4196] :
( ~ class_Int_Onumber__ring(X4196)
| c_Power_Opower__class_Opower(X4196,c_Int_Onumber__class_Onumber__of(X4196,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))),X4195)) = c_Groups_Oone__class_Oone(X4196) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).
fof(i_0_1248,plain,
! [X3548,X3549] :
( ~ class_Rings_Olinordered__idom(X3549)
| c_Orderings_Oord__class_Oless__eq(X3549,c_Groups_Ozero__class_Ozero(X3549),c_Power_Opower__class_Opower(X3549,X3548,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_1249,plain,
! [X4594] : 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))),X4594)),
inference(variable_rename,[status(thm)],[fact_two__realpow__ge__one]) ).
fof(i_0_1250,plain,
! [X4541,X4542] :
( ~ class_Rings_Olinordered__idom(X4542)
| c_Power_Opower__class_Opower(X4542,c_Groups_Oabs__class_Oabs(X4542,X4541),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Power_Opower__class_Opower(X4542,X4541,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_power2__abs])]) ).
fof(i_0_1251,plain,
! [X4589] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4589,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4589),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
fof(i_0_1252,plain,
! [X3512] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(X3512))) = 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))),X3512),
inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).
fof(i_0_1253,plain,
! [X2691,X2692] :
( ~ class_Groups_Omonoid__mult(X2692)
| c_Power_Opower__class_Opower(X2692,X2691,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X2692,c_Groups_Otimes__class_Otimes(X2692,X2691,X2691),X2691) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).
fof(i_0_1254,plain,
! [X4596] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4596)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4596,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| X4596 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4596 = 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_1255,plain,
! [X4102,X4103] :
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4103,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X4102
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4103)
| c_NthRoot_Osqrt(X4102) = X4103 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__unique])]) ).
fof(i_0_1256,plain,
! [X4105] :
( ( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4105),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != X4105
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4105) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4105)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4105),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4105 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__iff])]) ).
fof(i_0_1257,plain,
! [X3556] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3556,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| X3556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3556 = 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_1258,plain,
! [X2694,X2695] :
( ( c_Power_Opower__class_Opower(X2695,X2694,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X2695)
| X2694 = c_Groups_Ozero__class_Ozero(X2695)
| ~ class_Rings_Oring__1__no__zero__divisors(X2695) )
& ( X2694 != c_Groups_Ozero__class_Ozero(X2695)
| c_Power_Opower__class_Opower(X2695,X2694,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2695)
| ~ class_Rings_Oring__1__no__zero__divisors(X2695) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).
fof(i_0_1259,plain,
! [X2648,X2650,X2651] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2648)
| X2648 = 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(X2648)) )
& ( X2650 != 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))),X2651)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2650) ) ),
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_1260,plain,
! [X5055,X5056] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X5056)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OBit0(X5055))) = 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,X5056),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X5055))),
inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).
fof(i_0_1261,plain,
! [X3530] : 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))),X3530) = c_Nat_OSuc(c_Nat_OSuc(X3530)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).
fof(i_0_1262,plain,
! [X3529] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3529,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Nat_OSuc(c_Nat_OSuc(X3529)),
inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).
fof(i_0_1263,plain,
! [X2701,X2702] :
( ~ class_Groups_Omonoid__mult(X2702)
| ~ class_Int_Onumber(X2702)
| c_Power_Opower__class_Opower(X2702,c_Int_Onumber__class_Onumber__of(X2702,X2701),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X2702,c_Int_Onumber__class_Onumber__of(X2702,X2701),c_Int_Onumber__class_Onumber__of(X2702,X2701)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).
fof(i_0_1264,plain,
! [X4104] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4104)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4104),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X4104 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2])]) ).
fof(i_0_1265,plain,
! [X3524,X3525] :
( ~ class_Int_Onumber__ring(X3525)
| c_Groups_Otimes__class_Otimes(X3525,c_Int_Onumber__class_Onumber__of(X3525,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X3524) = c_Groups_Oplus__class_Oplus(X3525,X3524,X3524) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).
fof(i_0_1266,plain,
! [X3522,X3523] :
( ~ class_Int_Onumber__ring(X3523)
| c_Groups_Otimes__class_Otimes(X3523,X3522,c_Int_Onumber__class_Onumber__of(X3523,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X3523,X3522,X3522) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(i_0_1267,plain,
! [X2696,X2697] :
( ~ class_Groups_Omonoid__mult(X2697)
| c_Power_Opower__class_Opower(X2697,X2696,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Otimes__class_Otimes(X2697,X2696,X2696) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).
fof(i_0_1268,plain,
! [X2713,X2714] :
( ~ class_Rings_Ocomm__semiring__1(X2714)
| c_Groups_Otimes__class_Otimes(X2714,X2713,X2713) = c_Power_Opower__class_Opower(X2714,X2713,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_1269,plain,
! [X3532] : 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))),X3532) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3532,X3532),
inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).
fof(i_0_1270,plain,
! [X3531] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3531,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,X3531,X3531),
inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).
fof(i_0_1271,plain,
! [X4578] :
( ~ class_Rings_Osemiring__1(X4578)
| c_Power_Opower__class_Opower(X4578,c_Groups_Oone__class_Oone(X4578),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X4578) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).
fof(i_0_1272,plain,
! [X2693] :
( ~ class_Rings_Osemiring__1(X2693)
| c_Power_Opower__class_Opower(X2693,c_Groups_Ozero__class_Ozero(X2693),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2693) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).
fof(i_0_1273,plain,
! [X2715] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(X2715),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X2715,
inference(variable_rename,[status(thm)],[fact_csqrt]) ).
fof(i_0_1274,plain,
! [X4569] :
( ~ class_Int_Onumber__ring(X4569)
| c_Groups_Oplus__class_Oplus(X4569,c_Groups_Oone__class_Oone(X4569),c_Groups_Oone__class_Oone(X4569)) = c_Int_Onumber__class_Onumber__of(X4569,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_1275,plain,
! [X2652,X2654,X2655] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2652)
| X2652 = 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))),esk3_1(X2652))) )
& ( X2654 != 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))),X2655))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2654) ) ),
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_1180])])])])]) ).
fof(i_0_1276,plain,
! [X3476,X3477,X3478,X3479] :
( ~ class_Rings_Olinordered__semidom(X3479)
| ~ c_Orderings_Oord__class_Oless__eq(X3479,c_Power_Opower__class_Opower(X3479,X3478,c_Nat_OSuc(X3477)),c_Power_Opower__class_Opower(X3479,X3476,c_Nat_OSuc(X3477)))
| ~ c_Orderings_Oord__class_Oless__eq(X3479,c_Groups_Ozero__class_Ozero(X3479),X3476)
| c_Orderings_Oord__class_Oless__eq(X3479,X3478,X3476) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).
fof(i_0_1277,plain,
! [X3111,X3112] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3112),c_Int_OBit1(X3111))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3112,X3111) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3112,X3111)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3112),c_Int_OBit1(X3111)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).
fof(i_0_1278,plain,
! [X3109,X3110] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3110),c_Int_OBit1(X3109))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3110,X3109) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3110,X3109)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3110),c_Int_OBit1(X3109)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).
fof(i_0_1279,plain,
! [X3142,X3143] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3143),c_Int_OBit1(X3142))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3143,X3142) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3143,X3142)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3143),c_Int_OBit1(X3142)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).
fof(i_0_1280,plain,
! [X3140,X3141] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3141),c_Int_OBit1(X3140))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3141,X3140) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3141,X3140)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3141),c_Int_OBit1(X3140)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).
fof(i_0_1281,plain,
! [X3439,X3440,X3441] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3441),X3440),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3441),X3439))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3440,X3439) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3440,X3439)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3441),X3440),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3441),X3439)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).
fof(i_0_1282,plain,
! [X3442,X3443,X3444] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3444),X3443),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3444),X3442))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3443,X3442) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3443,X3442)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3444),X3443),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3444),X3442)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).
fof(i_0_1283,plain,
! [X27,X16,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(i_0_1284,plain,
! [X27,X16,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(i_0_1285,plain,
! [X16,X26,X27,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(i_0_1286,plain,
! [X16,X26,X27,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,c_Int_Onumber__class_Onumber__of(X2,X16)))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16)),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16))
=> ( ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,c_Int_Onumber__class_Onumber__of(X2,X16))) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(i_0_1287,plain,
! [X16,X48,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(i_0_1288,plain,
! [X16,X48,X26,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Int_Onumber__class_Onumber__of(X2,X16)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(i_0_1289,plain,
! [X48,X26,X16,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(i_0_1290,plain,
! [X48,X26,X16,X2] :
( ( class_Fields_Olinordered__field__inverse__zero(X2)
& class_Int_Onumber(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X16),X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(i_0_1291,plain,
! [X3374,X3375] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(X3375),c_Int_OBit0(X3374)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3375,X3374)),
inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).
fof(i_0_1292,plain,
! [X3372,X3373] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X3373),c_Int_OBit1(X3372)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3373,X3372)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).
fof(i_0_1293,plain,
! [X3485,X3486] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit1(X3486),X3485) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3486,X3485)),X3485),
inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).
fof(i_0_1294,plain,
! [X17,X18,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oplus__class_Oplus(X2,c_Groups_Otimes__class_Otimes(X2,X18,X18),c_Groups_Otimes__class_Otimes(X2,X17,X17)),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1295,plain,
! [X3561] :
( ( 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(X3561)))
| ~ 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,X3561)) )
& ( 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(X3561)))
| ~ 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,X3561)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).
fof(i_0_1296,plain,
! [X4576,X4577] :
( ~ class_Int_Onumber__ring(X4577)
| c_Groups_Oplus__class_Oplus(X4577,c_Int_Onumber__class_Onumber__of(X4577,X4576),c_Groups_Oone__class_Oone(X4577)) = c_Int_Onumber__class_Onumber__of(X4577,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4576,c_Int_OBit1(c_Int_OPls))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).
fof(i_0_1297,plain,
! [X4574,X4575] :
( ~ class_Int_Onumber__ring(X4575)
| c_Groups_Oplus__class_Oplus(X4575,c_Groups_Oone__class_Oone(X4575),c_Int_Onumber__class_Onumber__of(X4575,X4574)) = c_Int_Onumber__class_Onumber__of(X4575,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
fof(i_0_1298,plain,
! [X3396,X3397] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3397),c_Int_OBit0(X3396))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3397,X3396) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3397,X3396)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3397),c_Int_OBit0(X3396)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).
fof(i_0_1299,plain,
! [X3394,X3395] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3395),c_Int_OBit0(X3394))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3395,X3394) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3395,X3394)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3395),c_Int_OBit0(X3394)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).
fof(i_0_1300,plain,
! [X3016,X3017] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3017),c_Int_OBit0(X3016))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3017,X3016) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3017,X3016)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3017),c_Int_OBit0(X3016)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).
fof(i_0_1301,plain,
! [X3014,X3015] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3015),c_Int_OBit0(X3014))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3015,X3014) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3015,X3014)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3015),c_Int_OBit0(X3014)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).
fof(i_0_1302,plain,
! [X3012,X3013] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3013),c_Int_OBit1(X3012))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3013,X3012) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3013,X3012)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3013),c_Int_OBit1(X3012)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).
fof(i_0_1303,plain,
! [X3010,X3011] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3011),c_Int_OBit1(X3010))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3011,X3010) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3011,X3010)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3011),c_Int_OBit1(X3010)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).
fof(i_0_1304,plain,
! [X3410,X3411] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3411),c_Int_OBit1(X3410))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3411,X3410) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3411,X3410)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3411),c_Int_OBit1(X3410)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).
fof(i_0_1305,plain,
! [X3408,X3409] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3409),c_Int_OBit1(X3408))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3409,X3408) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3409,X3408)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3409),c_Int_OBit1(X3408)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).
fof(i_0_1306,plain,
! [X3505,X3506] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3506)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3505)
| 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,X3505,X3506)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).
fof(i_0_1307,plain,
! [X3507,X3508] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3508)
| ~ 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,X3508,X3507)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3507)
| ~ 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,X3508,X3507)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3508)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3507)
| 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,X3508,X3507)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).
fof(i_0_1308,plain,
! [X27,X48,X26,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).
fof(i_0_1309,plain,
! [X27,X48,X26,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Rings_Oinverse__class_Odivide(X2,X26,X48),X27)
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X27) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).
fof(i_0_1310,plain,
! [X48,X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).
fof(i_0_1311,plain,
! [X48,X26,X27,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X27,c_Rings_Oinverse__class_Odivide(X2,X26,X48))
<=> ( ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Otimes__class_Otimes(X2,X27,X48),X26) )
& ( ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X48)
=> ( ( c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X26,c_Groups_Otimes__class_Otimes(X2,X27,X48)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X48,c_Groups_Ozero__class_Ozero(X2))
=> c_Orderings_Oord__class_Oless__eq(X2,X27,c_Groups_Ozero__class_Ozero(X2)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).
fof(i_0_1312,plain,
! [X4423,X4424] :
( ~ class_Fields_Ofield(X4424)
| ~ class_Int_Onumber__ring(X4424)
| c_Rings_Oinverse__class_Odivide(X4424,X4423,c_Int_Onumber__class_Onumber__of(X4424,c_Int_OBit1(c_Int_OPls))) = X4423 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).
fof(i_0_1313,plain,
! [X4421,X4422] :
( ~ class_Fields_Ofield(X4422)
| ~ class_Int_Onumber__ring(X4422)
| c_Rings_Oinverse__class_Odivide(X4422,X4421,c_Int_Onumber__class_Onumber__of(X4422,c_Int_OBit1(c_Int_OPls))) = X4421 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).
fof(i_0_1314,plain,
! [X3472,X3473,X3474,X3475] :
( ~ class_Rings_Olinordered__semidom(X3475)
| c_Power_Opower__class_Opower(X3475,X3474,c_Nat_OSuc(X3473)) != c_Power_Opower__class_Opower(X3475,X3472,c_Nat_OSuc(X3473))
| ~ c_Orderings_Oord__class_Oless__eq(X3475,c_Groups_Ozero__class_Ozero(X3475),X3474)
| ~ c_Orderings_Oord__class_Oless__eq(X3475,c_Groups_Ozero__class_Ozero(X3475),X3472)
| X3474 = X3472 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).
fof(i_0_1315,plain,
! [X2577,X2578] :
( ~ class_Int_Onumber__ring(X2578)
| c_Groups_Otimes__class_Otimes(X2578,c_Int_Onumber__class_Onumber__of(X2578,c_Int_OBit1(c_Int_OPls)),X2577) = X2577 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).
fof(i_0_1316,plain,
! [X2575,X2576] :
( ~ class_Int_Onumber__ring(X2576)
| c_Groups_Otimes__class_Otimes(X2576,X2575,c_Int_Onumber__class_Onumber__of(X2576,c_Int_OBit1(c_Int_OPls))) = X2575 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).
fof(i_0_1317,plain,
! [X3503,X3504] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3504)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3503)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3504,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3504,X3503)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).
fof(i_0_1318,plain,
! [X3501,X3502] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3502)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3501)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3502,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3501,X3502)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).
fof(i_0_1319,plain,
! [X3382] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3382,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| X3382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3382 = 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_1320,plain,
! [X4572,X4573] :
( ( ~ c_Orderings_Oord__class_Oless(X4573,c_Int_Onumber__class_Onumber__of(X4573,X4572),c_Groups_Oone__class_Oone(X4573))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4572,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X4573)
| ~ class_Rings_Olinordered__idom(X4573) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4572,c_Int_OBit1(c_Int_OPls))
| c_Orderings_Oord__class_Oless(X4573,c_Int_Onumber__class_Onumber__of(X4573,X4572),c_Groups_Oone__class_Oone(X4573))
| ~ class_Int_Onumber__ring(X4573)
| ~ class_Rings_Olinordered__idom(X4573) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).
fof(i_0_1321,plain,
! [X4567,X4568] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4568,c_Int_Onumber__class_Onumber__of(X4568,X4567),c_Groups_Oone__class_Oone(X4568))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4567,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X4568)
| ~ class_Rings_Olinordered__idom(X4568) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4567,c_Int_OBit1(c_Int_OPls))
| c_Orderings_Oord__class_Oless__eq(X4568,c_Int_Onumber__class_Onumber__of(X4568,X4567),c_Groups_Oone__class_Oone(X4568))
| ~ class_Int_Onumber__ring(X4568)
| ~ class_Rings_Olinordered__idom(X4568) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).
fof(i_0_1322,plain,
! [X4570,X4571] :
( ( ~ c_Orderings_Oord__class_Oless(X4571,c_Groups_Oone__class_Oone(X4571),c_Int_Onumber__class_Onumber__of(X4571,X4570))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4570)
| ~ class_Int_Onumber__ring(X4571)
| ~ class_Rings_Olinordered__idom(X4571) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4570)
| c_Orderings_Oord__class_Oless(X4571,c_Groups_Oone__class_Oone(X4571),c_Int_Onumber__class_Onumber__of(X4571,X4570))
| ~ class_Int_Onumber__ring(X4571)
| ~ class_Rings_Olinordered__idom(X4571) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).
fof(i_0_1323,plain,
! [X4565,X4566] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4566,c_Groups_Oone__class_Oone(X4566),c_Int_Onumber__class_Onumber__of(X4566,X4565))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4565)
| ~ class_Int_Onumber__ring(X4566)
| ~ class_Rings_Olinordered__idom(X4566) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X4565)
| c_Orderings_Oord__class_Oless__eq(X4566,c_Groups_Oone__class_Oone(X4566),c_Int_Onumber__class_Onumber__of(X4566,X4565))
| ~ class_Int_Onumber__ring(X4566)
| ~ class_Rings_Olinordered__idom(X4566) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).
fof(i_0_1324,plain,
! [X3380] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3380),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3380,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3380,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3380),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_1325,plain,
! [X17,X74,X75,X76] :
( X76 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X75,X74),X17)
=> ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X17)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X17,X75) ) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X17)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X17,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) )
=> ( X75 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Divides_Odiv__class_Omod(tc_Int_Oint,X76,X75) = X17 ) ) ),
inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).
fof(i_0_1326,plain,
! [X2881] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X2881))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2881) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2881)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X2881)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).
fof(i_0_1327,plain,
! [X2884] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X2884))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X2884) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,X2884)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(X2884)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).
fof(i_0_1328,plain,
! [X3008] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X3008))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3008) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3008)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X3008)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).
fof(i_0_1329,plain,
! [X3403] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X3403))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3403) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3403)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(X3403)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).
fof(i_0_1330,plain,
! [X2882] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X2882),c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2882,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2882,c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X2882),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).
fof(i_0_1331,plain,
! [X3381] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3381),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3381,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3381,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(X3381),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).
fof(i_0_1332,plain,
! [X3009] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3009),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3009,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3009,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X3009),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).
fof(i_0_1333,plain,
! [X2885] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X2885),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2885,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2885,c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(X2885),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).
fof(i_0_1334,plain,
! [X2656,X2658,X2659] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2656)
| X2656 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk4_1(X2656)) )
& ( X2658 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2659)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2658) ) ),
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_1335,plain,
! [X4440,X4441] :
( ~ class_Int_Onumber__ring(X4441)
| c_Int_Onumber__class_Onumber__of(X4441,c_Int_OBit1(X4440)) = c_Groups_Oplus__class_Oplus(X4441,c_Groups_Oplus__class_Oplus(X4441,c_Groups_Oone__class_Oone(X4441),c_Int_Onumber__class_Onumber__of(X4441,X4440)),c_Int_Onumber__class_Onumber__of(X4441,X4440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).
fof(i_0_1336,plain,
! [X4505,X4506,X4507] :
( ~ class_Rings_Olinordered__semidom(X4507)
| ~ c_Orderings_Oord__class_Oless(X4507,c_Groups_Ozero__class_Ozero(X4507),X4506)
| ~ c_Orderings_Oord__class_Oless(X4507,X4506,c_Groups_Oone__class_Oone(X4507))
| c_Orderings_Oord__class_Oless(X4507,c_Power_Opower__class_Opower(X4507,X4506,c_Nat_OSuc(X4505)),c_Groups_Oone__class_Oone(X4507)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).
fof(i_0_1337,plain,
! [X4502,X4503,X4504] :
( ~ class_Rings_Olinordered__semidom(X4504)
| ~ c_Orderings_Oord__class_Oless__eq(X4504,c_Groups_Ozero__class_Ozero(X4504),X4503)
| ~ c_Orderings_Oord__class_Oless__eq(X4504,X4503,c_Groups_Oone__class_Oone(X4504))
| c_Orderings_Oord__class_Oless__eq(X4504,c_Power_Opower__class_Opower(X4504,X4503,c_Nat_OSuc(X4502)),X4503) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self])]) ).
fof(i_0_1338,plain,
! [X8,X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),X8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47),X8)) = 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,X22,X47)),X8) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).
fof(i_0_1339,plain,
! [X3401,X3402] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3402)
| 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,X3402,X3401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).
fof(i_0_1340,plain,
! [X3086,X3087] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(X3087),c_Int_OBit0(X3086)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3087,X3086)),
inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).
fof(i_0_1341,plain,
! [X2619,X2620] :
( ( c_Int_OBit1(X2620) != c_Int_OBit1(X2619)
| X2620 = X2619 )
& ( X2620 != X2619
| c_Int_OBit1(X2620) = c_Int_OBit1(X2619) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).
fof(i_0_1342,plain,
! [X2579,X2580,X2581] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2581),X2580) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2581),X2579)
| X2580 = X2579 )
& ( X2580 != X2579
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2581),X2580) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X2581),X2579) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).
fof(i_0_1343,plain,
! [X4442,X4443,X4444] :
( ~ class_Rings_Olinordered__semidom(X4444)
| ~ c_Orderings_Oord__class_Oless(X4444,c_Groups_Oone__class_Oone(X4444),X4443)
| c_Orderings_Oord__class_Oless(X4444,c_Groups_Oone__class_Oone(X4444),c_Power_Opower__class_Opower(X4444,X4443,c_Nat_OSuc(X4442))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).
fof(i_0_1344,plain,
! [X3138,X3139] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3139),c_Nat_OSuc(X3138))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3139,X3138) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).
fof(i_0_1345,plain,
! [X3121,X3122] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3122),c_Nat_OSuc(X3121))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3122,X3121) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3122,X3121)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3122),c_Nat_OSuc(X3121)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).
fof(i_0_1346,plain,
! [X3149,X3150] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3150),c_Nat_OSuc(X3149))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3150,X3149) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3150,X3149)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3150),c_Nat_OSuc(X3149)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).
fof(i_0_1347,plain,
! [X3115,X3116] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3116),c_Int_OBit0(X3115))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3116,X3115) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3116,X3115)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3116),c_Int_OBit0(X3115)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).
fof(i_0_1348,plain,
! [X3113,X3114] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3114),c_Int_OBit0(X3113))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3114,X3113) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3114,X3113)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3114),c_Int_OBit0(X3113)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).
fof(i_0_1349,plain,
! [X3159,X3160] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3160),c_Int_OBit0(X3159))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3160,X3159) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3160,X3159)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3160),c_Int_OBit0(X3159)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).
fof(i_0_1350,plain,
! [X3157,X3158] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3158),c_Int_OBit0(X3157))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3158,X3157) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3158,X3157)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3158),c_Int_OBit0(X3157)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).
fof(i_0_1351,plain,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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(X2) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__power__eq__number__of]) ).
fof(i_0_1352,plain,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,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(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__power__eq__number__of]) ).
fof(i_0_1353,plain,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X2))
<=> ( 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(X2,X15,c_Groups_Ozero__class_Ozero(X2)) )
| ( 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(X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__le__zero__eq__number__of]) ).
fof(i_0_1354,axiom,
! [X5,X3,X63] :
( hBOOL(hAPP(X63,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X5)))
<=> epred1_3(X63,X5,X3) ),
inference(apply_def,[status(thm)],[fact_split__zmod,c_0_1181]) ).
fof(i_0_1355,plain,
! [X2591,X2592] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OBit0(X2592),X2591) = c_Int_OBit0(c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2592,X2591)),
inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).
fof(i_0_1356,plain,
! [X16,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X15,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16)),c_Groups_Ozero__class_Ozero(X2))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X16))
& c_Orderings_Oord__class_Oless(X2,X15,c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__less__zero__eq__number__of]) ).
fof(i_0_1357,plain,
! [X3470,X3471] :
( ~ class_Int_Onumber__ring(X3471)
| c_Int_Onumber__class_Onumber__of(X3471,c_Int_OBit0(X3470)) = c_Groups_Oplus__class_Oplus(X3471,c_Groups_Oplus__class_Oplus(X3471,c_Groups_Ozero__class_Ozero(X3471),c_Int_Onumber__class_Onumber__of(X3471,X3470)),c_Int_Onumber__class_Onumber__of(X3471,X3470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).
fof(i_0_1358,plain,
! [X17,X18,X13,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X18,X13),c_Power_Opower__class_Opower(X2,X17,X13)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__mono__odd]) ).
fof(i_0_1359,plain,
! [X2889,X2890] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2890,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2890,X2889))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).
fof(i_0_1360,plain,
! [X2891,X2892] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2892,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2891,X2892))),
inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).
fof(i_0_1361,plain,
! [X3153,X3154] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3154,c_Nat_OSuc(X3153))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3154,X3153)
| X3154 = c_Nat_OSuc(X3153) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1182])]) ).
fof(i_0_1362,plain,
! [X3147,X3148] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3148,c_Nat_OSuc(X3147))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3148,X3147)
| X3148 = c_Nat_OSuc(X3147) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3148,X3147)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3148,c_Nat_OSuc(X3147)) )
& ( X3148 != c_Nat_OSuc(X3147)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3148,c_Nat_OSuc(X3147)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).
fof(i_0_1363,plain,
! [X2829,X2830] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2830,X2829)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2830),c_Nat_OSuc(X2829)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).
fof(i_0_1364,plain,
! [X16,X40,X2] :
( ( class_Int_Onumber(X2)
& class_Orderings_Olinorder(X2) )
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Int_Onumber__class_Onumber__of(X2,X40),c_Int_Onumber__class_Onumber__of(X2,X16))
<=> ~ c_Orderings_Oord__class_Oless(X2,c_Int_Onumber__class_Onumber__of(X2,X16),c_Int_Onumber__class_Onumber__of(X2,X40)) ) ),
inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).
fof(i_0_1365,plain,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> ( X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& X15 != c_Groups_Ozero__class_Ozero(X2) )
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__less__power__eq]) ).
fof(i_0_1366,plain,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
| ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__power__eq]) ).
fof(i_0_1367,plain,
! [X15,X3,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),c_Power_Opower__class_Opower(X2,X15,X3))
<=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_zero__le__odd__power]) ).
fof(i_0_1368,plain,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Power_Opower__class_Opower(X2,X15,X3),c_Groups_Ozero__class_Ozero(X2))
<=> ( X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless__eq(X2,X15,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& X15 = c_Groups_Ozero__class_Ozero(X2) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__le__zero__eq]) ).
fof(i_0_1369,plain,
! [X3383,X3384,X3386,X3387,X3388] :
( ( X3384 = c_Nat_OSuc(esk6_2(X3383,X3384))
| X3384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3384,c_Nat_OSuc(X3383)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk6_2(X3383,X3384),X3383)
| X3384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3384,c_Nat_OSuc(X3383)) )
& ( X3387 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3387,c_Nat_OSuc(X3386)) )
& ( X3387 != c_Nat_OSuc(X3388)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3388,X3386)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3387,c_Nat_OSuc(X3386)) ) ),
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_1370,plain,
! [X2909,X2910] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2909,c_Nat_OSuc(X2910))
| X2909 = X2910
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2910,X2909) )
& ( X2909 != X2910
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2909,c_Nat_OSuc(X2910))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2910,X2909) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).
fof(i_0_1371,plain,
! [X3145,X3146] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3146,X3145)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3145),X3146) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3145),X3146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3146,X3145) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1183])]) ).
fof(i_0_1372,plain,
! [X3117,X3118] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3118,X3117)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3117,c_Nat_OSuc(X3118)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3117,c_Nat_OSuc(X3118))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3118,X3117) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1184])]) ).
fof(i_0_1373,plain,
! [X4462] :
( ~ class_Int_Onumber__ring(X4462)
| c_Int_Onumber__class_Onumber__of(X4462,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X4462) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).
fof(i_0_1374,plain,
! [X4461] :
( ~ class_Int_Onumber__ring(X4461)
| c_Groups_Oone__class_Oone(X4461) = c_Int_Onumber__class_Onumber__of(X4461,c_Int_OBit1(c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).
fof(i_0_1375,plain,
! [X2584,X2585] : c_Int_OBit0(X2585) != c_Int_OBit1(X2584),
inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).
fof(i_0_1376,plain,
! [X2586,X2587] : c_Int_OBit1(X2587) != c_Int_OBit0(X2586),
inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).
fof(i_0_1377,plain,
! [X4512,X4513] :
( ~ class_Int_Onumber__ring(X4513)
| c_Groups_Otimes__class_Otimes(X4513,c_Groups_Oplus__class_Oplus(X4513,c_Groups_Oone__class_Oone(X4513),c_Groups_Oone__class_Oone(X4513)),c_Int_Onumber__class_Onumber__of(X4513,X4512)) = c_Int_Onumber__class_Onumber__of(X4513,c_Int_OBit0(X4512)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).
fof(i_0_1378,plain,
! [X2723,X2724,X2725] :
( ~ class_Groups_Omonoid__mult(X2725)
| c_Power_Opower__class_Opower(X2725,X2724,c_Nat_OSuc(X2723)) = c_Groups_Otimes__class_Otimes(X2725,c_Power_Opower__class_Opower(X2725,X2724,X2723),X2724) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).
fof(i_0_1379,plain,
! [X2720,X2721,X2722] :
( ~ class_Rings_Ocomm__semiring__1(X2722)
| c_Power_Opower__class_Opower(X2722,X2721,c_Nat_OSuc(X2720)) = c_Groups_Otimes__class_Otimes(X2722,X2721,c_Power_Opower__class_Opower(X2722,X2721,X2720)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).
fof(i_0_1380,plain,
! [X2717,X2718,X2719] :
( ~ class_Power_Opower(X2719)
| c_Power_Opower__class_Opower(X2719,X2718,c_Nat_OSuc(X2717)) = c_Groups_Otimes__class_Otimes(X2719,X2718,c_Power_Opower__class_Opower(X2719,X2718,X2717)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).
fof(i_0_1381,plain,
! [X2729,X2730,X2731] :
( ~ class_Rings_Ocomm__semiring__1(X2731)
| c_Groups_Otimes__class_Otimes(X2731,c_Power_Opower__class_Opower(X2731,X2730,X2729),X2730) = c_Power_Opower__class_Opower(X2731,X2730,c_Nat_OSuc(X2729)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).
fof(i_0_1382,plain,
! [X2726,X2727,X2728] :
( ~ class_Rings_Ocomm__semiring__1(X2728)
| c_Groups_Otimes__class_Otimes(X2728,X2727,c_Power_Opower__class_Opower(X2728,X2727,X2726)) = c_Power_Opower__class_Opower(X2728,X2727,c_Nat_OSuc(X2726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).
fof(i_0_1383,plain,
! [X3,X15,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( c_Orderings_Oord__class_Oless(X2,c_Power_Opower__class_Opower(X2,X15,X3),c_Groups_Ozero__class_Ozero(X2))
<=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
& c_Orderings_Oord__class_Oless(X2,X15,c_Groups_Ozero__class_Ozero(X2)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_power__less__zero__eq]) ).
fof(i_0_1384,plain,
! [X3131,X3132,X3133] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3133,X3132)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3132,X3131)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3133),X3131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).
fof(i_0_1385,plain,
! [X18] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X18),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(i_0_1386,plain,
! [X3092,X3093] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3093),X3092) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3093,c_Nat_OSuc(X3092)),
inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).
fof(i_0_1387,plain,
! [X3090,X3091] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X3091),X3090) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3091,X3090)),
inference(variable_rename,[status(thm)],[fact_add__Suc]) ).
fof(i_0_1388,plain,
! [X3088,X3089] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3089,c_Nat_OSuc(X3088)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3089,X3088)),
inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).
fof(i_0_1389,plain,
! [X3406,X3407] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X3407),X3406) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3406,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3407,X3406)),
inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).
fof(i_0_1390,plain,
! [X3404,X3405] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3405,c_Nat_OSuc(X3404)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3405,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3405,X3404)),
inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).
fof(i_0_1391,plain,
! [X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X47,c_Int_OPls)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X22,X47)) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).
fof(i_0_1392,plain,
! [X3134,X3135] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3135,c_Nat_OSuc(X3134))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3135,X3134)
| X3135 = X3134 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1185])]) ).
fof(i_0_1393,plain,
! [X3125,X3126] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3126,X3125)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3126,c_Nat_OSuc(X3125))
| X3125 = X3126 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1186])]) ).
fof(i_0_1394,plain,
! [X3123,X3124] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3124,c_Nat_OSuc(X3123))
| X3124 = X3123
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3124,X3123) )
& ( X3124 != X3123
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3124,c_Nat_OSuc(X3123))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3124,X3123) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1187])])]) ).
fof(i_0_1395,plain,
! [X3119,X3120] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3120,c_Nat_OSuc(X3119))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3120,X3119)
| X3120 = X3119 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3120,X3119)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3120,c_Nat_OSuc(X3119)) )
& ( X3120 != X3119
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3120,c_Nat_OSuc(X3119)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).
fof(i_0_1396,plain,
! [X3136,X3137] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3137),X3136)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3137,X3136) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).
fof(i_0_1397,plain,
! [X2911,X2912] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2912),X2911)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2912,X2911) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).
fof(i_0_1398,plain,
! [X2903,X2904] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2904),X2903)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2904,X2903) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2904,X2903)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2904),X2903) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).
fof(i_0_1399,plain,
! [X2899,X2900] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2900,X2899)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2900),X2899) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2900),X2899)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2900,X2899) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).
fof(i_0_1400,plain,
! [X3155,X3156] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3156),X3155)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3156,X3155) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).
fof(i_0_1401,plain,
! [X2901,X2902] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2902,c_Nat_OSuc(X2901))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2902,X2901) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2902,X2901)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2902,c_Nat_OSuc(X2901)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).
fof(i_0_1402,plain,
! [X3398] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3398),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3398,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3398,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3398),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_1403,plain,
! [X2893,X2894,X2896,X2897,X2898] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2894,X2893)
| X2893 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2894,esk5_2(X2893,X2894))) )
& ( X2896 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2897,X2898))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2897,X2896) ) ),
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_1404,plain,
! [X3129,X3130] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3130,X3129)
| c_Nat_OSuc(X3130) = X3129
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3130),X3129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).
fof(i_0_1405,plain,
! [X2611,X2612] :
( ( X2612 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2612,X2611) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2611 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2612,X2611) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2612 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2611 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2612,X2611) = 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_1406,plain,
! [X13,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X8),X13)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X10,X13)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X13) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1407,plain,
! [X3378,X3379] :
( ( X3379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3379 = 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,X3379,X3378) )
& ( X3378 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3379 = 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,X3379,X3378) )
& ( X3379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3378 = 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,X3379,X3378) )
& ( X3378 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3378 = 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,X3379,X3378) )
& ( X3379 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3378 != 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,X3379,X3378) )
& ( X3379 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3378 != 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,X3379,X3378) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).
fof(i_0_1408,plain,
! [X3376,X3377] :
( ( X3377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3377 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3376 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3377 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3376 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3377 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3376 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X3377 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3376 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3377,X3376) = 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_1409,plain,
! [X2883] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X2883))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2883) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2883)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X2883)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).
fof(i_0_1410,plain,
! [X2913] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X2913))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2913) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,X2913)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(X2913)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).
fof(i_0_1411,plain,
! [X3399] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3399))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3399) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3399)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3399)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).
fof(i_0_1412,plain,
! [X3412] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3412))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3412) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3412)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(X3412)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).
fof(i_0_1413,plain,
! [X3400] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3400),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3400,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3400,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X3400),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).
fof(i_0_1414,plain,
! [X2914] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X2914),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2914,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2914,c_Int_OMin)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(X2914),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).
fof(i_0_1415,plain,
! [X2886] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X2886),c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2886,c_Int_OMin) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2886,c_Int_OMin)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X2886),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).
fof(i_0_1416,plain,
! [X3413] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3413),c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3413,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3413,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(X3413),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).
fof(i_0_1417,plain,
! [X66,X67,X2,X31] :
( class_Orderings_Oord(X31)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X2,X31),X67,X66)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X67,X66)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X31),X66,X67) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1418,plain,
! [X1,X2] :
( class_Rings_Olinordered__ring(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Otimes__class_Otimes(X2,X1,X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1419,plain,
! [X3389] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| X3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3389,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_1420,plain,
! [X47,X22] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,c_Int_OPls)
=> c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X22),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X47)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X22,X47)) ) ),
inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).
fof(i_0_1421,plain,
! [X51,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X40),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X51))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,X51)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X40,c_Int_OPls) ) ),
inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).
fof(i_0_1422,plain,
! [X3071] :
( ( c_Int_OMin != c_Int_OBit1(X3071)
| c_Int_OMin = X3071 )
& ( c_Int_OMin != X3071
| c_Int_OMin = c_Int_OBit1(X3071) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).
fof(i_0_1423,plain,
! [X3072] :
( ( c_Int_OBit1(X3072) != c_Int_OMin
| X3072 = c_Int_OMin )
& ( X3072 != c_Int_OMin
| c_Int_OBit1(X3072) = c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).
fof(i_0_1424,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_1425,plain,
! [X3144] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X3144),X3144),
inference(variable_rename,[status(thm)],[i_0_1188]) ).
fof(i_0_1426,plain,
! [X2589] : c_Int_OBit1(X2589) != c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(i_0_1427,plain,
! [X2588] : c_Int_OPls != c_Int_OBit1(X2588),
inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(i_0_1428,plain,
! [X2907,X2908] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2908,X2907)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X2908),X2907) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).
fof(i_0_1429,plain,
! [X3127,X3128] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3128,X3127)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3128,c_Nat_OSuc(X3127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).
fof(i_0_1430,plain,
! [X2905,X2906] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2906,X2905)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2906,c_Nat_OSuc(X2905)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).
fof(i_0_1431,plain,
! [X3151,X3152] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3152,X3151)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3152,c_Nat_OSuc(X3151)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).
fof(i_0_1432,plain,
! [X55,X41] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X41,X55),X41),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1433,plain,
! [X41,X55] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X55,X41),X41),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1434,plain,
! [X2786,X2787] :
( ( c_Power_Opower__class_Opower(tc_Nat_Onat,X2787,X2786) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X2786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2787 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2786 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X2787,X2786) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X2787 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,X2787,X2786) = 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_1435,plain,
! [X2785] : c_Power_Opower__class_Opower(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2785) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).
fof(i_0_1436,plain,
! [X3,X4] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X3))
<=> ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4)
<=> ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3) ) ),
inference(fof_simplification,[status(thm)],[fact_odd__add]) ).
fof(i_0_1437,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_1438,plain,
! [X2662] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X2662))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2662) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2662)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Nat_OSuc(X2662)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1189])]) ).
fof(i_0_1439,plain,
! [X14,X15,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X2,X14,X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1440,plain,
! [X2799,X2800] :
( ~ class_Power_Opower(X2800)
| ~ class_Rings_Osemiring__0(X2800)
| c_Power_Opower__class_Opower(X2800,c_Groups_Ozero__class_Ozero(X2800),c_Nat_OSuc(X2799)) = c_Groups_Ozero__class_Ozero(X2800) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).
fof(i_0_1441,plain,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1442,plain,
! [X1,X25,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X25,X1)
=> ~ c_Orderings_Oord__class_Oless(X2,X1,X25) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1443,plain,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1444,plain,
! [X25,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X25)
=> ~ c_Orderings_Oord__class_Oless(X2,X25,X1) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1445,plain,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1446,plain,
! [X17,X18,X2] :
( class_Orderings_Opreorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ~ c_Orderings_Oord__class_Oless(X2,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1447,plain,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X2,X14,X15)
| X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1448,plain,
! [X18,X17,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> ~ c_Orderings_Oord__class_Oless(X2,X18,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1449,plain,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(X2,X14,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1450,plain,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> c_Orderings_Oord__class_Oless(X2,X14,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1451,plain,
! [X2623,X2624] :
( ( c_Nat_OSuc(X2624) != c_Nat_OSuc(X2623)
| X2624 = X2623 )
& ( X2624 != X2623
| c_Nat_OSuc(X2624) = c_Nat_OSuc(X2623) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).
fof(i_0_1452,plain,
! [X2621,X2622] :
( c_Nat_OSuc(X2622) != c_Nat_OSuc(X2621)
| X2622 = X2621 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).
fof(i_0_1453,plain,
! [X2627,X2628] :
( ( c_Int_OBit0(X2628) != c_Int_OBit0(X2627)
| X2628 = X2627 )
& ( X2628 != X2627
| c_Int_OBit0(X2628) = c_Int_OBit0(X2627) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).
fof(i_0_1454,plain,
! [X2831] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X2831)),
inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).
fof(i_0_1455,plain,
! [X2828] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2828,c_Nat_OSuc(X2828)),
inference(variable_rename,[status(thm)],[fact_lessI]) ).
fof(i_0_1456,plain,
! [X3390,X3392,X3393] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3390)
| X3390 = c_Nat_OSuc(esk7_1(X3390)) )
& ( X3392 != c_Nat_OSuc(X3393)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3392) ) ),
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_1457,plain,
! [X14,X15,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X2,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1458,plain,
! [X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_1459,plain,
! [X18,X2] :
( class_RealVector_Oreal__normed__vector(X2)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1460,plain,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> ( X18 != X17
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1461,plain,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( X18 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1462,plain,
! [X15,X14,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X14,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1463,plain,
! [X17,X18,X2] :
( class_Rings_Olinordered__idom(X2)
=> ( X18 != X17
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless(X2,X17,X18) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1464,plain,
! [X18,X17,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X17,X18)
=> c_Orderings_Oord__class_Oless(X2,X18,X17) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1465,plain,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1466,plain,
! [X17,X18,X2] :
( class_Orderings_Olinorder(X2)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X2,X18,X17)
=> c_Orderings_Oord__class_Oless__eq(X2,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1467,plain,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1468,plain,
! [X2] :
( class_Rings_Olinordered__semidom(X2)
=> ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oone__class_Oone(X2),c_Groups_Ozero__class_Ozero(X2)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1469,plain,
! [X4374] : c_Nat_OSuc(X4374) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4374),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).
fof(i_0_1470,plain,
! [X18,X2] :
( class_Int_Onumber__ring(X2)
=> ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin) ) ),
inference(fof_simplification,[status(thm)],[fact_neg__one__odd__power]) ).
fof(i_0_1471,plain,
! [X18,X2] :
( class_Int_Onumber__ring(X2)
=> ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Groups_Oone__class_Oone(X2) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X18)
=> c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin),X18) = c_Int_Onumber__class_Onumber__of(X2,c_Int_OMin) ) ) ),
inference(fof_simplification,[status(thm)],[fact_neg__one__even__odd__power]) ).
fof(i_0_1472,plain,
! [X17,X18] :
( X18 != X17
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1473,plain,
! [X18,X2] :
( class_Orderings_Opreorder(X2)
=> ~ c_Orderings_Oord__class_Oless(X2,X18,X18) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1474,plain,
! [X2596] : c_Nat_OSuc(X2596) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).
fof(i_0_1475,plain,
! [X2595] : c_Nat_OSuc(X2595) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).
fof(i_0_1476,plain,
! [X2593] : c_Nat_OSuc(X2593) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).
fof(i_0_1477,plain,
! [X2598] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2598),
inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).
fof(i_0_1478,plain,
! [X2597] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2597),
inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).
fof(i_0_1479,plain,
! [X2594] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X2594),
inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).
fof(i_0_1480,plain,
! [X2625] : c_Nat_OSuc(X2625) != X2625,
inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).
fof(i_0_1481,plain,
! [X2626] : X2626 != c_Nat_OSuc(X2626),
inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).
fof(i_0_1482,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1483,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1484,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1485,plain,
! [X2582] :
( ( c_Int_OPls != c_Int_OBit0(X2582)
| c_Int_OPls = X2582 )
& ( c_Int_OPls != X2582
| c_Int_OPls = c_Int_OBit0(X2582) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).
fof(i_0_1486,plain,
! [X2583] :
( ( c_Int_OBit0(X2583) != c_Int_OPls
| X2583 = c_Int_OPls )
& ( X2583 != c_Int_OPls
| c_Int_OBit0(X2583) = c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).
fof(i_0_1487,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X13),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1488,plain,
! [X13] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X13,X13),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1489,plain,
! [X3074] : c_Int_OBit0(X3074) != c_Int_OMin,
inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(i_0_1490,plain,
! [X3073] : c_Int_OMin != c_Int_OBit0(X3073),
inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(i_0_1491,plain,
! [X13] :
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X13)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) ),
inference(fof_simplification,[status(thm)],[fact_odd__pos]) ).
cnf(i_0_1492,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,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,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),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_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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,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,X4,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_1190]) ).
cnf(i_0_1493,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_1191]) ).
cnf(i_0_1494,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_1192]) ).
cnf(i_0_1495,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X4),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_NthRoot_Osqrt(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,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(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,X4,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_1193]) ).
cnf(i_0_1496,plain,
c_Transcendental_Oarctan(X1) = 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))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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)))))))))),
inference(split_conjunct,[status(thm)],[i_0_1194]) ).
cnf(i_0_1497,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1195]) ).
cnf(i_0_1498,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,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,X4,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_1196]) ).
cnf(i_0_1499,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(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,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(split_conjunct,[status(thm)],[i_0_1197]) ).
cnf(i_0_1500,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(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,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),X1)
| ~ 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,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1198]) ).
cnf(i_0_1501,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_NthRoot_Osqrt(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))))))),
inference(split_conjunct,[status(thm)],[i_0_1199]) ).
cnf(i_0_1502,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_NthRoot_Osqrt(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))))))),
inference(split_conjunct,[status(thm)],[i_0_1200]) ).
cnf(i_0_1503,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(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))))))),
inference(split_conjunct,[status(thm)],[i_0_1201]) ).
cnf(i_0_1504,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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))))))),
inference(split_conjunct,[status(thm)],[i_0_1202]) ).
cnf(i_0_1505,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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))))))),
inference(split_conjunct,[status(thm)],[i_0_1203]) ).
cnf(i_0_1506,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_1204]) ).
cnf(i_0_1507,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_1205]) ).
cnf(i_0_1508,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_1206]) ).
cnf(i_0_1509,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_1207]) ).
cnf(i_0_1510,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_1208]) ).
cnf(i_0_1511,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_1209]) ).
cnf(i_0_1512,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_1209]) ).
cnf(i_0_1513,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_1210]) ).
cnf(i_0_1514,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(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)))))) != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1211]) ).
cnf(i_0_1515,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(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)))))) != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1212]) ).
cnf(i_0_1516,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_1213]) ).
cnf(i_0_1517,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_1214]) ).
cnf(i_0_1518,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_1215]) ).
cnf(i_0_1519,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_1216]) ).
cnf(i_0_1520,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_1209]) ).
cnf(i_0_1521,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_1208]) ).
cnf(i_0_1522,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_1208]) ).
cnf(i_0_1523,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_1217]) ).
cnf(i_0_1524,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_1218]) ).
cnf(i_0_1525,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_1219]) ).
cnf(i_0_1526,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_1220]) ).
cnf(i_0_1527,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_1221]) ).
cnf(i_0_1528,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_1221]) ).
cnf(i_0_1529,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_1222]) ).
cnf(i_0_1530,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_1222]) ).
cnf(i_0_1531,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_1223]) ).
cnf(i_0_1532,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_1224]) ).
cnf(i_0_1533,plain,
( 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3)
| X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,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))),X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1225]) ).
cnf(i_0_1534,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_1226]) ).
cnf(i_0_1535,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_1227]) ).
cnf(i_0_1536,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_1221]) ).
cnf(i_0_1537,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_1222]) ).
cnf(i_0_1538,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_1228]) ).
cnf(i_0_1539,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1229]) ).
cnf(i_0_1540,plain,
( X1 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,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))),X3))
| 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1225]) ).
cnf(i_0_1541,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_1230]) ).
cnf(i_0_1542,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_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
cnf(i_0_1543,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_1232]) ).
cnf(i_0_1544,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_1233]) ).
cnf(i_0_1545,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_1234]) ).
cnf(i_0_1546,negated_conjecture,
v_na____ != 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(split_conjunct,[status(thm)],[i_0_1235]) ).
cnf(i_0_1547,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_1236]) ).
cnf(i_0_1548,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_1237]) ).
cnf(i_0_1549,plain,
( c_Groups_Oabs__class_Oabs(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,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_1238]) ).
cnf(i_0_1550,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_1239]) ).
cnf(i_0_1551,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_1239]) ).
cnf(i_0_1552,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1240]) ).
cnf(i_0_1553,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1241]) ).
cnf(i_0_1554,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_1242]) ).
cnf(i_0_1555,plain,
( c_Orderings_Oord__class_Oless(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_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1243]) ).
cnf(i_0_1556,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1244]) ).
cnf(i_0_1557,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1231]) ).
cnf(i_0_1558,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1245]) ).
cnf(i_0_1559,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1246]) ).
cnf(i_0_1560,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_1247]) ).
cnf(i_0_1561,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))),esk1_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1233]) ).
cnf(i_0_1562,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_1232]) ).
cnf(i_0_1563,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_1248]) ).
cnf(i_0_1564,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_1249]) ).
cnf(i_0_1565,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(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,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_1250]) ).
cnf(i_0_1566,plain,
c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[i_0_1251]) ).
cnf(i_0_1567,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_1236]) ).
cnf(i_0_1568,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__two__gt__one]) ).
cnf(i_0_1569,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__two__gt__zero]) ).
cnf(i_0_1570,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__two__ge__zero]) ).
cnf(i_0_1571,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_1252]) ).
cnf(i_0_1572,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_1253]) ).
cnf(i_0_1573,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_1574,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_1254]) ).
cnf(i_0_1575,plain,
( c_NthRoot_Osqrt(X2) = X1
| 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)))) != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1255]) ).
cnf(i_0_1576,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(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_1256]) ).
cnf(i_0_1577,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_1257]) ).
cnf(i_0_1578,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_1258]) ).
cnf(i_0_1579,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_1259]) ).
cnf(i_0_1580,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_1260]) ).
fof(i_0_1581,plain,
! [X3971,X3972,X3973,X3974,X3975] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3973,X3974),X3972,X3971)
| c_Orderings_Oord__class_Oless__eq(X3974,hAPP(X3972,X3975),hAPP(X3971,X3975))
| ~ class_Orderings_Oord(X3974) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3974,hAPP(X3972,esk9_4(X3971,X3972,X3973,X3974)),hAPP(X3971,esk9_4(X3971,X3972,X3973,X3974)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3973,X3974),X3972,X3971)
| ~ class_Orderings_Oord(X3974) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__fun__def])])])])]) ).
cnf(i_0_1582,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_1261]) ).
cnf(i_0_1583,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_1262]) ).
cnf(i_0_1584,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_1263]) ).
cnf(i_0_1585,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1256]) ).
cnf(i_0_1586,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1264]) ).
cnf(i_0_1587,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_1265]) ).
cnf(i_0_1588,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_1266]) ).
cnf(i_0_1589,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_1267]) ).
cnf(i_0_1590,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_1268]) ).
cnf(i_0_1591,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_1269]) ).
cnf(i_0_1592,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_1270]) ).
cnf(i_0_1593,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_1259]) ).
cnf(i_0_1594,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_1258]) ).
cnf(i_0_1595,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_1271]) ).
cnf(i_0_1596,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_1272]) ).
cnf(i_0_1597,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Complex_Oii,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(split_conjunct,[status(thm)],[fact_power2__i]) ).
cnf(i_0_1598,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_1273]) ).
cnf(i_0_1599,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_1600,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_1601,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_1602,plain,
! [X4623] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4623,v_na____)
| X4623 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,esk11_1(X4623),X4623)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IH])])]) ).
cnf(i_0_1603,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_1604,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_1605,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,esk12_0,v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_calculation])])]) ).
fof(i_0_1606,plain,
! [X3903,X3904,X3905,X3906,X3907,X3908] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3908,X3907),X3906) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3905,X3904),X3903)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3905,X3904),X3903),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3906,X3908)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3903)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3905)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3905,X3908)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3904,X3907) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1607,plain,
! [X3914,X3915,X3916,X3917,X3918,X3919] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3919,X3918),X3917) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3916,X3915),X3914)
| ~ 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,X3916,X3915),X3914))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3914,X3916)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3917)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3916)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3916,X3919)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3918,X3915) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
cnf(i_0_1608,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_1274]) ).
cnf(i_0_1609,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_1610,plain,
! [X3920,X3921,X3922,X3923,X3924] :
( ~ 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,X3924,X3923),X3922),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3924,X3921),X3920))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3922)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3922,X3924)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3920,X3924)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3923,X3921) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1611,plain,
! [X3909,X3910,X3911,X3912,X3913] :
( ~ 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,X3913,X3912),X3911),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3913,X3910),X3909))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3909,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3913,X3909)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3913,X3911)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3910,X3912) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
cnf(i_0_1612,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_1275]) ).
cnf(i_0_1613,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_1276]) ).
cnf(i_0_1614,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_1277]) ).
cnf(i_0_1615,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_1278]) ).
cnf(i_0_1616,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_1279]) ).
cnf(i_0_1617,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_1280]) ).
cnf(i_0_1618,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_1281]) ).
cnf(i_0_1619,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_1282]) ).
fof(i_0_1620,plain,
! [X5069,X5070,X5071,X5072] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5072)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5071)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5071,X5070)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5070,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5069,X5072)),X5071),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5070,X5072)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).
fof(i_0_1621,plain,
! [X5065,X5066,X5067,X5068] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5068)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5067,X5066)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5066,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5067,X5068),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5067,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5065,X5068)),X5066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).
fof(i_0_1622,plain,
! [X4100,X4101] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4101,X4101),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4100,X4100)))),
inference(variable_rename,[status(thm)],[fact_real__sqrt__mult__self__sum__ge__zero]) ).
fof(i_0_1623,plain,
! [X3969,X3970] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3970,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3970,X3970),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3969,X3969)))),
inference(variable_rename,[status(thm)],[fact_le__real__sqrt__sumsq]) ).
fof(i_0_1624,plain,
! [X5092,X5093,X5094,X5095,X5096,X5097,X5098,X5099,X5100,X5101] :
( ( X5093 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| hBOOL(hAPP(X5094,X5092))
| ~ epred1_3(X5094,X5093,X5092) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5093)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5096)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5096,X5093)
| X5092 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5093,X5095),X5096)
| hBOOL(hAPP(X5094,X5096))
| ~ epred1_3(X5094,X5093,X5092) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5093,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5093,X5098)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5098,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5092 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5093,X5097),X5098)
| hBOOL(hAPP(X5094,X5098))
| ~ epred1_3(X5094,X5093,X5092) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,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),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),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),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| X5100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,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),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),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),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X5099,X5100,X5101),X5100)
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk14_3(X5099,X5100,X5101)),esk15_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X5100,esk17_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X5099,X5100,X5101),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( X5099 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5100,esk16_3(X5099,X5100,X5101)),esk17_3(X5099,X5100,X5101))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) )
& ( ~ hBOOL(hAPP(X5101,esk17_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,esk15_3(X5099,X5100,X5101)))
| ~ hBOOL(hAPP(X5101,X5099))
| epred1_3(X5101,X5100,X5099) ) ),
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_1181])])])])])]) ).
fof(i_0_1625,plain,
! [X4559,X4560,X4561,X4562,X4563,X4564] :
( ~ class_Rings_Olinordered__semiring__1__strict(X4564)
| ~ c_Orderings_Oord__class_Oless(X4564,X4563,X4562)
| ~ c_Orderings_Oord__class_Oless(X4564,X4561,X4562)
| ~ c_Orderings_Oord__class_Oless__eq(X4564,c_Groups_Ozero__class_Ozero(X4564),X4560)
| ~ c_Orderings_Oord__class_Oless__eq(X4564,c_Groups_Ozero__class_Ozero(X4564),X4559)
| c_Groups_Oplus__class_Oplus(X4564,X4560,X4559) != c_Groups_Oone__class_Oone(X4564)
| c_Orderings_Oord__class_Oless(X4564,c_Groups_Oplus__class_Oplus(X4564,c_Groups_Otimes__class_Otimes(X4564,X4560,X4563),c_Groups_Otimes__class_Otimes(X4564,X4559,X4561)),X4562) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1626,plain,
! [X4493,X4494,X4495,X4496,X4497,X4498] :
( ~ class_Rings_Olinordered__semiring__1(X4498)
| ~ c_Orderings_Oord__class_Oless__eq(X4498,X4497,X4496)
| ~ c_Orderings_Oord__class_Oless__eq(X4498,X4495,X4496)
| ~ c_Orderings_Oord__class_Oless__eq(X4498,c_Groups_Ozero__class_Ozero(X4498),X4494)
| ~ c_Orderings_Oord__class_Oless__eq(X4498,c_Groups_Ozero__class_Ozero(X4498),X4493)
| c_Groups_Oplus__class_Oplus(X4498,X4494,X4493) != c_Groups_Oone__class_Oone(X4498)
| c_Orderings_Oord__class_Oless__eq(X4498,c_Groups_Oplus__class_Oplus(X4498,c_Groups_Otimes__class_Otimes(X4498,X4494,X4497),c_Groups_Otimes__class_Otimes(X4498,X4493,X4495)),X4496) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1627,plain,
! [X5061,X5062,X5063,X5064] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5064)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5063,X5062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5062,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,X5063,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5061,X5064)),X5062),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_1628,plain,
! [X5073,X5074,X5075,X5076] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5076)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5075)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5075,X5074)
| 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,X5074,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5073,X5076)),X5075)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).
fof(i_0_1629,plain,
! [X4489,X4490,X4491,X4492] :
( ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| ~ c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4491)
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| ~ c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),X4489)
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| ~ c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),X4489)
| c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4491)
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),X4489)
| ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4491)
| c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),c_Int_Onumber__class_Onumber__of(X4492,X4490))
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),X4489)
| c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Int_Onumber__class_Onumber__of(X4492,X4490),c_Groups_Ozero__class_Ozero(X4492))
| ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4491)
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) )
& ( ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Ozero__class_Ozero(X4492),X4489)
| ~ c_Orderings_Oord__class_Oless(X4492,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4491)
| ~ c_Orderings_Oord__class_Oless(X4492,X4491,c_Groups_Otimes__class_Otimes(X4492,X4489,c_Int_Onumber__class_Onumber__of(X4492,X4490)))
| c_Orderings_Oord__class_Oless(X4492,c_Rings_Oinverse__class_Odivide(X4492,X4491,c_Int_Onumber__class_Onumber__of(X4492,X4490)),X4489)
| ~ class_Fields_Olinordered__field__inverse__zero(X4492)
| ~ class_Int_Onumber(X4492) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1283])])]) ).
fof(i_0_1630,plain,
! [X4543,X4544,X4545,X4546] :
( ( ~ c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4545)
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Ozero__class_Ozero(X4546),X4543)
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Ozero__class_Ozero(X4546),X4543)
| c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4545)
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Ozero__class_Ozero(X4546),X4543)
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4545)
| c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Groups_Ozero__class_Ozero(X4546),c_Int_Onumber__class_Onumber__of(X4546,X4544))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Ozero__class_Ozero(X4546),X4543)
| c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless(X4546,c_Int_Onumber__class_Onumber__of(X4546,X4544),c_Groups_Ozero__class_Ozero(X4546))
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4545)
| ~ c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Ozero__class_Ozero(X4546),X4543)
| ~ c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4545)
| ~ c_Orderings_Oord__class_Oless__eq(X4546,X4545,c_Groups_Otimes__class_Otimes(X4546,X4543,c_Int_Onumber__class_Onumber__of(X4546,X4544)))
| c_Orderings_Oord__class_Oless__eq(X4546,c_Rings_Oinverse__class_Odivide(X4546,X4545,c_Int_Onumber__class_Onumber__of(X4546,X4544)),X4543)
| ~ class_Fields_Olinordered__field__inverse__zero(X4546)
| ~ class_Int_Onumber(X4546) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1284])])]) ).
fof(i_0_1631,plain,
! [X4477,X4478,X4479,X4480] :
( ( ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,X4478,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,X4478,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,X4478,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Ozero__class_Ozero(X4480),c_Int_Onumber__class_Onumber__of(X4480,X4477))
| ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Groups_Ozero__class_Ozero(X4480))
| c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,c_Int_Onumber__class_Onumber__of(X4480,X4477),c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,X4478,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) )
& ( ~ c_Orderings_Oord__class_Oless(X4480,X4479,c_Groups_Ozero__class_Ozero(X4480))
| ~ c_Orderings_Oord__class_Oless(X4480,X4478,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ c_Orderings_Oord__class_Oless(X4480,c_Groups_Otimes__class_Otimes(X4480,X4479,c_Int_Onumber__class_Onumber__of(X4480,X4477)),X4478)
| c_Orderings_Oord__class_Oless(X4480,X4479,c_Rings_Oinverse__class_Odivide(X4480,X4478,c_Int_Onumber__class_Onumber__of(X4480,X4477)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4480)
| ~ class_Int_Onumber(X4480) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1285])])]) ).
fof(i_0_1632,plain,
! [X4555,X4556,X4557,X4558] :
( ( ~ c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless__eq(X4558,X4556,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4556,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4556,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Groups_Ozero__class_Ozero(X4558),c_Int_Onumber__class_Onumber__of(X4558,X4555))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Groups_Ozero__class_Ozero(X4558))
| c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless(X4558,c_Int_Onumber__class_Onumber__of(X4558,X4555),c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4556,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Groups_Ozero__class_Ozero(X4558))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4556,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Otimes__class_Otimes(X4558,X4557,c_Int_Onumber__class_Onumber__of(X4558,X4555)),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,X4557,c_Rings_Oinverse__class_Odivide(X4558,X4556,c_Int_Onumber__class_Onumber__of(X4558,X4555)))
| ~ class_Fields_Olinordered__field__inverse__zero(X4558)
| ~ class_Int_Onumber(X4558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1286])])]) ).
fof(i_0_1633,plain,
! [X4485,X4486,X4487,X4488] :
( ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| ~ c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486),X4487)
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| ~ c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| ~ c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486),X4487)
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486),X4487)
| c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),X4486)
| ~ c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| ~ c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| ~ c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,X4486,c_Groups_Ozero__class_Ozero(X4488))
| ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486),X4487)
| ~ c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) )
& ( ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Ozero__class_Ozero(X4488),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ c_Orderings_Oord__class_Oless(X4488,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486),X4487)
| ~ c_Orderings_Oord__class_Oless(X4488,X4487,c_Groups_Otimes__class_Otimes(X4488,c_Int_Onumber__class_Onumber__of(X4488,X4485),X4486))
| c_Orderings_Oord__class_Oless(X4488,c_Rings_Oinverse__class_Odivide(X4488,X4487,X4486),c_Int_Onumber__class_Onumber__of(X4488,X4485))
| ~ class_Fields_Olinordered__field__inverse__zero(X4488)
| ~ class_Int_Onumber(X4488) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1287])])]) ).
fof(i_0_1634,plain,
! [X4547,X4548,X4549,X4550] :
( ( ~ c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548),X4549)
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548),X4549)
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548),X4549)
| c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,c_Groups_Ozero__class_Ozero(X4550),X4548)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless(X4550,X4548,c_Groups_Ozero__class_Ozero(X4550))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548),X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Ozero__class_Ozero(X4550),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ c_Orderings_Oord__class_Oless__eq(X4550,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548),X4549)
| ~ c_Orderings_Oord__class_Oless__eq(X4550,X4549,c_Groups_Otimes__class_Otimes(X4550,c_Int_Onumber__class_Onumber__of(X4550,X4547),X4548))
| c_Orderings_Oord__class_Oless__eq(X4550,c_Rings_Oinverse__class_Odivide(X4550,X4549,X4548),c_Int_Onumber__class_Onumber__of(X4550,X4547))
| ~ class_Fields_Olinordered__field__inverse__zero(X4550)
| ~ class_Int_Onumber(X4550) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1288])])]) ).
fof(i_0_1635,plain,
! [X4481,X4482,X4483,X4484] :
( ( ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,X4482,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,X4482,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,X4482,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481))
| c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Ozero__class_Ozero(X4484),X4481)
| ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Groups_Ozero__class_Ozero(X4484))
| c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,X4481,c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,X4482,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481))
| ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) )
& ( ~ c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Groups_Ozero__class_Ozero(X4484))
| ~ c_Orderings_Oord__class_Oless(X4484,X4482,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481))
| ~ c_Orderings_Oord__class_Oless(X4484,c_Groups_Otimes__class_Otimes(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),X4481),X4482)
| c_Orderings_Oord__class_Oless(X4484,c_Int_Onumber__class_Onumber__of(X4484,X4483),c_Rings_Oinverse__class_Odivide(X4484,X4482,X4481))
| ~ class_Fields_Olinordered__field__inverse__zero(X4484)
| ~ class_Int_Onumber(X4484) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1289])])]) ).
fof(i_0_1636,plain,
! [X4551,X4552,X4553,X4554] :
( ( ~ c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless__eq(X4554,X4552,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,X4552,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,X4552,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551))
| c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,c_Groups_Ozero__class_Ozero(X4554),X4551)
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Groups_Ozero__class_Ozero(X4554))
| c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless(X4554,X4551,c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,X4552,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Groups_Ozero__class_Ozero(X4554))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,X4552,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551))
| ~ c_Orderings_Oord__class_Oless__eq(X4554,c_Groups_Otimes__class_Otimes(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),X4551),X4552)
| c_Orderings_Oord__class_Oless__eq(X4554,c_Int_Onumber__class_Onumber__of(X4554,X4553),c_Rings_Oinverse__class_Odivide(X4554,X4552,X4551))
| ~ class_Fields_Olinordered__field__inverse__zero(X4554)
| ~ class_Int_Onumber(X4554) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])])]) ).
fof(i_0_1637,plain,
! [X4837,X4838,X4839,X4840,X4841] :
( ~ class_Fields_Ofield(X4841)
| X4840 = c_Groups_Ozero__class_Ozero(X4841)
| X4839 = c_Groups_Ozero__class_Ozero(X4841)
| c_Groups_Oplus__class_Oplus(X4841,c_Rings_Oinverse__class_Odivide(X4841,X4838,X4840),c_Rings_Oinverse__class_Odivide(X4841,X4837,X4839)) = c_Rings_Oinverse__class_Odivide(X4841,c_Groups_Oplus__class_Oplus(X4841,c_Groups_Otimes__class_Otimes(X4841,X4838,X4839),c_Groups_Otimes__class_Otimes(X4841,X4837,X4840)),c_Groups_Otimes__class_Otimes(X4841,X4840,X4839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).
fof(i_0_1638,plain,
! [X2940,X2941,X2942] :
( ( ~ c_Orderings_Oord__class_Oless(X2942,c_Groups_Ozero__class_Ozero(X2942),c_Groups_Oplus__class_Oplus(X2942,c_Groups_Otimes__class_Otimes(X2942,X2941,X2941),c_Groups_Otimes__class_Otimes(X2942,X2940,X2940)))
| X2941 != c_Groups_Ozero__class_Ozero(X2942)
| X2940 != c_Groups_Ozero__class_Ozero(X2942)
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( X2941 = c_Groups_Ozero__class_Ozero(X2942)
| c_Orderings_Oord__class_Oless(X2942,c_Groups_Ozero__class_Ozero(X2942),c_Groups_Oplus__class_Oplus(X2942,c_Groups_Otimes__class_Otimes(X2942,X2941,X2941),c_Groups_Otimes__class_Otimes(X2942,X2940,X2940)))
| ~ class_Rings_Olinordered__ring__strict(X2942) )
& ( X2940 = c_Groups_Ozero__class_Ozero(X2942)
| c_Orderings_Oord__class_Oless(X2942,c_Groups_Ozero__class_Ozero(X2942),c_Groups_Oplus__class_Oplus(X2942,c_Groups_Otimes__class_Otimes(X2942,X2941,X2941),c_Groups_Otimes__class_Otimes(X2942,X2940,X2940)))
| ~ class_Rings_Olinordered__ring__strict(X2942) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
cnf(i_0_1639,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_1291]) ).
cnf(i_0_1640,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_1292]) ).
cnf(i_0_1641,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_1293]) ).
fof(i_0_1642,plain,
! [X2946,X2947,X2948] :
( ( X2947 = c_Groups_Ozero__class_Ozero(X2948)
| ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Oplus__class_Oplus(X2948,c_Groups_Otimes__class_Otimes(X2948,X2947,X2947),c_Groups_Otimes__class_Otimes(X2948,X2946,X2946)),c_Groups_Ozero__class_Ozero(X2948))
| ~ class_Rings_Olinordered__ring__strict(X2948) )
& ( X2946 = c_Groups_Ozero__class_Ozero(X2948)
| ~ c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Oplus__class_Oplus(X2948,c_Groups_Otimes__class_Otimes(X2948,X2947,X2947),c_Groups_Otimes__class_Otimes(X2948,X2946,X2946)),c_Groups_Ozero__class_Ozero(X2948))
| ~ class_Rings_Olinordered__ring__strict(X2948) )
& ( X2947 != c_Groups_Ozero__class_Ozero(X2948)
| X2946 != c_Groups_Ozero__class_Ozero(X2948)
| c_Orderings_Oord__class_Oless__eq(X2948,c_Groups_Oplus__class_Oplus(X2948,c_Groups_Otimes__class_Otimes(X2948,X2947,X2947),c_Groups_Otimes__class_Otimes(X2948,X2946,X2946)),c_Groups_Ozero__class_Ozero(X2948))
| ~ class_Rings_Olinordered__ring__strict(X2948) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1643,plain,
! [X2943,X2944,X2945] :
( ~ class_Rings_Olinordered__ring(X2945)
| ~ c_Orderings_Oord__class_Oless(X2945,c_Groups_Oplus__class_Oplus(X2945,c_Groups_Otimes__class_Otimes(X2945,X2944,X2944),c_Groups_Otimes__class_Otimes(X2945,X2943,X2943)),c_Groups_Ozero__class_Ozero(X2945)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1294])]) ).
cnf(i_0_1644,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))),esk3_1(X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1275]) ).
fof(i_0_1645,plain,
! [X3044,X3045,X3046,X3047,X3048] :
( ~ class_Rings_Osemiring(X3048)
| c_Groups_Oplus__class_Oplus(X3048,c_Groups_Otimes__class_Otimes(X3048,X3047,X3046),c_Groups_Oplus__class_Oplus(X3048,c_Groups_Otimes__class_Otimes(X3048,X3045,X3046),X3044)) = c_Groups_Oplus__class_Oplus(X3048,c_Groups_Otimes__class_Otimes(X3048,c_Groups_Oplus__class_Oplus(X3048,X3047,X3045),X3046),X3044) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1646,plain,
! [X3053,X3054,X3055,X3056,X3057] :
( ( X3056 = X3055
| X3054 = X3053
| c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3054),c_Groups_Otimes__class_Otimes(X3057,X3055,X3053)) != c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3053),c_Groups_Otimes__class_Otimes(X3057,X3055,X3054))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3057) )
& ( X3056 != X3055
| c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3054),c_Groups_Otimes__class_Otimes(X3057,X3055,X3053)) = c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3053),c_Groups_Otimes__class_Otimes(X3057,X3055,X3054))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3057) )
& ( X3054 != X3053
| c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3054),c_Groups_Otimes__class_Otimes(X3057,X3055,X3053)) = c_Groups_Oplus__class_Oplus(X3057,c_Groups_Otimes__class_Otimes(X3057,X3056,X3053),c_Groups_Otimes__class_Otimes(X3057,X3055,X3054))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1647,plain,
! [X3066,X3067,X3068,X3069,X3070] :
( ( c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3068),c_Groups_Otimes__class_Otimes(X3070,X3067,X3066)) != c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3066),c_Groups_Otimes__class_Otimes(X3070,X3067,X3068))
| X3069 = X3067
| X3068 = X3066
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3070) )
& ( X3069 != X3067
| c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3068),c_Groups_Otimes__class_Otimes(X3070,X3067,X3066)) = c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3066),c_Groups_Otimes__class_Otimes(X3070,X3067,X3068))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3070) )
& ( X3068 != X3066
| c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3068),c_Groups_Otimes__class_Otimes(X3070,X3067,X3066)) = c_Groups_Oplus__class_Oplus(X3070,c_Groups_Otimes__class_Otimes(X3070,X3069,X3066),c_Groups_Otimes__class_Otimes(X3070,X3067,X3068))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3070) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
cnf(i_0_1648,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_1295]) ).
cnf(i_0_1649,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_1296]) ).
cnf(i_0_1650,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_1297]) ).
fof(i_0_1651,plain,
! [X3163,X3164,X3165,X3166] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3166,X3165),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3164,X3165),X3163)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3166,X3164),X3165),X3163),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1652,plain,
! [X3925,X3926,X3927] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3927,X3926),X3925),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),X3925)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3927)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3926,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_1653,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_1298]) ).
cnf(i_0_1654,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_1299]) ).
cnf(i_0_1655,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_1300]) ).
cnf(i_0_1656,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_1301]) ).
cnf(i_0_1657,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_1302]) ).
cnf(i_0_1658,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_1303]) ).
cnf(i_0_1659,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_1304]) ).
cnf(i_0_1660,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_1305]) ).
fof(i_0_1661,plain,
! [X3936,X3937,X3938] :
( ~ 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,X3938,X3937),X3936))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3936,X3938)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3938)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3937) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
cnf(i_0_1662,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_1306]) ).
cnf(i_0_1663,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_1307]) ).
cnf(i_0_1664,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_1277]) ).
cnf(i_0_1665,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_1278]) ).
cnf(i_0_1666,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_1279]) ).
cnf(i_0_1667,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_1280]) ).
cnf(i_0_1668,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_1281]) ).
cnf(i_0_1669,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_1282]) ).
fof(i_0_1670,plain,
! [X4785,X4786,X4787,X4788] :
( ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| ~ c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786),X4787)
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| ~ c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4785)
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| ~ c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4785)
| c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786),X4787)
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4785)
| ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786),X4787)
| c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4786)
| ~ c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| ~ c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4785)
| c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| ~ c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,X4786,c_Groups_Ozero__class_Ozero(X4788))
| ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786),X4787)
| ~ c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) )
& ( ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Ozero__class_Ozero(X4788),X4785)
| ~ c_Orderings_Oord__class_Oless(X4788,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786),X4787)
| ~ c_Orderings_Oord__class_Oless(X4788,X4787,c_Groups_Otimes__class_Otimes(X4788,X4785,X4786))
| c_Orderings_Oord__class_Oless(X4788,c_Rings_Oinverse__class_Odivide(X4788,X4787,X4786),X4785)
| ~ class_Fields_Olinordered__field__inverse__zero(X4788) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])])]) ).
fof(i_0_1671,plain,
! [X4883,X4884,X4885,X4886] :
( ( ~ c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884),X4885)
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Ozero__class_Ozero(X4886),X4883)
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Ozero__class_Ozero(X4886),X4883)
| c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884),X4885)
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Ozero__class_Ozero(X4886),X4883)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884),X4885)
| c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,c_Groups_Ozero__class_Ozero(X4886),X4884)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| ~ c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Ozero__class_Ozero(X4886),X4883)
| c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| ~ c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless(X4886,X4884,c_Groups_Ozero__class_Ozero(X4886))
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884),X4885)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Ozero__class_Ozero(X4886),X4883)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884),X4885)
| ~ c_Orderings_Oord__class_Oless__eq(X4886,X4885,c_Groups_Otimes__class_Otimes(X4886,X4883,X4884))
| c_Orderings_Oord__class_Oless__eq(X4886,c_Rings_Oinverse__class_Odivide(X4886,X4885,X4884),X4883)
| ~ class_Fields_Olinordered__field__inverse__zero(X4886) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1309])])]) ).
fof(i_0_1672,plain,
! [X4781,X4782,X4783,X4784] :
( ( ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4782,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,X4782,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,X4782,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781))
| c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Ozero__class_Ozero(X4784),X4781)
| ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Groups_Ozero__class_Ozero(X4784))
| c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4781,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,X4782,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781))
| ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) )
& ( ~ c_Orderings_Oord__class_Oless(X4784,X4783,c_Groups_Ozero__class_Ozero(X4784))
| ~ c_Orderings_Oord__class_Oless(X4784,X4782,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781))
| ~ c_Orderings_Oord__class_Oless(X4784,c_Groups_Otimes__class_Otimes(X4784,X4783,X4781),X4782)
| c_Orderings_Oord__class_Oless(X4784,X4783,c_Rings_Oinverse__class_Odivide(X4784,X4782,X4781))
| ~ class_Fields_Olinordered__field__inverse__zero(X4784) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1310])])]) ).
fof(i_0_1673,plain,
! [X4625,X4626,X4627,X4628] :
( ( ~ c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless__eq(X4628,X4626,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4626,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4626,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625))
| c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,c_Groups_Ozero__class_Ozero(X4628),X4625)
| ~ c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless(X4628,X4625,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4626,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Groups_Ozero__class_Ozero(X4628))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,X4626,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625))
| ~ c_Orderings_Oord__class_Oless__eq(X4628,c_Groups_Otimes__class_Otimes(X4628,X4627,X4625),X4626)
| c_Orderings_Oord__class_Oless__eq(X4628,X4627,c_Rings_Oinverse__class_Odivide(X4628,X4626,X4625))
| ~ class_Fields_Olinordered__field__inverse__zero(X4628) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1311])])]) ).
fof(i_0_1674,plain,
! [X5027,X5028,X5029,X5030] :
( ~ class_Divides_Osemiring__div(X5030)
| c_Divides_Odiv__class_Omod(X5030,c_Groups_Oplus__class_Oplus(X5030,X5029,X5028),X5027) = c_Divides_Odiv__class_Omod(X5030,c_Groups_Oplus__class_Oplus(X5030,c_Divides_Odiv__class_Omod(X5030,X5029,X5027),c_Divides_Odiv__class_Omod(X5030,X5028,X5027)),X5027) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).
fof(i_0_1675,plain,
! [X4922,X4923,X4924,X4925] :
( ~ class_Divides_Osemiring__div(X4925)
| c_Divides_Odiv__class_Omod(X4925,c_Groups_Otimes__class_Otimes(X4925,X4924,X4923),X4922) = c_Divides_Odiv__class_Omod(X4925,c_Groups_Otimes__class_Otimes(X4925,c_Divides_Odiv__class_Omod(X4925,X4924,X4922),c_Divides_Odiv__class_Omod(X4925,X4923,X4922)),X4922) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).
fof(i_0_1676,plain,
! [X4842,X4843,X4844] :
( ~ class_Fields_Olinordered__field(X4844)
| ~ c_Orderings_Oord__class_Oless(X4844,X4843,X4842)
| c_Orderings_Oord__class_Oless(X4844,c_Rings_Oinverse__class_Odivide(X4844,c_Groups_Oplus__class_Oplus(X4844,X4843,X4842),c_Groups_Oplus__class_Oplus(X4844,c_Groups_Oone__class_Oone(X4844),c_Groups_Oone__class_Oone(X4844))),X4842) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).
fof(i_0_1677,plain,
! [X4845,X4846,X4847] :
( ~ class_Fields_Olinordered__field(X4847)
| ~ c_Orderings_Oord__class_Oless(X4847,X4846,X4845)
| c_Orderings_Oord__class_Oless(X4847,X4846,c_Rings_Oinverse__class_Odivide(X4847,c_Groups_Oplus__class_Oplus(X4847,X4846,X4845),c_Groups_Oplus__class_Oplus(X4847,c_Groups_Oone__class_Oone(X4847),c_Groups_Oone__class_Oone(X4847)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).
cnf(i_0_1678,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Fields_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1312]) ).
cnf(i_0_1679,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Fields_Ofield(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1313]) ).
fof(i_0_1680,plain,
! [X4813,X4814,X4815,X4816] :
( ~ class_Fields_Olinordered__field(X4816)
| ~ c_Orderings_Oord__class_Oless(X4816,X4815,X4814)
| ~ c_Orderings_Oord__class_Oless(X4816,c_Groups_Ozero__class_Ozero(X4816),X4813)
| ~ c_Orderings_Oord__class_Oless(X4816,c_Groups_Ozero__class_Ozero(X4816),c_Groups_Otimes__class_Otimes(X4816,X4814,X4815))
| c_Orderings_Oord__class_Oless(X4816,c_Rings_Oinverse__class_Odivide(X4816,X4813,X4814),c_Rings_Oinverse__class_Odivide(X4816,X4813,X4815)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).
fof(i_0_1681,plain,
! [X4855,X4856,X4857,X4858] :
( ~ class_Fields_Olinordered__field(X4858)
| ~ c_Orderings_Oord__class_Oless__eq(X4858,X4857,X4856)
| ~ c_Orderings_Oord__class_Oless__eq(X4858,c_Groups_Ozero__class_Ozero(X4858),X4855)
| ~ c_Orderings_Oord__class_Oless(X4858,c_Groups_Ozero__class_Ozero(X4858),c_Groups_Otimes__class_Otimes(X4858,X4856,X4857))
| c_Orderings_Oord__class_Oless__eq(X4858,c_Rings_Oinverse__class_Odivide(X4858,X4855,X4856),c_Rings_Oinverse__class_Odivide(X4858,X4855,X4857)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).
fof(i_0_1682,plain,
! [X4817,X4818,X4819,X4820] :
( ~ class_Fields_Olinordered__field(X4820)
| ~ c_Orderings_Oord__class_Oless(X4820,X4819,X4818)
| ~ c_Orderings_Oord__class_Oless(X4820,X4817,c_Groups_Ozero__class_Ozero(X4820))
| ~ c_Orderings_Oord__class_Oless(X4820,c_Groups_Ozero__class_Ozero(X4820),c_Groups_Otimes__class_Otimes(X4820,X4819,X4818))
| c_Orderings_Oord__class_Oless(X4820,c_Rings_Oinverse__class_Odivide(X4820,X4817,X4819),c_Rings_Oinverse__class_Odivide(X4820,X4817,X4818)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).
fof(i_0_1683,plain,
! [X4851,X4852,X4853,X4854] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4854)
| ~ c_Orderings_Oord__class_Oless__eq(X4854,X4853,X4852)
| ~ c_Orderings_Oord__class_Oless__eq(X4854,X4851,c_Groups_Ozero__class_Ozero(X4854))
| ~ c_Orderings_Oord__class_Oless(X4854,c_Groups_Ozero__class_Ozero(X4854),c_Groups_Otimes__class_Otimes(X4854,X4853,X4852))
| c_Orderings_Oord__class_Oless__eq(X4854,c_Rings_Oinverse__class_Odivide(X4854,X4851,X4853),c_Rings_Oinverse__class_Odivide(X4854,X4851,X4852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).
cnf(i_0_1684,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_1314]) ).
cnf(i_0_1685,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_1315]) ).
cnf(i_0_1686,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_1316]) ).
cnf(i_0_1687,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_1317]) ).
cnf(i_0_1688,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_1318]) ).
fof(i_0_1689,plain,
! [X4637,X4638] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4638),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X4638,X4637)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4637))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
cnf(i_0_1690,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_1319]) ).
fof(i_0_1691,plain,
! [X4499,X4500,X4501] :
( ~ class_Rings_Olinordered__semidom(X4501)
| ~ c_Orderings_Oord__class_Oless(X4501,c_Groups_Ozero__class_Ozero(X4501),X4500)
| ~ c_Orderings_Oord__class_Oless(X4501,X4500,c_Groups_Oone__class_Oone(X4501))
| c_Orderings_Oord__class_Oless(X4501,c_Groups_Otimes__class_Otimes(X4501,X4500,c_Power_Opower__class_Opower(X4501,X4500,X4499)),c_Power_Opower__class_Opower(X4501,X4500,X4499)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
cnf(i_0_1692,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_1320]) ).
cnf(i_0_1693,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_1321]) ).
cnf(i_0_1694,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_1322]) ).
cnf(i_0_1695,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_1323]) ).
fof(i_0_1696,plain,
! [X5039,X5040,X5041,X5042,X5043,X5044] :
( ~ class_Divides_Osemiring__div(X5044)
| c_Divides_Odiv__class_Omod(X5044,X5043,X5042) != c_Divides_Odiv__class_Omod(X5044,X5041,X5042)
| c_Divides_Odiv__class_Omod(X5044,X5040,X5042) != c_Divides_Odiv__class_Omod(X5044,X5039,X5042)
| c_Divides_Odiv__class_Omod(X5044,c_Groups_Oplus__class_Oplus(X5044,X5043,X5040),X5042) = c_Divides_Odiv__class_Omod(X5044,c_Groups_Oplus__class_Oplus(X5044,X5041,X5039),X5042) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).
fof(i_0_1697,plain,
! [X4938,X4939,X4940,X4941,X4942,X4943] :
( ~ class_Divides_Osemiring__div(X4943)
| c_Divides_Odiv__class_Omod(X4943,X4942,X4941) != c_Divides_Odiv__class_Omod(X4943,X4940,X4941)
| c_Divides_Odiv__class_Omod(X4943,X4939,X4941) != c_Divides_Odiv__class_Omod(X4943,X4938,X4941)
| c_Divides_Odiv__class_Omod(X4943,c_Groups_Otimes__class_Otimes(X4943,X4942,X4939),X4941) = c_Divides_Odiv__class_Omod(X4943,c_Groups_Otimes__class_Otimes(X4943,X4940,X4938),X4941) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).
fof(i_0_1698,plain,
! [X4464] :
( ( ~ 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),X4464),X4464),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4464,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4464,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),X4464),X4464),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_1699,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_1324]) ).
fof(i_0_1700,plain,
! [X4668,X4669,X4670,X4671,X4672] :
( ~ class_RealVector_Oreal__normed__vector(X4672)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4672,X4671),X4670)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4672,X4669),X4668)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4672,c_Groups_Oplus__class_Oplus(X4672,X4671,X4669)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4670,X4668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
fof(i_0_1701,plain,
! [X4657,X4658,X4659,X4660,X4661] :
( ~ class_RealVector_Oreal__normed__algebra(X4661)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4661,X4660),X4659)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4661,X4658),X4657)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4661,c_Groups_Otimes__class_Otimes(X4661,X4660,X4658)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4659,X4657)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1702,plain,
! [X5057,X5058,X5059,X5060] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5059)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5059)
| X5059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5060,X5059) = X5057
| X5060 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5059,X5058),X5057) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5059,X5057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5057,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5059)
| X5059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5060,X5059) = X5057
| X5060 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5059,X5058),X5057) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5059)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5057)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5057,X5059)
| X5059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5060,X5059) = X5057
| X5060 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5059,X5058),X5057) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5059,X5057)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5057,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),X5057)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X5057,X5059)
| X5059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5060,X5059) = X5057
| X5060 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X5059,X5058),X5057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])])]) ).
fof(i_0_1703,plain,
! [X2738,X2739,X2740,X2741,X2742] :
( ~ class_Rings_Ocomm__semiring__1(X2742)
| c_Groups_Otimes__class_Otimes(X2742,c_Groups_Otimes__class_Otimes(X2742,X2741,X2740),c_Groups_Otimes__class_Otimes(X2742,X2739,X2738)) = c_Groups_Otimes__class_Otimes(X2742,X2739,c_Groups_Otimes__class_Otimes(X2742,c_Groups_Otimes__class_Otimes(X2742,X2741,X2740),X2738)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1704,plain,
! [X2743,X2744,X2745,X2746,X2747] :
( ~ class_Rings_Ocomm__semiring__1(X2747)
| c_Groups_Otimes__class_Otimes(X2747,c_Groups_Otimes__class_Otimes(X2747,X2746,X2745),c_Groups_Otimes__class_Otimes(X2747,X2744,X2743)) = c_Groups_Otimes__class_Otimes(X2747,X2746,c_Groups_Otimes__class_Otimes(X2747,X2745,c_Groups_Otimes__class_Otimes(X2747,X2744,X2743))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
cnf(i_0_1705,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_1326]) ).
cnf(i_0_1706,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_1327]) ).
cnf(i_0_1707,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_1328]) ).
cnf(i_0_1708,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_1329]) ).
cnf(i_0_1709,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_1330]) ).
cnf(i_0_1710,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_1331]) ).
cnf(i_0_1711,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_1332]) ).
cnf(i_0_1712,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_1333]) ).
fof(i_0_1713,plain,
! [X4770,X4771,X4772,X4773,X4774] :
( ~ class_Fields_Olinordered__field(X4774)
| ~ c_Orderings_Oord__class_Oless(X4774,c_Groups_Ozero__class_Ozero(X4774),X4773)
| ~ c_Orderings_Oord__class_Oless__eq(X4774,X4773,X4772)
| ~ c_Orderings_Oord__class_Oless(X4774,c_Groups_Ozero__class_Ozero(X4774),X4771)
| ~ c_Orderings_Oord__class_Oless(X4774,X4771,X4770)
| c_Orderings_Oord__class_Oless(X4774,c_Rings_Oinverse__class_Odivide(X4774,X4773,X4770),c_Rings_Oinverse__class_Odivide(X4774,X4772,X4771)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).
fof(i_0_1714,plain,
! [X4765,X4766,X4767,X4768,X4769] :
( ~ class_Fields_Olinordered__field(X4769)
| ~ c_Orderings_Oord__class_Oless__eq(X4769,c_Groups_Ozero__class_Ozero(X4769),X4768)
| ~ c_Orderings_Oord__class_Oless(X4769,X4768,X4767)
| ~ c_Orderings_Oord__class_Oless(X4769,c_Groups_Ozero__class_Ozero(X4769),X4766)
| ~ c_Orderings_Oord__class_Oless__eq(X4769,X4766,X4765)
| c_Orderings_Oord__class_Oless(X4769,c_Rings_Oinverse__class_Odivide(X4769,X4768,X4765),c_Rings_Oinverse__class_Odivide(X4769,X4767,X4766)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).
fof(i_0_1715,plain,
! [X2991,X2992,X2993,X2994,X2995] :
( ~ class_Rings_Olinordered__semiring__strict(X2995)
| ~ c_Orderings_Oord__class_Oless(X2995,X2994,X2993)
| ~ c_Orderings_Oord__class_Oless(X2995,X2992,X2991)
| ~ c_Orderings_Oord__class_Oless(X2995,c_Groups_Ozero__class_Ozero(X2995),X2993)
| ~ c_Orderings_Oord__class_Oless__eq(X2995,c_Groups_Ozero__class_Ozero(X2995),X2992)
| c_Orderings_Oord__class_Oless(X2995,c_Groups_Otimes__class_Otimes(X2995,X2994,X2992),c_Groups_Otimes__class_Otimes(X2995,X2993,X2991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1716,plain,
! [X2986,X2987,X2988,X2989,X2990] :
( ~ class_Rings_Olinordered__semiring__strict(X2990)
| ~ c_Orderings_Oord__class_Oless(X2990,X2989,X2988)
| ~ c_Orderings_Oord__class_Oless(X2990,X2987,X2986)
| ~ c_Orderings_Oord__class_Oless__eq(X2990,c_Groups_Ozero__class_Ozero(X2990),X2989)
| ~ c_Orderings_Oord__class_Oless__eq(X2990,c_Groups_Ozero__class_Ozero(X2990),X2987)
| c_Orderings_Oord__class_Oless(X2990,c_Groups_Otimes__class_Otimes(X2990,X2989,X2987),c_Groups_Otimes__class_Otimes(X2990,X2988,X2986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1717,plain,
! [X2976,X2977,X2978,X2979,X2980] :
( ~ class_Rings_Olinordered__semiring__strict(X2980)
| ~ c_Orderings_Oord__class_Oless__eq(X2980,X2979,X2978)
| ~ c_Orderings_Oord__class_Oless(X2980,X2977,X2976)
| ~ c_Orderings_Oord__class_Oless(X2980,c_Groups_Ozero__class_Ozero(X2980),X2979)
| ~ c_Orderings_Oord__class_Oless__eq(X2980,c_Groups_Ozero__class_Ozero(X2980),X2977)
| c_Orderings_Oord__class_Oless(X2980,c_Groups_Otimes__class_Otimes(X2980,X2979,X2977),c_Groups_Otimes__class_Otimes(X2980,X2978,X2976)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1718,plain,
! [X2981,X2982,X2983,X2984,X2985] :
( ~ class_Rings_Olinordered__semiring__strict(X2985)
| ~ c_Orderings_Oord__class_Oless(X2985,X2984,X2983)
| ~ c_Orderings_Oord__class_Oless__eq(X2985,X2982,X2981)
| ~ c_Orderings_Oord__class_Oless__eq(X2985,c_Groups_Ozero__class_Ozero(X2985),X2984)
| ~ c_Orderings_Oord__class_Oless(X2985,c_Groups_Ozero__class_Ozero(X2985),X2982)
| c_Orderings_Oord__class_Oless(X2985,c_Groups_Otimes__class_Otimes(X2985,X2984,X2982),c_Groups_Otimes__class_Otimes(X2985,X2983,X2981)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1719,plain,
! [X4760,X4761,X4762,X4763,X4764] :
( ~ class_Fields_Olinordered__field(X4764)
| ~ c_Orderings_Oord__class_Oless__eq(X4764,c_Groups_Ozero__class_Ozero(X4764),X4763)
| ~ c_Orderings_Oord__class_Oless__eq(X4764,X4763,X4762)
| ~ c_Orderings_Oord__class_Oless(X4764,c_Groups_Ozero__class_Ozero(X4764),X4761)
| ~ c_Orderings_Oord__class_Oless__eq(X4764,X4761,X4760)
| c_Orderings_Oord__class_Oless__eq(X4764,c_Rings_Oinverse__class_Odivide(X4764,X4763,X4760),c_Rings_Oinverse__class_Odivide(X4764,X4762,X4761)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).
fof(i_0_1720,plain,
! [X3302,X3303,X3304,X3305,X3306] :
( ~ class_Rings_Oordered__semiring(X3306)
| ~ c_Orderings_Oord__class_Oless__eq(X3306,X3305,X3304)
| ~ c_Orderings_Oord__class_Oless__eq(X3306,X3303,X3302)
| ~ c_Orderings_Oord__class_Oless__eq(X3306,c_Groups_Ozero__class_Ozero(X3306),X3305)
| ~ c_Orderings_Oord__class_Oless__eq(X3306,c_Groups_Ozero__class_Ozero(X3306),X3303)
| c_Orderings_Oord__class_Oless__eq(X3306,c_Groups_Otimes__class_Otimes(X3306,X3305,X3303),c_Groups_Otimes__class_Otimes(X3306,X3304,X3302)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1721,plain,
! [X3297,X3298,X3299,X3300,X3301] :
( ~ class_Rings_Oordered__semiring(X3301)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,X3300,X3299)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,X3298,X3297)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,c_Groups_Ozero__class_Ozero(X3301),X3299)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,c_Groups_Ozero__class_Ozero(X3301),X3298)
| c_Orderings_Oord__class_Oless__eq(X3301,c_Groups_Otimes__class_Otimes(X3301,X3300,X3298),c_Groups_Otimes__class_Otimes(X3301,X3299,X3297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
cnf(i_0_1722,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_1334]) ).
fof(i_0_1723,plain,
! [X4312,X4313,X4314,X4315,X4316] :
( ~ class_Rings_Olinordered__idom(X4316)
| ~ c_Orderings_Oord__class_Oless(X4316,c_Groups_Oabs__class_Oabs(X4316,X4315),X4314)
| ~ c_Orderings_Oord__class_Oless(X4316,c_Groups_Oabs__class_Oabs(X4316,X4313),X4312)
| c_Orderings_Oord__class_Oless(X4316,c_Groups_Otimes__class_Otimes(X4316,c_Groups_Oabs__class_Oabs(X4316,X4315),c_Groups_Oabs__class_Oabs(X4316,X4313)),c_Groups_Otimes__class_Otimes(X4316,X4314,X4312)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_1724,plain,
! [X2949,X2950,X2951] :
( ~ class_Rings_Olinordered__ring(X2951)
| c_Orderings_Oord__class_Oless__eq(X2951,c_Groups_Ozero__class_Ozero(X2951),c_Groups_Oplus__class_Oplus(X2951,c_Groups_Otimes__class_Otimes(X2951,X2950,X2950),c_Groups_Otimes__class_Otimes(X2951,X2949,X2949))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
cnf(i_0_1725,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_1307]) ).
cnf(i_0_1726,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_1307]) ).
cnf(i_0_1727,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_1335]) ).
cnf(i_0_1728,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_1336]) ).
fof(i_0_1729,plain,
! [X4435,X4436,X4437] :
( ~ class_Rings_Olinordered__semidom(X4437)
| ~ c_Orderings_Oord__class_Oless(X4437,c_Groups_Oone__class_Oone(X4437),X4436)
| c_Orderings_Oord__class_Oless(X4437,c_Power_Opower__class_Opower(X4437,X4436,X4435),c_Groups_Otimes__class_Otimes(X4437,X4436,c_Power_Opower__class_Opower(X4437,X4436,X4435))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
cnf(i_0_1730,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_1337]) ).
fof(i_0_1731,plain,
! [X2972,X2973,X2974,X2975] :
( ~ class_Rings_Olinordered__semiring(X2975)
| ~ c_Orderings_Oord__class_Oless(X2975,c_Groups_Otimes__class_Otimes(X2975,X2974,X2973),c_Groups_Otimes__class_Otimes(X2975,X2972,X2973))
| ~ c_Orderings_Oord__class_Oless__eq(X2975,c_Groups_Ozero__class_Ozero(X2975),X2973)
| c_Orderings_Oord__class_Oless(X2975,X2974,X2972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1732,plain,
! [X2968,X2969,X2970,X2971] :
( ~ class_Rings_Olinordered__semiring__strict(X2971)
| ~ c_Orderings_Oord__class_Oless(X2971,c_Groups_Otimes__class_Otimes(X2971,X2970,X2969),c_Groups_Otimes__class_Otimes(X2971,X2968,X2969))
| ~ c_Orderings_Oord__class_Oless__eq(X2971,c_Groups_Ozero__class_Ozero(X2971),X2969)
| c_Orderings_Oord__class_Oless(X2971,X2970,X2968) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1733,plain,
! [X3004,X3005,X3006,X3007] :
( ~ class_Rings_Olinordered__semidom(X3007)
| ~ c_Orderings_Oord__class_Oless(X3007,c_Power_Opower__class_Opower(X3007,X3006,X3005),c_Power_Opower__class_Opower(X3007,X3004,X3005))
| ~ c_Orderings_Oord__class_Oless__eq(X3007,c_Groups_Ozero__class_Ozero(X3007),X3004)
| c_Orderings_Oord__class_Oless(X3007,X3006,X3004) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1734,plain,
! [X2964,X2965,X2966,X2967] :
( ~ class_Rings_Olinordered__semiring(X2967)
| ~ c_Orderings_Oord__class_Oless(X2967,c_Groups_Otimes__class_Otimes(X2967,X2966,X2965),c_Groups_Otimes__class_Otimes(X2967,X2966,X2964))
| ~ c_Orderings_Oord__class_Oless__eq(X2967,c_Groups_Ozero__class_Ozero(X2967),X2966)
| c_Orderings_Oord__class_Oless(X2967,X2965,X2964) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1735,plain,
! [X2960,X2961,X2962,X2963] :
( ~ class_Rings_Olinordered__semiring__strict(X2963)
| ~ c_Orderings_Oord__class_Oless(X2963,c_Groups_Otimes__class_Otimes(X2963,X2962,X2961),c_Groups_Otimes__class_Otimes(X2963,X2962,X2960))
| ~ c_Orderings_Oord__class_Oless__eq(X2963,c_Groups_Ozero__class_Ozero(X2963),X2962)
| c_Orderings_Oord__class_Oless(X2963,X2961,X2960) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1736,plain,
! [X3277,X3278,X3279,X3280] :
( ( ~ c_Orderings_Oord__class_Oless(X3280,c_Groups_Otimes__class_Otimes(X3280,X3279,X3278),c_Groups_Otimes__class_Otimes(X3280,X3279,X3277))
| c_Orderings_Oord__class_Oless(X3280,X3278,X3277)
| ~ c_Orderings_Oord__class_Oless(X3280,c_Groups_Ozero__class_Ozero(X3280),X3279)
| ~ class_Rings_Olinordered__ring__strict(X3280) )
& ( ~ c_Orderings_Oord__class_Oless(X3280,X3278,X3277)
| c_Orderings_Oord__class_Oless(X3280,c_Groups_Otimes__class_Otimes(X3280,X3279,X3278),c_Groups_Otimes__class_Otimes(X3280,X3279,X3277))
| ~ c_Orderings_Oord__class_Oless(X3280,c_Groups_Ozero__class_Ozero(X3280),X3279)
| ~ class_Rings_Olinordered__ring__strict(X3280) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).
fof(i_0_1737,plain,
! [X2956,X2957,X2958,X2959] :
( ~ class_Rings_Olinordered__semiring__strict(X2959)
| ~ c_Orderings_Oord__class_Oless__eq(X2959,c_Groups_Otimes__class_Otimes(X2959,X2958,X2957),c_Groups_Otimes__class_Otimes(X2959,X2956,X2957))
| ~ c_Orderings_Oord__class_Oless(X2959,c_Groups_Ozero__class_Ozero(X2959),X2957)
| c_Orderings_Oord__class_Oless__eq(X2959,X2958,X2956) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1738,plain,
! [X2952,X2953,X2954,X2955] :
( ~ class_Rings_Olinordered__semiring__strict(X2955)
| ~ c_Orderings_Oord__class_Oless__eq(X2955,c_Groups_Otimes__class_Otimes(X2955,X2954,X2953),c_Groups_Otimes__class_Otimes(X2955,X2954,X2952))
| ~ c_Orderings_Oord__class_Oless(X2955,c_Groups_Ozero__class_Ozero(X2955),X2954)
| c_Orderings_Oord__class_Oless__eq(X2955,X2953,X2952) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1739,plain,
! [X3000,X3001,X3002,X3003] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3003,c_Groups_Otimes__class_Otimes(X3003,X3002,X3001),c_Groups_Otimes__class_Otimes(X3003,X3002,X3000))
| c_Orderings_Oord__class_Oless__eq(X3003,X3001,X3000)
| ~ c_Orderings_Oord__class_Oless(X3003,c_Groups_Ozero__class_Ozero(X3003),X3002)
| ~ class_Rings_Olinordered__ring__strict(X3003) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3003,X3001,X3000)
| c_Orderings_Oord__class_Oless__eq(X3003,c_Groups_Otimes__class_Otimes(X3003,X3002,X3001),c_Groups_Otimes__class_Otimes(X3003,X3002,X3000))
| ~ c_Orderings_Oord__class_Oless(X3003,c_Groups_Ozero__class_Ozero(X3003),X3002)
| ~ class_Rings_Olinordered__ring__strict(X3003) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1740,plain,
! [X3258,X3259,X3260,X3261] :
( ( ~ c_Orderings_Oord__class_Oless(X3261,c_Groups_Otimes__class_Otimes(X3261,X3260,X3259),c_Groups_Otimes__class_Otimes(X3261,X3260,X3258))
| c_Orderings_Oord__class_Oless(X3261,X3258,X3259)
| ~ c_Orderings_Oord__class_Oless(X3261,X3260,c_Groups_Ozero__class_Ozero(X3261))
| ~ class_Rings_Olinordered__ring__strict(X3261) )
& ( ~ c_Orderings_Oord__class_Oless(X3261,X3258,X3259)
| c_Orderings_Oord__class_Oless(X3261,c_Groups_Otimes__class_Otimes(X3261,X3260,X3259),c_Groups_Otimes__class_Otimes(X3261,X3260,X3258))
| ~ c_Orderings_Oord__class_Oless(X3261,X3260,c_Groups_Ozero__class_Ozero(X3261))
| ~ class_Rings_Olinordered__ring__strict(X3261) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1741,plain,
! [X2996,X2997,X2998,X2999] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2999,c_Groups_Otimes__class_Otimes(X2999,X2998,X2997),c_Groups_Otimes__class_Otimes(X2999,X2998,X2996))
| c_Orderings_Oord__class_Oless__eq(X2999,X2996,X2997)
| ~ c_Orderings_Oord__class_Oless(X2999,X2998,c_Groups_Ozero__class_Ozero(X2999))
| ~ class_Rings_Olinordered__ring__strict(X2999) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2999,X2996,X2997)
| c_Orderings_Oord__class_Oless__eq(X2999,c_Groups_Otimes__class_Otimes(X2999,X2998,X2997),c_Groups_Otimes__class_Otimes(X2999,X2998,X2996))
| ~ c_Orderings_Oord__class_Oless(X2999,X2998,c_Groups_Ozero__class_Ozero(X2999))
| ~ class_Rings_Olinordered__ring__strict(X2999) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1742,plain,
! [X4453,X4454,X4455,X4456] :
( ( ~ c_Orderings_Oord__class_Oless(X4456,c_Power_Opower__class_Opower(X4456,X4455,X4454),c_Power_Opower__class_Opower(X4456,X4455,X4453))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4454,X4453)
| ~ c_Orderings_Oord__class_Oless(X4456,c_Groups_Oone__class_Oone(X4456),X4455)
| ~ class_Rings_Olinordered__semidom(X4456) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4454,X4453)
| c_Orderings_Oord__class_Oless(X4456,c_Power_Opower__class_Opower(X4456,X4455,X4454),c_Power_Opower__class_Opower(X4456,X4455,X4453))
| ~ c_Orderings_Oord__class_Oless(X4456,c_Groups_Oone__class_Oone(X4456),X4455)
| ~ class_Rings_Olinordered__semidom(X4456) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1743,plain,
! [X4449,X4450,X4451,X4452] :
( ~ class_Rings_Olinordered__semidom(X4452)
| ~ c_Orderings_Oord__class_Oless(X4452,c_Groups_Oone__class_Oone(X4452),X4451)
| ~ c_Orderings_Oord__class_Oless(X4452,c_Power_Opower__class_Opower(X4452,X4451,X4450),c_Power_Opower__class_Opower(X4452,X4451,X4449))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4450,X4449) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1744,plain,
! [X4522,X4523,X4524,X4525] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4525,c_Power_Opower__class_Opower(X4525,X4524,X4523),c_Power_Opower__class_Opower(X4525,X4524,X4522))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4523,X4522)
| ~ c_Orderings_Oord__class_Oless(X4525,c_Groups_Oone__class_Oone(X4525),X4524)
| ~ class_Rings_Olinordered__semidom(X4525) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4523,X4522)
| c_Orderings_Oord__class_Oless__eq(X4525,c_Power_Opower__class_Opower(X4525,X4524,X4523),c_Power_Opower__class_Opower(X4525,X4524,X4522))
| ~ c_Orderings_Oord__class_Oless(X4525,c_Groups_Oone__class_Oone(X4525),X4524)
| ~ class_Rings_Olinordered__semidom(X4525) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1745,plain,
! [X4518,X4519,X4520,X4521] :
( ~ class_Rings_Olinordered__semidom(X4521)
| ~ c_Orderings_Oord__class_Oless(X4521,c_Groups_Oone__class_Oone(X4521),X4520)
| ~ c_Orderings_Oord__class_Oless__eq(X4521,c_Power_Opower__class_Opower(X4521,X4520,X4519),c_Power_Opower__class_Opower(X4521,X4520,X4518))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4519,X4518) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1746,plain,
! [X3228,X3229,X3230,X3231] :
( ~ class_Int_Onumber(X3231)
| ~ class_Rings_Osemiring(X3231)
| c_Groups_Otimes__class_Otimes(X3231,c_Groups_Oplus__class_Oplus(X3231,X3230,X3229),c_Int_Onumber__class_Onumber__of(X3231,X3228)) = c_Groups_Oplus__class_Oplus(X3231,c_Groups_Otimes__class_Otimes(X3231,X3230,c_Int_Onumber__class_Onumber__of(X3231,X3228)),c_Groups_Otimes__class_Otimes(X3231,X3229,c_Int_Onumber__class_Onumber__of(X3231,X3228))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).
fof(i_0_1747,plain,
! [X3224,X3225,X3226,X3227] :
( ~ class_Int_Onumber(X3227)
| ~ class_Rings_Osemiring(X3227)
| c_Groups_Otimes__class_Otimes(X3227,c_Int_Onumber__class_Onumber__of(X3227,X3226),c_Groups_Oplus__class_Oplus(X3227,X3225,X3224)) = c_Groups_Oplus__class_Oplus(X3227,c_Groups_Otimes__class_Otimes(X3227,c_Int_Onumber__class_Onumber__of(X3227,X3226),X3225),c_Groups_Otimes__class_Otimes(X3227,c_Int_Onumber__class_Onumber__of(X3227,X3226),X3224)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).
cnf(i_0_1748,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_1298]) ).
cnf(i_0_1749,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_1299]) ).
cnf(i_0_1750,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_1300]) ).
cnf(i_0_1751,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_1301]) ).
cnf(i_0_1752,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_1302]) ).
cnf(i_0_1753,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_1303]) ).
cnf(i_0_1754,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_1304]) ).
cnf(i_0_1755,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_1305]) ).
fof(i_0_1756,plain,
! [X3538,X3539,X3540] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3540,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3540),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3539),X3538)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3540,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3540),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3539),X3538)) = 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,X3540,X3539)),X3538) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1338])]) ).
fof(i_0_1757,plain,
! [X3765,X3766,X3767] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3766,X3767),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3765,X3767))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3766,X3765)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3767) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3766,X3765)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3766,X3767),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3765,X3767))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3767) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1758,plain,
! [X3104,X3105,X3106] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3106,X3105),c_Power_Opower__class_Opower(tc_Nat_Onat,X3106,X3104))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3105,X3104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1759,plain,
! [X3416,X3417,X3418] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3418,X3417),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3418,X3416))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3417,X3416)
| ~ 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,X3417,X3416)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3418,X3417),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3418,X3416))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3418) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1760,plain,
! [X3781,X3782,X3783] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3782,X3783),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3781,X3783))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3782,X3781)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3783) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3782,X3781)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3782,X3783),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3781,X3783))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3783) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1761,plain,
! [X3778,X3779,X3780] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3780,X3779),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3780,X3778))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3779,X3778)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3780) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3779,X3778)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3780,X3779),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3780,X3778))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3780) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1762,plain,
! [X3025,X3026,X3027] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3027,X3026),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3025,X3026))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3026)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3027,X3025) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3026)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3027,X3026),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3025,X3026)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3027,X3025)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3027,X3026),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3025,X3026)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1763,plain,
! [X3028,X3029,X3030] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3029),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3028))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3030)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3029,X3028) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3030)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3029),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3028)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3029,X3028)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3029),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3030,X3028)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1764,plain,
! [X3022,X3023,X3024] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3024,X3023),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3024,X3022))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3023,X3022)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3024) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3023,X3022)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3024,X3023),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3024,X3022))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3024) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1765,plain,
! [X4508,X4509,X4510,X4511] :
( ~ class_Rings_Olinordered__semidom(X4511)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4510,X4509)
| ~ c_Orderings_Oord__class_Oless(X4511,c_Groups_Ozero__class_Ozero(X4511),X4508)
| ~ c_Orderings_Oord__class_Oless(X4511,X4508,c_Groups_Oone__class_Oone(X4511))
| c_Orderings_Oord__class_Oless(X4511,c_Power_Opower__class_Opower(X4511,X4508,X4509),c_Power_Opower__class_Opower(X4511,X4508,X4510)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1766,plain,
! [X4514,X4515,X4516,X4517] :
( ~ class_Rings_Olinordered__semidom(X4517)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4516,X4515)
| ~ c_Orderings_Oord__class_Oless__eq(X4517,c_Groups_Ozero__class_Ozero(X4517),X4514)
| ~ c_Orderings_Oord__class_Oless__eq(X4517,X4514,c_Groups_Oone__class_Oone(X4517))
| c_Orderings_Oord__class_Oless__eq(X4517,c_Power_Opower__class_Opower(X4517,X4514,X4515),c_Power_Opower__class_Opower(X4517,X4514,X4516)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1767,plain,
! [X3281,X3282,X3283,X3284] :
( ( c_Orderings_Oord__class_Oless(X3284,X3283,c_Groups_Ozero__class_Ozero(X3284))
| c_Orderings_Oord__class_Oless(X3284,c_Groups_Ozero__class_Ozero(X3284),X3283)
| ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) )
& ( c_Orderings_Oord__class_Oless(X3284,X3281,X3282)
| c_Orderings_Oord__class_Oless(X3284,c_Groups_Ozero__class_Ozero(X3284),X3283)
| ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) )
& ( c_Orderings_Oord__class_Oless(X3284,X3283,c_Groups_Ozero__class_Ozero(X3284))
| c_Orderings_Oord__class_Oless(X3284,X3282,X3281)
| ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) )
& ( c_Orderings_Oord__class_Oless(X3284,X3281,X3282)
| c_Orderings_Oord__class_Oless(X3284,X3282,X3281)
| ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) )
& ( ~ c_Orderings_Oord__class_Oless(X3284,c_Groups_Ozero__class_Ozero(X3284),X3283)
| ~ c_Orderings_Oord__class_Oless(X3284,X3282,X3281)
| c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) )
& ( ~ c_Orderings_Oord__class_Oless(X3284,X3283,c_Groups_Ozero__class_Ozero(X3284))
| ~ c_Orderings_Oord__class_Oless(X3284,X3281,X3282)
| c_Orderings_Oord__class_Oless(X3284,c_Groups_Otimes__class_Otimes(X3284,X3283,X3282),c_Groups_Otimes__class_Otimes(X3284,X3283,X3281))
| ~ class_Rings_Olinordered__ring__strict(X3284) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1768,plain,
! [X3285,X3286,X3287,X3288] :
( ( c_Orderings_Oord__class_Oless(X3288,X3286,c_Groups_Ozero__class_Ozero(X3288))
| c_Orderings_Oord__class_Oless(X3288,c_Groups_Ozero__class_Ozero(X3288),X3286)
| ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) )
& ( c_Orderings_Oord__class_Oless(X3288,X3285,X3287)
| c_Orderings_Oord__class_Oless(X3288,c_Groups_Ozero__class_Ozero(X3288),X3286)
| ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) )
& ( c_Orderings_Oord__class_Oless(X3288,X3286,c_Groups_Ozero__class_Ozero(X3288))
| c_Orderings_Oord__class_Oless(X3288,X3287,X3285)
| ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) )
& ( c_Orderings_Oord__class_Oless(X3288,X3285,X3287)
| c_Orderings_Oord__class_Oless(X3288,X3287,X3285)
| ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) )
& ( ~ c_Orderings_Oord__class_Oless(X3288,c_Groups_Ozero__class_Ozero(X3288),X3286)
| ~ c_Orderings_Oord__class_Oless(X3288,X3287,X3285)
| c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) )
& ( ~ c_Orderings_Oord__class_Oless(X3288,X3286,c_Groups_Ozero__class_Ozero(X3288))
| ~ c_Orderings_Oord__class_Oless(X3288,X3285,X3287)
| c_Orderings_Oord__class_Oless(X3288,c_Groups_Otimes__class_Otimes(X3288,X3287,X3286),c_Groups_Otimes__class_Otimes(X3288,X3285,X3286))
| ~ class_Rings_Olinordered__ring__strict(X3288) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1769,plain,
! [X4833,X4834,X4835,X4836] :
( ~ class_Fields_Ofield(X4836)
| X4835 = c_Groups_Ozero__class_Ozero(X4836)
| c_Groups_Oplus__class_Oplus(X4836,c_Rings_Oinverse__class_Odivide(X4836,X4834,X4835),X4833) = c_Rings_Oinverse__class_Odivide(X4836,c_Groups_Oplus__class_Oplus(X4836,X4834,c_Groups_Otimes__class_Otimes(X4836,X4835,X4833)),X4835) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).
fof(i_0_1770,plain,
! [X4829,X4830,X4831,X4832] :
( ~ class_Fields_Ofield__inverse__zero(X4832)
| X4831 = c_Groups_Ozero__class_Ozero(X4832)
| c_Groups_Oplus__class_Oplus(X4832,c_Rings_Oinverse__class_Odivide(X4832,X4830,X4831),X4829) = c_Rings_Oinverse__class_Odivide(X4832,c_Groups_Oplus__class_Oplus(X4832,X4830,c_Groups_Otimes__class_Otimes(X4832,X4829,X4831)),X4831) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).
fof(i_0_1771,plain,
! [X4825,X4826,X4827,X4828] :
( ~ class_Fields_Ofield(X4828)
| X4827 = c_Groups_Ozero__class_Ozero(X4828)
| c_Groups_Oplus__class_Oplus(X4828,X4826,c_Rings_Oinverse__class_Odivide(X4828,X4825,X4827)) = c_Rings_Oinverse__class_Odivide(X4828,c_Groups_Oplus__class_Oplus(X4828,c_Groups_Otimes__class_Otimes(X4828,X4827,X4826),X4825),X4827) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).
fof(i_0_1772,plain,
! [X4821,X4822,X4823,X4824] :
( ~ class_Fields_Ofield__inverse__zero(X4824)
| X4823 = c_Groups_Ozero__class_Ozero(X4824)
| c_Groups_Oplus__class_Oplus(X4824,X4822,c_Rings_Oinverse__class_Odivide(X4824,X4821,X4823)) = c_Rings_Oinverse__class_Odivide(X4824,c_Groups_Oplus__class_Oplus(X4824,X4821,c_Groups_Otimes__class_Otimes(X4824,X4822,X4823)),X4823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
fof(i_0_1773,plain,
! [X2936,X2937,X2938,X2939] :
( ~ class_Rings_Olinordered__semidom(X2939)
| ~ c_Orderings_Oord__class_Oless(X2939,X2938,X2937)
| ~ c_Orderings_Oord__class_Oless__eq(X2939,c_Groups_Ozero__class_Ozero(X2939),X2938)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2936)
| c_Orderings_Oord__class_Oless(X2939,c_Power_Opower__class_Opower(X2939,X2938,X2936),c_Power_Opower__class_Opower(X2939,X2937,X2936)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1774,plain,
! [X4682,X4683,X4684,X4685,X4686] :
( ~ class_Fields_Ofield__inverse__zero(X4686)
| c_Groups_Otimes__class_Otimes(X4686,c_Rings_Oinverse__class_Odivide(X4686,X4685,X4684),c_Rings_Oinverse__class_Odivide(X4686,X4683,X4682)) = c_Rings_Oinverse__class_Odivide(X4686,c_Groups_Otimes__class_Otimes(X4686,X4685,X4683),c_Groups_Otimes__class_Otimes(X4686,X4684,X4682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).
fof(i_0_1775,plain,
! [X2867,X2868,X2869,X2870,X2871] :
( ~ class_Rings_Ocomm__semiring__1(X2871)
| c_Groups_Oplus__class_Oplus(X2871,c_Groups_Oplus__class_Oplus(X2871,X2870,X2869),c_Groups_Oplus__class_Oplus(X2871,X2868,X2867)) = c_Groups_Oplus__class_Oplus(X2871,c_Groups_Oplus__class_Oplus(X2871,X2870,X2868),c_Groups_Oplus__class_Oplus(X2871,X2869,X2867)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1776,plain,
! [X2733,X2734,X2735,X2736,X2737] :
( ~ class_Rings_Ocomm__semiring__1(X2737)
| c_Groups_Otimes__class_Otimes(X2737,c_Groups_Otimes__class_Otimes(X2737,X2736,X2735),c_Groups_Otimes__class_Otimes(X2737,X2734,X2733)) = c_Groups_Otimes__class_Otimes(X2737,c_Groups_Otimes__class_Otimes(X2737,X2736,X2734),c_Groups_Otimes__class_Otimes(X2737,X2735,X2733)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1777,plain,
! [X5035,X5036,X5037,X5038] :
( ~ class_Divides_Osemiring__div(X5038)
| c_Divides_Odiv__class_Omod(X5038,c_Groups_Oplus__class_Oplus(X5038,c_Divides_Odiv__class_Omod(X5038,X5037,X5036),X5035),X5036) = c_Divides_Odiv__class_Omod(X5038,c_Groups_Oplus__class_Oplus(X5038,X5037,X5035),X5036) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).
fof(i_0_1778,plain,
! [X4934,X4935,X4936,X4937] :
( ~ class_Divides_Osemiring__div(X4937)
| c_Divides_Odiv__class_Omod(X4937,c_Groups_Otimes__class_Otimes(X4937,c_Divides_Odiv__class_Omod(X4937,X4936,X4935),X4934),X4935) = c_Divides_Odiv__class_Omod(X4937,c_Groups_Otimes__class_Otimes(X4937,X4936,X4934),X4935) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).
fof(i_0_1779,plain,
! [X5031,X5032,X5033,X5034] :
( ~ class_Divides_Osemiring__div(X5034)
| c_Divides_Odiv__class_Omod(X5034,c_Groups_Oplus__class_Oplus(X5034,X5033,c_Divides_Odiv__class_Omod(X5034,X5032,X5031)),X5031) = c_Divides_Odiv__class_Omod(X5034,c_Groups_Oplus__class_Oplus(X5034,X5033,X5032),X5031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).
fof(i_0_1780,plain,
! [X5023,X5024,X5025,X5026] :
( ~ class_Divides_Osemiring__div(X5026)
| c_Divides_Odiv__class_Omod(X5026,c_Groups_Oplus__class_Oplus(X5026,X5025,X5024),X5023) = c_Divides_Odiv__class_Omod(X5026,c_Groups_Oplus__class_Oplus(X5026,c_Divides_Odiv__class_Omod(X5026,X5025,X5023),X5024),X5023) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).
fof(i_0_1781,plain,
! [X4918,X4919,X4920,X4921] :
( ~ class_Divides_Osemiring__div(X4921)
| c_Divides_Odiv__class_Omod(X4921,c_Groups_Otimes__class_Otimes(X4921,X4920,X4919),X4918) = c_Divides_Odiv__class_Omod(X4921,c_Groups_Otimes__class_Otimes(X4921,c_Divides_Odiv__class_Omod(X4921,X4920,X4918),X4919),X4918) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).
fof(i_0_1782,plain,
! [X5019,X5020,X5021,X5022] :
( ~ class_Divides_Osemiring__div(X5022)
| c_Divides_Odiv__class_Omod(X5022,c_Groups_Oplus__class_Oplus(X5022,X5021,X5020),X5019) = c_Divides_Odiv__class_Omod(X5022,c_Groups_Oplus__class_Oplus(X5022,X5021,c_Divides_Odiv__class_Omod(X5022,X5020,X5019)),X5019) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).
fof(i_0_1783,plain,
! [X4914,X4915,X4916,X4917] :
( ~ class_Divides_Osemiring__div(X4917)
| c_Divides_Odiv__class_Omod(X4917,c_Groups_Otimes__class_Otimes(X4917,X4916,X4915),X4914) = c_Divides_Odiv__class_Omod(X4917,c_Groups_Otimes__class_Otimes(X4917,X4916,c_Divides_Odiv__class_Omod(X4917,X4915,X4914)),X4914) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).
cnf(i_0_1784,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_1339]) ).
fof(i_0_1785,plain,
! [X2838,X2839,X2840,X2841] :
( ~ class_Int_Onumber__ring(X2841)
| c_Groups_Oplus__class_Oplus(X2841,c_Int_Onumber__class_Onumber__of(X2841,X2840),c_Groups_Oplus__class_Oplus(X2841,c_Int_Onumber__class_Onumber__of(X2841,X2839),X2838)) = c_Groups_Oplus__class_Oplus(X2841,c_Int_Onumber__class_Onumber__of(X2841,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2840,X2839)),X2838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).
fof(i_0_1786,plain,
! [X2634,X2635,X2636,X2637] :
( ~ class_Int_Onumber__ring(X2637)
| c_Groups_Otimes__class_Otimes(X2637,c_Int_Onumber__class_Onumber__of(X2637,X2636),c_Groups_Otimes__class_Otimes(X2637,c_Int_Onumber__class_Onumber__of(X2637,X2635),X2634)) = c_Groups_Otimes__class_Otimes(X2637,c_Int_Onumber__class_Onumber__of(X2637,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2636,X2635)),X2634) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).
fof(i_0_1787,plain,
! [X3218,X3219,X3220,X3221,X3222,X3223] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3223)
| X3222 = c_Groups_Ozero__class_Ozero(X3223)
| X3221 != X3220
| X3219 = X3218
| c_Groups_Oplus__class_Oplus(X3223,X3221,c_Groups_Otimes__class_Otimes(X3223,X3222,X3219)) != c_Groups_Oplus__class_Oplus(X3223,X3220,c_Groups_Otimes__class_Otimes(X3223,X3222,X3218)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
cnf(i_0_1788,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_1340]) ).
fof(i_0_1789,plain,
! [X4971,X4972,X4973] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4973,X4972),X4971),X4972) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X4973,X4971),X4972),
inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).
fof(i_0_1790,plain,
! [X4947,X4948,X4949] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4949,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4948,X4947)),X4947) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4949,X4948),X4947),
inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).
fof(i_0_1791,plain,
! [X4944,X4945,X4946] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4946,X4945),X4944) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4946,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4945,X4944)),X4944),
inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).
fof(i_0_1792,plain,
! [X4793,X4794,X4795,X4796] :
( ( ~ c_Orderings_Oord__class_Oless(X4796,c_Rings_Oinverse__class_Odivide(X4796,X4794,X4795),X4793)
| c_Orderings_Oord__class_Oless(X4796,X4794,c_Groups_Otimes__class_Otimes(X4796,X4793,X4795))
| ~ c_Orderings_Oord__class_Oless(X4796,c_Groups_Ozero__class_Ozero(X4796),X4795)
| ~ class_Fields_Olinordered__field(X4796) )
& ( ~ c_Orderings_Oord__class_Oless(X4796,X4794,c_Groups_Otimes__class_Otimes(X4796,X4793,X4795))
| c_Orderings_Oord__class_Oless(X4796,c_Rings_Oinverse__class_Odivide(X4796,X4794,X4795),X4793)
| ~ c_Orderings_Oord__class_Oless(X4796,c_Groups_Ozero__class_Ozero(X4796),X4795)
| ~ class_Fields_Olinordered__field(X4796) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).
fof(i_0_1793,plain,
! [X4797,X4798,X4799,X4800] :
( ~ class_Fields_Olinordered__field(X4800)
| ~ c_Orderings_Oord__class_Oless(X4800,c_Groups_Ozero__class_Ozero(X4800),X4799)
| ~ c_Orderings_Oord__class_Oless(X4800,X4798,c_Groups_Otimes__class_Otimes(X4800,X4797,X4799))
| c_Orderings_Oord__class_Oless(X4800,c_Rings_Oinverse__class_Odivide(X4800,X4798,X4799),X4797) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).
fof(i_0_1794,plain,
! [X4789,X4790,X4791,X4792] :
( ( ~ c_Orderings_Oord__class_Oless(X4792,X4790,c_Rings_Oinverse__class_Odivide(X4792,X4789,X4791))
| c_Orderings_Oord__class_Oless(X4792,c_Groups_Otimes__class_Otimes(X4792,X4790,X4791),X4789)
| ~ c_Orderings_Oord__class_Oless(X4792,c_Groups_Ozero__class_Ozero(X4792),X4791)
| ~ class_Fields_Olinordered__field(X4792) )
& ( ~ c_Orderings_Oord__class_Oless(X4792,c_Groups_Otimes__class_Otimes(X4792,X4790,X4791),X4789)
| c_Orderings_Oord__class_Oless(X4792,X4790,c_Rings_Oinverse__class_Odivide(X4792,X4789,X4791))
| ~ c_Orderings_Oord__class_Oless(X4792,c_Groups_Ozero__class_Ozero(X4792),X4791)
| ~ class_Fields_Olinordered__field(X4792) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).
fof(i_0_1795,plain,
! [X4875,X4876,X4877,X4878] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4878,c_Rings_Oinverse__class_Odivide(X4878,X4876,X4877),X4875)
| c_Orderings_Oord__class_Oless__eq(X4878,X4876,c_Groups_Otimes__class_Otimes(X4878,X4875,X4877))
| ~ c_Orderings_Oord__class_Oless(X4878,c_Groups_Ozero__class_Ozero(X4878),X4877)
| ~ class_Fields_Olinordered__field(X4878) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4878,X4876,c_Groups_Otimes__class_Otimes(X4878,X4875,X4877))
| c_Orderings_Oord__class_Oless__eq(X4878,c_Rings_Oinverse__class_Odivide(X4878,X4876,X4877),X4875)
| ~ c_Orderings_Oord__class_Oless(X4878,c_Groups_Ozero__class_Ozero(X4878),X4877)
| ~ class_Fields_Olinordered__field(X4878) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).
fof(i_0_1796,plain,
! [X4871,X4872,X4873,X4874] :
( ~ class_Fields_Olinordered__field(X4874)
| ~ c_Orderings_Oord__class_Oless(X4874,c_Groups_Ozero__class_Ozero(X4874),X4873)
| ~ c_Orderings_Oord__class_Oless__eq(X4874,X4872,c_Groups_Otimes__class_Otimes(X4874,X4871,X4873))
| c_Orderings_Oord__class_Oless__eq(X4874,c_Rings_Oinverse__class_Odivide(X4874,X4872,X4873),X4871) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).
fof(i_0_1797,plain,
! [X4879,X4880,X4881,X4882] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4882,X4880,c_Rings_Oinverse__class_Odivide(X4882,X4879,X4881))
| c_Orderings_Oord__class_Oless__eq(X4882,c_Groups_Otimes__class_Otimes(X4882,X4880,X4881),X4879)
| ~ c_Orderings_Oord__class_Oless(X4882,c_Groups_Ozero__class_Ozero(X4882),X4881)
| ~ class_Fields_Olinordered__field(X4882) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4882,c_Groups_Otimes__class_Otimes(X4882,X4880,X4881),X4879)
| c_Orderings_Oord__class_Oless__eq(X4882,X4880,c_Rings_Oinverse__class_Odivide(X4882,X4879,X4881))
| ~ c_Orderings_Oord__class_Oless(X4882,c_Groups_Ozero__class_Ozero(X4882),X4881)
| ~ class_Fields_Olinordered__field(X4882) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).
fof(i_0_1798,plain,
! [X4809,X4810,X4811,X4812] :
( ( ~ c_Orderings_Oord__class_Oless(X4812,c_Rings_Oinverse__class_Odivide(X4812,X4810,X4811),X4809)
| c_Orderings_Oord__class_Oless(X4812,c_Groups_Otimes__class_Otimes(X4812,X4809,X4811),X4810)
| ~ c_Orderings_Oord__class_Oless(X4812,X4811,c_Groups_Ozero__class_Ozero(X4812))
| ~ class_Fields_Olinordered__field(X4812) )
& ( ~ c_Orderings_Oord__class_Oless(X4812,c_Groups_Otimes__class_Otimes(X4812,X4809,X4811),X4810)
| c_Orderings_Oord__class_Oless(X4812,c_Rings_Oinverse__class_Odivide(X4812,X4810,X4811),X4809)
| ~ c_Orderings_Oord__class_Oless(X4812,X4811,c_Groups_Ozero__class_Ozero(X4812))
| ~ class_Fields_Olinordered__field(X4812) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).
fof(i_0_1799,plain,
! [X4859,X4860,X4861,X4862] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4862,c_Rings_Oinverse__class_Odivide(X4862,X4860,X4861),X4859)
| c_Orderings_Oord__class_Oless__eq(X4862,c_Groups_Otimes__class_Otimes(X4862,X4859,X4861),X4860)
| ~ c_Orderings_Oord__class_Oless(X4862,X4861,c_Groups_Ozero__class_Ozero(X4862))
| ~ class_Fields_Olinordered__field(X4862) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4862,c_Groups_Otimes__class_Otimes(X4862,X4859,X4861),X4860)
| c_Orderings_Oord__class_Oless__eq(X4862,c_Rings_Oinverse__class_Odivide(X4862,X4860,X4861),X4859)
| ~ c_Orderings_Oord__class_Oless(X4862,X4861,c_Groups_Ozero__class_Ozero(X4862))
| ~ class_Fields_Olinordered__field(X4862) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).
fof(i_0_1800,plain,
! [X4801,X4802,X4803,X4804] :
( ~ class_Fields_Olinordered__field(X4804)
| ~ c_Orderings_Oord__class_Oless(X4804,c_Groups_Ozero__class_Ozero(X4804),X4803)
| ~ c_Orderings_Oord__class_Oless(X4804,c_Groups_Otimes__class_Otimes(X4804,X4802,X4803),X4801)
| c_Orderings_Oord__class_Oless(X4804,X4802,c_Rings_Oinverse__class_Odivide(X4804,X4801,X4803)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).
fof(i_0_1801,plain,
! [X4867,X4868,X4869,X4870] :
( ~ class_Fields_Olinordered__field(X4870)
| ~ c_Orderings_Oord__class_Oless(X4870,c_Groups_Ozero__class_Ozero(X4870),X4869)
| ~ c_Orderings_Oord__class_Oless__eq(X4870,c_Groups_Otimes__class_Otimes(X4870,X4868,X4869),X4867)
| c_Orderings_Oord__class_Oless__eq(X4870,X4868,c_Rings_Oinverse__class_Odivide(X4870,X4867,X4869)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).
fof(i_0_1802,plain,
! [X4805,X4806,X4807,X4808] :
( ( ~ c_Orderings_Oord__class_Oless(X4808,X4806,c_Rings_Oinverse__class_Odivide(X4808,X4805,X4807))
| c_Orderings_Oord__class_Oless(X4808,X4805,c_Groups_Otimes__class_Otimes(X4808,X4806,X4807))
| ~ c_Orderings_Oord__class_Oless(X4808,X4807,c_Groups_Ozero__class_Ozero(X4808))
| ~ class_Fields_Olinordered__field(X4808) )
& ( ~ c_Orderings_Oord__class_Oless(X4808,X4805,c_Groups_Otimes__class_Otimes(X4808,X4806,X4807))
| c_Orderings_Oord__class_Oless(X4808,X4806,c_Rings_Oinverse__class_Odivide(X4808,X4805,X4807))
| ~ c_Orderings_Oord__class_Oless(X4808,X4807,c_Groups_Ozero__class_Ozero(X4808))
| ~ class_Fields_Olinordered__field(X4808) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).
fof(i_0_1803,plain,
! [X4863,X4864,X4865,X4866] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4866,X4864,c_Rings_Oinverse__class_Odivide(X4866,X4863,X4865))
| c_Orderings_Oord__class_Oless__eq(X4866,X4863,c_Groups_Otimes__class_Otimes(X4866,X4864,X4865))
| ~ c_Orderings_Oord__class_Oless(X4866,X4865,c_Groups_Ozero__class_Ozero(X4866))
| ~ class_Fields_Olinordered__field(X4866) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4866,X4863,c_Groups_Otimes__class_Otimes(X4866,X4864,X4865))
| c_Orderings_Oord__class_Oless__eq(X4866,X4864,c_Rings_Oinverse__class_Odivide(X4866,X4863,X4865))
| ~ c_Orderings_Oord__class_Oless(X4866,X4865,c_Groups_Ozero__class_Ozero(X4866))
| ~ class_Fields_Olinordered__field(X4866) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).
cnf(i_0_1804,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_1322]) ).
cnf(i_0_1805,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_1323]) ).
cnf(i_0_1806,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_1320]) ).
cnf(i_0_1807,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_1321]) ).
cnf(i_0_1808,plain,
( X1 = X2
| c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1341]) ).
cnf(i_0_1809,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_1342]) ).
fof(i_0_1810,plain,
! [X4317,X4318,X4319] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4319)
| c_Orderings_Oord__class_Oless__eq(X4319,c_Groups_Oabs__class_Oabs(X4319,c_Groups_Oplus__class_Oplus(X4319,X4318,X4317)),c_Groups_Oplus__class_Oplus(X4319,c_Groups_Oabs__class_Oabs(X4319,X4318),c_Groups_Oabs__class_Oabs(X4319,X4317))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
fof(i_0_1811,plain,
! [X4665,X4666,X4667] :
( ~ class_RealVector_Oreal__normed__vector(X4667)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4667,c_Groups_Oplus__class_Oplus(X4667,X4666,X4665)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4667,X4666),c_RealVector_Onorm__class_Onorm(X4667,X4665))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1812,plain,
! [X4654,X4655,X4656] :
( ~ class_RealVector_Oreal__normed__algebra(X4656)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4656,c_Groups_Otimes__class_Otimes(X4656,X4655,X4654)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4656,X4655),c_RealVector_Onorm__class_Onorm(X4656,X4654))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
cnf(i_0_1813,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_1343]) ).
fof(i_0_1814,plain,
! [X4432,X4433,X4434] :
( ~ class_Rings_Olinordered__semidom(X4434)
| ~ c_Orderings_Oord__class_Oless(X4434,c_Groups_Oone__class_Oone(X4434),X4433)
| c_Orderings_Oord__class_Oless(X4434,c_Groups_Oone__class_Oone(X4434),c_Groups_Otimes__class_Otimes(X4434,X4433,c_Power_Opower__class_Opower(X4434,X4433,X4432))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).
fof(i_0_1815,plain,
! [X3844,X3845,X3846,X3847] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3847)
| ~ c_Orderings_Oord__class_Oless(X3847,c_Groups_Oplus__class_Oplus(X3847,X3846,X3845),c_Groups_Oplus__class_Oplus(X3847,X3844,X3845))
| c_Orderings_Oord__class_Oless(X3847,X3846,X3844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1816,plain,
! [X3823,X3824,X3825,X3826] :
( ( ~ c_Orderings_Oord__class_Oless(X3826,c_Groups_Oplus__class_Oplus(X3826,X3825,X3824),c_Groups_Oplus__class_Oplus(X3826,X3823,X3824))
| c_Orderings_Oord__class_Oless(X3826,X3825,X3823)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3826) )
& ( ~ c_Orderings_Oord__class_Oless(X3826,X3825,X3823)
| c_Orderings_Oord__class_Oless(X3826,c_Groups_Oplus__class_Oplus(X3826,X3825,X3824),c_Groups_Oplus__class_Oplus(X3826,X3823,X3824))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3826) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1817,plain,
! [X3848,X3849,X3850,X3851] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3851)
| ~ c_Orderings_Oord__class_Oless(X3851,c_Groups_Oplus__class_Oplus(X3851,X3850,X3849),c_Groups_Oplus__class_Oplus(X3851,X3850,X3848))
| c_Orderings_Oord__class_Oless(X3851,X3849,X3848) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1818,plain,
! [X3827,X3828,X3829,X3830] :
( ( ~ c_Orderings_Oord__class_Oless(X3830,c_Groups_Oplus__class_Oplus(X3830,X3829,X3828),c_Groups_Oplus__class_Oplus(X3830,X3829,X3827))
| c_Orderings_Oord__class_Oless(X3830,X3828,X3827)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3830) )
& ( ~ c_Orderings_Oord__class_Oless(X3830,X3828,X3827)
| c_Orderings_Oord__class_Oless(X3830,c_Groups_Oplus__class_Oplus(X3830,X3829,X3828),c_Groups_Oplus__class_Oplus(X3830,X3829,X3827))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3830) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1819,plain,
! [X3815,X3816,X3817,X3818] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3818)
| ~ c_Orderings_Oord__class_Oless__eq(X3818,c_Groups_Oplus__class_Oplus(X3818,X3817,X3816),c_Groups_Oplus__class_Oplus(X3818,X3815,X3816))
| c_Orderings_Oord__class_Oless__eq(X3818,X3817,X3815) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1820,plain,
! [X3794,X3795,X3796,X3797] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Oplus__class_Oplus(X3797,X3796,X3795),c_Groups_Oplus__class_Oplus(X3797,X3794,X3795))
| c_Orderings_Oord__class_Oless__eq(X3797,X3796,X3794)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3797) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3797,X3796,X3794)
| c_Orderings_Oord__class_Oless__eq(X3797,c_Groups_Oplus__class_Oplus(X3797,X3796,X3795),c_Groups_Oplus__class_Oplus(X3797,X3794,X3795))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3797) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1821,plain,
! [X3819,X3820,X3821,X3822] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3822)
| ~ c_Orderings_Oord__class_Oless__eq(X3822,c_Groups_Oplus__class_Oplus(X3822,X3821,X3820),c_Groups_Oplus__class_Oplus(X3822,X3821,X3819))
| c_Orderings_Oord__class_Oless__eq(X3822,X3820,X3819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1822,plain,
! [X3798,X3799,X3800,X3801] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Oplus__class_Oplus(X3801,X3800,X3799),c_Groups_Oplus__class_Oplus(X3801,X3800,X3798))
| c_Orderings_Oord__class_Oless__eq(X3801,X3799,X3798)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3801) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3801,X3799,X3798)
| c_Orderings_Oord__class_Oless__eq(X3801,c_Groups_Oplus__class_Oplus(X3801,X3800,X3799),c_Groups_Oplus__class_Oplus(X3801,X3800,X3798))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X3801) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
cnf(i_0_1823,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_1344]) ).
cnf(i_0_1824,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_1345]) ).
cnf(i_0_1825,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_1346]) ).
fof(i_0_1826,plain,
! [X4579,X4580,X4581] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4581)
| X4581 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4580,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4581,X4579))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4580)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4579,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2])]) ).
fof(i_0_1827,plain,
! [X4582,X4583,X4584] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4584)
| X4584 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4583,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4584,X4582))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4583,X4584)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4582) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1828,plain,
! [X4678,X4679,X4680,X4681] :
( ~ class_RealVector_Oreal__normed__vector(X4681)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4680,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4681,X4679),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4680,c_RealVector_Onorm__class_Onorm(X4681,X4678)))
| X4679 = c_Groups_Ozero__class_Ozero(X4681) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
cnf(i_0_1829,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_1324]) ).
fof(i_0_1830,plain,
! [X3431,X3432,X3433] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3433)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3432),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3431)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3432,X3431)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3432),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3431)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3433)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3432,X3431)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3432),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3433,X3431)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1831,plain,
! [X3428,X3429,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,X3430,X3429),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3428,X3429)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3430,X3428)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3430,X3429),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3428,X3429)) )
& ( ~ 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,X3430,X3428)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3430,X3429),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3428,X3429)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1832,plain,
! [X4412,X4413,X4414,X4415] :
( ~ class_Rings_Olinordered__idom(X4415)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4414)
| ~ c_Orderings_Oord__class_Oless__eq(X4415,c_Groups_Oabs__class_Oabs(X4415,X4413),c_Groups_Oabs__class_Oabs(X4415,X4412))
| c_Orderings_Oord__class_Oless__eq(X4415,c_Power_Opower__class_Opower(X4415,X4413,X4414),c_Power_Opower__class_Opower(X4415,X4412,X4414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono__even])]) ).
cnf(i_0_1833,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_1347]) ).
cnf(i_0_1834,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_1348]) ).
fof(i_0_1835,plain,
! [X3629,X3630,X3631] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3630),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3629))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3630,X3629) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3630,X3629)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3630),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3629)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
cnf(i_0_1836,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_1349]) ).
cnf(i_0_1837,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_1350]) ).
fof(i_0_1838,plain,
! [X3632,X3633,X3634] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3634,X3633),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3634,X3632))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3633,X3632) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3633,X3632)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3634,X3633),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3634,X3632)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1839,plain,
! [X3210,X3211,X3212,X3213] :
( ~ class_Rings_Olinordered__semidom(X3213)
| c_Power_Opower__class_Opower(X3213,X3212,X3211) != c_Power_Opower__class_Opower(X3213,X3210,X3211)
| ~ c_Orderings_Oord__class_Oless__eq(X3213,c_Groups_Ozero__class_Ozero(X3213),X3212)
| ~ c_Orderings_Oord__class_Oless__eq(X3213,c_Groups_Ozero__class_Ozero(X3213),X3210)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3211)
| X3212 = X3210 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1840,plain,
! [X4722,X4723,X4724,X4725] :
( ~ class_Fields_Olinordered__field(X4725)
| ~ c_Orderings_Oord__class_Oless(X4725,X4724,X4723)
| ~ c_Orderings_Oord__class_Oless(X4725,c_Groups_Ozero__class_Ozero(X4725),X4722)
| c_Orderings_Oord__class_Oless(X4725,c_Rings_Oinverse__class_Odivide(X4725,X4724,X4722),c_Rings_Oinverse__class_Odivide(X4725,X4723,X4722)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).
fof(i_0_1841,plain,
! [X3248,X3249,X3250,X3251] :
( ~ class_Rings_Olinordered__semiring__strict(X3251)
| ~ c_Orderings_Oord__class_Oless(X3251,X3250,X3249)
| ~ c_Orderings_Oord__class_Oless(X3251,c_Groups_Ozero__class_Ozero(X3251),X3248)
| c_Orderings_Oord__class_Oless(X3251,c_Groups_Otimes__class_Otimes(X3251,X3250,X3248),c_Groups_Otimes__class_Otimes(X3251,X3249,X3248)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1842,plain,
! [X3240,X3241,X3242,X3243] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3243)
| ~ c_Orderings_Oord__class_Oless(X3243,X3242,X3241)
| ~ c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),X3240)
| c_Orderings_Oord__class_Oless(X3243,c_Groups_Otimes__class_Otimes(X3243,X3240,X3242),c_Groups_Otimes__class_Otimes(X3243,X3240,X3241)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1843,plain,
! [X3244,X3245,X3246,X3247] :
( ~ class_Rings_Olinordered__semiring__strict(X3247)
| ~ c_Orderings_Oord__class_Oless(X3247,X3246,X3245)
| ~ c_Orderings_Oord__class_Oless(X3247,c_Groups_Ozero__class_Ozero(X3247),X3244)
| c_Orderings_Oord__class_Oless(X3247,c_Groups_Otimes__class_Otimes(X3247,X3244,X3246),c_Groups_Otimes__class_Otimes(X3247,X3244,X3245)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1844,plain,
! [X4694,X4695,X4696,X4697] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4697)
| ~ c_Orderings_Oord__class_Oless__eq(X4697,X4696,X4695)
| ~ c_Orderings_Oord__class_Oless__eq(X4697,c_Groups_Ozero__class_Ozero(X4697),X4694)
| c_Orderings_Oord__class_Oless__eq(X4697,c_Rings_Oinverse__class_Odivide(X4697,X4696,X4694),c_Rings_Oinverse__class_Odivide(X4697,X4695,X4694)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).
fof(i_0_1845,plain,
! [X3360,X3361,X3362,X3363] :
( ~ class_Rings_Olinordered__semidom(X3363)
| ~ c_Orderings_Oord__class_Oless__eq(X3363,X3362,X3361)
| ~ c_Orderings_Oord__class_Oless__eq(X3363,c_Groups_Ozero__class_Ozero(X3363),X3362)
| c_Orderings_Oord__class_Oless__eq(X3363,c_Power_Opower__class_Opower(X3363,X3362,X3360),c_Power_Opower__class_Opower(X3363,X3361,X3360)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1846,plain,
! [X3323,X3324,X3325,X3326] :
( ~ class_Rings_Oordered__semiring(X3326)
| ~ c_Orderings_Oord__class_Oless__eq(X3326,X3325,X3324)
| ~ c_Orderings_Oord__class_Oless__eq(X3326,c_Groups_Ozero__class_Ozero(X3326),X3323)
| c_Orderings_Oord__class_Oless__eq(X3326,c_Groups_Otimes__class_Otimes(X3326,X3325,X3323),c_Groups_Otimes__class_Otimes(X3326,X3324,X3323)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1847,plain,
! [X3315,X3316,X3317,X3318] :
( ~ class_Rings_Oordered__comm__semiring(X3318)
| ~ c_Orderings_Oord__class_Oless__eq(X3318,X3317,X3316)
| ~ c_Orderings_Oord__class_Oless__eq(X3318,c_Groups_Ozero__class_Ozero(X3318),X3315)
| c_Orderings_Oord__class_Oless__eq(X3318,c_Groups_Otimes__class_Otimes(X3318,X3315,X3317),c_Groups_Otimes__class_Otimes(X3318,X3315,X3316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1848,plain,
! [X3319,X3320,X3321,X3322] :
( ~ class_Rings_Oordered__semiring(X3322)
| ~ c_Orderings_Oord__class_Oless__eq(X3322,X3321,X3320)
| ~ c_Orderings_Oord__class_Oless__eq(X3322,c_Groups_Ozero__class_Ozero(X3322),X3319)
| c_Orderings_Oord__class_Oless__eq(X3322,c_Groups_Otimes__class_Otimes(X3322,X3319,X3321),c_Groups_Otimes__class_Otimes(X3322,X3319,X3320)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1849,plain,
! [X4726,X4727,X4728,X4729] :
( ~ class_Fields_Olinordered__field(X4729)
| ~ c_Orderings_Oord__class_Oless(X4729,X4728,X4727)
| ~ c_Orderings_Oord__class_Oless(X4729,X4726,c_Groups_Ozero__class_Ozero(X4729))
| c_Orderings_Oord__class_Oless(X4729,c_Rings_Oinverse__class_Odivide(X4729,X4727,X4726),c_Rings_Oinverse__class_Odivide(X4729,X4728,X4726)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).
fof(i_0_1850,plain,
! [X3236,X3237,X3238,X3239] :
( ~ class_Rings_Olinordered__ring__strict(X3239)
| ~ c_Orderings_Oord__class_Oless(X3239,X3238,X3237)
| ~ c_Orderings_Oord__class_Oless(X3239,X3236,c_Groups_Ozero__class_Ozero(X3239))
| c_Orderings_Oord__class_Oless(X3239,c_Groups_Otimes__class_Otimes(X3239,X3237,X3236),c_Groups_Otimes__class_Otimes(X3239,X3238,X3236)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1851,plain,
! [X3232,X3233,X3234,X3235] :
( ~ class_Rings_Olinordered__ring__strict(X3235)
| ~ c_Orderings_Oord__class_Oless(X3235,X3234,X3233)
| ~ c_Orderings_Oord__class_Oless(X3235,X3232,c_Groups_Ozero__class_Ozero(X3235))
| c_Orderings_Oord__class_Oless(X3235,c_Groups_Otimes__class_Otimes(X3235,X3232,X3233),c_Groups_Otimes__class_Otimes(X3235,X3232,X3234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1852,plain,
! [X4690,X4691,X4692,X4693] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4693)
| ~ c_Orderings_Oord__class_Oless__eq(X4693,X4692,X4691)
| ~ c_Orderings_Oord__class_Oless__eq(X4693,X4690,c_Groups_Ozero__class_Ozero(X4693))
| c_Orderings_Oord__class_Oless__eq(X4693,c_Rings_Oinverse__class_Odivide(X4693,X4691,X4690),c_Rings_Oinverse__class_Odivide(X4693,X4692,X4690)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).
fof(i_0_1853,plain,
! [X3311,X3312,X3313,X3314] :
( ~ class_Rings_Oordered__ring(X3314)
| ~ c_Orderings_Oord__class_Oless__eq(X3314,X3313,X3312)
| ~ c_Orderings_Oord__class_Oless__eq(X3314,X3311,c_Groups_Ozero__class_Ozero(X3314))
| c_Orderings_Oord__class_Oless__eq(X3314,c_Groups_Otimes__class_Otimes(X3314,X3312,X3311),c_Groups_Otimes__class_Otimes(X3314,X3313,X3311)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1854,plain,
! [X3307,X3308,X3309,X3310] :
( ~ class_Rings_Oordered__ring(X3310)
| ~ c_Orderings_Oord__class_Oless__eq(X3310,X3309,X3308)
| ~ c_Orderings_Oord__class_Oless__eq(X3310,X3307,c_Groups_Ozero__class_Ozero(X3310))
| c_Orderings_Oord__class_Oless__eq(X3310,c_Groups_Otimes__class_Otimes(X3310,X3307,X3308),c_Groups_Otimes__class_Otimes(X3310,X3307,X3309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
cnf(i_0_1855,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_1330]) ).
cnf(i_0_1856,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_1331]) ).
cnf(i_0_1857,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_1333]) ).
cnf(i_0_1858,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_1332]) ).
cnf(i_0_1859,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_1326]) ).
cnf(i_0_1860,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_1328]) ).
cnf(i_0_1861,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_1327]) ).
cnf(i_0_1862,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_1329]) ).
fof(i_0_1863,plain,
! [X4428,X4429,X4430] :
( ~ class_Rings_Olinordered__idom(X4430)
| ~ c_Orderings_Oord__class_Oless__eq(X4430,c_Groups_Ozero__class_Ozero(X4430),X4429)
| ~ c_Orderings_Oord__class_Oless__eq(X4430,c_Groups_Ozero__class_Ozero(X4430),X4428)
| ~ c_Orderings_Oord__class_Oless__eq(X4430,X4428,c_Groups_Oone__class_Oone(X4430))
| c_Orderings_Oord__class_Oless__eq(X4430,c_Groups_Otimes__class_Otimes(X4430,X4429,X4428),X4429) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1864,plain,
! [X4425,X4426,X4427] :
( ~ class_Rings_Olinordered__idom(X4427)
| ~ c_Orderings_Oord__class_Oless__eq(X4427,c_Groups_Ozero__class_Ozero(X4427),X4426)
| ~ c_Orderings_Oord__class_Oless__eq(X4427,c_Groups_Ozero__class_Ozero(X4427),X4425)
| ~ c_Orderings_Oord__class_Oless__eq(X4427,X4425,c_Groups_Oone__class_Oone(X4427))
| c_Orderings_Oord__class_Oless__eq(X4427,c_Groups_Otimes__class_Otimes(X4427,X4425,X4426),X4426) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1865,plain,
! [X4673,X4674,X4675] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4675)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4675,c_Power_Opower__class_Opower(X4675,X4674,X4673)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4675,X4674),X4673)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1866,plain,
! [X4445,X4446,X4447,X4448] :
( ~ class_Rings_Olinordered__semidom(X4448)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X4447,X4446)
| ~ c_Orderings_Oord__class_Oless(X4448,c_Groups_Oone__class_Oone(X4448),X4445)
| c_Orderings_Oord__class_Oless(X4448,c_Power_Opower__class_Opower(X4448,X4445,X4447),c_Power_Opower__class_Opower(X4448,X4445,X4446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1867,plain,
! [X4457,X4458,X4459,X4460] :
( ~ class_Rings_Olinordered__semidom(X4460)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4459,X4458)
| ~ c_Orderings_Oord__class_Oless__eq(X4460,c_Groups_Oone__class_Oone(X4460),X4457)
| c_Orderings_Oord__class_Oless__eq(X4460,c_Power_Opower__class_Opower(X4460,X4457,X4459),c_Power_Opower__class_Opower(X4460,X4457,X4458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1868,plain,
! [X3526,X3527,X3528] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),X3527)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| X3527 != c_Groups_Ozero__class_Ozero(X3528)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),X3527)
| X3527 != c_Groups_Ozero__class_Ozero(X3528)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| X3527 = c_Groups_Ozero__class_Ozero(X3528)
| c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526))
| ~ c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),X3527)
| c_Orderings_Oord__class_Oless(X3528,c_Groups_Ozero__class_Ozero(X3528),c_Power_Opower__class_Opower(X3528,X3527,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3526)))
| ~ class_Rings_Olinordered__idom(X3528) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1351])])]) ).
fof(i_0_1869,plain,
! [X3839,X3840,X3841,X3842,X3843] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3843)
| ~ c_Orderings_Oord__class_Oless(X3843,X3842,X3841)
| ~ c_Orderings_Oord__class_Oless(X3843,X3840,X3839)
| c_Orderings_Oord__class_Oless(X3843,c_Groups_Oplus__class_Oplus(X3843,X3842,X3840),c_Groups_Oplus__class_Oplus(X3843,X3841,X3839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1870,plain,
! [X3892,X3893,X3894,X3895,X3896] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3896)
| ~ c_Orderings_Oord__class_Oless__eq(X3896,X3895,X3894)
| ~ c_Orderings_Oord__class_Oless(X3896,X3893,X3892)
| c_Orderings_Oord__class_Oless(X3896,c_Groups_Oplus__class_Oplus(X3896,X3895,X3893),c_Groups_Oplus__class_Oplus(X3896,X3894,X3892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1871,plain,
! [X3887,X3888,X3889,X3890,X3891] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3891)
| ~ c_Orderings_Oord__class_Oless(X3891,X3890,X3889)
| ~ c_Orderings_Oord__class_Oless__eq(X3891,X3888,X3887)
| c_Orderings_Oord__class_Oless(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__less__le__mono])]) ).
fof(i_0_1872,plain,
! [X3810,X3811,X3812,X3813,X3814] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3814)
| ~ c_Orderings_Oord__class_Oless__eq(X3814,X3813,X3812)
| ~ c_Orderings_Oord__class_Oless__eq(X3814,X3811,X3810)
| c_Orderings_Oord__class_Oless__eq(X3814,c_Groups_Oplus__class_Oplus(X3814,X3813,X3811),c_Groups_Oplus__class_Oplus(X3814,X3812,X3810)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1873,plain,
! [X4616,X4617,X4618] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4618,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4617),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4618,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4616)))
| X4617 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma])]) ).
fof(i_0_1874,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__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5054,X5053),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X5054,X5053) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X5054,X5053) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).
fof(i_0_1875,plain,
! [X4336,X4337,X4338,X4339] :
( ~ class_Fields_Ofield(X4339)
| X4338 = c_Groups_Ozero__class_Ozero(X4339)
| c_Power_Opower__class_Opower(X4339,c_Rings_Oinverse__class_Odivide(X4339,X4337,X4338),X4336) = c_Rings_Oinverse__class_Odivide(X4339,c_Power_Opower__class_Opower(X4339,X4337,X4336),c_Power_Opower__class_Opower(X4339,X4338,X4336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).
fof(i_0_1876,plain,
! [X3215,X3216,X3217] :
( ( X3216 = c_Groups_Ozero__class_Ozero(X3217)
| c_Groups_Oplus__class_Oplus(X3217,c_Groups_Otimes__class_Otimes(X3217,X3216,X3216),c_Groups_Otimes__class_Otimes(X3217,X3215,X3215)) != c_Groups_Ozero__class_Ozero(X3217)
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( X3215 = c_Groups_Ozero__class_Ozero(X3217)
| c_Groups_Oplus__class_Oplus(X3217,c_Groups_Otimes__class_Otimes(X3217,X3216,X3216),c_Groups_Otimes__class_Otimes(X3217,X3215,X3215)) != c_Groups_Ozero__class_Ozero(X3217)
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( X3216 != c_Groups_Ozero__class_Ozero(X3217)
| X3215 != c_Groups_Ozero__class_Ozero(X3217)
| c_Groups_Oplus__class_Oplus(X3217,c_Groups_Otimes__class_Otimes(X3217,X3216,X3216),c_Groups_Otimes__class_Otimes(X3217,X3215,X3215)) = c_Groups_Ozero__class_Ozero(X3217)
| ~ class_Rings_Olinordered__ring__strict(X3217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).
fof(i_0_1877,plain,
! [X3519,X3520,X3521] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519))
| ~ c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),c_Power_Opower__class_Opower(X3521,X3520,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519)))
| ~ class_Rings_Olinordered__idom(X3521) )
& ( c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),X3520)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519))
| ~ c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),c_Power_Opower__class_Opower(X3521,X3520,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519)))
| ~ class_Rings_Olinordered__idom(X3521) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519))
| c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),c_Power_Opower__class_Opower(X3521,X3520,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519)))
| ~ class_Rings_Olinordered__idom(X3521) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519))
| ~ c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),X3520)
| c_Orderings_Oord__class_Oless__eq(X3521,c_Groups_Ozero__class_Ozero(X3521),c_Power_Opower__class_Opower(X3521,X3520,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3519)))
| ~ class_Rings_Olinordered__idom(X3521) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1352])])]) ).
fof(i_0_1878,plain,
! [X3533,X3534,X3535] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| ~ c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( X3534 = c_Groups_Ozero__class_Ozero(X3535)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| ~ c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| c_Orderings_Oord__class_Oless__eq(X3535,X3534,c_Groups_Ozero__class_Ozero(X3535))
| ~ c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( X3534 = c_Groups_Ozero__class_Ozero(X3535)
| c_Orderings_Oord__class_Oless__eq(X3535,X3534,c_Groups_Ozero__class_Ozero(X3535))
| ~ c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| ~ c_Orderings_Oord__class_Oless__eq(X3535,X3534,c_Groups_Ozero__class_Ozero(X3535))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533))
| X3534 != c_Groups_Ozero__class_Ozero(X3535)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3535,c_Power_Opower__class_Opower(X3535,X3534,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3533)),c_Groups_Ozero__class_Ozero(X3535))
| ~ class_Rings_Olinordered__idom(X3535) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1353])])]) ).
fof(i_0_1879,plain,
! [X4930,X4931,X4932,X4933] :
( ~ class_Divides_Osemiring__div(X4933)
| c_Divides_Odiv__class_Omod(X4933,c_Groups_Otimes__class_Otimes(X4933,X4932,X4931),c_Groups_Otimes__class_Otimes(X4933,X4930,X4931)) = c_Groups_Otimes__class_Otimes(X4933,c_Divides_Odiv__class_Omod(X4933,X4932,X4930),X4931) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).
fof(i_0_1880,plain,
! [X3062,X3063,X3064,X3065] :
( ~ class_Rings_Ocomm__semiring__1(X3065)
| c_Groups_Oplus__class_Oplus(X3065,c_Groups_Otimes__class_Otimes(X3065,X3064,X3063),c_Groups_Otimes__class_Otimes(X3065,X3062,X3063)) = c_Groups_Otimes__class_Otimes(X3065,c_Groups_Oplus__class_Oplus(X3065,X3064,X3062),X3063) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1881,plain,
! [X4926,X4927,X4928,X4929] :
( ~ class_Divides_Osemiring__div(X4929)
| c_Divides_Odiv__class_Omod(X4929,c_Groups_Otimes__class_Otimes(X4929,X4928,X4927),c_Groups_Otimes__class_Otimes(X4929,X4928,X4926)) = c_Groups_Otimes__class_Otimes(X4929,X4928,c_Divides_Odiv__class_Omod(X4929,X4927,X4926)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).
fof(i_0_1882,plain,
! [X4258,X4259,X4260,X4261] :
( ~ class_RealVector_Oreal__normed__field(X4261)
| c_Rings_Oinverse__class_Odivide(X4261,c_Groups_Oplus__class_Oplus(X4261,X4260,X4259),X4258) = c_Groups_Oplus__class_Oplus(X4261,c_Rings_Oinverse__class_Odivide(X4261,X4260,X4258),c_Rings_Oinverse__class_Odivide(X4261,X4259,X4258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Oadd])]) ).
fof(i_0_1883,plain,
! [X4254,X4255,X4256,X4257] :
( ~ class_Rings_Odivision__ring(X4257)
| c_Rings_Oinverse__class_Odivide(X4257,c_Groups_Oplus__class_Oplus(X4257,X4256,X4255),X4254) = c_Groups_Oplus__class_Oplus(X4257,c_Rings_Oinverse__class_Odivide(X4257,X4256,X4254),c_Rings_Oinverse__class_Odivide(X4257,X4255,X4254)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).
fof(i_0_1884,plain,
! [X4262,X4263,X4264,X4265] :
( ~ class_Fields_Ofield__inverse__zero(X4265)
| c_Power_Opower__class_Opower(X4265,c_Rings_Oinverse__class_Odivide(X4265,X4264,X4263),X4262) = c_Rings_Oinverse__class_Odivide(X4265,c_Power_Opower__class_Opower(X4265,X4264,X4262),c_Power_Opower__class_Opower(X4265,X4263,X4262)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
fof(i_0_1885,plain,
! [X2778,X2779,X2780,X2781] :
( ~ class_Groups_Ocomm__monoid__mult(X2781)
| c_Power_Opower__class_Opower(X2781,c_Groups_Otimes__class_Otimes(X2781,X2780,X2779),X2778) = c_Groups_Otimes__class_Otimes(X2781,c_Power_Opower__class_Opower(X2781,X2780,X2778),c_Power_Opower__class_Opower(X2781,X2779,X2778)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1886,plain,
! [X2774,X2775,X2776,X2777] :
( ~ class_Rings_Ocomm__semiring__1(X2777)
| c_Power_Opower__class_Opower(X2777,c_Groups_Otimes__class_Otimes(X2777,X2776,X2775),X2774) = c_Groups_Otimes__class_Otimes(X2777,c_Power_Opower__class_Opower(X2777,X2776,X2774),c_Power_Opower__class_Opower(X2777,X2775,X2774)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1887,plain,
! [X3040,X3041,X3042,X3043] :
( ~ class_Rings_Ocomm__semiring(X3043)
| c_Groups_Otimes__class_Otimes(X3043,c_Groups_Oplus__class_Oplus(X3043,X3042,X3041),X3040) = c_Groups_Oplus__class_Oplus(X3043,c_Groups_Otimes__class_Otimes(X3043,X3042,X3040),c_Groups_Otimes__class_Otimes(X3043,X3041,X3040)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1888,plain,
! [X2930,X2931,X2932,X2933] :
( ~ class_RealVector_Oreal__normed__algebra(X2933)
| c_Groups_Otimes__class_Otimes(X2933,c_Groups_Oplus__class_Oplus(X2933,X2932,X2931),X2930) = c_Groups_Oplus__class_Oplus(X2933,c_Groups_Otimes__class_Otimes(X2933,X2932,X2930),c_Groups_Otimes__class_Otimes(X2933,X2931,X2930)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1889,plain,
! [X2926,X2927,X2928,X2929] :
( ~ class_RealVector_Oreal__normed__algebra(X2929)
| c_Groups_Otimes__class_Otimes(X2929,c_Groups_Oplus__class_Oplus(X2929,X2928,X2927),X2926) = c_Groups_Oplus__class_Oplus(X2929,c_Groups_Otimes__class_Otimes(X2929,X2928,X2926),c_Groups_Otimes__class_Otimes(X2929,X2927,X2926)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1890,plain,
! [X3058,X3059,X3060,X3061] :
( ~ class_Rings_Ocomm__semiring__1(X3061)
| c_Groups_Otimes__class_Otimes(X3061,c_Groups_Oplus__class_Oplus(X3061,X3060,X3059),X3058) = c_Groups_Oplus__class_Oplus(X3061,c_Groups_Otimes__class_Otimes(X3061,X3060,X3058),c_Groups_Otimes__class_Otimes(X3061,X3059,X3058)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1891,plain,
! [X2922,X2923,X2924,X2925] :
( ~ class_RealVector_Oreal__normed__algebra(X2925)
| c_Groups_Otimes__class_Otimes(X2925,X2924,c_Groups_Oplus__class_Oplus(X2925,X2923,X2922)) = c_Groups_Oplus__class_Oplus(X2925,c_Groups_Otimes__class_Otimes(X2925,X2924,X2923),c_Groups_Otimes__class_Otimes(X2925,X2924,X2922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1892,plain,
! [X2918,X2919,X2920,X2921] :
( ~ class_RealVector_Oreal__normed__algebra(X2921)
| c_Groups_Otimes__class_Otimes(X2921,X2920,c_Groups_Oplus__class_Oplus(X2921,X2919,X2918)) = c_Groups_Oplus__class_Oplus(X2921,c_Groups_Otimes__class_Otimes(X2921,X2920,X2919),c_Groups_Otimes__class_Otimes(X2921,X2920,X2918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1893,plain,
! [X3049,X3050,X3051,X3052] :
( ~ class_Rings_Ocomm__semiring__1(X3052)
| c_Groups_Otimes__class_Otimes(X3052,X3051,c_Groups_Oplus__class_Oplus(X3052,X3050,X3049)) = c_Groups_Oplus__class_Oplus(X3052,c_Groups_Otimes__class_Otimes(X3052,X3051,X3050),c_Groups_Otimes__class_Otimes(X3052,X3051,X3049)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).
fof(i_0_1894,plain,
! [X5045,X5046,X5047,X5048] :
( ~ class_Divides_Osemiring__div(X5048)
| c_Divides_Odiv__class_Omod(X5048,c_Groups_Oplus__class_Oplus(X5048,X5047,c_Groups_Otimes__class_Otimes(X5048,X5046,X5045)),X5046) = c_Divides_Odiv__class_Omod(X5048,X5047,X5046) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).
fof(i_0_1895,plain,
! [X5049,X5050,X5051,X5052] :
( ~ class_Divides_Osemiring__div(X5052)
| c_Divides_Odiv__class_Omod(X5052,c_Groups_Oplus__class_Oplus(X5052,X5051,c_Groups_Otimes__class_Otimes(X5052,X5050,X5049)),X5049) = c_Divides_Odiv__class_Omod(X5052,X5051,X5049) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).
fof(i_0_1896,plain,
! [X3368,X3369,X3370,X3371] :
( ~ class_Rings_Ocomm__semiring__1(X3371)
| c_Groups_Otimes__class_Otimes(X3371,c_Power_Opower__class_Opower(X3371,X3370,X3369),c_Power_Opower__class_Opower(X3371,X3370,X3368)) = c_Power_Opower__class_Opower(X3371,X3370,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3369,X3368)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1897,plain,
! [X3364,X3365,X3366,X3367] :
( ~ class_Groups_Omonoid__mult(X3367)
| c_Power_Opower__class_Opower(X3367,X3366,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3365,X3364)) = c_Groups_Otimes__class_Otimes(X3367,c_Power_Opower__class_Opower(X3367,X3366,X3365),c_Power_Opower__class_Opower(X3367,X3366,X3364)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1898,plain,
! [X3770,X3771,X3772] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3772)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3771,X3770)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3772,X3771),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3772,X3770)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1899,plain,
! [X3436,X3437,X3438] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3438,X3437)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3436)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3436,X3438),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3436,X3437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1900,plain,
! [X3425,X3426,X3427] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3427,X3426)
| ~ 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,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3427,X3425),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3426,X3425)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1901,plain,
! [X3422,X3423,X3424] :
( ~ 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),X3422)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3424),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3422,X3423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1902,plain,
! [X5077,X5078,X5079] :
( ( ~ hBOOL(hAPP(X5079,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5078,X5077)))
| epred1_3(X5079,X5077,X5078) )
& ( ~ epred1_3(X5079,X5077,X5078)
| hBOOL(hAPP(X5079,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5078,X5077))) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1354])]) ).
fof(i_0_1903,plain,
! [X3686,X3687,X3688,X3689] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3689,X3688)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3687,X3686)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3689,X3687),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3688,X3686)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1904,plain,
! [X3682,X3683,X3684,X3685] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3685,X3684)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3683,X3682)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3685,X3683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3684,X3682)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1905,plain,
! [X3690,X3691,X3692,X3693] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3693,X3692)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3691,X3690)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3693,X3691),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3692,X3690)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1906,plain,
! [X3190,X3191,X3192,X3193] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3193,X3192)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3191,X3190)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3193,X3191),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3192,X3190)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1907,plain,
! [X3262,X3263,X3264] :
( ~ class_Rings_Olinordered__semiring__strict(X3264)
| ~ c_Orderings_Oord__class_Oless(X3264,c_Groups_Ozero__class_Ozero(X3264),c_Groups_Otimes__class_Otimes(X3264,X3263,X3262))
| ~ c_Orderings_Oord__class_Oless(X3264,c_Groups_Ozero__class_Ozero(X3264),X3262)
| c_Orderings_Oord__class_Oless(X3264,c_Groups_Ozero__class_Ozero(X3264),X3263) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1908,plain,
! [X3265,X3266,X3267] :
( ~ class_Rings_Olinordered__semiring__strict(X3267)
| ~ c_Orderings_Oord__class_Oless(X3267,c_Groups_Ozero__class_Ozero(X3267),c_Groups_Otimes__class_Otimes(X3267,X3266,X3265))
| ~ c_Orderings_Oord__class_Oless(X3267,c_Groups_Ozero__class_Ozero(X3267),X3266)
| c_Orderings_Oord__class_Oless(X3267,c_Groups_Ozero__class_Ozero(X3267),X3265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1909,plain,
! [X4387,X4388,X4389] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4389,c_Groups_Ozero__class_Ozero(X4389),X4387)
| ~ c_Orderings_Oord__class_Oless__eq(X4389,c_Groups_Ozero__class_Ozero(X4389),X4388)
| c_Groups_Oabs__class_Oabs(X4389,c_Groups_Otimes__class_Otimes(X4389,X4388,X4387)) = c_Groups_Otimes__class_Otimes(X4389,c_Groups_Oabs__class_Oabs(X4389,X4388),c_Groups_Oabs__class_Oabs(X4389,X4387))
| ~ class_Rings_Oordered__ring__abs(X4389) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4389,X4387,c_Groups_Ozero__class_Ozero(X4389))
| ~ c_Orderings_Oord__class_Oless__eq(X4389,c_Groups_Ozero__class_Ozero(X4389),X4388)
| c_Groups_Oabs__class_Oabs(X4389,c_Groups_Otimes__class_Otimes(X4389,X4388,X4387)) = c_Groups_Otimes__class_Otimes(X4389,c_Groups_Oabs__class_Oabs(X4389,X4388),c_Groups_Oabs__class_Oabs(X4389,X4387))
| ~ class_Rings_Oordered__ring__abs(X4389) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4389,c_Groups_Ozero__class_Ozero(X4389),X4387)
| ~ c_Orderings_Oord__class_Oless__eq(X4389,X4388,c_Groups_Ozero__class_Ozero(X4389))
| c_Groups_Oabs__class_Oabs(X4389,c_Groups_Otimes__class_Otimes(X4389,X4388,X4387)) = c_Groups_Otimes__class_Otimes(X4389,c_Groups_Oabs__class_Oabs(X4389,X4388),c_Groups_Oabs__class_Oabs(X4389,X4387))
| ~ class_Rings_Oordered__ring__abs(X4389) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4389,X4387,c_Groups_Ozero__class_Ozero(X4389))
| ~ c_Orderings_Oord__class_Oless__eq(X4389,X4388,c_Groups_Ozero__class_Ozero(X4389))
| c_Groups_Oabs__class_Oabs(X4389,c_Groups_Otimes__class_Otimes(X4389,X4388,X4387)) = c_Groups_Otimes__class_Otimes(X4389,c_Groups_Oabs__class_Oabs(X4389,X4388),c_Groups_Oabs__class_Oabs(X4389,X4387))
| ~ class_Rings_Oordered__ring__abs(X4389) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
cnf(i_0_1910,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk4_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1334]) ).
fof(i_0_1911,plain,
! [X3776,X3777] :
( ( X3777 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3777,X3777),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3776,X3776)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3776 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3777,X3777),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3776,X3776)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3777 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3776 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3777,X3777),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3776,X3776)) = 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_1912,plain,
! [X3773,X3774,X3775] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3775,X3774),X3773) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3775,X3773),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3774,X3773)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
cnf(i_0_1913,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_1355]) ).
fof(i_0_1914,plain,
! [X3176,X3177,X3178] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3178,X3177),X3176) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3178,X3176),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3177,X3176)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1915,plain,
! [X3170,X3171,X3172] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3172,X3171),X3170) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3172,X3170),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3171,X3170)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1916,plain,
! [X3452,X3453,X3454] : c_Power_Opower__class_Opower(tc_Int_Oint,X3454,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3453,X3452)) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X3454,X3453),c_Power_Opower__class_Opower(tc_Int_Oint,X3454,X3452)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1917,plain,
! [X3173,X3174,X3175] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3175,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3174,X3173)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3175,X3174),c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3175,X3173)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1918,plain,
! [X3167,X3168,X3169] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3169,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3168,X3167)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3169,X3168),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3169,X3167)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
cnf(i_0_1919,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_1295]) ).
fof(i_0_1920,plain,
! [X3513,X3514,X3515] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3513))
| ~ c_Orderings_Oord__class_Oless(X3515,c_Power_Opower__class_Opower(X3515,X3514,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3513)),c_Groups_Ozero__class_Ozero(X3515))
| ~ class_Rings_Olinordered__idom(X3515) )
& ( c_Orderings_Oord__class_Oless(X3515,X3514,c_Groups_Ozero__class_Ozero(X3515))
| ~ c_Orderings_Oord__class_Oless(X3515,c_Power_Opower__class_Opower(X3515,X3514,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3513)),c_Groups_Ozero__class_Ozero(X3515))
| ~ class_Rings_Olinordered__idom(X3515) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3513))
| ~ c_Orderings_Oord__class_Oless(X3515,X3514,c_Groups_Ozero__class_Ozero(X3515))
| c_Orderings_Oord__class_Oless(X3515,c_Power_Opower__class_Opower(X3515,X3514,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3513)),c_Groups_Ozero__class_Ozero(X3515))
| ~ class_Rings_Olinordered__idom(X3515) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1356])])]) ).
fof(i_0_1921,plain,
! [X3414,X3415] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3415,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3414)))
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3414) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3415) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3414) != 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,X3415,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3414))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3415)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3415,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3414))) ) ),
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_1922,plain,
! [X4707,X4708,X4709] :
( ( c_Orderings_Oord__class_Oless(X4709,X4708,c_Groups_Ozero__class_Ozero(X4709))
| c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4708)
| ~ c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) )
& ( c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4707)
| c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4708)
| ~ c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) )
& ( c_Orderings_Oord__class_Oless(X4709,X4708,c_Groups_Ozero__class_Ozero(X4709))
| c_Orderings_Oord__class_Oless(X4709,X4707,c_Groups_Ozero__class_Ozero(X4709))
| ~ c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) )
& ( c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4707)
| c_Orderings_Oord__class_Oless(X4709,X4707,c_Groups_Ozero__class_Ozero(X4709))
| ~ c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) )
& ( ~ c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4708)
| ~ c_Orderings_Oord__class_Oless(X4709,X4707,c_Groups_Ozero__class_Ozero(X4709))
| c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) )
& ( ~ c_Orderings_Oord__class_Oless(X4709,X4708,c_Groups_Ozero__class_Ozero(X4709))
| ~ c_Orderings_Oord__class_Oless(X4709,c_Groups_Ozero__class_Ozero(X4709),X4707)
| c_Orderings_Oord__class_Oless(X4709,c_Rings_Oinverse__class_Odivide(X4709,X4708,X4707),c_Groups_Ozero__class_Ozero(X4709))
| ~ class_Fields_Olinordered__field__inverse__zero(X4709) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).
fof(i_0_1923,plain,
! [X4698,X4699,X4700] :
( ( c_Orderings_Oord__class_Oless__eq(X4700,X4699,c_Groups_Ozero__class_Ozero(X4700))
| c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4699)
| ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) )
& ( c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4698)
| c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4699)
| ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) )
& ( c_Orderings_Oord__class_Oless__eq(X4700,X4699,c_Groups_Ozero__class_Ozero(X4700))
| c_Orderings_Oord__class_Oless__eq(X4700,X4698,c_Groups_Ozero__class_Ozero(X4700))
| ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) )
& ( c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4698)
| c_Orderings_Oord__class_Oless__eq(X4700,X4698,c_Groups_Ozero__class_Ozero(X4700))
| ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4699)
| ~ c_Orderings_Oord__class_Oless__eq(X4700,X4698,c_Groups_Ozero__class_Ozero(X4700))
| c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4700,X4699,c_Groups_Ozero__class_Ozero(X4700))
| ~ c_Orderings_Oord__class_Oless__eq(X4700,c_Groups_Ozero__class_Ozero(X4700),X4698)
| c_Orderings_Oord__class_Oless__eq(X4700,c_Rings_Oinverse__class_Odivide(X4700,X4699,X4698),c_Groups_Ozero__class_Ozero(X4700))
| ~ class_Fields_Olinordered__field__inverse__zero(X4700) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).
fof(i_0_1924,plain,
! [X3342,X3343,X3344] :
( ( c_Orderings_Oord__class_Oless__eq(X3344,X3343,c_Groups_Ozero__class_Ozero(X3344))
| c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3343)
| ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) )
& ( c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3342)
| c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3343)
| ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) )
& ( c_Orderings_Oord__class_Oless__eq(X3344,X3343,c_Groups_Ozero__class_Ozero(X3344))
| c_Orderings_Oord__class_Oless__eq(X3344,X3342,c_Groups_Ozero__class_Ozero(X3344))
| ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) )
& ( c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3342)
| c_Orderings_Oord__class_Oless__eq(X3344,X3342,c_Groups_Ozero__class_Ozero(X3344))
| ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3343)
| ~ c_Orderings_Oord__class_Oless__eq(X3344,X3342,c_Groups_Ozero__class_Ozero(X3344))
| c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3344,X3343,c_Groups_Ozero__class_Ozero(X3344))
| ~ c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Ozero__class_Ozero(X3344),X3342)
| c_Orderings_Oord__class_Oless__eq(X3344,c_Groups_Otimes__class_Otimes(X3344,X3343,X3342),c_Groups_Ozero__class_Ozero(X3344))
| ~ class_Rings_Olinordered__ring__strict(X3344) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1925,plain,
! [X4704,X4705,X4706] :
( ( c_Orderings_Oord__class_Oless(X4706,X4705,c_Groups_Ozero__class_Ozero(X4706))
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4705)
| ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) )
& ( c_Orderings_Oord__class_Oless(X4706,X4704,c_Groups_Ozero__class_Ozero(X4706))
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4705)
| ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) )
& ( c_Orderings_Oord__class_Oless(X4706,X4705,c_Groups_Ozero__class_Ozero(X4706))
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4704)
| ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) )
& ( c_Orderings_Oord__class_Oless(X4706,X4704,c_Groups_Ozero__class_Ozero(X4706))
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4704)
| ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) )
& ( ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4705)
| ~ c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),X4704)
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) )
& ( ~ c_Orderings_Oord__class_Oless(X4706,X4705,c_Groups_Ozero__class_Ozero(X4706))
| ~ c_Orderings_Oord__class_Oless(X4706,X4704,c_Groups_Ozero__class_Ozero(X4706))
| c_Orderings_Oord__class_Oless(X4706,c_Groups_Ozero__class_Ozero(X4706),c_Rings_Oinverse__class_Odivide(X4706,X4705,X4704))
| ~ class_Fields_Olinordered__field__inverse__zero(X4706) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).
fof(i_0_1926,plain,
! [X4701,X4702,X4703] :
( ( c_Orderings_Oord__class_Oless__eq(X4703,X4702,c_Groups_Ozero__class_Ozero(X4703))
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4702)
| ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) )
& ( c_Orderings_Oord__class_Oless__eq(X4703,X4701,c_Groups_Ozero__class_Ozero(X4703))
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4702)
| ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) )
& ( c_Orderings_Oord__class_Oless__eq(X4703,X4702,c_Groups_Ozero__class_Ozero(X4703))
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4701)
| ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) )
& ( c_Orderings_Oord__class_Oless__eq(X4703,X4701,c_Groups_Ozero__class_Ozero(X4703))
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4701)
| ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4702)
| ~ c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),X4701)
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4703,X4702,c_Groups_Ozero__class_Ozero(X4703))
| ~ c_Orderings_Oord__class_Oless__eq(X4703,X4701,c_Groups_Ozero__class_Ozero(X4703))
| c_Orderings_Oord__class_Oless__eq(X4703,c_Groups_Ozero__class_Ozero(X4703),c_Rings_Oinverse__class_Odivide(X4703,X4702,X4701))
| ~ class_Fields_Olinordered__field__inverse__zero(X4703) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).
fof(i_0_1927,plain,
! [X3345,X3346,X3347] :
( ( c_Orderings_Oord__class_Oless__eq(X3347,X3346,c_Groups_Ozero__class_Ozero(X3347))
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3346)
| ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) )
& ( c_Orderings_Oord__class_Oless__eq(X3347,X3345,c_Groups_Ozero__class_Ozero(X3347))
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3346)
| ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) )
& ( c_Orderings_Oord__class_Oless__eq(X3347,X3346,c_Groups_Ozero__class_Ozero(X3347))
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3345)
| ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) )
& ( c_Orderings_Oord__class_Oless__eq(X3347,X3345,c_Groups_Ozero__class_Ozero(X3347))
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3345)
| ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3346)
| ~ c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),X3345)
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3347,X3346,c_Groups_Ozero__class_Ozero(X3347))
| ~ c_Orderings_Oord__class_Oless__eq(X3347,X3345,c_Groups_Ozero__class_Ozero(X3347))
| c_Orderings_Oord__class_Oless__eq(X3347,c_Groups_Ozero__class_Ozero(X3347),c_Groups_Otimes__class_Otimes(X3347,X3346,X3345))
| ~ class_Rings_Olinordered__ring__strict(X3347) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
cnf(i_0_1928,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]) ).
cnf(i_0_1929,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_1357]) ).
fof(i_0_1930,plain,
! [X3445,X3446,X3447,X3448] :
( ~ class_Rings_Olinordered__idom(X3448)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3447)
| ~ c_Orderings_Oord__class_Oless__eq(X3448,X3446,X3445)
| c_Orderings_Oord__class_Oless__eq(X3448,c_Power_Opower__class_Opower(X3448,X3446,X3447),c_Power_Opower__class_Opower(X3448,X3445,X3447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1358])]) ).
cnf(i_0_1931,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_1359]) ).
cnf(i_0_1932,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_1360]) ).
cnf(i_0_1933,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_1361]) ).
cnf(i_0_1934,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_1362]) ).
fof(i_0_1935,plain,
! [X4716,X4717,X4718] :
( ~ class_Fields_Olinordered__field(X4718)
| ~ c_Orderings_Oord__class_Oless(X4718,X4717,c_Groups_Ozero__class_Ozero(X4718))
| ~ c_Orderings_Oord__class_Oless(X4718,c_Groups_Ozero__class_Ozero(X4718),X4716)
| c_Orderings_Oord__class_Oless(X4718,c_Rings_Oinverse__class_Odivide(X4718,X4717,X4716),c_Groups_Ozero__class_Ozero(X4718)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).
fof(i_0_1936,plain,
! [X4713,X4714,X4715] :
( ~ class_Fields_Olinordered__field(X4715)
| ~ c_Orderings_Oord__class_Oless(X4715,c_Groups_Ozero__class_Ozero(X4715),X4714)
| ~ c_Orderings_Oord__class_Oless(X4715,X4713,c_Groups_Ozero__class_Ozero(X4715))
| c_Orderings_Oord__class_Oless(X4715,c_Rings_Oinverse__class_Odivide(X4715,X4714,X4713),c_Groups_Ozero__class_Ozero(X4715)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).
fof(i_0_1937,plain,
! [X3255,X3256,X3257] :
( ~ class_Rings_Olinordered__semiring__strict(X3257)
| ~ c_Orderings_Oord__class_Oless(X3257,X3256,c_Groups_Ozero__class_Ozero(X3257))
| ~ c_Orderings_Oord__class_Oless(X3257,c_Groups_Ozero__class_Ozero(X3257),X3255)
| c_Orderings_Oord__class_Oless(X3257,c_Groups_Otimes__class_Otimes(X3257,X3256,X3255),c_Groups_Ozero__class_Ozero(X3257)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1938,plain,
! [X3271,X3272,X3273] :
( ~ class_Rings_Olinordered__semiring__strict(X3273)
| ~ c_Orderings_Oord__class_Oless(X3273,c_Groups_Ozero__class_Ozero(X3273),X3272)
| ~ c_Orderings_Oord__class_Oless(X3273,X3271,c_Groups_Ozero__class_Ozero(X3273))
| c_Orderings_Oord__class_Oless(X3273,c_Groups_Otimes__class_Otimes(X3273,X3272,X3271),c_Groups_Ozero__class_Ozero(X3273)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1939,plain,
! [X3268,X3269,X3270] :
( ~ class_Rings_Olinordered__semiring__strict(X3270)
| ~ c_Orderings_Oord__class_Oless(X3270,c_Groups_Ozero__class_Ozero(X3270),X3269)
| ~ c_Orderings_Oord__class_Oless(X3270,X3268,c_Groups_Ozero__class_Ozero(X3270))
| c_Orderings_Oord__class_Oless(X3270,c_Groups_Otimes__class_Otimes(X3270,X3268,X3269),c_Groups_Ozero__class_Ozero(X3270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1940,plain,
! [X4775,X4776,X4777] :
( ~ class_Fields_Olinordered__field(X4777)
| ~ c_Orderings_Oord__class_Oless__eq(X4777,c_Groups_Ozero__class_Ozero(X4777),X4776)
| ~ c_Orderings_Oord__class_Oless(X4777,X4775,c_Groups_Ozero__class_Ozero(X4777))
| c_Orderings_Oord__class_Oless__eq(X4777,c_Rings_Oinverse__class_Odivide(X4777,X4776,X4775),c_Groups_Ozero__class_Ozero(X4777)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).
fof(i_0_1941,plain,
! [X4757,X4758,X4759] :
( ~ class_Fields_Olinordered__field(X4759)
| ~ c_Orderings_Oord__class_Oless__eq(X4759,X4758,c_Groups_Ozero__class_Ozero(X4759))
| ~ c_Orderings_Oord__class_Oless(X4759,c_Groups_Ozero__class_Ozero(X4759),X4757)
| c_Orderings_Oord__class_Oless__eq(X4759,c_Rings_Oinverse__class_Odivide(X4759,X4758,X4757),c_Groups_Ozero__class_Ozero(X4759)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).
fof(i_0_1942,plain,
! [X3330,X3331,X3332] :
( ~ class_Rings_Oordered__cancel__semiring(X3332)
| ~ c_Orderings_Oord__class_Oless__eq(X3332,X3331,c_Groups_Ozero__class_Ozero(X3332))
| ~ c_Orderings_Oord__class_Oless__eq(X3332,c_Groups_Ozero__class_Ozero(X3332),X3330)
| c_Orderings_Oord__class_Oless__eq(X3332,c_Groups_Otimes__class_Otimes(X3332,X3331,X3330),c_Groups_Ozero__class_Ozero(X3332)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1943,plain,
! [X3291,X3292,X3293] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3293,c_Groups_Ozero__class_Ozero(X3293),X3292)
| ~ c_Orderings_Oord__class_Oless__eq(X3293,X3291,c_Groups_Ozero__class_Ozero(X3293))
| c_Orderings_Oord__class_Oless__eq(X3293,c_Groups_Otimes__class_Otimes(X3293,X3292,X3291),c_Groups_Ozero__class_Ozero(X3293))
| ~ class_Rings_Oordered__cancel__semiring(X3293) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3293,X3292,c_Groups_Ozero__class_Ozero(X3293))
| ~ c_Orderings_Oord__class_Oless__eq(X3293,c_Groups_Ozero__class_Ozero(X3293),X3291)
| c_Orderings_Oord__class_Oless__eq(X3293,c_Groups_Otimes__class_Otimes(X3293,X3292,X3291),c_Groups_Ozero__class_Ozero(X3293))
| ~ class_Rings_Oordered__cancel__semiring(X3293) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1944,plain,
! [X3336,X3337,X3338] :
( ~ class_Rings_Oordered__cancel__semiring(X3338)
| ~ c_Orderings_Oord__class_Oless__eq(X3338,c_Groups_Ozero__class_Ozero(X3338),X3337)
| ~ c_Orderings_Oord__class_Oless__eq(X3338,X3336,c_Groups_Ozero__class_Ozero(X3338))
| c_Orderings_Oord__class_Oless__eq(X3338,c_Groups_Otimes__class_Otimes(X3338,X3337,X3336),c_Groups_Ozero__class_Ozero(X3338)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1945,plain,
! [X3333,X3334,X3335] :
( ~ class_Rings_Oordered__cancel__semiring(X3335)
| ~ c_Orderings_Oord__class_Oless__eq(X3335,c_Groups_Ozero__class_Ozero(X3335),X3334)
| ~ c_Orderings_Oord__class_Oless__eq(X3335,X3333,c_Groups_Ozero__class_Ozero(X3335))
| c_Orderings_Oord__class_Oless__eq(X3335,c_Groups_Otimes__class_Otimes(X3335,X3333,X3334),c_Groups_Ozero__class_Ozero(X3335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1946,plain,
! [X3877,X3878,X3879] :
( ~ class_Groups_Oordered__comm__monoid__add(X3879)
| ~ c_Orderings_Oord__class_Oless(X3879,X3878,c_Groups_Ozero__class_Ozero(X3879))
| ~ c_Orderings_Oord__class_Oless(X3879,X3877,c_Groups_Ozero__class_Ozero(X3879))
| c_Orderings_Oord__class_Oless(X3879,c_Groups_Oplus__class_Oplus(X3879,X3878,X3877),c_Groups_Ozero__class_Ozero(X3879)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1947,plain,
! [X3897,X3898,X3899] :
( ~ class_Groups_Oordered__comm__monoid__add(X3899)
| ~ c_Orderings_Oord__class_Oless__eq(X3899,X3898,c_Groups_Ozero__class_Ozero(X3899))
| ~ c_Orderings_Oord__class_Oless(X3899,X3897,c_Groups_Ozero__class_Ozero(X3899))
| c_Orderings_Oord__class_Oless(X3899,c_Groups_Oplus__class_Oplus(X3899,X3898,X3897),c_Groups_Ozero__class_Ozero(X3899)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1948,plain,
! [X3900,X3901,X3902] :
( ~ class_Groups_Oordered__comm__monoid__add(X3902)
| ~ c_Orderings_Oord__class_Oless(X3902,X3901,c_Groups_Ozero__class_Ozero(X3902))
| ~ c_Orderings_Oord__class_Oless__eq(X3902,X3900,c_Groups_Ozero__class_Ozero(X3902))
| c_Orderings_Oord__class_Oless(X3902,c_Groups_Oplus__class_Oplus(X3902,X3901,X3900),c_Groups_Ozero__class_Ozero(X3902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1949,plain,
! [X3856,X3857,X3858] :
( ~ class_Groups_Oordered__comm__monoid__add(X3858)
| ~ c_Orderings_Oord__class_Oless__eq(X3858,X3857,c_Groups_Ozero__class_Ozero(X3858))
| ~ c_Orderings_Oord__class_Oless__eq(X3858,X3856,c_Groups_Ozero__class_Ozero(X3858))
| c_Orderings_Oord__class_Oless__eq(X3858,c_Groups_Oplus__class_Oplus(X3858,X3857,X3856),c_Groups_Ozero__class_Ozero(X3858)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1950,plain,
! [X4347,X4348,X4349] :
( ~ class_Rings_Olinordered__semidom(X4349)
| ~ c_Orderings_Oord__class_Oless(X4349,c_Groups_Oone__class_Oone(X4349),X4348)
| ~ c_Orderings_Oord__class_Oless(X4349,c_Groups_Oone__class_Oone(X4349),X4347)
| c_Orderings_Oord__class_Oless(X4349,c_Groups_Oone__class_Oone(X4349),c_Groups_Otimes__class_Otimes(X4349,X4348,X4347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1951,plain,
! [X4710,X4711,X4712] :
( ~ class_Fields_Olinordered__field(X4712)
| ~ c_Orderings_Oord__class_Oless(X4712,c_Groups_Ozero__class_Ozero(X4712),X4711)
| ~ c_Orderings_Oord__class_Oless(X4712,c_Groups_Ozero__class_Ozero(X4712),X4710)
| c_Orderings_Oord__class_Oless(X4712,c_Groups_Ozero__class_Ozero(X4712),c_Rings_Oinverse__class_Odivide(X4712,X4711,X4710)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).
fof(i_0_1952,plain,
! [X3880,X3881,X3882] :
( ~ class_Groups_Oordered__comm__monoid__add(X3882)
| ~ c_Orderings_Oord__class_Oless(X3882,c_Groups_Ozero__class_Ozero(X3882),X3881)
| ~ c_Orderings_Oord__class_Oless(X3882,c_Groups_Ozero__class_Ozero(X3882),X3880)
| c_Orderings_Oord__class_Oless(X3882,c_Groups_Ozero__class_Ozero(X3882),c_Groups_Oplus__class_Oplus(X3882,X3881,X3880)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1953,plain,
! [X3565,X3566,X3567] :
( ~ class_Groups_Oordered__comm__monoid__add(X3567)
| ~ c_Orderings_Oord__class_Oless__eq(X3567,c_Groups_Ozero__class_Ozero(X3567),X3566)
| ~ c_Orderings_Oord__class_Oless(X3567,c_Groups_Ozero__class_Ozero(X3567),X3565)
| c_Orderings_Oord__class_Oless(X3567,c_Groups_Ozero__class_Ozero(X3567),c_Groups_Oplus__class_Oplus(X3567,X3566,X3565)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1954,plain,
! [X3562,X3563,X3564] :
( ~ class_Groups_Oordered__comm__monoid__add(X3564)
| ~ c_Orderings_Oord__class_Oless(X3564,c_Groups_Ozero__class_Ozero(X3564),X3563)
| ~ c_Orderings_Oord__class_Oless__eq(X3564,c_Groups_Ozero__class_Ozero(X3564),X3562)
| c_Orderings_Oord__class_Oless(X3564,c_Groups_Ozero__class_Ozero(X3564),c_Groups_Oplus__class_Oplus(X3564,X3563,X3562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1955,plain,
! [X3274,X3275,X3276] :
( ~ class_Rings_Olinordered__semiring__strict(X3276)
| ~ c_Orderings_Oord__class_Oless(X3276,c_Groups_Ozero__class_Ozero(X3276),X3275)
| ~ c_Orderings_Oord__class_Oless(X3276,c_Groups_Ozero__class_Ozero(X3276),X3274)
| c_Orderings_Oord__class_Oless(X3276,c_Groups_Ozero__class_Ozero(X3276),c_Groups_Otimes__class_Otimes(X3276,X3275,X3274)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1956,plain,
! [X4778,X4779,X4780] :
( ~ class_Fields_Olinordered__field(X4780)
| ~ c_Orderings_Oord__class_Oless__eq(X4780,c_Groups_Ozero__class_Ozero(X4780),X4779)
| ~ c_Orderings_Oord__class_Oless(X4780,c_Groups_Ozero__class_Ozero(X4780),X4778)
| c_Orderings_Oord__class_Oless__eq(X4780,c_Groups_Ozero__class_Ozero(X4780),c_Rings_Oinverse__class_Odivide(X4780,X4779,X4778)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).
fof(i_0_1957,plain,
! [X3870,X3871,X3872] :
( ~ class_Groups_Oordered__comm__monoid__add(X3872)
| ~ c_Orderings_Oord__class_Oless__eq(X3872,c_Groups_Ozero__class_Ozero(X3872),X3871)
| ~ c_Orderings_Oord__class_Oless__eq(X3872,c_Groups_Ozero__class_Ozero(X3872),X3870)
| c_Orderings_Oord__class_Oless__eq(X3872,c_Groups_Ozero__class_Ozero(X3872),c_Groups_Oplus__class_Oplus(X3872,X3871,X3870)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1958,plain,
! [X3294,X3295,X3296] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3296,c_Groups_Ozero__class_Ozero(X3296),X3295)
| ~ c_Orderings_Oord__class_Oless__eq(X3296,c_Groups_Ozero__class_Ozero(X3296),X3294)
| c_Orderings_Oord__class_Oless__eq(X3296,c_Groups_Ozero__class_Ozero(X3296),c_Groups_Otimes__class_Otimes(X3296,X3295,X3294))
| ~ class_Rings_Oordered__ring(X3296) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3296,X3295,c_Groups_Ozero__class_Ozero(X3296))
| ~ c_Orderings_Oord__class_Oless__eq(X3296,X3294,c_Groups_Ozero__class_Ozero(X3296))
| c_Orderings_Oord__class_Oless__eq(X3296,c_Groups_Ozero__class_Ozero(X3296),c_Groups_Otimes__class_Otimes(X3296,X3295,X3294))
| ~ class_Rings_Oordered__ring(X3296) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1959,plain,
! [X3339,X3340,X3341] :
( ~ class_Rings_Oordered__cancel__semiring(X3341)
| ~ c_Orderings_Oord__class_Oless__eq(X3341,c_Groups_Ozero__class_Ozero(X3341),X3340)
| ~ c_Orderings_Oord__class_Oless__eq(X3341,c_Groups_Ozero__class_Ozero(X3341),X3339)
| c_Orderings_Oord__class_Oless__eq(X3341,c_Groups_Ozero__class_Ozero(X3341),c_Groups_Otimes__class_Otimes(X3341,X3340,X3339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1960,plain,
! [X4719,X4720,X4721] :
( ~ class_Fields_Olinordered__field(X4721)
| ~ c_Orderings_Oord__class_Oless(X4721,X4720,c_Groups_Ozero__class_Ozero(X4721))
| ~ c_Orderings_Oord__class_Oless(X4721,X4719,c_Groups_Ozero__class_Ozero(X4721))
| c_Orderings_Oord__class_Oless(X4721,c_Groups_Ozero__class_Ozero(X4721),c_Rings_Oinverse__class_Odivide(X4721,X4720,X4719)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).
fof(i_0_1961,plain,
! [X3252,X3253,X3254] :
( ~ class_Rings_Olinordered__ring__strict(X3254)
| ~ c_Orderings_Oord__class_Oless(X3254,X3253,c_Groups_Ozero__class_Ozero(X3254))
| ~ c_Orderings_Oord__class_Oless(X3254,X3252,c_Groups_Ozero__class_Ozero(X3254))
| c_Orderings_Oord__class_Oless(X3254,c_Groups_Ozero__class_Ozero(X3254),c_Groups_Otimes__class_Otimes(X3254,X3253,X3252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1962,plain,
! [X4754,X4755,X4756] :
( ~ class_Fields_Olinordered__field(X4756)
| ~ c_Orderings_Oord__class_Oless__eq(X4756,X4755,c_Groups_Ozero__class_Ozero(X4756))
| ~ c_Orderings_Oord__class_Oless(X4756,X4754,c_Groups_Ozero__class_Ozero(X4756))
| c_Orderings_Oord__class_Oless__eq(X4756,c_Groups_Ozero__class_Ozero(X4756),c_Rings_Oinverse__class_Odivide(X4756,X4755,X4754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).
fof(i_0_1963,plain,
! [X3327,X3328,X3329] :
( ~ class_Rings_Oordered__ring(X3329)
| ~ c_Orderings_Oord__class_Oless__eq(X3329,X3328,c_Groups_Ozero__class_Ozero(X3329))
| ~ c_Orderings_Oord__class_Oless__eq(X3329,X3327,c_Groups_Ozero__class_Ozero(X3329))
| c_Orderings_Oord__class_Oless__eq(X3329,c_Groups_Ozero__class_Ozero(X3329),c_Groups_Otimes__class_Otimes(X3329,X3328,X3327)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1964,plain,
! [X2887,X2888] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2888,X2887))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2888)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2887) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2888)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2888,X2887)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2887)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2888,X2887)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1965,plain,
! [X4350,X4351] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4351,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4350)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4351)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4350,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4351)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4351,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4350,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4351,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4351)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4350)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4350,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4350)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4351,X4350)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff])])]) ).
fof(i_0_1966,plain,
! [X3183] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3183,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3183,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3183,X3183))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1967,plain,
! [X3831,X3832,X3833,X3834] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3834)
| ~ c_Orderings_Oord__class_Oless(X3834,X3833,X3832)
| c_Orderings_Oord__class_Oless(X3834,c_Groups_Oplus__class_Oplus(X3834,X3833,X3831),c_Groups_Oplus__class_Oplus(X3834,X3832,X3831)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1968,plain,
! [X3835,X3836,X3837,X3838] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X3838)
| ~ c_Orderings_Oord__class_Oless(X3838,X3837,X3836)
| c_Orderings_Oord__class_Oless(X3838,c_Groups_Oplus__class_Oplus(X3838,X3835,X3837),c_Groups_Oplus__class_Oplus(X3838,X3835,X3836)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1969,plain,
! [X3802,X3803,X3804,X3805] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3805)
| ~ c_Orderings_Oord__class_Oless__eq(X3805,X3804,X3803)
| c_Orderings_Oord__class_Oless__eq(X3805,c_Groups_Oplus__class_Oplus(X3805,X3804,X3802),c_Groups_Oplus__class_Oplus(X3805,X3803,X3802)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1970,plain,
! [X3806,X3807,X3808,X3809] :
( ~ class_Groups_Oordered__ab__semigroup__add(X3809)
| ~ c_Orderings_Oord__class_Oless__eq(X3809,X3808,X3807)
| c_Orderings_Oord__class_Oless__eq(X3809,c_Groups_Oplus__class_Oplus(X3809,X3806,X3808),c_Groups_Oplus__class_Oplus(X3809,X3806,X3807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1971,plain,
! [X4526,X4527,X4528] :
( ~ class_Rings_Olinordered__semidom(X4528)
| ~ c_Orderings_Oord__class_Oless(X4528,c_Groups_Oone__class_Oone(X4528),X4527)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4526)
| c_Orderings_Oord__class_Oless(X4528,c_Groups_Oone__class_Oone(X4528),c_Power_Opower__class_Opower(X4528,X4527,X4526)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
cnf(i_0_1972,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_1345]) ).
cnf(i_0_1973,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_1363]) ).
cnf(i_0_1974,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_1346]) ).
fof(i_0_1975,plain,
! [X3572,X3573,X3574,X3575] :
( ~ class_Groups_Oordered__comm__monoid__add(X3575)
| ~ c_Orderings_Oord__class_Oless__eq(X3575,c_Groups_Ozero__class_Ozero(X3575),X3574)
| ~ c_Orderings_Oord__class_Oless(X3575,X3573,X3572)
| c_Orderings_Oord__class_Oless(X3575,X3573,c_Groups_Oplus__class_Oplus(X3575,X3574,X3572)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1976,plain,
! [X3568,X3569,X3570,X3571] :
( ~ class_Groups_Oordered__comm__monoid__add(X3571)
| ~ c_Orderings_Oord__class_Oless(X3571,c_Groups_Ozero__class_Ozero(X3571),X3570)
| ~ c_Orderings_Oord__class_Oless__eq(X3571,X3569,X3568)
| c_Orderings_Oord__class_Oless(X3571,X3569,c_Groups_Oplus__class_Oplus(X3571,X3570,X3568)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1977,plain,
! [X2832,X2833,X2834,X2835] :
( ~ class_Rings_Olinordered__semidom(X2835)
| ~ c_Orderings_Oord__class_Oless(X2835,c_Groups_Ozero__class_Ozero(X2835),X2834)
| ~ c_Orderings_Oord__class_Oless(X2835,X2833,X2832)
| c_Orderings_Oord__class_Oless(X2835,X2833,c_Groups_Oplus__class_Oplus(X2835,X2834,X2832)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1978,plain,
! [X3863,X3864,X3865,X3866] :
( ~ class_Groups_Oordered__comm__monoid__add(X3866)
| ~ c_Orderings_Oord__class_Oless__eq(X3866,c_Groups_Ozero__class_Ozero(X3866),X3865)
| ~ c_Orderings_Oord__class_Oless__eq(X3866,X3864,X3863)
| c_Orderings_Oord__class_Oless__eq(X3866,X3864,c_Groups_Oplus__class_Oplus(X3866,X3865,X3863)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1979,plain,
! [X3859,X3860,X3861,X3862] :
( ~ class_Groups_Oordered__comm__monoid__add(X3862)
| ~ c_Orderings_Oord__class_Oless__eq(X3862,c_Groups_Ozero__class_Ozero(X3862),X3861)
| ~ c_Orderings_Oord__class_Oless__eq(X3862,X3860,X3859)
| c_Orderings_Oord__class_Oless__eq(X3862,X3860,c_Groups_Oplus__class_Oplus(X3862,X3859,X3861)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1980,plain,
! [X2872,X2873,X2874] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2873),c_Int_Onumber__class_Onumber__of(X2874,X2872))
| ~ c_Orderings_Oord__class_Oless(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2872),c_Int_Onumber__class_Onumber__of(X2874,X2873))
| ~ class_Int_Onumber(X2874)
| ~ class_Orderings_Olinorder(X2874) )
& ( c_Orderings_Oord__class_Oless(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2872),c_Int_Onumber__class_Onumber__of(X2874,X2873))
| c_Orderings_Oord__class_Oless__eq(X2874,c_Int_Onumber__class_Onumber__of(X2874,X2873),c_Int_Onumber__class_Onumber__of(X2874,X2872))
| ~ class_Int_Onumber(X2874)
| ~ class_Orderings_Olinorder(X2874) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1364])])]) ).
fof(i_0_1981,plain,
! [X3509,X3510,X3511] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| X3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),X3510)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| X3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| X3510 != c_Groups_Ozero__class_Ozero(X3511)
| X3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),X3510)
| X3510 != c_Groups_Ozero__class_Ozero(X3511)
| X3509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( X3509 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| X3510 = c_Groups_Ozero__class_Ozero(X3511)
| c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3509)
| ~ c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),X3510)
| c_Orderings_Oord__class_Oless(X3511,c_Groups_Ozero__class_Ozero(X3511),c_Power_Opower__class_Opower(X3511,X3510,X3509))
| ~ class_Rings_Olinordered__idom(X3511) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1365])])]) ).
fof(i_0_1982,plain,
! [X4291,X4292,X4293] :
( ~ class_Fields_Ofield__inverse__zero(X4293)
| c_Rings_Oinverse__class_Odivide(X4293,c_Groups_Oone__class_Oone(X4293),c_Power_Opower__class_Opower(X4293,X4292,X4291)) = c_Power_Opower__class_Opower(X4293,c_Rings_Oinverse__class_Odivide(X4293,c_Groups_Oone__class_Oone(X4293),X4292),X4291) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).
fof(i_0_1983,plain,
! [X3496,X3497,X3498] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3496)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3496)
| ~ c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),c_Power_Opower__class_Opower(X3498,X3497,X3496))
| ~ class_Rings_Olinordered__idom(X3498) )
& ( c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),X3497)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3496)
| ~ c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),c_Power_Opower__class_Opower(X3498,X3497,X3496))
| ~ class_Rings_Olinordered__idom(X3498) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3496)
| c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),c_Power_Opower__class_Opower(X3498,X3497,X3496))
| ~ class_Rings_Olinordered__idom(X3498) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3496)
| ~ c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),X3497)
| c_Orderings_Oord__class_Oless__eq(X3498,c_Groups_Ozero__class_Ozero(X3498),c_Power_Opower__class_Opower(X3498,X3497,X3496))
| ~ class_Rings_Olinordered__idom(X3498) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1366])])]) ).
fof(i_0_1984,plain,
! [X3493,X3494,X3495] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3495,c_Groups_Ozero__class_Ozero(X3495),c_Power_Opower__class_Opower(X3495,X3494,X3493))
| c_Orderings_Oord__class_Oless__eq(X3495,c_Groups_Ozero__class_Ozero(X3495),X3494)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3493)
| ~ class_Rings_Olinordered__idom(X3495) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3495,c_Groups_Ozero__class_Ozero(X3495),X3494)
| c_Orderings_Oord__class_Oless__eq(X3495,c_Groups_Ozero__class_Ozero(X3495),c_Power_Opower__class_Opower(X3495,X3494,X3493))
| ~ class_Rings_Olinordered__idom(X3495) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3493)
| c_Orderings_Oord__class_Oless__eq(X3495,c_Groups_Ozero__class_Ozero(X3495),c_Power_Opower__class_Opower(X3495,X3494,X3493))
| ~ class_Rings_Olinordered__idom(X3495) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__iff])])]) ).
fof(i_0_1985,plain,
! [X3487,X3488,X3489] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3489,c_Groups_Ozero__class_Ozero(X3489),c_Power_Opower__class_Opower(X3489,X3487,X3488))
| c_Orderings_Oord__class_Oless__eq(X3489,c_Groups_Ozero__class_Ozero(X3489),X3487)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3488)
| ~ class_Rings_Olinordered__idom(X3489) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3489,c_Groups_Ozero__class_Ozero(X3489),X3487)
| c_Orderings_Oord__class_Oless__eq(X3489,c_Groups_Ozero__class_Ozero(X3489),c_Power_Opower__class_Opower(X3489,X3487,X3488))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3488)
| ~ class_Rings_Olinordered__idom(X3489) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1367])])]) ).
fof(i_0_1986,plain,
! [X3516,X3517,X3518] :
( ( X3516 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| ~ c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( X3517 = c_Groups_Ozero__class_Ozero(X3518)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| ~ c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| c_Orderings_Oord__class_Oless__eq(X3518,X3517,c_Groups_Ozero__class_Ozero(X3518))
| ~ c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( X3517 = c_Groups_Ozero__class_Ozero(X3518)
| c_Orderings_Oord__class_Oless__eq(X3518,X3517,c_Groups_Ozero__class_Ozero(X3518))
| ~ c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| ~ c_Orderings_Oord__class_Oless__eq(X3518,X3517,c_Groups_Ozero__class_Ozero(X3518))
| X3516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3516)
| X3517 != c_Groups_Ozero__class_Ozero(X3518)
| X3516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(X3518,c_Power_Opower__class_Opower(X3518,X3517,X3516),c_Groups_Ozero__class_Ozero(X3518))
| ~ class_Rings_Olinordered__idom(X3518) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1368])])]) ).
cnf(i_0_1987,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_1347]) ).
cnf(i_0_1988,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_1348]) ).
fof(i_0_1989,plain,
! [X3658,X3659,X3660] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3660,X3659)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3660,X3658),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3659,X3658)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1990,plain,
! [X3661,X3662,X3663] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3663,X3662)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3663,X3661),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3662,X3661)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1991,plain,
! [X3715,X3716,X3717] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3717,X3716)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3715,X3717),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3715,X3716)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
cnf(i_0_1992,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_1349]) ).
cnf(i_0_1993,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_1350]) ).
fof(i_0_1994,plain,
! [X3667,X3668,X3669] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3669,X3668)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3667,X3669),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3667,X3668)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1995,plain,
! [X3664,X3665,X3666] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3666,X3665)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3666,X3664),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3665,X3664)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1996,plain,
! [X3184,X3185,X3186] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3186,X3185)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3186,X3184),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3185,X3184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1997,plain,
! [X3187,X3188,X3189] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3189,X3188)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3187,X3189),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3187,X3188)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
cnf(i_0_1998,plain,
( X1 = c_Nat_OSuc(esk6_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_1369]) ).
cnf(i_0_1999,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_1370]) ).
fof(i_0_2000,plain,
! [X4359,X4360,X4361] :
( ~ class_Rings_Ocomm__semiring__1(X4361)
| c_Groups_Oplus__class_Oplus(X4361,c_Groups_Otimes__class_Otimes(X4361,X4360,X4359),X4359) = c_Groups_Otimes__class_Otimes(X4361,c_Groups_Oplus__class_Oplus(X4361,X4360,c_Groups_Oone__class_Oone(X4361)),X4359) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).
fof(i_0_2001,plain,
! [X4356,X4357,X4358] :
( ~ class_Rings_Ocomm__semiring__1(X4358)
| c_Groups_Oplus__class_Oplus(X4358,X4357,c_Groups_Otimes__class_Otimes(X4358,X4356,X4357)) = c_Groups_Otimes__class_Otimes(X4358,c_Groups_Oplus__class_Oplus(X4358,X4356,c_Groups_Oone__class_Oone(X4358)),X4357) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).
cnf(i_0_2002,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_1371]) ).
cnf(i_0_2003,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_1372]) ).
cnf(i_0_2004,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_1373]) ).
cnf(i_0_2005,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_1374]) ).
cnf(i_0_2006,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk6_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_1369]) ).
cnf(i_0_2007,plain,
c_Int_OBit0(X1) != c_Int_OBit1(X2),
inference(split_conjunct,[status(thm)],[i_0_1375]) ).
cnf(i_0_2008,plain,
c_Int_OBit1(X1) != c_Int_OBit0(X2),
inference(split_conjunct,[status(thm)],[i_0_1376]) ).
fof(i_0_2009,plain,
! [X4209,X4210,X4211] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4211)
| c_Groups_Oabs__class_Oabs(X4211,c_Groups_Oplus__class_Oplus(X4211,c_Groups_Oabs__class_Oabs(X4211,X4210),c_Groups_Oabs__class_Oabs(X4211,X4209))) = c_Groups_Oplus__class_Oplus(X4211,c_Groups_Oabs__class_Oabs(X4211,X4210),c_Groups_Oabs__class_Oabs(X4211,X4209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_2010,plain,
! [X3768,X3769] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3769)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3768)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3769,X3768)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_2011,plain,
! [X3434,X3435] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3435)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3435,X3434)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3434)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3435,X3434)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3435)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3434)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3435,X3434)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).
fof(i_0_2012,plain,
! [X4998,X4999] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4999)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4998)
| 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,X4999,X4998)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).
fof(i_0_2013,plain,
! [X3752,X3753] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3753)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3752)
| 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,X3753,X3752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).
fof(i_0_2014,plain,
! [X3852,X3853] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3853)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3852)
| 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,X3853,X3852)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).
cnf(i_0_2015,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_1369]) ).
cnf(i_0_2016,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_1377]) ).
fof(i_0_2017,plain,
! [X4735,X4736,X4737,X4738] :
( ~ class_Fields_Ofield__inverse__zero(X4738)
| X4737 = c_Groups_Ozero__class_Ozero(X4738)
| c_Rings_Oinverse__class_Odivide(X4738,c_Groups_Otimes__class_Otimes(X4738,X4737,X4736),c_Groups_Otimes__class_Otimes(X4738,X4737,X4735)) = c_Rings_Oinverse__class_Odivide(X4738,X4736,X4735) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).
fof(i_0_2018,plain,
! [X4739,X4740,X4741,X4742] :
( ~ class_Fields_Ofield__inverse__zero(X4742)
| X4741 = c_Groups_Ozero__class_Ozero(X4742)
| c_Rings_Oinverse__class_Odivide(X4742,c_Groups_Otimes__class_Otimes(X4742,X4740,X4741),c_Groups_Otimes__class_Otimes(X4742,X4739,X4741)) = c_Rings_Oinverse__class_Odivide(X4742,X4740,X4739) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).
fof(i_0_2019,plain,
! [X4608,X4609] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4609),X4608))
| X4609 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4609 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4609),X4608)) )
& ( X4608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4609),X4608)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).
cnf(i_0_2020,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_1378]) ).
cnf(i_0_2021,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_1379]) ).
cnf(i_0_2022,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_1380]) ).
cnf(i_0_2023,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_1381]) ).
cnf(i_0_2024,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_1382]) ).
fof(i_0_2025,plain,
! [X3885,X3886] :
( ( ~ c_Orderings_Oord__class_Oless(X3886,c_Groups_Ozero__class_Ozero(X3886),c_Groups_Oplus__class_Oplus(X3886,X3885,X3885))
| c_Orderings_Oord__class_Oless(X3886,c_Groups_Ozero__class_Ozero(X3886),X3885)
| ~ class_Groups_Olinordered__ab__group__add(X3886) )
& ( ~ c_Orderings_Oord__class_Oless(X3886,c_Groups_Ozero__class_Ozero(X3886),X3885)
| c_Orderings_Oord__class_Oless(X3886,c_Groups_Ozero__class_Ozero(X3886),c_Groups_Oplus__class_Oplus(X3886,X3885,X3885))
| ~ class_Groups_Olinordered__ab__group__add(X3886) ) ),
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_2026,plain,
! [X3875,X3876] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3876,c_Groups_Ozero__class_Ozero(X3876),c_Groups_Oplus__class_Oplus(X3876,X3875,X3875))
| c_Orderings_Oord__class_Oless__eq(X3876,c_Groups_Ozero__class_Ozero(X3876),X3875)
| ~ class_Groups_Olinordered__ab__group__add(X3876) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3876,c_Groups_Ozero__class_Ozero(X3876),X3875)
| c_Orderings_Oord__class_Oless__eq(X3876,c_Groups_Ozero__class_Ozero(X3876),c_Groups_Oplus__class_Oplus(X3876,X3875,X3875))
| ~ class_Groups_Olinordered__ab__group__add(X3876) ) ),
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_2027,plain,
! [X3883,X3884] :
( ( ~ c_Orderings_Oord__class_Oless(X3884,c_Groups_Oplus__class_Oplus(X3884,X3883,X3883),c_Groups_Ozero__class_Ozero(X3884))
| c_Orderings_Oord__class_Oless(X3884,X3883,c_Groups_Ozero__class_Ozero(X3884))
| ~ class_Groups_Olinordered__ab__group__add(X3884) )
& ( ~ c_Orderings_Oord__class_Oless(X3884,X3883,c_Groups_Ozero__class_Ozero(X3884))
| c_Orderings_Oord__class_Oless(X3884,c_Groups_Oplus__class_Oplus(X3884,X3883,X3883),c_Groups_Ozero__class_Ozero(X3884))
| ~ class_Groups_Olinordered__ab__group__add(X3884) ) ),
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_2028,plain,
! [X2836,X2837] :
( ( ~ c_Orderings_Oord__class_Oless(X2837,c_Groups_Oplus__class_Oplus(X2837,X2836,X2836),c_Groups_Ozero__class_Ozero(X2837))
| c_Orderings_Oord__class_Oless(X2837,X2836,c_Groups_Ozero__class_Ozero(X2837))
| ~ class_Rings_Olinordered__idom(X2837) )
& ( ~ c_Orderings_Oord__class_Oless(X2837,X2836,c_Groups_Ozero__class_Ozero(X2837))
| c_Orderings_Oord__class_Oless(X2837,c_Groups_Oplus__class_Oplus(X2837,X2836,X2836),c_Groups_Ozero__class_Ozero(X2837))
| ~ class_Rings_Olinordered__idom(X2837) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_2029,plain,
! [X3482,X3483,X3484] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3482)
| ~ c_Orderings_Oord__class_Oless(X3484,c_Power_Opower__class_Opower(X3484,X3483,X3482),c_Groups_Ozero__class_Ozero(X3484))
| ~ class_Rings_Olinordered__idom(X3484) )
& ( c_Orderings_Oord__class_Oless(X3484,X3483,c_Groups_Ozero__class_Ozero(X3484))
| ~ c_Orderings_Oord__class_Oless(X3484,c_Power_Opower__class_Opower(X3484,X3483,X3482),c_Groups_Ozero__class_Ozero(X3484))
| ~ class_Rings_Olinordered__idom(X3484) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3482)
| ~ c_Orderings_Oord__class_Oless(X3484,X3483,c_Groups_Ozero__class_Ozero(X3484))
| c_Orderings_Oord__class_Oless(X3484,c_Power_Opower__class_Opower(X3484,X3483,X3482),c_Groups_Ozero__class_Ozero(X3484))
| ~ class_Rings_Olinordered__idom(X3484) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1383])])]) ).
fof(i_0_2030,plain,
! [X3873,X3874] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3874,c_Groups_Oplus__class_Oplus(X3874,X3873,X3873),c_Groups_Ozero__class_Ozero(X3874))
| c_Orderings_Oord__class_Oless__eq(X3874,X3873,c_Groups_Ozero__class_Ozero(X3874))
| ~ class_Groups_Olinordered__ab__group__add(X3874) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3874,X3873,c_Groups_Ozero__class_Ozero(X3874))
| c_Orderings_Oord__class_Oless__eq(X3874,c_Groups_Oplus__class_Oplus(X3874,X3873,X3873),c_Groups_Ozero__class_Ozero(X3874))
| ~ class_Groups_Olinordered__ab__group__add(X3874) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero])])]) ).
cnf(i_0_2031,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_1384]) ).
fof(i_0_2032,plain,
! [X2863,X2864,X2865,X2866] :
( ~ class_Rings_Ocomm__semiring__1(X2866)
| c_Groups_Oplus__class_Oplus(X2866,c_Groups_Oplus__class_Oplus(X2866,X2865,X2864),X2863) = c_Groups_Oplus__class_Oplus(X2866,c_Groups_Oplus__class_Oplus(X2866,X2865,X2863),X2864) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).
fof(i_0_2033,plain,
! [X2748,X2749,X2750,X2751] :
( ~ class_Rings_Ocomm__semiring__1(X2751)
| c_Groups_Otimes__class_Otimes(X2751,c_Groups_Otimes__class_Otimes(X2751,X2750,X2749),X2748) = c_Groups_Otimes__class_Otimes(X2751,c_Groups_Otimes__class_Otimes(X2751,X2750,X2748),X2749) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_2034,plain,
! [X3728,X3729,X3730,X3731] :
( ~ class_Groups_Oab__semigroup__add(X3731)
| c_Groups_Oplus__class_Oplus(X3731,c_Groups_Oplus__class_Oplus(X3731,X3730,X3729),X3728) = c_Groups_Oplus__class_Oplus(X3731,X3730,c_Groups_Oplus__class_Oplus(X3731,X3729,X3728)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_2035,plain,
! [X2859,X2860,X2861,X2862] :
( ~ class_Rings_Ocomm__semiring__1(X2862)
| c_Groups_Oplus__class_Oplus(X2862,c_Groups_Oplus__class_Oplus(X2862,X2861,X2860),X2859) = c_Groups_Oplus__class_Oplus(X2862,X2861,c_Groups_Oplus__class_Oplus(X2862,X2860,X2859)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_2036,plain,
! [X2782,X2783,X2784] :
( ~ class_Groups_Omonoid__mult(X2784)
| c_Groups_Otimes__class_Otimes(X2784,c_Power_Opower__class_Opower(X2784,X2783,X2782),X2783) = c_Groups_Otimes__class_Otimes(X2784,X2783,c_Power_Opower__class_Opower(X2784,X2783,X2782)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_2037,plain,
! [X3724,X3725,X3726,X3727] :
( ~ class_Groups_Oab__semigroup__mult(X3727)
| c_Groups_Otimes__class_Otimes(X3727,c_Groups_Otimes__class_Otimes(X3727,X3726,X3725),X3724) = c_Groups_Otimes__class_Otimes(X3727,X3726,c_Groups_Otimes__class_Otimes(X3727,X3725,X3724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_2038,plain,
! [X2752,X2753,X2754,X2755] :
( ~ class_Rings_Ocomm__semiring__1(X2755)
| c_Groups_Otimes__class_Otimes(X2755,c_Groups_Otimes__class_Otimes(X2755,X2754,X2753),X2752) = c_Groups_Otimes__class_Otimes(X2755,X2754,c_Groups_Otimes__class_Otimes(X2755,X2753,X2752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_2039,plain,
! [X2855,X2856,X2857,X2858] :
( ~ class_Rings_Ocomm__semiring__1(X2858)
| c_Groups_Oplus__class_Oplus(X2858,X2857,c_Groups_Oplus__class_Oplus(X2858,X2856,X2855)) = c_Groups_Oplus__class_Oplus(X2858,c_Groups_Oplus__class_Oplus(X2858,X2857,X2856),X2855) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).
fof(i_0_2040,plain,
! [X4250,X4251,X4252,X4253] :
( ~ class_Rings_Odivision__ring(X4253)
| c_Groups_Otimes__class_Otimes(X4253,X4252,c_Rings_Oinverse__class_Odivide(X4253,X4251,X4250)) = c_Rings_Oinverse__class_Odivide(X4253,c_Groups_Otimes__class_Otimes(X4253,X4252,X4251),X4250) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).
fof(i_0_2041,plain,
! [X2756,X2757,X2758,X2759] :
( ~ class_Rings_Ocomm__semiring__1(X2759)
| c_Groups_Otimes__class_Otimes(X2759,X2758,c_Groups_Otimes__class_Otimes(X2759,X2757,X2756)) = c_Groups_Otimes__class_Otimes(X2759,c_Groups_Otimes__class_Otimes(X2759,X2758,X2757),X2756) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).
fof(i_0_2042,plain,
! [X2851,X2852,X2853,X2854] :
( ~ class_Rings_Ocomm__semiring__1(X2854)
| c_Groups_Oplus__class_Oplus(X2854,X2853,c_Groups_Oplus__class_Oplus(X2854,X2852,X2851)) = c_Groups_Oplus__class_Oplus(X2854,X2852,c_Groups_Oplus__class_Oplus(X2854,X2853,X2851)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).
fof(i_0_2043,plain,
! [X2760,X2761,X2762,X2763] :
( ~ class_Rings_Ocomm__semiring__1(X2763)
| c_Groups_Otimes__class_Otimes(X2763,X2762,c_Groups_Otimes__class_Otimes(X2763,X2761,X2760)) = c_Groups_Otimes__class_Otimes(X2763,X2761,c_Groups_Otimes__class_Otimes(X2763,X2762,X2760)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).
cnf(i_0_2044,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_2045,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_2046,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_2047,plain,
! [X4212] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4212),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X4212),
inference(variable_rename,[status(thm)],[i_0_1385]) ).
fof(i_0_2048,plain,
! [X2792,X2793,X2794,X2795] :
( ~ class_Groups_Omonoid__mult(X2795)
| c_Power_Opower__class_Opower(X2795,X2794,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2793,X2792)) = c_Power_Opower__class_Opower(X2795,c_Power_Opower__class_Opower(X2795,X2794,X2793),X2792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_2049,plain,
! [X2788,X2789,X2790,X2791] :
( ~ class_Rings_Ocomm__semiring__1(X2791)
| c_Power_Opower__class_Opower(X2791,c_Power_Opower__class_Opower(X2791,X2790,X2789),X2788) = c_Power_Opower__class_Opower(X2791,X2790,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2789,X2788)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).
cnf(i_0_2050,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_1386]) ).
cnf(i_0_2051,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_1387]) ).
cnf(i_0_2052,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_1388]) ).
cnf(i_0_2053,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_1389]) ).
cnf(i_0_2054,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_1390]) ).
fof(i_0_2055,plain,
! [X2934,X2935] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2935,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2934)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2934) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2934,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2934)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2935)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2935,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2934,c_Int_OPls)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2934)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2935,X2934))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2935,c_Int_OPls) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1391])])]) ).
fof(i_0_2056,plain,
! [X4272,X4273] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4273,X4272),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4273,X4273)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4272,X4273),
inference(variable_rename,[status(thm)],[fact_real__divide__square__eq]) ).
fof(i_0_2057,plain,
! [X3620,X3621,X3622] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3622,X3621),X3620) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3622,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3621,X3620)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_2058,plain,
! [X3617,X3618,X3619] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3619,X3618),X3617) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3619,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3618,X3617)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_2059,plain,
! [X2685,X2686,X2687] : c_Power_Opower__class_Opower(tc_Int_Oint,c_Power_Opower__class_Opower(tc_Int_Oint,X2687,X2686),X2685) = c_Power_Opower__class_Opower(tc_Int_Oint,X2687,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2686,X2685)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_2060,plain,
! [X3756,X3757,X3758] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3758,X3757),X3756) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3758,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3757,X3756)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_2061,plain,
! [X2682,X2683,X2684] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2684,X2683),X2682) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2684,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2683,X2682)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_2062,plain,
! [X2629,X2630,X2631] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2631,X2630),X2629) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2631,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2630,X2629)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_2063,plain,
! [X3611,X3612,X3613] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3613,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3612,X3611)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3612,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3613,X3611)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_2064,plain,
! [X3614,X3615,X3616] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3616,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3615,X3614)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3615,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3616,X3614)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_2065,plain,
! [X4380,X4381] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4381,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4380,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4381,X4380)
| X4381 = X4380 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4381,X4380)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4381,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4380,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X4381 != X4380
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4381,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4380,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_2066,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_1392]) ).
cnf(i_0_2067,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_1393]) ).
cnf(i_0_2068,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_1394]) ).
cnf(i_0_2069,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_1395]) ).
fof(i_0_2070,plain,
! [X3102,X3103] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3103,X3102))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3103)
| X3102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3103)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3103,X3102)) )
& ( X3102 != 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,X3103,X3102)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_2071,plain,
! [X3094,X3095] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3095,X3094))
| X3094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3095) )
& ( X3094 != 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,X3095,X3094)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3095)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Power_Opower__class_Opower(tc_Nat_Onat,X3095,X3094)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_2072,plain,
! [X4469,X4470] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4470,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4469)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4470,X4469) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4470,X4469)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4470,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4469) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
cnf(i_0_2073,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_1396]) ).
cnf(i_0_2074,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_1397]) ).
cnf(i_0_2075,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_1398]) ).
cnf(i_0_2076,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_1399]) ).
cnf(i_0_2077,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_1400]) ).
fof(i_0_2078,plain,
! [X4471,X4472] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4472,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4471,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4472,X4471) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4472,X4471)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4472,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4471,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_2079,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_1401]) ).
cnf(i_0_2080,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_1402]) ).
cnf(i_0_2081,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_1403]) ).
fof(i_0_2082,plain,
! [X4848,X4849,X4850] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4850)
| ~ c_Orderings_Oord__class_Oless(X4850,c_Groups_Ozero__class_Ozero(X4850),X4849)
| c_Rings_Oinverse__class_Odivide(X4850,c_Groups_Oabs__class_Oabs(X4850,X4848),X4849) = c_Groups_Oabs__class_Oabs(X4850,c_Rings_Oinverse__class_Odivide(X4850,X4848,X4849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).
fof(i_0_2083,plain,
! [X4390,X4391,X4392] :
( ~ class_Rings_Olinordered__idom(X4392)
| ~ c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ozero__class_Ozero(X4392),X4391)
| c_Groups_Otimes__class_Otimes(X4392,c_Groups_Oabs__class_Oabs(X4392,X4390),X4391) = c_Groups_Oabs__class_Oabs(X4392,c_Groups_Otimes__class_Otimes(X4392,X4390,X4391)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
cnf(i_0_2084,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_1404]) ).
fof(i_0_2085,plain,
! [X3694,X3695,X3696,X3697] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3697,X3696)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3695,X3696) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3697,X3694)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3695,X3694) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
cnf(i_0_2086,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_1405]) ).
fof(i_0_2087,plain,
! [X3698,X3699,X3700] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3700,X3699),X3698)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3700,X3698) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_2088,plain,
! [X3707,X3708,X3709] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3709,X3707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3709,X3708),X3707) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3708,X3707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3709,X3708),X3707) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1406])])]) ).
fof(i_0_2089,plain,
! [X3704,X3705,X3706] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3706,X3705),X3704)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3706,X3704) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_2090,plain,
! [X3701,X3702,X3703] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3703,X3702),X3701)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3702,X3701) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_2091,plain,
! [X4730,X4731,X4732,X4733,X4734] :
( ( c_Rings_Oinverse__class_Odivide(X4734,X4731,X4733) != c_Rings_Oinverse__class_Odivide(X4734,X4730,X4732)
| c_Groups_Otimes__class_Otimes(X4734,X4731,X4732) = c_Groups_Otimes__class_Otimes(X4734,X4730,X4733)
| X4732 = c_Groups_Ozero__class_Ozero(X4734)
| X4733 = c_Groups_Ozero__class_Ozero(X4734)
| ~ class_Fields_Ofield(X4734) )
& ( c_Groups_Otimes__class_Otimes(X4734,X4731,X4732) != c_Groups_Otimes__class_Otimes(X4734,X4730,X4733)
| c_Rings_Oinverse__class_Odivide(X4734,X4731,X4733) = c_Rings_Oinverse__class_Odivide(X4734,X4730,X4732)
| X4732 = c_Groups_Ozero__class_Ozero(X4734)
| X4733 = c_Groups_Ozero__class_Ozero(X4734)
| ~ class_Fields_Ofield(X4734) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).
cnf(i_0_2092,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_1407]) ).
cnf(i_0_2093,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_1408]) ).
cnf(i_0_2094,plain,
( X2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk5_2(X2,X1)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1403]) ).
fof(i_0_2095,plain,
! [X3867,X3868,X3869] :
( ( X3868 = c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,X3868,X3867) != c_Groups_Ozero__class_Ozero(X3869)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3867)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3868)
| ~ class_Groups_Oordered__comm__monoid__add(X3869) )
& ( X3867 = c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,X3868,X3867) != c_Groups_Ozero__class_Ozero(X3869)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3867)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3868)
| ~ class_Groups_Oordered__comm__monoid__add(X3869) )
& ( X3868 != c_Groups_Ozero__class_Ozero(X3869)
| X3867 != c_Groups_Ozero__class_Ozero(X3869)
| c_Groups_Oplus__class_Oplus(X3869,X3868,X3867) = c_Groups_Ozero__class_Ozero(X3869)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3867)
| ~ c_Orderings_Oord__class_Oless__eq(X3869,c_Groups_Ozero__class_Ozero(X3869),X3868)
| ~ class_Groups_Oordered__comm__monoid__add(X3869) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
cnf(i_0_2096,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_1409]) ).
cnf(i_0_2097,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_1410]) ).
cnf(i_0_2098,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_1411]) ).
cnf(i_0_2099,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_1412]) ).
cnf(i_0_2100,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_1413]) ).
cnf(i_0_2101,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_1414]) ).
cnf(i_0_2102,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_1415]) ).
cnf(i_0_2103,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_1416]) ).
fof(i_0_2104,plain,
! [X4199,X4200,X4201,X4202] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X4201,X4202),X4200,X4199)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4201,X4202),X4200,X4199)
| ~ class_Orderings_Oord(X4202) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4201,X4202),X4199,X4200)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X4201,X4202),X4200,X4199)
| ~ class_Orderings_Oord(X4202) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4201,X4202),X4200,X4199)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4201,X4202),X4199,X4200)
| c_Orderings_Oord__class_Oless(tc_fun(X4201,X4202),X4200,X4199)
| ~ class_Orderings_Oord(X4202) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1417])])]) ).
fof(i_0_2105,plain,
! [X3018,X3019] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3019,X3018)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3018)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3019),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3018)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3019,X3018)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3019),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3018)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3019,X3018)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3019,X3018)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3019),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3018)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3018)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3019,X3018)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3019),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3018)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).
fof(i_0_2106,plain,
! [X4365,X4366,X4367,X4368] :
( ( c_Power_Opower__class_Opower(X4368,X4367,X4366) != c_Power_Opower__class_Opower(X4368,X4367,X4365)
| X4366 = X4365
| ~ c_Orderings_Oord__class_Oless(X4368,c_Groups_Oone__class_Oone(X4368),X4367)
| ~ class_Rings_Olinordered__semidom(X4368) )
& ( X4366 != X4365
| c_Power_Opower__class_Opower(X4368,X4367,X4366) = c_Power_Opower__class_Opower(X4368,X4367,X4365)
| ~ c_Orderings_Oord__class_Oless(X4368,c_Groups_Oone__class_Oone(X4368),X4367)
| ~ class_Rings_Olinordered__semidom(X4368) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_2107,plain,
! [X3289,X3290] :
( ~ class_Rings_Olinordered__ring(X3290)
| ~ c_Orderings_Oord__class_Oless(X3290,c_Groups_Otimes__class_Otimes(X3290,X3289,X3289),c_Groups_Ozero__class_Ozero(X3290)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1418])]) ).
fof(i_0_2108,plain,
! [X3354,X3355,X3356] :
( ~ class_Rings_Olinordered__semidom(X3356)
| ~ c_Orderings_Oord__class_Oless(X3356,c_Groups_Ozero__class_Ozero(X3356),X3355)
| c_Orderings_Oord__class_Oless(X3356,c_Groups_Ozero__class_Ozero(X3356),c_Power_Opower__class_Opower(X3356,X3355,X3354)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_2109,plain,
! [X4362,X4363,X4364] :
( ~ class_Rings_Olinordered__semidom(X4364)
| ~ c_Orderings_Oord__class_Oless__eq(X4364,c_Groups_Oone__class_Oone(X4364),X4363)
| c_Orderings_Oord__class_Oless__eq(X4364,c_Groups_Oone__class_Oone(X4364),c_Power_Opower__class_Opower(X4364,X4363,X4362)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_2110,plain,
! [X3357,X3358,X3359] :
( ~ class_Rings_Olinordered__semidom(X3359)
| ~ c_Orderings_Oord__class_Oless__eq(X3359,c_Groups_Ozero__class_Ozero(X3359),X3358)
| c_Orderings_Oord__class_Oless__eq(X3359,c_Groups_Ozero__class_Ozero(X3359),c_Power_Opower__class_Opower(X3359,X3358,X3357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
cnf(i_0_2111,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_1419]) ).
fof(i_0_2112,plain,
! [X3536,X3537] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3537,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3537),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3536)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3537,c_Int_OPls)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3537),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3536)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3537,X3536)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1420])]) ).
fof(i_0_2113,plain,
! [X3020,X3021] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3021),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3020))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3021,X3020)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3021,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3021,X3020)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3021),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3020)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3021,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3021),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3020)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1421])])]) ).
fof(i_0_2114,plain,
! [X4379] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4379),X4379) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
cnf(i_0_2115,plain,
( c_Int_OMin = X1
| c_Int_OMin != c_Int_OBit1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1422]) ).
cnf(i_0_2116,plain,
( X1 = c_Int_OMin
| c_Int_OBit1(X1) != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_1423]) ).
fof(i_0_2117,plain,
! [X3179] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3179,X3179))
| X3179 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3179 != 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,X3179,X3179)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1424])]) ).
fof(i_0_2118,plain,
! [X3419,X3420,X3421] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3421,X3420) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3421,X3419)
| X3420 = X3419
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3421) )
& ( X3420 != X3419
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3421,X3420) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3421,X3419)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3421) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
cnf(i_0_2119,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_1425]) ).
cnf(i_0_2120,plain,
c_Int_OBit1(X1) != c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_1426]) ).
cnf(i_0_2121,plain,
c_Int_OPls != c_Int_OBit1(X1),
inference(split_conjunct,[status(thm)],[i_0_1427]) ).
fof(i_0_2122,plain,
! [X4535] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4535)
| 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),X4535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
cnf(i_0_2123,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_1362]) ).
cnf(i_0_2124,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_1370]) ).
cnf(i_0_2125,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_1402]) ).
fof(i_0_2126,plain,
! [X4900,X4901] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4900,X4901),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4901,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4901,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4900,X4901))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4901,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_2127,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__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4902,X4903),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__sign])]) ).
fof(i_0_2128,plain,
! [X4906,X4907] :
( ( 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,X4906,X4907))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4907) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4906,X4907),X4907)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4907) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).
fof(i_0_2129,plain,
! [X4908,X4909] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4909)
| 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,X4908,X4909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).
fof(i_0_2130,plain,
! [X3854,X3855] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3855)
| 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,X3855,X3854)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_2131,plain,
! [X4354,X4355] :
( ~ class_Rings_Ocomm__semiring__1(X4355)
| c_Groups_Oplus__class_Oplus(X4355,X4354,X4354) = c_Groups_Otimes__class_Otimes(X4355,c_Groups_Oplus__class_Oplus(X4355,c_Groups_Oone__class_Oone(X4355),c_Groups_Oone__class_Oone(X4355)),X4354) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).
fof(i_0_2132,plain,
! [X4467,X4468] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4468,X4467)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4468,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4467) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
cnf(i_0_2133,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_1428]) ).
cnf(i_0_2134,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_1398]) ).
cnf(i_0_2135,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_1399]) ).
cnf(i_0_2136,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_1429]) ).
cnf(i_0_2137,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_1395]) ).
cnf(i_0_2138,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_1430]) ).
cnf(i_0_2139,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_1401]) ).
cnf(i_0_2140,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_1431]) ).
cnf(i_0_2141,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_1362]) ).
fof(i_0_2142,plain,
! [X3577,X3578] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3578,X3577),X3578),
inference(variable_rename,[status(thm)],[i_0_1432]) ).
fof(i_0_2143,plain,
! [X3579,X3580] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3580,X3579),X3579),
inference(variable_rename,[status(thm)],[i_0_1433]) ).
fof(i_0_2144,plain,
! [X4996,X4997] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4997)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4996,X4997),X4997) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).
fof(i_0_2145,plain,
! [X5000,X5001] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5001)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Omod(tc_Int_Oint,X5001,X5000),X5001) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).
fof(i_0_2146,plain,
! [X4994,X4995] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4995,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4995,c_Divides_Odiv__class_Omod(tc_Int_Oint,X4994,X4995)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).
fof(i_0_2147,plain,
! [X4418,X4419,X4420] :
( ~ class_Rings_Olinordered__idom(X4420)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4419))
| c_Power_Opower__class_Opower(X4420,c_Groups_Oabs__class_Oabs(X4420,X4418),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4419)) = c_Power_Opower__class_Opower(X4420,X4418,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4419)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__abs__number__of])]) ).
fof(i_0_2148,plain,
! [X4408,X4409,X4410,X4411] :
( ( c_Int_Onumber__class_Onumber__of(X4411,X4409) = c_Groups_Ozero__class_Ozero(X4411)
| X4410 = c_Groups_Otimes__class_Otimes(X4411,X4408,c_Int_Onumber__class_Onumber__of(X4411,X4409))
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) != X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) )
& ( c_Int_Onumber__class_Onumber__of(X4411,X4409) != c_Groups_Ozero__class_Ozero(X4411)
| X4408 = c_Groups_Ozero__class_Ozero(X4411)
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) != X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) )
& ( c_Int_Onumber__class_Onumber__of(X4411,X4409) = c_Groups_Ozero__class_Ozero(X4411)
| c_Int_Onumber__class_Onumber__of(X4411,X4409) != c_Groups_Ozero__class_Ozero(X4411)
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) = X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) )
& ( X4408 != c_Groups_Ozero__class_Ozero(X4411)
| c_Int_Onumber__class_Onumber__of(X4411,X4409) != c_Groups_Ozero__class_Ozero(X4411)
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) = X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) )
& ( c_Int_Onumber__class_Onumber__of(X4411,X4409) = c_Groups_Ozero__class_Ozero(X4411)
| X4410 != c_Groups_Otimes__class_Otimes(X4411,X4408,c_Int_Onumber__class_Onumber__of(X4411,X4409))
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) = X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) )
& ( X4408 != c_Groups_Ozero__class_Ozero(X4411)
| X4410 != c_Groups_Otimes__class_Otimes(X4411,X4408,c_Int_Onumber__class_Onumber__of(X4411,X4409))
| c_Rings_Oinverse__class_Odivide(X4411,X4410,c_Int_Onumber__class_Onumber__of(X4411,X4409)) = X4408
| ~ class_Fields_Ofield__inverse__zero(X4411)
| ~ class_Int_Onumber(X4411) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).
fof(i_0_2149,plain,
! [X4396,X4397,X4398,X4399] :
( ( c_Int_Onumber__class_Onumber__of(X4399,X4396) = c_Groups_Ozero__class_Ozero(X4399)
| c_Groups_Otimes__class_Otimes(X4399,X4398,c_Int_Onumber__class_Onumber__of(X4399,X4396)) = X4397
| X4398 != c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) )
& ( c_Int_Onumber__class_Onumber__of(X4399,X4396) != c_Groups_Ozero__class_Ozero(X4399)
| X4398 = c_Groups_Ozero__class_Ozero(X4399)
| X4398 != c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) )
& ( c_Int_Onumber__class_Onumber__of(X4399,X4396) = c_Groups_Ozero__class_Ozero(X4399)
| c_Int_Onumber__class_Onumber__of(X4399,X4396) != c_Groups_Ozero__class_Ozero(X4399)
| X4398 = c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) )
& ( X4398 != c_Groups_Ozero__class_Ozero(X4399)
| c_Int_Onumber__class_Onumber__of(X4399,X4396) != c_Groups_Ozero__class_Ozero(X4399)
| X4398 = c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) )
& ( c_Int_Onumber__class_Onumber__of(X4399,X4396) = c_Groups_Ozero__class_Ozero(X4399)
| c_Groups_Otimes__class_Otimes(X4399,X4398,c_Int_Onumber__class_Onumber__of(X4399,X4396)) != X4397
| X4398 = c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) )
& ( X4398 != c_Groups_Ozero__class_Ozero(X4399)
| c_Groups_Otimes__class_Otimes(X4399,X4398,c_Int_Onumber__class_Onumber__of(X4399,X4396)) != X4397
| X4398 = c_Rings_Oinverse__class_Odivide(X4399,X4397,c_Int_Onumber__class_Onumber__of(X4399,X4396))
| ~ class_Fields_Ofield__inverse__zero(X4399)
| ~ class_Int_Onumber(X4399) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).
fof(i_0_2150,plain,
! [X4024,X4025,X4026,X4027,X4028] :
( ~ class_Orderings_Oord(X4028)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4027,X4028),X4026,X4025)
| c_Orderings_Oord__class_Oless__eq(X4028,hAPP(X4026,X4024),hAPP(X4025,X4024)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_2151,plain,
! [X3986,X3987,X3988,X3989,X3990] :
( ~ class_Orderings_Oord(X3990)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3989,X3990),X3988,X3987)
| c_Orderings_Oord__class_Oless__eq(X3990,hAPP(X3988,X3986),hAPP(X3987,X3986)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_2152,plain,
! [X3646,X3647,X3648] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3648,X3647)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3648,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3647,X3646)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_2153,plain,
! [X3649,X3650,X3651] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3651,X3650)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3651,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3649,X3650)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_2154,plain,
! [X3652,X3653,X3654] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3654,X3653)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3654,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3653,X3652)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_2155,plain,
! [X3655,X3656,X3657] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3657,X3656)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3657,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3655,X3656)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
cnf(i_0_2156,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_1407]) ).
cnf(i_0_2157,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_1407]) ).
cnf(i_0_2158,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_1408]) ).
cnf(i_0_2159,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_1408]) ).
cnf(i_0_2160,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_1434]) ).
fof(i_0_2161,plain,
! [X4639,X4640,X4641] :
( ~ class_Fields_Ofield__inverse__zero(X4641)
| ~ class_RealVector_Oreal__normed__field(X4641)
| c_RealVector_Onorm__class_Onorm(X4641,c_Rings_Oinverse__class_Odivide(X4641,X4640,X4639)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4641,X4640),c_RealVector_Onorm__class_Onorm(X4641,X4639)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__divide])]) ).
fof(i_0_2162,plain,
! [X4404,X4405,X4406,X4407] :
( ( X4405 = c_Groups_Ozero__class_Ozero(X4407)
| X4406 = c_Groups_Otimes__class_Otimes(X4407,c_Int_Onumber__class_Onumber__of(X4407,X4404),X4405)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) != c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) )
& ( X4405 != c_Groups_Ozero__class_Ozero(X4407)
| c_Int_Onumber__class_Onumber__of(X4407,X4404) = c_Groups_Ozero__class_Ozero(X4407)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) != c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) )
& ( X4405 = c_Groups_Ozero__class_Ozero(X4407)
| X4405 != c_Groups_Ozero__class_Ozero(X4407)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) = c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) )
& ( c_Int_Onumber__class_Onumber__of(X4407,X4404) != c_Groups_Ozero__class_Ozero(X4407)
| X4405 != c_Groups_Ozero__class_Ozero(X4407)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) = c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) )
& ( X4405 = c_Groups_Ozero__class_Ozero(X4407)
| X4406 != c_Groups_Otimes__class_Otimes(X4407,c_Int_Onumber__class_Onumber__of(X4407,X4404),X4405)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) = c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) )
& ( c_Int_Onumber__class_Onumber__of(X4407,X4404) != c_Groups_Ozero__class_Ozero(X4407)
| X4406 != c_Groups_Otimes__class_Otimes(X4407,c_Int_Onumber__class_Onumber__of(X4407,X4404),X4405)
| c_Rings_Oinverse__class_Odivide(X4407,X4406,X4405) = c_Int_Onumber__class_Onumber__of(X4407,X4404)
| ~ class_Fields_Ofield__inverse__zero(X4407)
| ~ class_Int_Onumber(X4407) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).
fof(i_0_2163,plain,
! [X4400,X4401,X4402,X4403] :
( ( X4400 = c_Groups_Ozero__class_Ozero(X4403)
| c_Groups_Otimes__class_Otimes(X4403,c_Int_Onumber__class_Onumber__of(X4403,X4402),X4400) = X4401
| c_Int_Onumber__class_Onumber__of(X4403,X4402) != c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) )
& ( X4400 != c_Groups_Ozero__class_Ozero(X4403)
| c_Int_Onumber__class_Onumber__of(X4403,X4402) = c_Groups_Ozero__class_Ozero(X4403)
| c_Int_Onumber__class_Onumber__of(X4403,X4402) != c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) )
& ( X4400 = c_Groups_Ozero__class_Ozero(X4403)
| X4400 != c_Groups_Ozero__class_Ozero(X4403)
| c_Int_Onumber__class_Onumber__of(X4403,X4402) = c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) )
& ( c_Int_Onumber__class_Onumber__of(X4403,X4402) != c_Groups_Ozero__class_Ozero(X4403)
| X4400 != c_Groups_Ozero__class_Ozero(X4403)
| c_Int_Onumber__class_Onumber__of(X4403,X4402) = c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) )
& ( X4400 = c_Groups_Ozero__class_Ozero(X4403)
| c_Groups_Otimes__class_Otimes(X4403,c_Int_Onumber__class_Onumber__of(X4403,X4402),X4400) != X4401
| c_Int_Onumber__class_Onumber__of(X4403,X4402) = c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) )
& ( c_Int_Onumber__class_Onumber__of(X4403,X4402) != c_Groups_Ozero__class_Ozero(X4403)
| c_Groups_Otimes__class_Otimes(X4403,c_Int_Onumber__class_Onumber__of(X4403,X4402),X4400) != X4401
| c_Int_Onumber__class_Onumber__of(X4403,X4402) = c_Rings_Oinverse__class_Odivide(X4403,X4401,X4400)
| ~ class_Fields_Ofield__inverse__zero(X4403)
| ~ class_Int_Onumber(X4403) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).
fof(i_0_2164,plain,
! [X4751,X4752,X4753] :
( ~ class_Fields_Olinordered__field(X4753)
| X4752 = c_Groups_Ozero__class_Ozero(X4753)
| c_Groups_Oabs__class_Oabs(X4753,c_Rings_Oinverse__class_Odivide(X4753,X4751,X4752)) = c_Rings_Oinverse__class_Odivide(X4753,c_Groups_Oabs__class_Oabs(X4753,X4751),c_Groups_Oabs__class_Oabs(X4753,X4752)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).
fof(i_0_2165,plain,
! [X3449,X3450] :
( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3450)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3450,X3449)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3449)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3450,X3449)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3450)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3449)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Power_Opower__class_Opower(tc_Nat_Onat,X3450,X3449)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__power__nat])])]) ).
fof(i_0_2166,plain,
! [X4982,X4983,X4984] :
( ~ class_Fields_Ofield__inverse__zero(X4984)
| ~ class_RealVector_Oreal__field(X4984)
| c_RealVector_Oof__real(X4984,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4983,X4982)) = c_Rings_Oinverse__class_Odivide(X4984,c_RealVector_Oof__real(X4984,X4983),c_RealVector_Oof__real(X4984,X4982)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__divide])]) ).
fof(i_0_2167,plain,
! [X5010,X5011,X5012] :
( ~ class_RealVector_Oreal__algebra__1(X5012)
| ~ class_RealVector_Oreal__normed__vector(X5012)
| c_RealVector_Oof__real(X5012,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5011,X5010)) = c_Groups_Oplus__class_Oplus(X5012,c_RealVector_Oof__real(X5012,X5011),c_RealVector_Oof__real(X5012,X5010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Oadd])]) ).
fof(i_0_2168,plain,
! [X4662,X4663,X4664] :
( ~ class_RealVector_Oreal__normed__field(X4664)
| X4663 = c_Groups_Ozero__class_Ozero(X4664)
| c_RealVector_Onorm__class_Onorm(X4664,c_Rings_Oinverse__class_Odivide(X4664,X4662,X4663)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4664,X4662),c_RealVector_Onorm__class_Onorm(X4664,X4663)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__divide])]) ).
cnf(i_0_2169,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_1414]) ).
cnf(i_0_2170,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_1413]) ).
cnf(i_0_2171,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_1415]) ).
cnf(i_0_2172,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_1416]) ).
cnf(i_0_2173,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_1409]) ).
cnf(i_0_2174,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_1411]) ).
cnf(i_0_2175,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_1410]) ).
cnf(i_0_2176,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_1412]) ).
cnf(i_0_2177,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_1405]) ).
cnf(i_0_2178,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_1405]) ).
fof(i_0_2179,plain,
! [X2875,X2876,X2877] :
( ( ~ c_Orderings_Oord__class_Oless(X2877,c_Int_Onumber__class_Onumber__of(X2877,X2876),c_Int_Onumber__class_Onumber__of(X2877,X2875))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2876,X2875)
| ~ class_Int_Onumber__ring(X2877)
| ~ class_Rings_Olinordered__idom(X2877) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X2876,X2875)
| c_Orderings_Oord__class_Oless(X2877,c_Int_Onumber__class_Onumber__of(X2877,X2876),c_Int_Onumber__class_Onumber__of(X2877,X2875))
| ~ class_Int_Onumber__ring(X2877)
| ~ class_Rings_Olinordered__idom(X2877) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).
fof(i_0_2180,plain,
! [X2878,X2879,X2880] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2880,c_Int_Onumber__class_Onumber__of(X2880,X2879),c_Int_Onumber__class_Onumber__of(X2880,X2878))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2879,X2878)
| ~ class_Int_Onumber__ring(X2880)
| ~ class_Rings_Olinordered__idom(X2880) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2879,X2878)
| c_Orderings_Oord__class_Oless__eq(X2880,c_Int_Onumber__class_Onumber__of(X2880,X2879),c_Int_Onumber__class_Onumber__of(X2880,X2878))
| ~ class_Int_Onumber__ring(X2880)
| ~ class_Rings_Olinordered__idom(X2880) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).
fof(i_0_2181,plain,
! [X4910,X4911,X4912] :
( ~ class_RealVector_Oreal__field(X4912)
| X4911 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X4912,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4910,X4911)) = c_Rings_Oinverse__class_Odivide(X4912,c_RealVector_Oof__real(X4912,X4910),c_RealVector_Oof__real(X4912,X4911)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__of__real__divide])]) ).
fof(i_0_2182,plain,
! [X4086,X4087,X4088,X4089] :
( ~ class_Orderings_Opreorder(X4089)
| ~ c_Orderings_Oord__class_Oless(X4089,X4088,X4087)
| ~ c_Orderings_Oord__class_Oless(X4089,X4087,X4086)
| c_Orderings_Oord__class_Oless(X4089,X4088,X4086) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_2183,plain,
! [X4182,X4183,X4184,X4185] :
( ~ class_Orderings_Opreorder(X4185)
| ~ c_Orderings_Oord__class_Oless__eq(X4185,X4184,X4183)
| ~ c_Orderings_Oord__class_Oless(X4185,X4183,X4182)
| c_Orderings_Oord__class_Oless(X4185,X4184,X4182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_2184,plain,
! [X4174,X4175,X4176,X4177] :
( ~ class_Orderings_Opreorder(X4177)
| ~ c_Orderings_Oord__class_Oless(X4177,X4176,X4175)
| ~ c_Orderings_Oord__class_Oless__eq(X4177,X4175,X4174)
| c_Orderings_Oord__class_Oless(X4177,X4176,X4174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_2185,plain,
! [X4090,X4091,X4092,X4093] :
( ~ class_Orderings_Oorder(X4093)
| ~ c_Orderings_Oord__class_Oless(X4093,X4092,X4091)
| ~ c_Orderings_Oord__class_Oless(X4093,X4090,X4092)
| c_Orderings_Oord__class_Oless(X4093,X4090,X4091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_2186,plain,
! [X4186,X4187,X4188,X4189] :
( ~ class_Orderings_Oorder(X4189)
| ~ c_Orderings_Oord__class_Oless__eq(X4189,X4188,X4187)
| ~ c_Orderings_Oord__class_Oless(X4189,X4186,X4188)
| c_Orderings_Oord__class_Oless(X4189,X4186,X4187) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_2187,plain,
! [X4178,X4179,X4180,X4181] :
( ~ class_Orderings_Oorder(X4181)
| ~ c_Orderings_Oord__class_Oless(X4181,X4180,X4179)
| ~ c_Orderings_Oord__class_Oless__eq(X4181,X4178,X4180)
| c_Orderings_Oord__class_Oless(X4181,X4178,X4179) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_2188,plain,
! [X4013,X4014,X4015,X4016] :
( ~ class_Orderings_Opreorder(X4016)
| ~ c_Orderings_Oord__class_Oless__eq(X4016,X4015,X4014)
| ~ c_Orderings_Oord__class_Oless__eq(X4016,X4014,X4013)
| c_Orderings_Oord__class_Oless__eq(X4016,X4015,X4013) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_2189,plain,
! [X4020,X4021,X4022,X4023] :
( ~ class_Orderings_Oorder(X4023)
| ~ c_Orderings_Oord__class_Oless__eq(X4023,X4022,X4021)
| ~ c_Orderings_Oord__class_Oless__eq(X4023,X4020,X4022)
| c_Orderings_Oord__class_Oless__eq(X4023,X4020,X4021) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_2190,plain,
! [X4687,X4688,X4689] :
( ~ class_Fields_Olinordered__field__inverse__zero(X4689)
| c_Groups_Oabs__class_Oabs(X4689,c_Rings_Oinverse__class_Odivide(X4689,X4688,X4687)) = c_Rings_Oinverse__class_Odivide(X4689,c_Groups_Oabs__class_Oabs(X4689,X4688),c_Groups_Oabs__class_Oabs(X4689,X4687)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).
fof(i_0_2191,plain,
! [X4238,X4239,X4240] :
( ~ class_Rings_Olinordered__idom(X4240)
| c_Groups_Oabs__class_Oabs(X4240,c_Groups_Otimes__class_Otimes(X4240,X4239,X4238)) = c_Groups_Otimes__class_Otimes(X4240,c_Groups_Oabs__class_Oabs(X4240,X4239),c_Groups_Oabs__class_Oabs(X4240,X4238)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_2192,plain,
! [X4634,X4635,X4636] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4636)
| c_RealVector_Onorm__class_Onorm(X4636,c_Groups_Otimes__class_Otimes(X4636,X4635,X4634)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4636,X4635),c_RealVector_Onorm__class_Onorm(X4636,X4634)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_2193,plain,
! [X2842,X2843,X2844] :
( ~ class_Int_Onumber__ring(X2844)
| c_Groups_Oplus__class_Oplus(X2844,c_Int_Onumber__class_Onumber__of(X2844,X2843),c_Int_Onumber__class_Onumber__of(X2844,X2842)) = c_Int_Onumber__class_Onumber__of(X2844,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2843,X2842)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).
fof(i_0_2194,plain,
! [X2638,X2639,X2640] :
( ~ class_Int_Onumber__ring(X2640)
| c_Groups_Otimes__class_Otimes(X2640,c_Int_Onumber__class_Onumber__of(X2640,X2639),c_Int_Onumber__class_Onumber__of(X2640,X2638)) = c_Int_Onumber__class_Onumber__of(X2640,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2639,X2638)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).
fof(i_0_2195,plain,
! [X5007,X5008,X5009] :
( ~ class_RealVector_Oreal__algebra__1(X5009)
| c_RealVector_Oof__real(X5009,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5008,X5007)) = c_Groups_Oplus__class_Oplus(X5009,c_RealVector_Oof__real(X5009,X5008),c_RealVector_Oof__real(X5009,X5007)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__add])]) ).
fof(i_0_2196,plain,
! [X4960,X4961,X4962] :
( ~ class_RealVector_Oreal__algebra__1(X4962)
| c_RealVector_Oof__real(X4962,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4961,X4960)) = c_Groups_Otimes__class_Otimes(X4962,c_RealVector_Oof__real(X4962,X4961),c_RealVector_Oof__real(X4962,X4960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__mult])]) ).
fof(i_0_2197,plain,
! [X2845,X2846,X2847] :
( ~ class_Int_Onumber__ring(X2847)
| c_Int_Onumber__class_Onumber__of(X2847,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2846,X2845)) = c_Groups_Oplus__class_Oplus(X2847,c_Int_Onumber__class_Onumber__of(X2847,X2846),c_Int_Onumber__class_Onumber__of(X2847,X2845)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
fof(i_0_2198,plain,
! [X2641,X2642,X2643] :
( ~ class_Int_Onumber__ring(X2643)
| c_Int_Onumber__class_Onumber__of(X2643,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2642,X2641)) = c_Groups_Otimes__class_Otimes(X2643,c_Int_Onumber__class_Onumber__of(X2643,X2642),c_Int_Onumber__class_Onumber__of(X2643,X2641)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).
cnf(i_0_2199,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_1435]) ).
fof(i_0_2200,plain,
! [X4393,X4394,X4395] :
( ~ class_Rings_Olinordered__idom(X4395)
| c_Orderings_Oord__class_Oless__eq(X4395,c_Groups_Ozero__class_Ozero(X4395),c_Power_Opower__class_Opower(X4395,c_Groups_Oabs__class_Oabs(X4395,X4394),X4393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_2201,plain,
! [X4904,X4905] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4905)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4905,X4904)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4905,X4904) = X4905 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).
fof(i_0_2202,plain,
! [X4898,X4899] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4899,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4898,X4899)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4899,X4898) = X4899 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).
fof(i_0_2203,plain,
! [X4974,X4975,X4976] :
( ~ class_Divides_Osemiring__div(X4976)
| c_Divides_Odiv__class_Omod(X4976,c_Divides_Odiv__class_Omod(X4976,X4975,X4974),X4974) = c_Divides_Odiv__class_Omod(X4976,X4975,X4974) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).
fof(i_0_2204,plain,
! [X5016,X5017,X5018] :
( ~ class_Divides_Osemiring__div(X5018)
| c_Divides_Odiv__class_Omod(X5018,c_Groups_Oplus__class_Oplus(X5018,X5017,X5016),X5017) = c_Divides_Odiv__class_Omod(X5018,X5016,X5017) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).
fof(i_0_2205,plain,
! [X5013,X5014,X5015] :
( ~ class_Divides_Osemiring__div(X5015)
| c_Divides_Odiv__class_Omod(X5015,c_Groups_Oplus__class_Oplus(X5015,X5014,X5013),X5013) = c_Divides_Odiv__class_Omod(X5015,X5014,X5013) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).
fof(i_0_2206,plain,
! [X3930,X3931,X3932] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3932,X3931)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3931,X3930)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3932,X3930) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_2207,plain,
! [X3672,X3673,X3674] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3674,X3673)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3673,X3672)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3674,X3672) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_2208,plain,
! [X3675,X3676,X3677] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3677,X3676)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3676,X3675)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3677,X3675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
cnf(i_0_2209,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_1394]) ).
fof(i_0_2210,plain,
! [X3200,X3201] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3201)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3200)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3201,X3200)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3200)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3201)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3201,X3200)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3201)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3200)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3201,X3200)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3201)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3200)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3201,X3200)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1436])])]) ).
fof(i_0_2211,plain,
! [X3198,X3199] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3199)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3198)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3199,X3198)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3198)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3199)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3199,X3198)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3199)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3198)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3199,X3198)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3199)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3198)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3199,X3198)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__add])])]) ).
fof(i_0_2212,plain,
! [X3196,X3197] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3197)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3196)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3197,X3196)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1437])])]) ).
cnf(i_0_2213,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_1371]) ).
cnf(i_0_2214,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_1372]) ).
fof(i_0_2215,plain,
! [X3161,X3162] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3162),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3161)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3162,X3161)),
inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).
fof(i_0_2216,plain,
! [X2680,X2681] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2681),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2680)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2681,X2680)),
inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).
cnf(i_0_2217,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_1438]) ).
cnf(i_0_2218,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_1407]) ).
cnf(i_0_2219,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_1407]) ).
cnf(i_0_2220,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_1408]) ).
cnf(i_0_2221,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_1408]) ).
fof(i_0_2222,plain,
! [X4294] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4294))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(i_0_2223,plain,
! [X2660,X2661] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2661,X2660))
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2661)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2660) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2661)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2661,X2660)) )
& ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2660)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2661,X2660)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__product__nat])])]) ).
fof(i_0_2224,plain,
! [X3180,X3181] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3181),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3180))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3181,X3180) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3181,X3180)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3181),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3180)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).
fof(i_0_2225,plain,
! [X3194,X3195] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3195),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3194))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3195,X3194) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3195,X3194)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3195),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X3194)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).
fof(i_0_2226,plain,
! [X4241,X4242,X4243] :
( ~ class_Rings_Olinordered__idom(X4243)
| c_Groups_Oabs__class_Oabs(X4243,c_Power_Opower__class_Opower(X4243,X4242,X4241)) = c_Power_Opower__class_Opower(X4243,c_Groups_Oabs__class_Oabs(X4243,X4242),X4241) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_2227,plain,
! [X4642,X4643,X4644] :
( ~ class_RealVector_Oreal__normed__div__algebra(X4644)
| c_RealVector_Onorm__class_Onorm(X4644,c_Power_Opower__class_Opower(X4644,X4643,X4642)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4644,X4643),X4642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
cnf(i_0_2228,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_1434]) ).
fof(i_0_2229,plain,
! [X4606,X4607] : 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,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4607),X4606)),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_2230,plain,
! [X4991,X4992,X4993] :
( ~ class_RealVector_Oreal__algebra__1(X4993)
| c_RealVector_Oof__real(X4993,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4992,X4991)) = c_Power_Opower__class_Opower(X4993,c_RealVector_Oof__real(X4993,X4992),X4991) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__power])]) ).
fof(i_0_2231,plain,
! [X4135,X4136,X4137] :
( ( c_Orderings_Oord__class_Oless__eq(X4137,X4136,X4135)
| ~ c_Orderings_Oord__class_Oless(X4137,X4136,X4135)
| ~ class_Orderings_Opreorder(X4137) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4137,X4135,X4136)
| ~ c_Orderings_Oord__class_Oless(X4137,X4136,X4135)
| ~ class_Orderings_Opreorder(X4137) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4137,X4136,X4135)
| c_Orderings_Oord__class_Oless__eq(X4137,X4135,X4136)
| c_Orderings_Oord__class_Oless(X4137,X4136,X4135)
| ~ class_Orderings_Opreorder(X4137) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1439])])]) ).
fof(i_0_2232,plain,
! [X3202,X3203] :
( ( ~ c_Orderings_Oord__class_Oless(X3203,c_Groups_Ozero__class_Ozero(X3203),c_Int_Onumber__class_Onumber__of(X3203,X3202))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3202)
| ~ class_Int_Onumber__ring(X3203)
| ~ class_Rings_Olinordered__idom(X3203) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3202)
| c_Orderings_Oord__class_Oless(X3203,c_Groups_Ozero__class_Ozero(X3203),c_Int_Onumber__class_Onumber__of(X3203,X3202))
| ~ class_Int_Onumber__ring(X3203)
| ~ class_Rings_Olinordered__idom(X3203) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).
fof(i_0_2233,plain,
! [X3206,X3207] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3207,c_Groups_Ozero__class_Ozero(X3207),c_Int_Onumber__class_Onumber__of(X3207,X3206))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3206)
| ~ class_Int_Onumber__ring(X3207)
| ~ class_Rings_Olinordered__idom(X3207) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X3206)
| c_Orderings_Oord__class_Oless__eq(X3207,c_Groups_Ozero__class_Ozero(X3207),c_Int_Onumber__class_Onumber__of(X3207,X3206))
| ~ class_Int_Onumber__ring(X3207)
| ~ class_Rings_Olinordered__idom(X3207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).
fof(i_0_2234,plain,
! [X3204,X3205] :
( ( ~ c_Orderings_Oord__class_Oless(X3205,c_Int_Onumber__class_Onumber__of(X3205,X3204),c_Groups_Ozero__class_Ozero(X3205))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3204,c_Int_OPls)
| ~ class_Int_Onumber__ring(X3205)
| ~ class_Rings_Olinordered__idom(X3205) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3204,c_Int_OPls)
| c_Orderings_Oord__class_Oless(X3205,c_Int_Onumber__class_Onumber__of(X3205,X3204),c_Groups_Ozero__class_Ozero(X3205))
| ~ class_Int_Onumber__ring(X3205)
| ~ class_Rings_Olinordered__idom(X3205) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).
fof(i_0_2235,plain,
! [X3208,X3209] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3209,c_Int_Onumber__class_Onumber__of(X3209,X3208),c_Groups_Ozero__class_Ozero(X3209))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3208,c_Int_OPls)
| ~ class_Int_Onumber__ring(X3209)
| ~ class_Rings_Olinordered__idom(X3209) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3208,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(X3209,c_Int_Onumber__class_Onumber__of(X3209,X3208),c_Groups_Ozero__class_Ozero(X3209))
| ~ class_Int_Onumber__ring(X3209)
| ~ class_Rings_Olinordered__idom(X3209) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).
fof(i_0_2236,plain,
! [X3490,X3491,X3492] :
( ~ class_Groups_Omonoid__mult(X3492)
| ~ class_Rings_Olinordered__ring(X3492)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3491)
| c_Orderings_Oord__class_Oless__eq(X3492,c_Groups_Ozero__class_Ozero(X3492),c_Power_Opower__class_Opower(X3492,X3490,X3491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power])]) ).
fof(i_0_2237,plain,
! [X4603,X4604] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4604,X4603)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4604) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1])]) ).
fof(i_0_2238,plain,
! [X4431] :
( ~ class_Rings_Olinordered__semidom(X4431)
| c_Orderings_Oord__class_Oless(X4431,c_Groups_Ozero__class_Ozero(X4431),c_Groups_Oplus__class_Oplus(X4431,c_Groups_Oone__class_Oone(X4431),c_Groups_Oone__class_Oone(X4431))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_2239,plain,
! [X4980,X4981] : c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X4981),X4980) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4981,X4980)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__power]) ).
fof(i_0_2240,plain,
! [X3712,X3713,X3714] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3713,X3714)
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| X3714 = X3713
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3714,X3713) )
& ( ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| X3714 = X3713
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3714,X3713) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3713,X3714)
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3714,X3713) )
& ( ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3714,X3713) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3713,X3714)
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| X3714 = X3713
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714)) )
& ( ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| X3714 = X3713
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3713,X3714)
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714)) )
& ( ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714))
| ~ hBOOL(hAPP(hAPP(X3712,X3713),X3714)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_2241,plain,
! [X4297,X4298,X4299] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4299)
| ~ c_Orderings_Oord__class_Oless__eq(X4299,c_Groups_Oabs__class_Oabs(X4299,X4298),X4297)
| c_Orderings_Oord__class_Oless__eq(X4299,X4298,X4297) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
cnf(i_0_2242,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_1440]) ).
fof(i_0_2243,plain,
! [X4203,X4204] :
( ~ class_Int_Onumber__ring(X4204)
| ~ class_Rings_Olinordered__idom(X4204)
| c_Groups_Oabs__class_Oabs(X4204,c_Power_Opower__class_Opower(X4204,c_Int_Onumber__class_Onumber__of(X4204,c_Int_OMin),X4203)) = c_Groups_Oone__class_Oone(X4204) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).
cnf(i_0_2244,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_1407]) ).
cnf(i_0_2245,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_1408]) ).
fof(i_0_2246,plain,
! [X4162,X4163,X4164] :
( ( c_Orderings_Oord__class_Oless(X4164,X4163,X4162)
| X4163 = X4162
| ~ c_Orderings_Oord__class_Oless__eq(X4164,X4163,X4162)
| ~ class_Orderings_Olinorder(X4164) )
& ( X4163 != X4162
| ~ c_Orderings_Oord__class_Oless(X4164,X4163,X4162)
| ~ c_Orderings_Oord__class_Oless__eq(X4164,X4163,X4162)
| ~ class_Orderings_Olinorder(X4164) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1441])])]) ).
fof(i_0_2247,plain,
! [X4017,X4018,X4019] :
( ~ class_Orderings_Oorder(X4019)
| ~ c_Orderings_Oord__class_Oless__eq(X4019,X4018,X4017)
| ~ c_Orderings_Oord__class_Oless__eq(X4019,X4017,X4018)
| X4017 = X4018 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_2248,plain,
! [X4010,X4011,X4012] :
( ~ class_Orderings_Oorder(X4012)
| ~ c_Orderings_Oord__class_Oless__eq(X4012,X4011,X4010)
| ~ c_Orderings_Oord__class_Oless__eq(X4012,X4010,X4011)
| X4011 = X4010 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_2249,plain,
! [X3991,X3992,X3993] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3993,X3991,X3992)
| X3991 = X3992
| ~ c_Orderings_Oord__class_Oless__eq(X3993,X3992,X3991)
| ~ class_Orderings_Oorder(X3993) )
& ( X3991 != X3992
| c_Orderings_Oord__class_Oless__eq(X3993,X3991,X3992)
| ~ c_Orderings_Oord__class_Oless__eq(X3993,X3992,X3991)
| ~ class_Orderings_Oorder(X3993) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_2250,plain,
! [X3980,X3981,X3982] :
( ( c_Orderings_Oord__class_Oless__eq(X3982,X3981,X3980)
| X3981 != X3980
| ~ class_Orderings_Oorder(X3982) )
& ( c_Orderings_Oord__class_Oless__eq(X3982,X3980,X3981)
| X3981 != X3980
| ~ class_Orderings_Oorder(X3982) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3982,X3981,X3980)
| ~ c_Orderings_Oord__class_Oless__eq(X3982,X3980,X3981)
| X3981 = X3980
| ~ class_Orderings_Oorder(X3982) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_2251,plain,
! [X4352,X4353] :
( ~ class_Rings_Olinordered__semidom(X4353)
| c_Orderings_Oord__class_Oless(X4353,X4352,c_Groups_Oplus__class_Oplus(X4353,X4352,c_Groups_Oone__class_Oone(X4353))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_2252,plain,
! [X2688,X2689,X2690] :
( ( X2689 = c_Groups_Ozero__class_Ozero(X2690)
| c_Power_Opower__class_Opower(X2690,X2689,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2688)) != c_Groups_Ozero__class_Ozero(X2690)
| ~ class_Power_Opower(X2690)
| ~ class_Rings_Omult__zero(X2690)
| ~ class_Rings_Ono__zero__divisors(X2690)
| ~ class_Rings_Ozero__neq__one(X2690) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2688) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2690,X2689,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2688)) != c_Groups_Ozero__class_Ozero(X2690)
| ~ class_Power_Opower(X2690)
| ~ class_Rings_Omult__zero(X2690)
| ~ class_Rings_Ono__zero__divisors(X2690)
| ~ class_Rings_Ozero__neq__one(X2690) )
& ( X2689 != c_Groups_Ozero__class_Ozero(X2690)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2690,X2689,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2688)) = c_Groups_Ozero__class_Ozero(X2690)
| ~ class_Power_Opower(X2690)
| ~ class_Rings_Omult__zero(X2690)
| ~ class_Rings_Ono__zero__divisors(X2690)
| ~ class_Rings_Ozero__neq__one(X2690) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff__number__of])])]) ).
fof(i_0_2253,plain,
! [X3748,X3749,X3750,X3751] :
( ~ class_Groups_Ocancel__semigroup__add(X3751)
| c_Groups_Oplus__class_Oplus(X3751,X3750,X3749) != c_Groups_Oplus__class_Oplus(X3751,X3748,X3749)
| X3750 = X3748 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_2254,plain,
! [X3736,X3737,X3738,X3739] :
( ( c_Groups_Oplus__class_Oplus(X3739,X3738,X3737) != c_Groups_Oplus__class_Oplus(X3739,X3736,X3737)
| X3738 = X3736
| ~ class_Groups_Ocancel__semigroup__add(X3739) )
& ( X3738 != X3736
| c_Groups_Oplus__class_Oplus(X3739,X3738,X3737) = c_Groups_Oplus__class_Oplus(X3739,X3736,X3737)
| ~ class_Groups_Ocancel__semigroup__add(X3739) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_2255,plain,
! [X3744,X3745,X3746,X3747] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X3747)
| c_Groups_Oplus__class_Oplus(X3747,X3746,X3745) != c_Groups_Oplus__class_Oplus(X3747,X3746,X3744)
| X3745 = X3744 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_2256,plain,
! [X3740,X3741,X3742,X3743] :
( ~ class_Groups_Ocancel__semigroup__add(X3743)
| c_Groups_Oplus__class_Oplus(X3743,X3742,X3741) != c_Groups_Oplus__class_Oplus(X3743,X3742,X3740)
| X3741 = X3740 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_2257,plain,
! [X3732,X3733,X3734,X3735] :
( ( c_Groups_Oplus__class_Oplus(X3735,X3734,X3733) != c_Groups_Oplus__class_Oplus(X3735,X3734,X3732)
| X3733 = X3732
| ~ class_Groups_Ocancel__semigroup__add(X3735) )
& ( X3733 != X3732
| c_Groups_Oplus__class_Oplus(X3735,X3734,X3733) = c_Groups_Oplus__class_Oplus(X3735,X3734,X3732)
| ~ class_Groups_Ocancel__semigroup__add(X3735) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_2258,plain,
! [X4465,X4466] :
( ( X4466 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4466,X4465) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4466) )
& ( X4465 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4466,X4465) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4466) )
& ( X4466 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4465 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4466,X4465) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4466) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
fof(i_0_2259,plain,
! [X4067,X4068,X4069] :
( ~ class_Orderings_Oorder(X4069)
| ~ c_Orderings_Oord__class_Oless(X4069,X4068,X4067)
| ~ c_Orderings_Oord__class_Oless(X4069,X4067,X4068) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1442])]) ).
fof(i_0_2260,plain,
! [X4094,X4095,X4096] :
( ~ class_Orderings_Opreorder(X4096)
| ~ c_Orderings_Oord__class_Oless(X4096,X4095,X4094)
| ~ c_Orderings_Oord__class_Oless(X4096,X4094,X4095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1443])]) ).
fof(i_0_2261,plain,
! [X4064,X4065,X4066] :
( ~ class_Orderings_Opreorder(X4066)
| ~ c_Orderings_Oord__class_Oless(X4066,X4065,X4064)
| ~ c_Orderings_Oord__class_Oless(X4066,X4064,X4065) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1444])]) ).
fof(i_0_2262,plain,
! [X4055,X4056,X4057] :
( ~ class_Orderings_Opreorder(X4057)
| ~ c_Orderings_Oord__class_Oless(X4057,X4056,X4055)
| ~ c_Orderings_Oord__class_Oless(X4057,X4055,X4056) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1445])]) ).
fof(i_0_2263,plain,
! [X4052,X4053,X4054] :
( ~ class_Orderings_Opreorder(X4054)
| ~ c_Orderings_Oord__class_Oless(X4054,X4053,X4052)
| ~ c_Orderings_Oord__class_Oless(X4054,X4052,X4053) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1446])]) ).
fof(i_0_2264,plain,
! [X4037,X4038,X4039] :
( ( c_Orderings_Oord__class_Oless(X4039,X4038,X4037)
| c_Orderings_Oord__class_Oless(X4039,X4037,X4038)
| X4038 = X4037
| ~ class_Orderings_Olinorder(X4039) )
& ( ~ c_Orderings_Oord__class_Oless(X4039,X4037,X4038)
| ~ c_Orderings_Oord__class_Oless(X4039,X4038,X4037)
| ~ class_Orderings_Olinorder(X4039) )
& ( X4038 != X4037
| ~ c_Orderings_Oord__class_Oless(X4039,X4038,X4037)
| ~ class_Orderings_Olinorder(X4039) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1447])])]) ).
fof(i_0_2265,plain,
! [X4156,X4157,X4158] :
( ~ class_Orderings_Olinorder(X4158)
| ~ c_Orderings_Oord__class_Oless__eq(X4158,X4157,X4156)
| ~ c_Orderings_Oord__class_Oless(X4158,X4156,X4157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1448])]) ).
fof(i_0_2266,plain,
! [X4123,X4124,X4125] :
( ( c_Orderings_Oord__class_Oless(X4125,X4124,X4123)
| c_Orderings_Oord__class_Oless__eq(X4125,X4123,X4124)
| ~ class_Orderings_Olinorder(X4125) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4125,X4123,X4124)
| ~ c_Orderings_Oord__class_Oless(X4125,X4124,X4123)
| ~ class_Orderings_Olinorder(X4125) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1449])])]) ).
fof(i_0_2267,plain,
! [X4126,X4127,X4128] :
( ( c_Orderings_Oord__class_Oless__eq(X4128,X4127,X4126)
| c_Orderings_Oord__class_Oless(X4128,X4126,X4127)
| ~ class_Orderings_Olinorder(X4128) )
& ( ~ c_Orderings_Oord__class_Oless(X4128,X4126,X4127)
| ~ c_Orderings_Oord__class_Oless__eq(X4128,X4127,X4126)
| ~ class_Orderings_Olinorder(X4128) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1450])])]) ).
cnf(i_0_2268,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1451]) ).
cnf(i_0_2269,plain,
( X1 = X2
| c_Nat_OSuc(X1) != c_Nat_OSuc(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1452]) ).
fof(i_0_2270,plain,
! [X3214] :
( ( ~ 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,X3214))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3214) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X3214)
| 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,X3214)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).
cnf(i_0_2271,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_1419]) ).
fof(i_0_2272,plain,
! [X3348,X3349] :
( ~ class_Rings_Olinordered__ring(X3349)
| c_Orderings_Oord__class_Oless__eq(X3349,c_Groups_Ozero__class_Ozero(X3349),c_Groups_Otimes__class_Otimes(X3349,X3348,X3348)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_2273,plain,
! [X4206,X4207] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X4207,X4206)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4207),c_NthRoot_Osqrt(X4206)),
inference(variable_rename,[status(thm)],[fact_real__sqrt__divide]) ).
fof(i_0_2274,plain,
! [X3953,X3954] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3954,X3953)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3954),c_NthRoot_Osqrt(X3953)),
inference(variable_rename,[status(thm)],[fact_real__sqrt__mult]) ).
fof(i_0_2275,plain,
! [X3759,X3760,X3761] :
( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3760,X3761) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3759,X3761)
| X3760 = X3759
| X3761 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3760 != X3759
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3760,X3761) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3759,X3761)
| X3761 = 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_2276,plain,
! [X2599,X2600,X2601] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2601,X2600) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2599,X2600)
| X2601 = X2599
| X2600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2601 != X2599
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2601,X2600) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2599,X2600) )
& ( X2600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2601,X2600) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2599,X2600) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_2277,plain,
! [X3762,X3763,X3764] :
( ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3764,X3763) != c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3764,X3762)
| X3763 = X3762
| X3764 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3763 != X3762
| c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3764,X3763) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3764,X3762)
| X3764 = 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_2278,plain,
! [X2663,X2664,X2665] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2664) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2663)
| X2665 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2664 = X2663 )
& ( X2665 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2664) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2663) )
& ( X2664 != X2663
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2664) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2665,X2663) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_2279,plain,
! [X2602,X2603,X2604] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2603) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2602)
| X2603 = X2602
| X2604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2603 != X2602
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2603) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2602) )
& ( X2604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2603) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2604,X2602) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_2280,plain,
! [X4953,X4954,X4955] :
( ~ class_Divides_Osemiring__div(X4955)
| c_Divides_Odiv__class_Omod(X4955,c_Groups_Otimes__class_Otimes(X4955,X4954,X4953),X4954) = c_Groups_Ozero__class_Ozero(X4955) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).
fof(i_0_2281,plain,
! [X4950,X4951,X4952] :
( ~ class_Divides_Osemiring__div(X4952)
| c_Divides_Odiv__class_Omod(X4952,c_Groups_Otimes__class_Otimes(X4952,X4951,X4950),X4950) = c_Groups_Ozero__class_Ozero(X4952) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).
fof(i_0_2282,plain,
! [X3928,X3929] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3929,X3928)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3928,X3929)
| X3929 = X3928 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_2283,plain,
! [X3680,X3681] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3681,X3680)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3680,X3681)
| X3681 = X3680 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_2284,plain,
! [X3678,X3679] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3679,X3678)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3678,X3679)
| X3679 = X3678 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
cnf(i_0_2285,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_1369]) ).
cnf(i_0_2286,plain,
( X1 = X2
| c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1453]) ).
fof(i_0_2287,plain,
! [X3626,X3627,X3628] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3628,X3627) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3626,X3627)
| X3628 = X3626 )
& ( X3628 != X3626
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3628,X3627) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3626,X3627) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_2288,plain,
! [X3623,X3624,X3625] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3625,X3624) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3625,X3623)
| X3624 = X3623 )
& ( X3624 != X3623
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3625,X3624) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3625,X3623) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_2289,plain,
! [X4236,X4237] :
( ~ class_Rings_Olinordered__idom(X4237)
| c_Groups_Otimes__class_Otimes(X4237,c_Groups_Oabs__class_Oabs(X4237,X4236),c_Groups_Oabs__class_Oabs(X4237,X4236)) = c_Groups_Otimes__class_Otimes(X4237,X4236,X4236) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_2290,plain,
! [X4985,X4986,X4988,X4989,X4990] :
( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X4986,X4985) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4986 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4985,esk13_2(X4985,X4986)) )
& ( X4989 != c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4988,X4990)
| c_Divides_Odiv__class_Omod(tc_Int_Oint,X4989,X4988) = 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_2291,plain,
! [X3951,X3952] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3952,X3951)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3952),X3951),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
cnf(i_0_2292,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1395]) ).
cnf(i_0_2293,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_1454]) ).
cnf(i_0_2294,plain,
( c_Int_OBit1(X1) = c_Int_OMin
| X1 != c_Int_OMin ),
inference(split_conjunct,[status(thm)],[i_0_1423]) ).
cnf(i_0_2295,plain,
( c_Int_OMin = c_Int_OBit1(X1)
| c_Int_OMin != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1422]) ).
fof(i_0_2296,plain,
! [X4610,X4611,X4613,X4614,X4615] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4611,X4610)
| X4610 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4611,esk10_2(X4610,X4611)) )
& ( X4613 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4614,X4615)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4614,X4613) ) ),
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__Suc__ex__iff])])])])]) ).
fof(i_0_2297,plain,
! [X3589,X3590,X3592,X3593,X3594] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3590,X3589)
| X3589 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3590,esk8_2(X3589,X3590)) )
& ( X3592 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3593,X3594)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3593,X3592) ) ),
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_2298,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X1)),
inference(split_conjunct,[status(thm)],[i_0_1455]) ).
fof(i_0_2299,plain,
! [X4340,X4341,X4342] :
( ~ class_Rings_Olinordered__idom(X4342)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4341)
| c_Power_Opower__class_Opower(X4342,c_Groups_Oabs__class_Oabs(X4342,X4340),X4341) = c_Power_Opower__class_Opower(X4342,X4340,X4341) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__even__abs])]) ).
fof(i_0_2300,plain,
! [X4743,X4744,X4745,X4746] :
( ( X4744 = c_Groups_Ozero__class_Ozero(X4746)
| X4745 = c_Groups_Otimes__class_Otimes(X4746,X4743,X4744)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) != X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) )
& ( X4744 != c_Groups_Ozero__class_Ozero(X4746)
| X4743 = c_Groups_Ozero__class_Ozero(X4746)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) != X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) )
& ( X4744 = c_Groups_Ozero__class_Ozero(X4746)
| X4744 != c_Groups_Ozero__class_Ozero(X4746)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) = X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) )
& ( X4743 != c_Groups_Ozero__class_Ozero(X4746)
| X4744 != c_Groups_Ozero__class_Ozero(X4746)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) = X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) )
& ( X4744 = c_Groups_Ozero__class_Ozero(X4746)
| X4745 != c_Groups_Otimes__class_Otimes(X4746,X4743,X4744)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) = X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) )
& ( X4743 != c_Groups_Ozero__class_Ozero(X4746)
| X4745 != c_Groups_Otimes__class_Otimes(X4746,X4743,X4744)
| c_Rings_Oinverse__class_Odivide(X4746,X4745,X4744) = X4743
| ~ class_Fields_Ofield__inverse__zero(X4746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).
fof(i_0_2301,plain,
! [X4747,X4748,X4749,X4750] :
( ( X4747 = c_Groups_Ozero__class_Ozero(X4750)
| c_Groups_Otimes__class_Otimes(X4750,X4749,X4747) = X4748
| X4749 != c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) )
& ( X4747 != c_Groups_Ozero__class_Ozero(X4750)
| X4749 = c_Groups_Ozero__class_Ozero(X4750)
| X4749 != c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) )
& ( X4747 = c_Groups_Ozero__class_Ozero(X4750)
| X4747 != c_Groups_Ozero__class_Ozero(X4750)
| X4749 = c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) )
& ( X4749 != c_Groups_Ozero__class_Ozero(X4750)
| X4747 != c_Groups_Ozero__class_Ozero(X4750)
| X4749 = c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) )
& ( X4747 = c_Groups_Ozero__class_Ozero(X4750)
| c_Groups_Otimes__class_Otimes(X4750,X4749,X4747) != X4748
| X4749 = c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) )
& ( X4749 != c_Groups_Ozero__class_Ozero(X4750)
| c_Groups_Otimes__class_Otimes(X4750,X4749,X4747) != X4748
| X4749 = c_Rings_Oinverse__class_Odivide(X4750,X4748,X4747)
| ~ class_Fields_Ofield__inverse__zero(X4750) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).
cnf(i_0_2302,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).
fof(i_0_2303,plain,
! [X3585,X3586] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3586,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3586,X3585)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_2304,plain,
! [X3583,X3584] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3584,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3583,X3584)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_2305,plain,
! [X3182] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3182,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X3182,X3182)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_2306,plain,
! [X3959,X3960] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3960),c_NthRoot_Osqrt(X3959))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3960,X3959) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3960,X3959)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3960),c_NthRoot_Osqrt(X3959)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__iff])]) ).
fof(i_0_2307,plain,
! [X3945,X3946] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3946),c_NthRoot_Osqrt(X3945))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3946,X3945) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3946,X3945)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3946),c_NthRoot_Osqrt(X3945)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__iff])]) ).
fof(i_0_2308,plain,
! [X4324,X4325,X4326,X4327] :
( ~ class_Rings_Odivision__ring(X4327)
| X4326 = c_Groups_Ozero__class_Ozero(X4327)
| X4325 != c_Groups_Otimes__class_Otimes(X4327,X4324,X4326)
| c_Rings_Oinverse__class_Odivide(X4327,X4325,X4326) = X4324 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).
fof(i_0_2309,plain,
! [X4328,X4329,X4330,X4331] :
( ( c_Rings_Oinverse__class_Odivide(X4331,X4329,X4330) != X4328
| X4329 = c_Groups_Otimes__class_Otimes(X4331,X4328,X4330)
| X4330 = c_Groups_Ozero__class_Ozero(X4331)
| ~ class_Rings_Odivision__ring(X4331) )
& ( X4329 != c_Groups_Otimes__class_Otimes(X4331,X4328,X4330)
| c_Rings_Oinverse__class_Odivide(X4331,X4329,X4330) = X4328
| X4330 = c_Groups_Ozero__class_Ozero(X4331)
| ~ class_Rings_Odivision__ring(X4331) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).
fof(i_0_2310,plain,
! [X4332,X4333,X4334,X4335] :
( ( X4333 != c_Rings_Oinverse__class_Odivide(X4335,X4332,X4334)
| c_Groups_Otimes__class_Otimes(X4335,X4333,X4334) = X4332
| X4334 = c_Groups_Ozero__class_Ozero(X4335)
| ~ class_Rings_Odivision__ring(X4335) )
& ( c_Groups_Otimes__class_Otimes(X4335,X4333,X4334) != X4332
| X4333 = c_Rings_Oinverse__class_Odivide(X4335,X4332,X4334)
| X4334 = c_Groups_Ozero__class_Ozero(X4335)
| ~ class_Rings_Odivision__ring(X4335) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).
fof(i_0_2311,plain,
! [X4320,X4321,X4322,X4323] :
( ~ class_Rings_Odivision__ring(X4323)
| X4322 = c_Groups_Ozero__class_Ozero(X4323)
| c_Groups_Otimes__class_Otimes(X4323,X4321,X4322) != X4320
| X4321 = c_Rings_Oinverse__class_Odivide(X4323,X4320,X4322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).
fof(i_0_2312,plain,
! [X4385] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4385))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4385) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4385)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4385)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__1__iff])]) ).
fof(i_0_2313,plain,
! [X3965] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3965))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3965) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3965)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3965)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__0__iff])]) ).
fof(i_0_2314,plain,
! [X4384] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4384))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4384) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4384)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4384)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__1__iff])]) ).
fof(i_0_2315,plain,
! [X3964] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3964))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3964) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3964)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3964)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff])]) ).
fof(i_0_2316,plain,
! [X4386] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4386),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4386,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4386,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4386),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__1__iff])]) ).
fof(i_0_2317,plain,
! [X3966] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3966),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3966,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3966,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3966),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__0__iff])]) ).
fof(i_0_2318,plain,
! [X4383] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4383),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4383,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4383,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X4383),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__1__iff])]) ).
fof(i_0_2319,plain,
! [X3963] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3963),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3963,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3963,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3963),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__0__iff])]) ).
fof(i_0_2320,plain,
! [X4308,X4309] :
( ( ~ c_Orderings_Oord__class_Oless(X4309,c_Groups_Ozero__class_Ozero(X4309),c_Groups_Oabs__class_Oabs(X4309,X4308))
| X4308 != c_Groups_Ozero__class_Ozero(X4309)
| ~ class_Groups_Oordered__ab__group__add__abs(X4309) )
& ( X4308 = c_Groups_Ozero__class_Ozero(X4309)
| c_Orderings_Oord__class_Oless(X4309,c_Groups_Ozero__class_Ozero(X4309),c_Groups_Oabs__class_Oabs(X4309,X4308))
| ~ class_Groups_Oordered__ab__group__add__abs(X4309) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
cnf(i_0_2321,plain,
( X1 = c_Nat_OSuc(esk7_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_1456]) ).
fof(i_0_2322,plain,
! [X3968] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3968)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3968)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__zero])]) ).
fof(i_0_2323,plain,
! [X4382] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4382)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X4382)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__one])]) ).
fof(i_0_2324,plain,
! [X3962] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3962)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X3962)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__zero])]) ).
fof(i_0_2325,plain,
! [X4171,X4172,X4173] :
( ~ class_Orderings_Oorder(X4173)
| ~ c_Orderings_Oord__class_Oless__eq(X4173,X4172,X4171)
| X4171 = X4172
| c_Orderings_Oord__class_Oless(X4173,X4172,X4171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_2326,plain,
! [X4168,X4169,X4170] :
( ~ class_Orderings_Oorder(X4170)
| ~ c_Orderings_Oord__class_Oless__eq(X4170,X4169,X4168)
| X4169 = X4168
| c_Orderings_Oord__class_Oless(X4170,X4169,X4168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_2327,plain,
! [X4165,X4166,X4167] :
( ~ class_Orderings_Oorder(X4167)
| ~ c_Orderings_Oord__class_Oless__eq(X4167,X4166,X4165)
| c_Orderings_Oord__class_Oless(X4167,X4166,X4165)
| X4166 = X4165 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_2328,plain,
! [X4150,X4151,X4152] :
( ~ class_Orderings_Oorder(X4152)
| X4151 = X4150
| ~ c_Orderings_Oord__class_Oless__eq(X4152,X4151,X4150)
| c_Orderings_Oord__class_Oless(X4152,X4151,X4150) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_2329,plain,
! [X4138,X4139,X4140] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4140,X4139,X4138)
| c_Orderings_Oord__class_Oless(X4140,X4139,X4138)
| X4139 = X4138
| ~ class_Orderings_Oorder(X4140) )
& ( ~ c_Orderings_Oord__class_Oless(X4140,X4139,X4138)
| c_Orderings_Oord__class_Oless__eq(X4140,X4139,X4138)
| ~ class_Orderings_Oorder(X4140) )
& ( X4139 != X4138
| c_Orderings_Oord__class_Oless__eq(X4140,X4139,X4138)
| ~ class_Orderings_Oorder(X4140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_2330,plain,
! [X4132,X4133,X4134] :
( ( c_Orderings_Oord__class_Oless__eq(X4134,X4133,X4132)
| ~ c_Orderings_Oord__class_Oless(X4134,X4133,X4132)
| ~ class_Orderings_Oorder(X4134) )
& ( X4133 != X4132
| ~ c_Orderings_Oord__class_Oless(X4134,X4133,X4132)
| ~ class_Orderings_Oorder(X4134) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4134,X4133,X4132)
| X4133 = X4132
| c_Orderings_Oord__class_Oless(X4134,X4133,X4132)
| ~ class_Orderings_Oorder(X4134) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_2331,plain,
! [X4147,X4148,X4149] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4149,X4148,X4147)
| X4148 = X4147
| c_Orderings_Oord__class_Oless(X4149,X4148,X4147)
| ~ class_Orderings_Olinorder(X4149) )
& ( X4148 != X4147
| c_Orderings_Oord__class_Oless__eq(X4149,X4148,X4147)
| c_Orderings_Oord__class_Oless(X4149,X4148,X4147)
| ~ class_Orderings_Olinorder(X4149) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1457])])]) ).
fof(i_0_2332,plain,
! [X4153,X4154,X4155] :
( ~ class_Orderings_Oorder(X4155)
| X4154 = X4153
| ~ c_Orderings_Oord__class_Oless__eq(X4155,X4153,X4154)
| c_Orderings_Oord__class_Oless(X4155,X4153,X4154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_2333,plain,
! [X4892,X4893] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X4893,X4892)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X4893),c_Transcendental_Oarctan(X4892)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arctan__monotone])]) ).
fof(i_0_2334,plain,
! [X3957,X3958] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3958,X3957)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3958),c_NthRoot_Osqrt(X3957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__mono])]) ).
fof(i_0_2335,plain,
! [X4890,X4891] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X4891,X4890)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X4891),c_Transcendental_Oarctan(X4890)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arctan__monotone_H])]) ).
fof(i_0_2336,plain,
! [X3947,X3948] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3948,X3947)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X3948),c_NthRoot_Osqrt(X3947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__mono])]) ).
fof(i_0_2337,plain,
! [X4302,X4303] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4303,c_Groups_Oabs__class_Oabs(X4303,X4302),c_Groups_Ozero__class_Ozero(X4303))
| X4302 = c_Groups_Ozero__class_Ozero(X4303)
| ~ class_Groups_Oordered__ab__group__add__abs(X4303) )
& ( X4302 != c_Groups_Ozero__class_Ozero(X4303)
| c_Orderings_Oord__class_Oless__eq(X4303,c_Groups_Oabs__class_Oabs(X4303,X4302),c_Groups_Ozero__class_Ozero(X4303))
| ~ class_Groups_Oordered__ab__group__add__abs(X4303) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_2338,plain,
! [X4159,X4160,X4161] :
( ~ class_Orderings_Opreorder(X4161)
| ~ c_Orderings_Oord__class_Oless(X4161,X4160,X4159)
| c_Orderings_Oord__class_Oless__eq(X4161,X4160,X4159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
cnf(i_0_2339,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_1456]) ).
fof(i_0_2340,plain,
! [X4463] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4463)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4463) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4463)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4463) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_2341,plain,
! [X4652,X4653] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4653,X4652))
| X4652 != c_Groups_Ozero__class_Ozero(X4653)
| ~ class_RealVector_Oreal__normed__vector(X4653) )
& ( X4652 = c_Groups_Ozero__class_Ozero(X4653)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4653,X4652))
| ~ class_RealVector_Oreal__normed__vector(X4653) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_2342,plain,
! [X4306,X4307] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4307)
| ~ c_Orderings_Oord__class_Oless(X4307,c_Groups_Oabs__class_Oabs(X4307,X4306),c_Groups_Ozero__class_Ozero(X4307)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1458])]) ).
fof(i_0_2343,plain,
! [X4650,X4651] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4651,X4650),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X4650 = c_Groups_Ozero__class_Ozero(X4651)
| ~ class_RealVector_Oreal__normed__vector(X4651) )
& ( X4650 != c_Groups_Ozero__class_Ozero(X4651)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4651,X4650),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X4651) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_2344,plain,
! [X3720,X3721] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3721,X3720)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3721,X3720) )
& ( X3721 != X3720
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3721,X3720) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3721,X3720)
| X3721 = X3720
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3721,X3720) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_2345,plain,
! [X3718,X3719] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3719,X3718)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3719,X3718)
| X3719 = X3718 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3719,X3718)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3719,X3718) )
& ( X3719 != X3718
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3719,X3718) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_2346,plain,
! [X3605,X3606] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3606,X3605)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3606,X3605) )
& ( X3606 != X3605
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X3606,X3605) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3606,X3605)
| X3606 = X3605
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3606,X3605) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_2347,plain,
! [X3670,X3671] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3671,X3670)
| X3671 = X3670
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3671,X3670) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_2348,plain,
! [X3607,X3608] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3608,X3607)
| X3608 = X3607 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3608,X3607)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607) )
& ( X3608 != X3607
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_2349,plain,
! [X3603,X3604] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3604,X3603)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3604,X3603) )
& ( X3604 != X3603
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3604,X3603) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3604,X3603)
| X3604 = X3603
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3604,X3603) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_2350,plain,
! [X3710,X3711] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3711,X3710)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3711,X3710) )
& ( X3711 != X3710
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3711,X3710) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2351,plain,
! [X3644,X3645] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3645,X3644)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3645,X3644) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2352,plain,
! [X4645,X4646] :
( ~ class_RealVector_Oreal__normed__vector(X4646)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4646,X4645),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1459])]) ).
cnf(i_0_2353,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_1438]) ).
fof(i_0_2354,plain,
! [X4605] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4605),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X4605 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X4605 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4605),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff])]) ).
fof(i_0_2355,plain,
! [X2796,X2797,X2798] :
( ( X2797 = c_Groups_Ozero__class_Ozero(X2798)
| c_Power_Opower__class_Opower(X2798,X2797,X2796) != c_Groups_Ozero__class_Ozero(X2798)
| ~ class_Power_Opower(X2798)
| ~ class_Rings_Omult__zero(X2798)
| ~ class_Rings_Ono__zero__divisors(X2798)
| ~ class_Rings_Ozero__neq__one(X2798) )
& ( X2796 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2798,X2797,X2796) != c_Groups_Ozero__class_Ozero(X2798)
| ~ class_Power_Opower(X2798)
| ~ class_Rings_Omult__zero(X2798)
| ~ class_Rings_Ono__zero__divisors(X2798)
| ~ class_Rings_Ozero__neq__one(X2798) )
& ( X2797 != c_Groups_Ozero__class_Ozero(X2798)
| X2796 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X2798,X2797,X2796) = c_Groups_Ozero__class_Ozero(X2798)
| ~ class_Power_Opower(X2798)
| ~ class_Rings_Omult__zero(X2798)
| ~ class_Rings_Ono__zero__divisors(X2798)
| ~ class_Rings_Ozero__neq__one(X2798) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2356,plain,
! [X4529,X4530] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4529) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4530,c_Groups_Ozero__class_Ozero(X4530),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4529)) = c_Groups_Oone__class_Oone(X4530)
| ~ class_Power_Opower(X4530)
| ~ class_Rings_Osemiring__0(X4530) )
& ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4530,c_Groups_Ozero__class_Ozero(X4530),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X4529)) = c_Groups_Ozero__class_Ozero(X4530)
| ~ class_Power_Opower(X4530)
| ~ class_Rings_Osemiring__0(X4530) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left__number__of])])]) ).
fof(i_0_2357,plain,
! [X4369] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4369,X4369)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4369),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(i_0_2358,plain,
! [X4034,X4035,X4036] :
( ( X4035 = X4034
| c_Orderings_Oord__class_Oless(X4036,X4035,X4034)
| c_Orderings_Oord__class_Oless(X4036,X4034,X4035)
| ~ class_Orderings_Olinorder(X4036) )
& ( ~ c_Orderings_Oord__class_Oless(X4036,X4035,X4034)
| X4035 != X4034
| ~ class_Orderings_Olinorder(X4036) )
& ( ~ c_Orderings_Oord__class_Oless(X4036,X4034,X4035)
| X4035 != X4034
| ~ class_Orderings_Olinorder(X4036) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2359,plain,
! [X4097,X4098,X4099] :
( ~ class_Orderings_Olinorder(X4099)
| c_Orderings_Oord__class_Oless(X4099,X4098,X4097)
| X4098 = X4097
| c_Orderings_Oord__class_Oless(X4099,X4097,X4098) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1460])]) ).
fof(i_0_2360,plain,
! [X4046,X4047,X4048] :
( ~ class_Orderings_Olinorder(X4048)
| X4047 = X4046
| c_Orderings_Oord__class_Oless(X4048,X4047,X4046)
| c_Orderings_Oord__class_Oless(X4048,X4046,X4047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1461])]) ).
fof(i_0_2361,plain,
! [X4043,X4044,X4045] :
( ( c_Orderings_Oord__class_Oless(X4045,X4043,X4044)
| X4043 = X4044
| c_Orderings_Oord__class_Oless(X4045,X4044,X4043)
| ~ class_Orderings_Olinorder(X4045) )
& ( X4043 != X4044
| ~ c_Orderings_Oord__class_Oless(X4045,X4043,X4044)
| c_Orderings_Oord__class_Oless(X4045,X4044,X4043)
| ~ class_Orderings_Olinorder(X4045) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1462])])]) ).
fof(i_0_2362,plain,
! [X4040,X4041,X4042] :
( ~ class_Orderings_Olinorder(X4042)
| c_Orderings_Oord__class_Oless(X4042,X4041,X4040)
| X4041 = X4040
| c_Orderings_Oord__class_Oless(X4042,X4040,X4041) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2363,plain,
! [X2915,X2916,X2917] :
( ~ class_Rings_Olinordered__idom(X2917)
| X2916 = X2915
| c_Orderings_Oord__class_Oless(X2917,X2916,X2915)
| c_Orderings_Oord__class_Oless(X2917,X2915,X2916) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1463])]) ).
fof(i_0_2364,plain,
! [X4310,X4311] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4311)
| ~ c_Orderings_Oord__class_Oless(X4311,c_Groups_Ozero__class_Ozero(X4311),X4310)
| c_Groups_Oabs__class_Oabs(X4311,X4310) = X4310 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_2365,plain,
! [X4304,X4305] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4305)
| ~ c_Orderings_Oord__class_Oless__eq(X4305,c_Groups_Ozero__class_Ozero(X4305),X4304)
| c_Groups_Oabs__class_Oabs(X4305,X4304) = X4304 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
cnf(i_0_2366,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_1434]) ).
fof(i_0_2367,plain,
! [X4144,X4145,X4146] :
( ~ class_Orderings_Olinorder(X4146)
| c_Orderings_Oord__class_Oless__eq(X4146,X4145,X4144)
| c_Orderings_Oord__class_Oless(X4146,X4144,X4145) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1464])]) ).
fof(i_0_2368,plain,
! [X4129,X4130,X4131] :
( ~ class_Orderings_Olinorder(X4131)
| c_Orderings_Oord__class_Oless__eq(X4131,X4130,X4129)
| c_Orderings_Oord__class_Oless(X4131,X4129,X4130) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2369,plain,
! [X4141,X4142,X4143] :
( ~ class_Orderings_Olinorder(X4143)
| c_Orderings_Oord__class_Oless(X4143,X4142,X4141)
| c_Orderings_Oord__class_Oless__eq(X4143,X4141,X4142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1465])]) ).
fof(i_0_2370,plain,
! [X4029,X4030,X4031] :
( ~ class_Orderings_Olinorder(X4031)
| c_Orderings_Oord__class_Oless__eq(X4031,X4030,X4029)
| c_Orderings_Oord__class_Oless__eq(X4031,X4029,X4030) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1466])]) ).
fof(i_0_2371,plain,
! [X3977,X3978,X3979] :
( ~ class_Orderings_Olinorder(X3979)
| c_Orderings_Oord__class_Oless__eq(X3979,X3978,X3977)
| c_Orderings_Oord__class_Oless__eq(X3979,X3977,X3978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2372,plain,
! [X2848,X2849,X2850] :
( ~ class_Rings_Ocomm__semiring__1(X2850)
| c_Groups_Oplus__class_Oplus(X2850,X2849,X2848) = c_Groups_Oplus__class_Oplus(X2850,X2848,X2849) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2373,plain,
! [X2764,X2765,X2766] :
( ~ class_Rings_Ocomm__semiring__1(X2766)
| c_Groups_Otimes__class_Otimes(X2766,X2765,X2764) = c_Groups_Otimes__class_Otimes(X2766,X2764,X2765) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2374,plain,
! [X4345] :
( ~ class_Rings_Olinordered__semidom(X4345)
| ~ c_Orderings_Oord__class_Oless(X4345,c_Groups_Oone__class_Oone(X4345),c_Groups_Ozero__class_Ozero(X4345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1467])]) ).
fof(i_0_2375,plain,
! [X4343] :
( ~ class_Rings_Olinordered__semidom(X4343)
| ~ c_Orderings_Oord__class_Oless__eq(X4343,c_Groups_Oone__class_Oone(X4343),c_Groups_Ozero__class_Ozero(X4343)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1468])]) ).
cnf(i_0_2376,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_1469]) ).
fof(i_0_2377,plain,
! [X2675,X2676,X2677] :
( ( c_Groups_Otimes__class_Otimes(X2677,X2676,X2675) != c_Groups_Ozero__class_Ozero(X2677)
| X2676 = c_Groups_Ozero__class_Ozero(X2677)
| X2675 = c_Groups_Ozero__class_Ozero(X2677)
| ~ class_Rings_Oring__no__zero__divisors(X2677) )
& ( X2676 != c_Groups_Ozero__class_Ozero(X2677)
| c_Groups_Otimes__class_Otimes(X2677,X2676,X2675) = c_Groups_Ozero__class_Ozero(X2677)
| ~ class_Rings_Oring__no__zero__divisors(X2677) )
& ( X2675 != c_Groups_Ozero__class_Ozero(X2677)
| c_Groups_Otimes__class_Otimes(X2677,X2676,X2675) = c_Groups_Ozero__class_Ozero(X2677)
| ~ class_Rings_Oring__no__zero__divisors(X2677) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2378,plain,
! [X2672,X2673,X2674] :
( ~ class_Rings_Ono__zero__divisors(X2674)
| X2673 = c_Groups_Ozero__class_Ozero(X2674)
| X2672 = c_Groups_Ozero__class_Ozero(X2674)
| c_Groups_Otimes__class_Otimes(X2674,X2673,X2672) != c_Groups_Ozero__class_Ozero(X2674) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2379,plain,
! [X2669,X2670,X2671] :
( ~ class_Rings_Ono__zero__divisors(X2671)
| c_Groups_Otimes__class_Otimes(X2671,X2670,X2669) != c_Groups_Ozero__class_Ozero(X2671)
| X2670 = c_Groups_Ozero__class_Ozero(X2671)
| X2669 = c_Groups_Ozero__class_Ozero(X2671) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2380,plain,
! [X3480,X3481] :
( ~ class_Int_Onumber__ring(X3481)
| c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3480)
| c_Power_Opower__class_Opower(X3481,c_Int_Onumber__class_Onumber__of(X3481,c_Int_OMin),X3480) = c_Int_Onumber__class_Onumber__of(X3481,c_Int_OMin) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1470])]) ).
fof(i_0_2381,plain,
! [X4533,X4534] :
( ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4533)
| c_Power_Opower__class_Opower(X4534,c_Int_Onumber__class_Onumber__of(X4534,c_Int_OMin),X4533) = c_Groups_Oone__class_Oone(X4534)
| ~ class_Int_Onumber__ring(X4534) )
& ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4533)
| c_Power_Opower__class_Opower(X4534,c_Int_Onumber__class_Onumber__of(X4534,c_Int_OMin),X4533) = c_Int_Onumber__class_Onumber__of(X4534,c_Int_OMin)
| ~ class_Int_Onumber__ring(X4534) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1471])])]) ).
fof(i_0_2382,plain,
! [X4531,X4532] :
( ~ class_Int_Onumber__ring(X4532)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X4531)
| c_Power_Opower__class_Opower(X4532,c_Int_Onumber__class_Onumber__of(X4532,c_Int_OMin),X4531) = c_Groups_Oone__class_Oone(X4532) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__one__even__power])]) ).
fof(i_0_2383,plain,
! [X3609,X3610] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X3610,X3609)
| X3610 = X3609
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3609,X3610) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2384,plain,
! [X3635,X3636] :
( X3636 = X3635
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3636,X3635)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3635,X3636) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1472])]) ).
fof(i_0_2385,plain,
! [X3587,X3588] :
( ( X3588 = X3587
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3588,X3587)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3587,X3588) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3588,X3587)
| X3588 != X3587 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3587,X3588)
| X3588 != X3587 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2386,plain,
! [X4228,X4229,X4230] :
( ( c_Rings_Oinverse__class_Odivide(X4230,X4228,X4229) != c_Groups_Oone__class_Oone(X4230)
| X4228 = X4229
| X4229 = c_Groups_Ozero__class_Ozero(X4230)
| ~ class_Rings_Odivision__ring(X4230) )
& ( X4228 != X4229
| c_Rings_Oinverse__class_Odivide(X4230,X4228,X4229) = c_Groups_Oone__class_Oone(X4230)
| X4229 = c_Groups_Ozero__class_Ozero(X4230)
| ~ class_Rings_Odivision__ring(X4230) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).
fof(i_0_2387,plain,
! [X3933,X3934] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3934,X3933)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3933,X3934) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2388,plain,
! [X3601,X3602] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3602,X3601)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3601,X3602) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2389,plain,
! [X3599,X3600] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3600,X3599)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3599,X3600) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2390,plain,
! [X3597,X3598] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3598,X3597) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3597,X3598),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2391,plain,
! [X3595,X3596] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3596,X3595) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3595,X3596),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2392,plain,
! [X3754,X3755] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3755,X3754) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3754,X3755),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2393,plain,
! [X2678,X2679] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2679,X2678) = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2678,X2679),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2394,plain,
! [X2632,X2633] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2633,X2632) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2632,X2633),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2395,plain,
! [X3031,X3032] :
( ( c_Groups_Oplus__class_Oplus(X3032,X3031,X3031) != c_Groups_Ozero__class_Ozero(X3032)
| X3031 = c_Groups_Ozero__class_Ozero(X3032)
| ~ class_Groups_Olinordered__ab__group__add(X3032) )
& ( X3031 != c_Groups_Ozero__class_Ozero(X3032)
| c_Groups_Oplus__class_Oplus(X3032,X3031,X3031) = c_Groups_Ozero__class_Ozero(X3032)
| ~ class_Groups_Olinordered__ab__group__add(X3032) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2396,plain,
! [X2771,X2772,X2773] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2773)
| X2772 = c_Groups_Ozero__class_Ozero(X2773)
| c_Power_Opower__class_Opower(X2773,X2772,X2771) != c_Groups_Ozero__class_Ozero(X2773) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2397,plain,
! [X3788,X3789] :
( ( c_Groups_Ozero__class_Ozero(X3789) != c_Groups_Oplus__class_Oplus(X3789,X3788,X3788)
| X3788 = c_Groups_Ozero__class_Ozero(X3789)
| ~ class_Groups_Olinordered__ab__group__add(X3789) )
& ( X3788 != c_Groups_Ozero__class_Ozero(X3789)
| c_Groups_Ozero__class_Ozero(X3789) = c_Groups_Oplus__class_Oplus(X3789,X3788,X3788)
| ~ class_Groups_Olinordered__ab__group__add(X3789) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2398,plain,
! [X4475,X4476] :
( c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4476,X4475) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4476 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4476 = 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_2399,plain,
! [X4473,X4474] :
( ( X4474 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X4474 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X4473 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X4474 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X4474 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X4473 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X4473 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X4473 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X4474 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4473 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( X4474 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| X4473 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4474,X4473) = 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_2400,plain,
! [X3961] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3961)
| c_NthRoot_Osqrt(X3961) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3961 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__zero__cancel])]) ).
fof(i_0_2401,plain,
! [X3033,X3034,X3035] :
( ( X3034 != c_Groups_Oplus__class_Oplus(X3035,X3034,X3033)
| X3033 = c_Groups_Ozero__class_Ozero(X3035)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3035) )
& ( X3033 != c_Groups_Ozero__class_Ozero(X3035)
| X3034 = c_Groups_Oplus__class_Oplus(X3035,X3034,X3033)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X3035) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2402,plain,
! [X3967] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3967)
| c_NthRoot_Osqrt(X3967) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__not__eq__zero])]) ).
fof(i_0_2403,plain,
! [X4061,X4062,X4063] :
( ~ class_Orderings_Oorder(X4063)
| ~ c_Orderings_Oord__class_Oless(X4063,X4062,X4061)
| X4061 != X4062 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2404,plain,
! [X4058,X4059,X4060] :
( ~ class_Orderings_Oorder(X4060)
| ~ c_Orderings_Oord__class_Oless(X4060,X4059,X4058)
| X4059 != X4058 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2405,plain,
! [X4049,X4050,X4051] :
( ~ class_Orderings_Oorder(X4051)
| ~ c_Orderings_Oord__class_Oless(X4051,X4050,X4049)
| X4050 != X4049 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2406,plain,
! [X3500] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3500) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3500,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3500,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3500) = 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_2407,plain,
! [X3499] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3499)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3499,c_Int_OPls) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3499,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X3499) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).
fof(i_0_2408,plain,
! [X4416,X4417] :
( ~ class_Fields_Ofield__inverse__zero(X4417)
| ~ class_Int_Onumber__ring(X4417)
| c_Rings_Oinverse__class_Odivide(X4417,X4416,c_Int_Onumber__class_Onumber__of(X4417,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X4417) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).
fof(i_0_2409,plain,
! [X2605,X2606] :
( ( c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2606,X2605) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2606,X2605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X2605 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2606,X2605) = 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_2410,plain,
! [X3100] :
( ( X3100 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3100) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3100)
| X3100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).
fof(i_0_2411,plain,
! [X4300,X4301] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4301)
| c_Orderings_Oord__class_Oless__eq(X4301,c_Groups_Ozero__class_Ozero(X4301),c_Groups_Oabs__class_Oabs(X4301,X4300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_2412,plain,
! [X4032,X4033] :
( ~ class_Orderings_Opreorder(X4033)
| ~ c_Orderings_Oord__class_Oless(X4033,X4032,X4032) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1473])]) ).
fof(i_0_2413,plain,
! [X4376,X4377] :
( X4377 != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4377,X4376)
| X4376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4377 = 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_2414,plain,
! [X3107] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3107,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3107 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3107,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_2415,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1474]) ).
cnf(i_0_2416,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1475]) ).
cnf(i_0_2417,plain,
c_Nat_OSuc(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1476]) ).
cnf(i_0_2418,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1477]) ).
cnf(i_0_2419,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1478]) ).
cnf(i_0_2420,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1479]) ).
fof(i_0_2421,plain,
! [X4280,X4281] :
( ( X4281 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4281,X4280) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4280 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4281,X4280) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4281 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4280 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4281,X4280) = 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_2422,plain,
! [X3077,X3078] :
( ( X3078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3078,X3077) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3078,X3077) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3078 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3078,X3077) = 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_2423,plain,
! [X4283,X4284] :
( ( X4284 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4284,X4283) )
& ( X4283 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4284,X4283) )
& ( X4284 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X4283 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4284,X4283) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).
fof(i_0_2424,plain,
! [X3097,X3098] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3098,X3097)
| X3097 != 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_2425,plain,
c_Nat_OSuc(X1) != X1,
inference(split_conjunct,[status(thm)],[i_0_1480]) ).
cnf(i_0_2426,plain,
X1 != c_Nat_OSuc(X1),
inference(split_conjunct,[status(thm)],[i_0_1481]) ).
fof(i_0_2427,plain,
! [X4676,X4677] :
( ~ class_Int_Onumber__ring(X4677)
| ~ class_RealVector_Oreal__normed__algebra__1(X4677)
| c_RealVector_Onorm__class_Onorm(X4677,c_Int_Onumber__class_Onumber__of(X4677,X4676)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X4676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__number__of])]) ).
fof(i_0_2428,plain,
! [X4647,X4648] :
( ~ class_RealVector_Oreal__normed__vector(X4648)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4648,X4647)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2429,plain,
! [X3075,X3076] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3076,X3075) != X3076
| X3075 = 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_2430,plain,
! [X3101] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3101,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1482]) ).
fof(i_0_2431,plain,
! [X3099] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3099,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1483]) ).
fof(i_0_2432,plain,
! [X2826] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2826,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1484]) ).
fof(i_0_2433,plain,
! [X4295,X4296] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4296)
| c_Orderings_Oord__class_Oless__eq(X4296,X4295,c_Groups_Oabs__class_Oabs(X4296,X4295)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_2434,plain,
! [X3640,X3641] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3641,X3640)
| X3641 != X3640 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2435,plain,
! [X3638,X3639] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3639,X3638)
| X3638 != X3639 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2436,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_2437,plain,
! [X3352,X3353] :
( ~ class_Int_Onumber__ring(X3353)
| c_Groups_Oplus__class_Oplus(X3353,c_Int_Onumber__class_Onumber__of(X3353,c_Int_OPls),X3352) = X3352 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).
fof(i_0_2438,plain,
! [X3350,X3351] :
( ~ class_Int_Onumber__ring(X3351)
| c_Groups_Oplus__class_Oplus(X3351,X3350,c_Int_Onumber__class_Onumber__of(X3351,c_Int_OPls)) = X3350 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).
cnf(i_0_2439,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Int_OBit0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1485]) ).
cnf(i_0_2440,plain,
( X1 = c_Int_OPls
| c_Int_OBit0(X1) != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_1486]) ).
fof(i_0_2441,plain,
! [X4438,X4439] :
( ( X4438 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4439,c_Groups_Ozero__class_Ozero(X4439),X4438) = c_Groups_Oone__class_Oone(X4439)
| ~ class_Power_Opower(X4439)
| ~ class_Rings_Osemiring__0(X4439) )
& ( X4438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(X4439,c_Groups_Ozero__class_Ozero(X4439),X4438) = c_Groups_Ozero__class_Ozero(X4439)
| ~ class_Power_Opower(X4439)
| ~ class_Rings_Osemiring__0(X4439) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2442,plain,
! [X3637] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3637,X3637),
inference(variable_rename,[status(thm)],[i_0_1487]) ).
fof(i_0_2443,plain,
! [X3576] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3576,X3576),
inference(variable_rename,[status(thm)],[i_0_1488]) ).
cnf(i_0_2444,plain,
c_Int_OBit0(X1) != c_Int_OMin,
inference(split_conjunct,[status(thm)],[i_0_1489]) ).
cnf(i_0_2445,plain,
c_Int_OMin != c_Int_OBit0(X1),
inference(split_conjunct,[status(thm)],[i_0_1490]) ).
fof(i_0_2446,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_2447,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_2448,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_2449,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_2450,plain,
! [X4913] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4913,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_2451,plain,
! [X4233,X4234] :
( ( X4233 != c_Groups_Ozero__class_Ozero(X4234)
| c_Rings_Oinverse__class_Odivide(X4234,X4233,X4233) = c_Groups_Ozero__class_Ozero(X4234)
| ~ class_Rings_Odivision__ring__inverse__zero(X4234) )
& ( X4233 = c_Groups_Ozero__class_Ozero(X4234)
| c_Rings_Oinverse__class_Odivide(X4234,X4233,X4233) = c_Groups_Oone__class_Oone(X4234)
| ~ class_Rings_Odivision__ring__inverse__zero(X4234) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).
fof(i_0_2452,plain,
! [X4346] :
( ~ class_Rings_Olinordered__semidom(X4346)
| c_Orderings_Oord__class_Oless(X4346,c_Groups_Ozero__class_Ozero(X4346),c_Groups_Oone__class_Oone(X4346)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2453,plain,
! [X4344] :
( ~ class_Rings_Olinordered__semidom(X4344)
| c_Orderings_Oord__class_Oless__eq(X4344,c_Groups_Ozero__class_Ozero(X4344),c_Groups_Oone__class_Oone(X4344)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2454,plain,
! [X4969,X4970] :
( ~ class_Divides_Osemiring__div(X4970)
| c_Divides_Odiv__class_Omod(X4970,c_Groups_Ozero__class_Ozero(X4970),X4969) = c_Groups_Ozero__class_Ozero(X4970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).
fof(i_0_2455,plain,
! [X4248,X4249] :
( ~ class_RealVector_Oreal__normed__field(X4249)
| c_Rings_Oinverse__class_Odivide(X4249,c_Groups_Ozero__class_Ozero(X4249),X4248) = c_Groups_Ozero__class_Ozero(X4249) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide_Ozero])]) ).
fof(i_0_2456,plain,
! [X4244,X4245] :
( ~ class_Rings_Odivision__ring(X4245)
| c_Rings_Oinverse__class_Odivide(X4245,c_Groups_Ozero__class_Ozero(X4245),X4244) = c_Groups_Ozero__class_Ozero(X4245) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(i_0_2457,plain,
! [X4274,X4275] :
( ~ class_Groups_Omonoid__mult(X4275)
| c_Power_Opower__class_Opower(X4275,c_Groups_Oone__class_Oone(X4275),X4274) = c_Groups_Oone__class_Oone(X4275) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2458,plain,
! [X2824,X2825] :
( ~ class_RealVector_Oreal__normed__algebra(X2825)
| c_Groups_Otimes__class_Otimes(X2825,c_Groups_Ozero__class_Ozero(X2825),X2824) = c_Groups_Ozero__class_Ozero(X2825) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2459,plain,
! [X2822,X2823] :
( ~ class_RealVector_Oreal__normed__algebra(X2823)
| c_Groups_Otimes__class_Otimes(X2823,c_Groups_Ozero__class_Ozero(X2823),X2822) = c_Groups_Ozero__class_Ozero(X2823) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2460,plain,
! [X2769,X2770] :
( ~ class_Rings_Ocomm__semiring__1(X2770)
| c_Groups_Otimes__class_Otimes(X2770,c_Groups_Ozero__class_Ozero(X2770),X2769) = c_Groups_Ozero__class_Ozero(X2770) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).
fof(i_0_2461,plain,
! [X2703,X2704] :
( ~ class_Rings_Omult__zero(X2704)
| c_Groups_Otimes__class_Otimes(X2704,c_Groups_Ozero__class_Ozero(X2704),X2703) = c_Groups_Ozero__class_Ozero(X2704) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2462,plain,
! [X5004,X5005] :
( ~ class_Divides_Osemiring__div(X5005)
| c_Divides_Odiv__class_Omod(X5005,X5004,c_Groups_Oone__class_Oone(X5005)) = c_Groups_Ozero__class_Ozero(X5005) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).
fof(i_0_2463,plain,
! [X4246,X4247] :
( ~ class_Rings_Odivision__ring__inverse__zero(X4247)
| c_Rings_Oinverse__class_Odivide(X4247,X4246,c_Groups_Ozero__class_Ozero(X4247)) = c_Groups_Ozero__class_Ozero(X4247) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).
fof(i_0_2464,plain,
! [X2820,X2821] :
( ~ class_RealVector_Oreal__normed__algebra(X2821)
| c_Groups_Otimes__class_Otimes(X2821,X2820,c_Groups_Ozero__class_Ozero(X2821)) = c_Groups_Ozero__class_Ozero(X2821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2465,plain,
! [X2818,X2819] :
( ~ class_RealVector_Oreal__normed__algebra(X2819)
| c_Groups_Otimes__class_Otimes(X2819,X2818,c_Groups_Ozero__class_Ozero(X2819)) = c_Groups_Ozero__class_Ozero(X2819) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2466,plain,
! [X2767,X2768] :
( ~ class_Rings_Ocomm__semiring__1(X2768)
| c_Groups_Otimes__class_Otimes(X2768,X2767,c_Groups_Ozero__class_Ozero(X2768)) = c_Groups_Ozero__class_Ozero(X2768) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).
fof(i_0_2467,plain,
! [X2705,X2706] :
( ~ class_Rings_Omult__zero(X2706)
| c_Groups_Otimes__class_Otimes(X2706,X2705,c_Groups_Ozero__class_Ozero(X2706)) = c_Groups_Ozero__class_Ozero(X2706) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2468,plain,
! [X4231,X4232] :
( ~ class_Rings_Odivision__ring(X4232)
| X4231 = c_Groups_Ozero__class_Ozero(X4232)
| c_Rings_Oinverse__class_Odivide(X4232,X4231,X4231) = c_Groups_Oone__class_Oone(X4232) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
fof(i_0_2469,plain,
! [X3451] :
( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3451)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1491])]) ).
fof(i_0_2470,plain,
! [X4372,X4373] :
( ~ class_Rings_Ocomm__semiring__1(X4373)
| c_Power_Opower__class_Opower(X4373,X4372,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4373) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).
fof(i_0_2471,plain,
! [X4370,X4371] :
( ~ class_Power_Opower(X4371)
| c_Power_Opower__class_Opower(X4371,X4370,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4371) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2472,plain,
! [X3786,X3787] :
( ~ class_Groups_Ocomm__monoid__add(X3787)
| c_Groups_Oplus__class_Oplus(X3787,c_Groups_Ozero__class_Ozero(X3787),X3786) = X3786 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2473,plain,
! [X3784,X3785] :
( ~ class_Groups_Omonoid__add(X3785)
| c_Groups_Oplus__class_Oplus(X3785,c_Groups_Ozero__class_Ozero(X3785),X3784) = X3784 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2474,plain,
! [X3038,X3039] :
( ~ class_Rings_Ocomm__semiring__1(X3039)
| c_Groups_Oplus__class_Oplus(X3039,c_Groups_Ozero__class_Ozero(X3039),X3038) = X3038 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2475,plain,
! [X4215,X4216] :
( ~ class_Groups_Ocomm__monoid__mult(X4216)
| c_Groups_Otimes__class_Otimes(X4216,c_Groups_Oone__class_Oone(X4216),X4215) = X4215 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2476,plain,
! [X4270,X4271] :
( ~ class_Rings_Ocomm__semiring__1(X4271)
| c_Groups_Otimes__class_Otimes(X4271,c_Groups_Oone__class_Oone(X4271),X4270) = X4270 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).
fof(i_0_2477,plain,
! [X4213,X4214] :
( ~ class_Groups_Omonoid__mult(X4214)
| c_Groups_Otimes__class_Otimes(X4214,c_Groups_Oone__class_Oone(X4214),X4213) = X4213 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2478,plain,
! [X4967,X4968] :
( ~ class_Divides_Osemiring__div(X4968)
| c_Divides_Odiv__class_Omod(X4968,X4967,c_Groups_Ozero__class_Ozero(X4968)) = X4967 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).
fof(i_0_2479,plain,
! [X4289,X4290] :
( ~ class_Rings_Odivision__ring(X4290)
| c_Rings_Oinverse__class_Odivide(X4290,X4289,c_Groups_Oone__class_Oone(X4290)) = X4289 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(i_0_2480,plain,
! [X3792,X3793] :
( ~ class_Groups_Ocomm__monoid__add(X3793)
| c_Groups_Oplus__class_Oplus(X3793,X3792,c_Groups_Ozero__class_Ozero(X3793)) = X3792 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2481,plain,
! [X3790,X3791] :
( ~ class_Groups_Omonoid__add(X3791)
| c_Groups_Oplus__class_Oplus(X3791,X3790,c_Groups_Ozero__class_Ozero(X3791)) = X3790 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2482,plain,
! [X3036,X3037] :
( ~ class_Rings_Ocomm__semiring__1(X3037)
| c_Groups_Oplus__class_Oplus(X3037,X3036,c_Groups_Ozero__class_Ozero(X3037)) = X3036 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2483,plain,
! [X4219,X4220] :
( ~ class_Groups_Ocomm__monoid__mult(X4220)
| c_Groups_Otimes__class_Otimes(X4220,X4219,c_Groups_Oone__class_Oone(X4220)) = X4219 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2484,plain,
! [X4268,X4269] :
( ~ class_Rings_Ocomm__semiring__1(X4269)
| c_Groups_Otimes__class_Otimes(X4269,X4268,c_Groups_Oone__class_Oone(X4269)) = X4268 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).
fof(i_0_2485,plain,
! [X4217,X4218] :
( ~ class_Groups_Omonoid__mult(X4218)
| c_Groups_Otimes__class_Otimes(X4218,X4217,c_Groups_Oone__class_Oone(X4218)) = X4217 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2486,plain,
! [X4278,X4279] :
( ~ class_Rings_Ocomm__semiring__1(X4279)
| c_Power_Opower__class_Opower(X4279,X4278,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4278 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).
fof(i_0_2487,plain,
! [X4276,X4277] :
( ~ class_Groups_Omonoid__mult(X4277)
| c_Power_Opower__class_Opower(X4277,X4276,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4276 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2488,plain,
! [X4965,X4966] :
( ~ class_Divides_Osemiring__div(X4966)
| c_Divides_Odiv__class_Omod(X4966,X4965,X4965) = c_Groups_Ozero__class_Ozero(X4966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).
fof(i_0_2489,plain,
! [X3983,X3984,X3985] :
( ~ class_Orderings_Opreorder(X3985)
| X3984 != X3983
| c_Orderings_Oord__class_Oless__eq(X3985,X3984,X3983) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2490,plain,
! [X5002,X5003] :
( ~ class_Int_Onumber__ring(X5003)
| ~ class_RealVector_Oreal__algebra__1(X5003)
| c_RealVector_Oof__real(X5003,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X5002)) = c_Int_Onumber__class_Onumber__of(X5003,X5002) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__number__of__eq])]) ).
fof(i_0_2491,plain,
! [X3939,X3940] :
( ~ class_Orderings_Opreorder(X3940)
| c_Orderings_Oord__class_Oless__eq(X3940,X3939,X3939) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
cnf(i_0_2492,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_2493,plain,
! [X4221,X4222] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4222)
| c_Groups_Oabs__class_Oabs(X4222,c_Groups_Oabs__class_Oabs(X4222,X4221)) = c_Groups_Oabs__class_Oabs(X4222,X4221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_2494,plain,
! [X2613,X2614,X2615] :
( ( c_Int_Onumber__class_Onumber__of(X2615,X2614) != c_Int_Onumber__class_Onumber__of(X2615,X2613)
| X2614 = X2613
| ~ class_Int_Onumber__ring(X2615)
| ~ class_Int_Oring__char__0(X2615) )
& ( X2614 != X2613
| c_Int_Onumber__class_Onumber__of(X2615,X2614) = c_Int_Onumber__class_Onumber__of(X2615,X2613)
| ~ class_Int_Onumber__ring(X2615)
| ~ class_Int_Oring__char__0(X2615) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).
fof(i_0_2495,plain,
! [X3096] :
( X3096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2496,plain,
! [X4629,X4630] :
( ~ class_RealVector_Oreal__normed__vector(X4630)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4630,X4629)) = c_RealVector_Onorm__class_Onorm(X4630,X4629) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(i_0_2497,plain,
! [X4896,X4897] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4897)
| c_RealVector_Onorm__class_Onorm(X4897,c_RealVector_Oof__real(X4897,X4896)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4896) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(i_0_2498,plain,
! [X4964] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4964) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).
fof(i_0_2499,plain,
! [X2608] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2608) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2500,plain,
! [X2607] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2607,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_2501,plain,
! [X3082] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3082) = X3082,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2502,plain,
! [X3080] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3080) = X3080,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2503,plain,
! [X4235] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4235) = X4235,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2504,plain,
! [X4287] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4287) = X4287,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2505,plain,
! [X4285] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X4285) = X4285,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2506,plain,
! [X3081] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3081,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X3081,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2507,plain,
! [X3079] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3079,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3079,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2508,plain,
! [X4286] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,X4286,c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4286,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2509,plain,
! [X4282] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X4282,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4282,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2510,plain,
! [X3642,X3643] :
( X3643 != X3642
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3643,X3642) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2511,plain,
! [X3108] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3108),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2512,plain,
! [X2827] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2827),
inference(variable_rename,[status(thm)],[fact_le0]) ).
cnf(i_0_2513,plain,
( c_Int_OBit0(X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(split_conjunct,[status(thm)],[i_0_1486]) ).
cnf(i_0_2514,plain,
( c_Int_OPls = c_Int_OBit0(X1)
| c_Int_OPls != X1 ),
inference(split_conjunct,[status(thm)],[i_0_1485]) ).
fof(i_0_2515,plain,
! [X4963] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X4963,X4963) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zmod__self]) ).
fof(i_0_2516,plain,
! [X4208] :
( ~ class_Int_Onumber__ring(X4208)
| ~ class_Rings_Olinordered__idom(X4208)
| c_Groups_Oabs__class_Oabs(X4208,c_Int_Onumber__class_Onumber__of(X4208,c_Int_OMin)) = c_Groups_Oone__class_Oone(X4208) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).
fof(i_0_2517,plain,
! [X4977,X4978,X4979] :
( ( c_RealVector_Oof__real(X4979,X4978) != c_RealVector_Oof__real(X4979,X4977)
| X4978 = X4977
| ~ class_RealVector_Oreal__algebra__1(X4979) )
& ( X4978 != X4977
| c_RealVector_Oof__real(X4979,X4978) = c_RealVector_Oof__real(X4979,X4977)
| ~ class_RealVector_Oreal__algebra__1(X4979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__iff])])]) ).
fof(i_0_2518,plain,
! [X3935] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3935,X3935),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2519,plain,
! [X3582] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3582,X3582),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2520,plain,
! [X3581] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3581,X3581),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2521,plain,
! [X3083] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X3083) = X3083,
inference(variable_rename,[status(thm)],[fact_add__Pls]) ).
fof(i_0_2522,plain,
! [X3084] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3084,c_Int_OPls) = X3084,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(i_0_2523,plain,
! [X2590] : c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X2590) = c_Int_OPls,
inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).
cnf(i_0_2524,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).
fof(i_0_2525,plain,
! [X4225,X4226] :
( ( c_Groups_Oabs__class_Oabs(X4226,X4225) != c_Groups_Ozero__class_Ozero(X4226)
| X4225 = c_Groups_Ozero__class_Ozero(X4226)
| ~ class_Groups_Oordered__ab__group__add__abs(X4226) )
& ( X4225 != c_Groups_Ozero__class_Ozero(X4226)
| c_Groups_Oabs__class_Oabs(X4226,X4225) = c_Groups_Ozero__class_Ozero(X4226)
| ~ class_Groups_Oordered__ab__group__add__abs(X4226) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_2526,plain,
! [X4958,X4959] :
( ( c_RealVector_Oof__real(X4959,X4958) != c_Groups_Ozero__class_Ozero(X4959)
| X4958 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X4959) )
& ( X4958 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X4959,X4958) = c_Groups_Ozero__class_Ozero(X4959)
| ~ class_RealVector_Oreal__algebra__1(X4959) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__0__iff])])]) ).
fof(i_0_2527,plain,
! [X4632,X4633] :
( ( c_RealVector_Onorm__class_Onorm(X4633,X4632) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X4632 = c_Groups_Ozero__class_Ozero(X4633)
| ~ class_RealVector_Oreal__normed__vector(X4633) )
& ( X4632 != c_Groups_Ozero__class_Ozero(X4633)
| c_RealVector_Onorm__class_Onorm(X4633,X4632) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X4633) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2528,plain,
! [X5087,X5088] :
( ~ class_Orderings_Oorder(X5088)
| class_Orderings_Oorder(tc_fun(X5087,X5088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2529,plain,
! [X5089,X5090] :
( ~ class_Orderings_Oord(X5090)
| class_Orderings_Oord(tc_fun(X5089,X5090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2530,plain,
! [X5085,X5086] :
( ~ class_Orderings_Opreorder(X5086)
| class_Orderings_Opreorder(tc_fun(X5085,X5086)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2531,plain,
! [X4957] :
( ~ class_RealVector_Oreal__algebra__1(X4957)
| ~ class_RealVector_Oreal__normed__vector(X4957)
| c_RealVector_Oof__real(X4957,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X4957) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ozero])]) ).
fof(i_0_2532,plain,
! [X4288] :
( ~ class_Rings_Olinordered__idom(X4288)
| c_Groups_Oabs__class_Oabs(X4288,c_Groups_Oone__class_Oone(X4288)) = c_Groups_Oone__class_Oone(X4288) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_2533,plain,
! [X4227] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4227)
| c_Groups_Oabs__class_Oabs(X4227,c_Groups_Ozero__class_Ozero(X4227)) = c_Groups_Ozero__class_Ozero(X4227) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_2534,plain,
! [X4649] :
( ~ class_RealVector_Oreal__normed__algebra__1(X4649)
| c_RealVector_Onorm__class_Onorm(X4649,c_Groups_Oone__class_Oone(X4649)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__one])]) ).
fof(i_0_2535,plain,
! [X4631] :
( ~ class_RealVector_Oreal__normed__vector(X4631)
| c_RealVector_Onorm__class_Onorm(X4631,c_Groups_Ozero__class_Ozero(X4631)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__zero])]) ).
fof(i_0_2536,plain,
! [X5006] :
( ~ class_RealVector_Oreal__algebra__1(X5006)
| c_RealVector_Oof__real(X5006,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X5006) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])]) ).
fof(i_0_2537,plain,
! [X4956] :
( ~ class_RealVector_Oreal__algebra__1(X4956)
| c_RealVector_Oof__real(X4956,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X4956) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__0])]) ).
fof(i_0_2538,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_2539,plain,
! [X4889] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4889) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4889),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(i_0_2540,plain,
! [X2609] :
( ~ class_Int_Onumber__ring(X2609)
| c_Int_Onumber__class_Onumber__of(X2609,c_Int_OPls) = c_Groups_Ozero__class_Ozero(X2609) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).
fof(i_0_2541,plain,
! [X2610] :
( ~ class_Int_Onumber__ring(X2610)
| c_Groups_Ozero__class_Ozero(X2610) = c_Int_Onumber__class_Onumber__of(X2610,c_Int_OPls) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).
fof(i_0_2542,plain,
! [X4267] :
( ~ class_Rings_Ozero__neq__one(X4267)
| c_Groups_Ozero__class_Ozero(X4267) != c_Groups_Oone__class_Oone(X4267) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2543,plain,
! [X4266] :
( ~ class_Rings_Ozero__neq__one(X4266)
| c_Groups_Oone__class_Oone(X4266) != c_Groups_Ozero__class_Ozero(X4266) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2544,plain,
! [X3956] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X3956),
inference(variable_rename,[status(thm)],[fact_complex__i__not__number__of]) ).
fof(i_0_2545,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(fof_simplification,[status(thm)],[fact_o]) ).
fof(i_0_2546,plain,
! [X3949,X3950] :
( ( c_NthRoot_Osqrt(X3950) != c_NthRoot_Osqrt(X3949)
| X3950 = X3949 )
& ( X3950 != X3949
| c_NthRoot_Osqrt(X3950) = c_NthRoot_Osqrt(X3949) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__iff])]) ).
fof(i_0_2547,plain,
! [X4205] :
( ( c_NthRoot_Osqrt(X4205) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X4205 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( X4205 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X4205) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff])]) ).
fof(i_0_2548,plain,
! [X3955] :
( ( c_NthRoot_Osqrt(X3955) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3955 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3955 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X3955) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__0__iff])]) ).
fof(i_0_2549,plain,
! [X2732] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X2732) = X2732,
inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).
cnf(i_0_2550,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(tc_RealDef_Oreal,X4,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_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_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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(tc_RealDef_Oreal,X4,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)],[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_1492,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2551,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X4),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_NthRoot_Osqrt(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,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_NthRoot_Osqrt(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,X4,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1495,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2552,plain,
c_Transcendental_Oarctan(X1) = 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))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(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)))))))))),
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_1496,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2553,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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_Oone__class_Oone(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_1497,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2554,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,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(tc_RealDef_Oreal,X4,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)],[i_0_1498,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2555,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(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,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)))))),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_NthRoot_Osqrt(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))))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,c_NthRoot_Osqrt(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)))))) ),
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_1499,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2556,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(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,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)))))),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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,X3,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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))))) ),
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_1500,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2557,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_NthRoot_Osqrt(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))))))),
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_1501,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2558,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_NthRoot_Osqrt(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))))))),
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_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2559,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(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))))))),
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_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2560,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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))))))),
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_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2561,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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))))))),
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_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2562,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_1506,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2563,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_1507,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2564,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_1508,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2565,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_1510,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2566,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_1511,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2567,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_1512,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2568,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_1513,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2569,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(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)))))) != 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_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2570,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(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)))))) != 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_1515,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2571,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_1516,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2572,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_1517,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2573,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_1518,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2574,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_1519,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2575,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_1520,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2576,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_1521,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2577,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_1522,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2578,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_1523,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2579,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_1524,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2580,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_1525,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2581,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_1526,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2582,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_1527,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2583,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_1528,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2584,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_1529,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2585,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_1530,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2586,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_1531,c_0_1493]),c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2587,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_1532,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2588,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_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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3)
| X1 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,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))),X3)) ),
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_1533,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2589,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_1534,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2590,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_1535,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2591,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_1536,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2592,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_1537,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2593,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1538,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2594,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1539,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2595,plain,
( X1 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,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))),X3))
| 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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3) ),
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_1540,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2596,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_1541,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2597,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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))))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1542,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2598,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_1543,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2599,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_1544,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2600,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_1545,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2601,negated_conjecture,
v_na____ != 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1546,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2602,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_1547,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2603,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_1548,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2604,plain,
( c_Groups_Oabs__class_Oabs(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,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1549,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2605,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_1550,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),
[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,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_1551,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2607,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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)))),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1552,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2608,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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)))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1553,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2609,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_1554,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2610,plain,
( c_Orderings_Oord__class_Oless(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_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1555,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2611,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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)))))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1556,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2612,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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)))))
| ~ class_Int_Onumber__ring(X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1557,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2613,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(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_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1558,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2614,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1559,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2615,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_1560,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2616,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))),esk1_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_1561,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2617,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_1562,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2618,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_1563,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2619,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_1564,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2620,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(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,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1565,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2621,plain,
c_NthRoot_Osqrt(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_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1566,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2622,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_1567,c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2623,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(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))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1568,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2624,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(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))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1569,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2625,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(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))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1570,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2626,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_1571,c_0_1509]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2627,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_1572,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2628,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_1573,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2629,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_1574,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2630,plain,
( c_NthRoot_Osqrt(X2) = X1
| 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)))) != X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1575,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2631,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(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_1576,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2632,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_1577,c_0_1493]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2633,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_1578,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2634,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_1579,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2635,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_1580,c_0_1493]),c_0_1493]),c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2636,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk9_4(X3,X2,X4,X1)),hAPP(X3,esk9_4(X3,X2,X4,X1)))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_2637,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_1582,c_0_1493]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2638,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_1583,c_0_1493]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2639,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_1584,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2640,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(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
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1585,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2641,plain,
( c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(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
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1586,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2642,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_1587,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2643,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_1588,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2644,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_1589,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2645,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_1590,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2646,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_1591,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2647,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_1592,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2648,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_1593,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2649,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_1594,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2650,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_1595,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2651,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_1596,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2652,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_Complex_Oii,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_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1597,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2653,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_1598,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2654,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_1599,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2655,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_1600,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2656,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_1601,c_0_1509]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2657,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,esk11_1(X1),X1)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,v_na____) ),
inference(split_conjunct,[status(thm)],[i_0_1602]),
[final] ).
cnf(i_0_2658,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_1603,c_0_1493]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2659,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_1604,c_0_1493]),c_0_1509]),c_0_1509]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2660,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,v_b,c_Power_Opower__class_Opower(tc_Complex_Ocomplex,esk12_0,v_na____)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____) ),
inference(split_conjunct,[status(thm)],[i_0_1605]),
[final] ).
cnf(i_0_2661,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_1606]),
[final] ).
cnf(i_0_2662,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_1607]),
[final] ).
cnf(i_0_2663,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_1608,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2664,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_1609,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2665,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_1610]),
[final] ).
cnf(i_0_2666,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_1611]),
[final] ).
cnf(i_0_2667,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_1612,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2668,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_1613,c_0_1509]),c_0_1509]),
[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_1614,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2670,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_1615,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2671,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_1616,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2672,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_1617,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2673,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_1618,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2674,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_1619,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2675,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_1620]),
[final] ).
cnf(i_0_2676,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_1621]),
[final] ).
cnf(i_0_2677,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(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)))),
inference(split_conjunct,[status(thm)],[i_0_1622]),
[final] ).
cnf(i_0_2678,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_NthRoot_Osqrt(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)))),
inference(split_conjunct,[status(thm)],[i_0_1623]),
[final] ).
cnf(i_0_2679,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk14_3(X1,X2,X3)),esk15_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2680,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_1625]),
[final] ).
cnf(i_0_2681,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_1626]),
[final] ).
cnf(i_0_2682,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_1627]),
[final] ).
cnf(i_0_2683,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_1628]),
[final] ).
cnf(i_0_2684,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2685,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2686,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2687,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2688,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk14_3(X1,X2,X3)),esk15_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2689,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2690,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2691,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2692,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2693,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ 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,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2694,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ 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,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2695,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2696,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2697,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X5,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),c_Groups_Otimes__class_Otimes(X1,X5,X2)),c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1637]),
[final] ).
cnf(i_0_2698,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2699,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2700,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2701,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2702,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk15_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2703,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk14_3(X2,X3,X1)),esk15_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2704,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_1638]),
[final] ).
cnf(i_0_2705,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_1639,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2706,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_1640,c_0_1493]),c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2707,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_1641,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2708,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_1642]),
[final] ).
cnf(i_0_2709,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_1642]),
[final] ).
cnf(i_0_2710,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_1643]),
[final] ).
cnf(i_0_2711,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk15_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2712,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X3,esk14_3(X2,X3,X1)),esk15_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2713,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2714,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)),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)],[i_0_1644,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2715,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_1645]),
[final] ).
cnf(i_0_2716,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_1646]),
[final] ).
cnf(i_0_2717,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_1647]),
[final] ).
cnf(i_0_2718,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_1648,c_0_1494]),
[final] ).
cnf(i_0_2719,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_1649,c_0_1494]),
[final] ).
cnf(i_0_2720,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_1650,c_0_1494]),
[final] ).
cnf(i_0_2721,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_1651]),
[final] ).
cnf(i_0_2722,plain,
( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,esk15_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2723,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_1652]),
[final] ).
cnf(i_0_2724,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_1653,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2725,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_1654,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2726,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_1655,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2727,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_1656,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2728,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_1657,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2729,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_1658,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2730,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_1659,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2731,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_1660,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2732,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_1661]),
[final] ).
cnf(i_0_2733,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_1662,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2734,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_1663,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2735,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2736,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2737,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2738,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2739,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2740,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2741,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2742,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2743,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_1664,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2744,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_1665,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2745,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_1666,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2746,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_1667,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_2747,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_1668,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2748,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_1669,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2749,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2750,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2751,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2752,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2753,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2754,plain,
( c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2755,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2756,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2757,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_1674]),
[final] ).
cnf(i_0_2758,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_1675]),
[final] ).
cnf(i_0_2759,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2760,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2761,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2762,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ 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,X2,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2763,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ 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,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2764,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ 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,c_Int_Onumber__class_Onumber__of(X1,X3)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2765,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X4))
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2766,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X4))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X4)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2767,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk14_3(X1,X2,X3)),esk15_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2768,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2769,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X1,X2,X3),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2770,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk14_3(X2,X1,X3)),esk15_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2771,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2772,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2773,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2774,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2775,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2776,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2777,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2778,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2779,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))),X3)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1676]),
[final] ).
cnf(i_0_2780,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1))))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1677]),
[final] ).
cnf(i_0_2781,plain,
( c_Rings_Oinverse__class_Odivide(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)
| ~ class_Fields_Ofield(X1) ),
inference(rw,[status(thm)],[i_0_1678,c_0_1494]),
[final] ).
cnf(i_0_2782,plain,
( c_Rings_Oinverse__class_Odivide(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)
| ~ class_Fields_Ofield(X1) ),
inference(rw,[status(thm)],[i_0_1679,c_0_1494]),
[final] ).
cnf(i_0_2783,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ 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_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1680]),
[final] ).
cnf(i_0_2784,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1681]),
[final] ).
cnf(i_0_2785,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1682]),
[final] ).
cnf(i_0_2786,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Otimes__class_Otimes(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1683]),
[final] ).
cnf(i_0_2787,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_1684,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2788,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_1685,c_0_1494]),
[final] ).
cnf(i_0_2789,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_1686,c_0_1494]),
[final] ).
cnf(i_0_2790,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2791,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2792,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2793,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2794,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2795,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2796,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2797,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2798,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk14_3(X1,X2,X3)),esk15_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2799,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2800,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2801,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| X2 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X1,esk14_3(X2,X1,X3)),esk15_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2802,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2803,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2804,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2805,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2806,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_1687,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2807,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_1688,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2808,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X2)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2))),
inference(split_conjunct,[status(thm)],[i_0_1689]),
[final] ).
cnf(i_0_2809,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_1690,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2810,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_1691]),
[final] ).
cnf(i_0_2811,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2812,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2813,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2814,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2815,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_1692,c_0_1494]),
[final] ).
cnf(i_0_2816,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_1693,c_0_1494]),
[final] ).
cnf(i_0_2817,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_1694,c_0_1494]),
[final] ).
cnf(i_0_2818,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_1695,c_0_1494]),
[final] ).
cnf(i_0_2819,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_1696]),
[final] ).
cnf(i_0_2820,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_1697]),
[final] ).
cnf(i_0_2821,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_1698]),
[final] ).
cnf(i_0_2822,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_1699,c_0_1494]),
[final] ).
cnf(i_0_2823,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X4)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3,X5))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1700]),
[final] ).
cnf(i_0_2824,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X5))
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_2825,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_1702]),
[final] ).
cnf(i_0_2826,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_1703]),
[final] ).
cnf(i_0_2827,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_1704]),
[final] ).
cnf(i_0_2828,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk15_3(X1,X2,X3)))
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2829,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X2,X3,X1))
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2830,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X2,X3,X1),X3)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2831,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk15_3(X2,X1,X3)))
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2832,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_1705,c_0_1494]),
[final] ).
cnf(i_0_2833,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_1706,c_0_1494]),
[final] ).
cnf(i_0_2834,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_1707,c_0_1494]),
[final] ).
cnf(i_0_2835,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_1708,c_0_1494]),
[final] ).
cnf(i_0_2836,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_1709,c_0_1494]),
[final] ).
cnf(i_0_2837,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_1710,c_0_1494]),
[final] ).
cnf(i_0_2838,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_1711,c_0_1494]),
[final] ).
cnf(i_0_2839,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_1712,c_0_1494]),
[final] ).
cnf(i_0_2840,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1713]),
[final] ).
cnf(i_0_2841,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ 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__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1714]),
[final] ).
cnf(i_0_2842,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_1715]),
[final] ).
cnf(i_0_2843,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_1716]),
[final] ).
cnf(i_0_2844,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_1717]),
[final] ).
cnf(i_0_2845,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_1718]),
[final] ).
cnf(i_0_2846,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X5),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1719]),
[final] ).
cnf(i_0_2847,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_1720]),
[final] ).
cnf(i_0_2848,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_1721]),
[final] ).
cnf(i_0_2849,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2850,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,esk14_3(X2,X1,X3)),esk15_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2851,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_1722,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2852,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Int_Onumber__class_Onumber__of(X1,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2853,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Int_Onumber__class_Onumber__of(X1,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2854,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ 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,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2855,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2856,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X4)),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X4),X5) ),
inference(split_conjunct,[status(thm)],[i_0_1723]),
[final] ).
cnf(i_0_2857,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,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2858,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,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2859,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_1642]),
[final] ).
cnf(i_0_2860,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_2861,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X3),X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_2862,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Int_Onumber__class_Onumber__of(X1,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_2863,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X4),X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Int_Onumber__class_Onumber__of(X1,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_2864,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_1638]),
[final] ).
cnf(i_0_2865,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_1638]),
[final] ).
cnf(i_0_2866,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,esk15_3(X1,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2867,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X2,X3,X1))
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2868,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X2,X3,X1),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2869,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,esk15_3(X2,X1,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2870,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_1724]),
[final] ).
cnf(i_0_2871,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_1725,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2872,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_1726,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2873,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_1727,c_0_1494]),
[final] ).
cnf(i_0_2874,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk16_3(X1,X2,X3)),esk17_3(X1,X2,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,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2875,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,esk14_3(X2,X1,X3)),esk15_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2876,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_1728,c_0_1509]),
[final] ).
cnf(i_0_2877,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_1729]),
[final] ).
cnf(i_0_2878,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_2879,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(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(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_2880,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_2881,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(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(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2882,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_1730,c_0_1509]),
[final] ).
cnf(i_0_2883,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2884,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2885,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2886,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2887,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2888,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2889,plain,
( c_Orderings_Oord__class_Oless(X1,X3,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2890,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2891,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,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,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2892,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless__eq(X1,X4,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2893,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2894,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2895,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2896,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,c_Groups_Otimes__class_Otimes(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2897,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2898,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ 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,X2,X3),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2899,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_1731]),
[final] ).
cnf(i_0_2900,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_1732]),
[final] ).
cnf(i_0_2901,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_1733]),
[final] ).
cnf(i_0_2902,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_1734]),
[final] ).
cnf(i_0_2903,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_1735]),
[final] ).
cnf(i_0_2904,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_1736]),
[final] ).
cnf(i_0_2905,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_1737]),
[final] ).
cnf(i_0_2906,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_1738]),
[final] ).
cnf(i_0_2907,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_1739]),
[final] ).
cnf(i_0_2908,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_1740]),
[final] ).
cnf(i_0_2909,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_1741]),
[final] ).
cnf(i_0_2910,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_1742]),
[final] ).
cnf(i_0_2911,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_1743]),
[final] ).
cnf(i_0_2912,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_1744]),
[final] ).
cnf(i_0_2913,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_1745]),
[final] ).
cnf(i_0_2914,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_1746]),
[final] ).
cnf(i_0_2915,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_1747]),
[final] ).
cnf(i_0_2916,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_1702]),
[final] ).
cnf(i_0_2917,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_1748,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2918,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_1749,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2919,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_1750,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2920,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_1751,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2921,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_1752,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2922,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_1753,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2923,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_1754,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2924,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_1755,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_2925,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_1756]),
[final] ).
cnf(i_0_2926,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_1757]),
[final] ).
cnf(i_0_2927,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_1758]),
[final] ).
cnf(i_0_2928,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_1759]),
[final] ).
cnf(i_0_2929,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_1760]),
[final] ).
cnf(i_0_2930,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_1761]),
[final] ).
cnf(i_0_2931,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_1762]),
[final] ).
cnf(i_0_2932,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_1763]),
[final] ).
cnf(i_0_2933,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_1764]),
[final] ).
cnf(i_0_2934,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_1765]),
[final] ).
cnf(i_0_2935,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_1766]),
[final] ).
cnf(i_0_2936,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_1767]),
[final] ).
cnf(i_0_2937,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_1768]),
[final] ).
cnf(i_0_2938,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4)),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1769]),
[final] ).
cnf(i_0_2939,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2)),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1770]),
[final] ).
cnf(i_0_2940,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4),X2)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1771]),
[final] ).
cnf(i_0_2941,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,X2)),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1772]),
[final] ).
cnf(i_0_2942,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_1647]),
[final] ).
cnf(i_0_2943,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_1646]),
[final] ).
cnf(i_0_2944,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_1773]),
[final] ).
cnf(i_0_2945,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_1768]),
[final] ).
cnf(i_0_2946,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_1767]),
[final] ).
cnf(i_0_2947,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_1767]),
[final] ).
cnf(i_0_2948,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_1768]),
[final] ).
cnf(i_0_2949,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X5)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),c_Groups_Otimes__class_Otimes(X1,X3,X5))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1774]),
[final] ).
cnf(i_0_2950,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_1775]),
[final] ).
cnf(i_0_2951,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_1776]),
[final] ).
cnf(i_0_2952,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_1777]),
[final] ).
cnf(i_0_2953,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_1778]),
[final] ).
cnf(i_0_2954,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_1779]),
[final] ).
cnf(i_0_2955,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_1780]),
[final] ).
cnf(i_0_2956,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_1781]),
[final] ).
cnf(i_0_2957,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_1782]),
[final] ).
cnf(i_0_2958,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_1783]),
[final] ).
cnf(i_0_2959,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2960,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| epred1_3(X2,X1,X3)
| ~ hBOOL(hAPP(X2,esk15_3(X3,X1,X2)))
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_2961,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_1784,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_2962,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_1768]),
[final] ).
cnf(i_0_2963,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_1767]),
[final] ).
cnf(i_0_2964,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_1702]),
[final] ).
cnf(i_0_2965,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_1785]),
[final] ).
cnf(i_0_2966,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_1786]),
[final] ).
cnf(i_0_2967,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_1787]),
[final] ).
cnf(i_0_2968,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_1788,c_0_1493]),c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_2969,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_1789]),
[final] ).
cnf(i_0_2970,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_1790]),
[final] ).
cnf(i_0_2971,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_1791]),
[final] ).
cnf(i_0_2972,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_2973,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1793]),
[final] ).
cnf(i_0_2974,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2975,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_2976,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2977,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_2978,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1796]),
[final] ).
cnf(i_0_2979,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2980,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X4),X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X4)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_2981,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2982,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_2983,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1798]),
[final] ).
cnf(i_0_2984,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_2985,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1799]),
[final] ).
cnf(i_0_2986,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1794]),
[final] ).
cnf(i_0_2987,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1792]),
[final] ).
cnf(i_0_2988,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(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),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1800]),
[final] ).
cnf(i_0_2989,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ 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),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2990,plain,
( c_Orderings_Oord__class_Oless(X1,X3,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,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_2991,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1797]),
[final] ).
cnf(i_0_2992,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Otimes__class_Otimes(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1795]),
[final] ).
cnf(i_0_2993,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1801]),
[final] ).
cnf(i_0_2994,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2995,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,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__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_2996,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_2997,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1802]),
[final] ).
cnf(i_0_2998,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Otimes__class_Otimes(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_2999,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Otimes__class_Otimes(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X4,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1803]),
[final] ).
cnf(i_0_3000,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_1804,c_0_1494]),
[final] ).
cnf(i_0_3001,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_1805,c_0_1494]),
[final] ).
cnf(i_0_3002,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_1806,c_0_1494]),
[final] ).
cnf(i_0_3003,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_1807,c_0_1494]),
[final] ).
cnf(i_0_3004,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),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_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3005,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3006,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),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_3007,plain,
( c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_3008,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_1808,c_0_1494]),c_0_1494]),
[final] ).
cnf(i_0_3009,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_1809,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3010,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1810]),
[final] ).
cnf(i_0_3011,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1811]),
[final] ).
cnf(i_0_3012,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1812]),
[final] ).
cnf(i_0_3013,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
| X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,esk17_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3014,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,X1,X3)
| ~ hBOOL(hAPP(X2,esk15_3(X3,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3015,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1629]),
[final] ).
cnf(i_0_3016,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1630]),
[final] ).
cnf(i_0_3017,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1631]),
[final] ).
cnf(i_0_3018,plain,
( c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X3),c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X3)))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_3019,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_1813,c_0_1509]),
[final] ).
cnf(i_0_3020,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_1814]),
[final] ).
cnf(i_0_3021,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_1815]),
[final] ).
cnf(i_0_3022,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_1816]),
[final] ).
cnf(i_0_3023,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_1817]),
[final] ).
cnf(i_0_3024,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_1818]),
[final] ).
cnf(i_0_3025,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_1819]),
[final] ).
cnf(i_0_3026,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_1820]),
[final] ).
cnf(i_0_3027,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_1821]),
[final] ).
cnf(i_0_3028,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_1822]),
[final] ).
cnf(i_0_3029,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_1823,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3030,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_1824,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3031,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_1825,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3032,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_1826]),
[final] ).
cnf(i_0_3033,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_1827]),
[final] ).
cnf(i_0_3034,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,c_RealVector_Onorm__class_Onorm(X1,X4))) ),
inference(split_conjunct,[status(thm)],[i_0_1828]),
[final] ).
cnf(i_0_3035,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_1698]),
[final] ).
cnf(i_0_3036,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_1829,c_0_1494]),
[final] ).
cnf(i_0_3037,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_1830]),
[final] ).
cnf(i_0_3038,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_1831]),
[final] ).
cnf(i_0_3039,plain,
( 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_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_1832]),
[final] ).
cnf(i_0_3040,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_1833,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3041,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_1834,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3042,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_1831]),
[final] ).
cnf(i_0_3043,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_1830]),
[final] ).
cnf(i_0_3044,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_1835]),
[final] ).
cnf(i_0_3045,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_1836,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3046,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_1837,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3047,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_1838]),
[final] ).
cnf(i_0_3048,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_1839]),
[final] ).
cnf(i_0_3049,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1633]),
[final] ).
cnf(i_0_3050,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1634]),
[final] ).
cnf(i_0_3051,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1635]),
[final] ).
cnf(i_0_3052,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1636]),
[final] ).
cnf(i_0_3053,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field(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_1840]),
[final] ).
cnf(i_0_3054,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_1767]),
[final] ).
cnf(i_0_3055,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_1841]),
[final] ).
cnf(i_0_3056,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_1768]),
[final] ).
cnf(i_0_3057,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_1842]),
[final] ).
cnf(i_0_3058,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_1843]),
[final] ).
cnf(i_0_3059,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_1736]),
[final] ).
cnf(i_0_3060,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(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_1844]),
[final] ).
cnf(i_0_3061,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_1845]),
[final] ).
cnf(i_0_3062,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_1846]),
[final] ).
cnf(i_0_3063,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_1847]),
[final] ).
cnf(i_0_3064,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_1848]),
[final] ).
cnf(i_0_3065,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_1739]),
[final] ).
cnf(i_0_3066,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X4),c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ class_Fields_Olinordered__field(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_1849]),
[final] ).
cnf(i_0_3067,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_1767]),
[final] ).
cnf(i_0_3068,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_1850]),
[final] ).
cnf(i_0_3069,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_1768]),
[final] ).
cnf(i_0_3070,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_1740]),
[final] ).
cnf(i_0_3071,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_1851]),
[final] ).
cnf(i_0_3072,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X4),c_Rings_Oinverse__class_Odivide(X1,X2,X4))
| ~ class_Fields_Olinordered__field__inverse__zero(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_1852]),
[final] ).
cnf(i_0_3073,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_1853]),
[final] ).
cnf(i_0_3074,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_1854]),
[final] ).
cnf(i_0_3075,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_1741]),
[final] ).
cnf(i_0_3076,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_1855,c_0_1494]),
[final] ).
cnf(i_0_3077,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_1856,c_0_1494]),
[final] ).
cnf(i_0_3078,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_1857,c_0_1494]),
[final] ).
cnf(i_0_3079,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_1858,c_0_1494]),
[final] ).
cnf(i_0_3080,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_1859,c_0_1494]),
[final] ).
cnf(i_0_3081,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_1860,c_0_1494]),
[final] ).
cnf(i_0_3082,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_1861,c_0_1494]),
[final] ).
cnf(i_0_3083,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_1862,c_0_1494]),
[final] ).
cnf(i_0_3084,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_1863]),
[final] ).
cnf(i_0_3085,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_1864]),
[final] ).
cnf(i_0_3086,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Power_Opower__class_Opower(X1,X2,X3)),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1865]),
[final] ).
cnf(i_0_3087,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_1866]),
[final] ).
cnf(i_0_3088,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_1742]),
[final] ).
cnf(i_0_3089,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_1867]),
[final] ).
cnf(i_0_3090,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_1744]),
[final] ).
cnf(i_0_3091,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_1868]),
[final] ).
cnf(i_0_3092,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_1869]),
[final] ).
cnf(i_0_3093,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_1870]),
[final] ).
cnf(i_0_3094,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_1871]),
[final] ).
cnf(i_0_3095,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_1872]),
[final] ).
cnf(i_0_3096,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1873]),
[final] ).
cnf(i_0_3097,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_1874]),
[final] ).
cnf(i_0_3098,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),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3099,plain,
( c_Orderings_Oord__class_Oless(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(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X2),X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_3100,plain,
( 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_3101,plain,
( 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3102,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Power_Opower__class_Opower(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Power_Opower__class_Opower(X1,X3,X4),c_Power_Opower__class_Opower(X1,X2,X4))
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1875]),
[final] ).
cnf(i_0_3103,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_1876]),
[final] ).
cnf(i_0_3104,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_1876]),
[final] ).
cnf(i_0_3105,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_1877]),
[final] ).
cnf(i_0_3106,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_1878]),
[final] ).
cnf(i_0_3107,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_1879]),
[final] ).
cnf(i_0_3108,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_1880]),
[final] ).
cnf(i_0_3109,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_1881]),
[final] ).
cnf(i_0_3110,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1882]),
[final] ).
cnf(i_0_3111,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),X4) = c_Groups_Oplus__class_Oplus(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X4),c_Rings_Oinverse__class_Odivide(X1,X3,X4))
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1883]),
[final] ).
cnf(i_0_3112,plain,
( c_Power_Opower__class_Opower(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),X4) = c_Rings_Oinverse__class_Odivide(X1,c_Power_Opower__class_Opower(X1,X2,X4),c_Power_Opower__class_Opower(X1,X3,X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1884]),
[final] ).
cnf(i_0_3113,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_1885]),
[final] ).
cnf(i_0_3114,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_1886]),
[final] ).
cnf(i_0_3115,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_1887]),
[final] ).
cnf(i_0_3116,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_1888]),
[final] ).
cnf(i_0_3117,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_1889]),
[final] ).
cnf(i_0_3118,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_1890]),
[final] ).
cnf(i_0_3119,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_1891]),
[final] ).
cnf(i_0_3120,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_1892]),
[final] ).
cnf(i_0_3121,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_1893]),
[final] ).
cnf(i_0_3122,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_1894]),
[final] ).
cnf(i_0_3123,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_1895]),
[final] ).
cnf(i_0_3124,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_1896]),
[final] ).
cnf(i_0_3125,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_1897]),
[final] ).
cnf(i_0_3126,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_1898]),
[final] ).
cnf(i_0_3127,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_1757]),
[final] ).
cnf(i_0_3128,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_1899]),
[final] ).
cnf(i_0_3129,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_1830]),
[final] ).
cnf(i_0_3130,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_1900]),
[final] ).
cnf(i_0_3131,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_1831]),
[final] ).
cnf(i_0_3132,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_1901]),
[final] ).
cnf(i_0_3133,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_1759]),
[final] ).
cnf(i_0_3134,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_1760]),
[final] ).
cnf(i_0_3135,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_1761]),
[final] ).
cnf(i_0_3136,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_1764]),
[final] ).
cnf(i_0_3137,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_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),esk15_3(X1,X2,X3))
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3138,plain,
( epred1_3(X1,X3,X2)
| ~ hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3139,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_1903]),
[final] ).
cnf(i_0_3140,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_1904]),
[final] ).
cnf(i_0_3141,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_1905]),
[final] ).
cnf(i_0_3142,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_1906]),
[final] ).
cnf(i_0_3143,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_1907]),
[final] ).
cnf(i_0_3144,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_1908]),
[final] ).
cnf(i_0_3145,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_1868]),
[final] ).
cnf(i_0_3146,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,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),X3)
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3147,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(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_Ozero__class_Ozero(X1),X3)
| ~ class_Rings_Oordered__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3148,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ 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__ring__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3149,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ 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__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1909]),
[final] ).
cnf(i_0_3150,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X1,X2,X3),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3151,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3152,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X2,X1,X3),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3153,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_1868]),
[final] ).
cnf(i_0_3154,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)),esk4_1(X1))
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_1910,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3155,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_1911]),
[final] ).
cnf(i_0_3156,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_1911]),
[final] ).
cnf(i_0_3157,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_1912]),
[final] ).
cnf(i_0_3158,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_1913,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3159,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_1914]),
[final] ).
cnf(i_0_3160,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_1915]),
[final] ).
cnf(i_0_3161,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_1916]),
[final] ).
cnf(i_0_3162,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_1917]),
[final] ).
cnf(i_0_3163,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_1918]),
[final] ).
cnf(i_0_3164,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_1919,c_0_1493]),
[final] ).
cnf(i_0_3165,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_1878]),
[final] ).
cnf(i_0_3166,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_1878]),
[final] ).
cnf(i_0_3167,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_1920]),
[final] ).
cnf(i_0_3168,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_1920]),
[final] ).
cnf(i_0_3169,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_1921]),
[final] ).
cnf(i_0_3170,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),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3171,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_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3172,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_1924]),
[final] ).
cnf(i_0_3173,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_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3174,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3175,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_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3176,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_Rings_Oinverse__class_Odivide(X1,X3,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3177,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_1924]),
[final] ).
cnf(i_0_3178,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_1924]),
[final] ).
cnf(i_0_3179,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_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3180,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_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3181,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),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3182,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),X3)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3183,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_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3184,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_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3185,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_1927]),
[final] ).
cnf(i_0_3186,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_1927]),
[final] ).
cnf(i_0_3187,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_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3188,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_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3189,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_1927]),
[final] ).
cnf(i_0_3190,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_1927]),
[final] ).
cnf(i_0_3191,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3192,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_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3193,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_1924]),
[final] ).
cnf(i_0_3194,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1670]),
[final] ).
cnf(i_0_3195,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X4,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1671]),
[final] ).
cnf(i_0_3196,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_3197,plain,
( c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless__eq(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_3198,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_1928,c_0_1509]),c_0_1494]),
[final] ).
cnf(i_0_3199,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_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),esk15_3(X1,X2,X3))
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3200,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_3(X1,X2,X3),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X1,X2,X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3201,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),esk15_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3202,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,esk15_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3203,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_1929,c_0_1493]),
[final] ).
cnf(i_0_3204,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_1930]),
[final] ).
cnf(i_0_3205,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_1931,c_0_1509]),
[final] ).
cnf(i_0_3206,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_1932,c_0_1509]),
[final] ).
cnf(i_0_3207,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_1878]),
[final] ).
cnf(i_0_3208,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_1933,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3209,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_1934,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3210,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_1878]),
[final] ).
cnf(i_0_3211,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(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_1935]),
[final] ).
cnf(i_0_3212,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(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_1936]),
[final] ).
cnf(i_0_3213,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(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)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3214,plain,
( c_Orderings_Oord__class_Oless(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),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,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1922]),
[final] ).
cnf(i_0_3215,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_1937]),
[final] ).
cnf(i_0_3216,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_1938]),
[final] ).
cnf(i_0_3217,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_1939]),
[final] ).
cnf(i_0_3218,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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_1940]),
[final] ).
cnf(i_0_3219,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field(X1)
| ~ c_Orderings_Oord__class_Oless__eq(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_1941]),
[final] ).
cnf(i_0_3220,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3221,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1923]),
[final] ).
cnf(i_0_3222,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_1942]),
[final] ).
cnf(i_0_3223,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_1943]),
[final] ).
cnf(i_0_3224,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_1944]),
[final] ).
cnf(i_0_3225,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_1943]),
[final] ).
cnf(i_0_3226,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_1924]),
[final] ).
cnf(i_0_3227,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_1924]),
[final] ).
cnf(i_0_3228,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_1945]),
[final] ).
cnf(i_0_3229,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_1946]),
[final] ).
cnf(i_0_3230,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_1947]),
[final] ).
cnf(i_0_3231,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_1948]),
[final] ).
cnf(i_0_3232,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_1949]),
[final] ).
cnf(i_0_3233,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_1950]),
[final] ).
cnf(i_0_3234,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1951]),
[final] ).
cnf(i_0_3235,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ 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)
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3236,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_1952]),
[final] ).
cnf(i_0_3237,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_1953]),
[final] ).
cnf(i_0_3238,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_1954]),
[final] ).
cnf(i_0_3239,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_1955]),
[final] ).
cnf(i_0_3240,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1956]),
[final] ).
cnf(i_0_3241,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3242,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_1957]),
[final] ).
cnf(i_0_3243,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_1958]),
[final] ).
cnf(i_0_3244,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_1959]),
[final] ).
cnf(i_0_3245,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_1927]),
[final] ).
cnf(i_0_3246,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1960]),
[final] ).
cnf(i_0_3247,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ 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))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3248,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_1961]),
[final] ).
cnf(i_0_3249,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3))
| ~ class_Fields_Olinordered__field(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_1962]),
[final] ).
cnf(i_0_3250,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Rings_Oinverse__class_Odivide(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_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1926]),
[final] ).
cnf(i_0_3251,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_1963]),
[final] ).
cnf(i_0_3252,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_1958]),
[final] ).
cnf(i_0_3253,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_1927]),
[final] ).
cnf(i_0_3254,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_1964]),
[final] ).
cnf(i_0_3255,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3256,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3257,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_1966]),
[final] ).
cnf(i_0_3258,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_1967]),
[final] ).
cnf(i_0_3259,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_1816]),
[final] ).
cnf(i_0_3260,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_1968]),
[final] ).
cnf(i_0_3261,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_1818]),
[final] ).
cnf(i_0_3262,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_1969]),
[final] ).
cnf(i_0_3263,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_1820]),
[final] ).
cnf(i_0_3264,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_1970]),
[final] ).
cnf(i_0_3265,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_1822]),
[final] ).
cnf(i_0_3266,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_1971]),
[final] ).
cnf(i_0_3267,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_1972,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3268,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_1973,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3269,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_1974,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3270,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_1920]),
[final] ).
cnf(i_0_3271,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_1868]),
[final] ).
cnf(i_0_3272,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_1877]),
[final] ).
cnf(i_0_3273,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_1975]),
[final] ).
cnf(i_0_3274,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_1976]),
[final] ).
cnf(i_0_3275,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_1977]),
[final] ).
cnf(i_0_3276,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_1978]),
[final] ).
cnf(i_0_3277,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_1979]),
[final] ).
cnf(i_0_3278,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_1980]),
[final] ).
cnf(i_0_3279,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_1981]),
[final] ).
cnf(i_0_3280,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oone__class_Oone(X1),X2),X3)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1982]),
[final] ).
cnf(i_0_3281,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_1983]),
[final] ).
cnf(i_0_3282,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_1984]),
[final] ).
cnf(i_0_3283,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_1985]),
[final] ).
cnf(i_0_3284,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_1986]),
[final] ).
cnf(i_0_3285,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_1987,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3286,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_1988,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3287,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_1989]),
[final] ).
cnf(i_0_3288,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_1990]),
[final] ).
cnf(i_0_3289,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_1835]),
[final] ).
cnf(i_0_3290,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_1991]),
[final] ).
cnf(i_0_3291,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_1992,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3292,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_1993,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3293,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_1994]),
[final] ).
cnf(i_0_3294,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_1995]),
[final] ).
cnf(i_0_3295,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_1838]),
[final] ).
cnf(i_0_3296,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_1996]),
[final] ).
cnf(i_0_3297,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_1762]),
[final] ).
cnf(i_0_3298,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_1997]),
[final] ).
cnf(i_0_3299,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_1763]),
[final] ).
cnf(i_0_3300,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_1981]),
[final] ).
cnf(i_0_3301,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk6_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_1998,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3302,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_1999,c_0_1509]),
[final] ).
cnf(i_0_3303,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_2000]),
[final] ).
cnf(i_0_3304,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_2001]),
[final] ).
cnf(i_0_3305,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_2002,c_0_1509]),
[final] ).
cnf(i_0_3306,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_2003,c_0_1509]),
[final] ).
cnf(i_0_3307,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_2004,c_0_1494]),
[final] ).
cnf(i_0_3308,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_2005,c_0_1494]),
[final] ).
cnf(i_0_3309,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,esk6_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_2006,c_0_1509]),
[final] ).
cnf(i_0_3310,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_2007,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_3311,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_2008,c_0_1493]),c_0_1494]),
[final] ).
cnf(i_0_3312,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2009]),
[final] ).
cnf(i_0_3313,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_2010]),
[final] ).
cnf(i_0_3314,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_2011]),
[final] ).
cnf(i_0_3315,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3316,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_2012]),
[final] ).
cnf(i_0_3317,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_2013]),
[final] ).
cnf(i_0_3318,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_2014]),
[final] ).
cnf(i_0_3319,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3320,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3321,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1965]),
[final] ).
cnf(i_0_3322,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_1986]),
[final] ).
cnf(i_0_3323,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_2015,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3324,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_2016,c_0_1493]),
[final] ).
cnf(i_0_3325,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),c_Groups_Otimes__class_Otimes(X1,X2,X4)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3326,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),c_Groups_Otimes__class_Otimes(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,X3,X4)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2018]),
[final] ).
cnf(i_0_3327,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),X2))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3328,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_2020,c_0_1509]),
[final] ).
cnf(i_0_3329,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_2021,c_0_1509]),
[final] ).
cnf(i_0_3330,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_2022,c_0_1509]),
[final] ).
cnf(i_0_3331,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_2023,c_0_1509]),
[final] ).
cnf(i_0_3332,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_2024,c_0_1509]),
[final] ).
cnf(i_0_3333,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_2025]),
[final] ).
cnf(i_0_3334,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_2026]),
[final] ).
cnf(i_0_3335,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_2027]),
[final] ).
cnf(i_0_3336,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_2028]),
[final] ).
cnf(i_0_3337,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_2029]),
[final] ).
cnf(i_0_3338,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_2030]),
[final] ).
cnf(i_0_3339,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_2031,c_0_1509]),
[final] ).
cnf(i_0_3340,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_2032]),
[final] ).
cnf(i_0_3341,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_2033]),
[final] ).
cnf(i_0_3342,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_2034]),
[final] ).
cnf(i_0_3343,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_2035]),
[final] ).
cnf(i_0_3344,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_2036]),
[final] ).
cnf(i_0_3345,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_2037]),
[final] ).
cnf(i_0_3346,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_2038]),
[final] ).
cnf(i_0_3347,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_2039]),
[final] ).
cnf(i_0_3348,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Rings_Oinverse__class_Odivide(X1,X3,X4)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3),X4)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2040]),
[final] ).
cnf(i_0_3349,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_2041]),
[final] ).
cnf(i_0_3350,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_2042]),
[final] ).
cnf(i_0_3351,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_2043]),
[final] ).
cnf(i_0_3352,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_2044,c_0_1494]),
[final] ).
cnf(i_0_3353,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_2045,c_0_1494]),
[final] ).
cnf(i_0_3354,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_2046,c_0_1494]),
[final] ).
cnf(i_0_3355,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),
inference(split_conjunct,[status(thm)],[i_0_2047]),
[final] ).
cnf(i_0_3356,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_2048]),
[final] ).
cnf(i_0_3357,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_2049]),
[final] ).
cnf(i_0_3358,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_2050,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3359,plain,
( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Int_Oint,X3,X2)))
| ~ epred1_3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1902]),
[final] ).
cnf(i_0_3360,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_2051,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3361,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_2052,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3362,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_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),X2)
| epred1_3(X3,X2,X1)
| ~ hBOOL(hAPP(X3,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3363,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),esk15_3(X2,X1,X3))
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3364,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_2053,c_0_1509]),
[final] ).
cnf(i_0_3365,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_2054,c_0_1509]),
[final] ).
cnf(i_0_3366,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3367,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,esk15_3(X2,X1,X3),X1)
| epred1_3(X3,X1,X2)
| ~ hBOOL(hAPP(X3,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3368,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_2055]),
[final] ).
cnf(i_0_3369,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_1763]),
[final] ).
cnf(i_0_3370,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_1762]),
[final] ).
cnf(i_0_3371,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[i_0_2056]),
[final] ).
cnf(i_0_3372,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_2057]),
[final] ).
cnf(i_0_3373,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_2058]),
[final] ).
cnf(i_0_3374,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_2059]),
[final] ).
cnf(i_0_3375,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_2060]),
[final] ).
cnf(i_0_3376,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_2061]),
[final] ).
cnf(i_0_3377,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_2062]),
[final] ).
cnf(i_0_3378,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_2063]),
[final] ).
cnf(i_0_3379,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_2064]),
[final] ).
cnf(i_0_3380,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_2065]),
[final] ).
cnf(i_0_3381,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_2066,c_0_1509]),
[final] ).
cnf(i_0_3382,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_2067,c_0_1509]),
[final] ).
cnf(i_0_3383,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_2068,c_0_1509]),
[final] ).
cnf(i_0_3384,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_2069,c_0_1509]),
[final] ).
cnf(i_0_3385,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_2070]),
[final] ).
cnf(i_0_3386,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_2071]),
[final] ).
cnf(i_0_3387,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_2072]),
[final] ).
cnf(i_0_3388,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_2073,c_0_1509]),
[final] ).
cnf(i_0_3389,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_2074,c_0_1509]),
[final] ).
cnf(i_0_3390,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_2075,c_0_1509]),
[final] ).
cnf(i_0_3391,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_2076,c_0_1509]),
[final] ).
cnf(i_0_3392,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_2077,c_0_1509]),
[final] ).
cnf(i_0_3393,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_2078]),
[final] ).
cnf(i_0_3394,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_2079,c_0_1509]),
[final] ).
cnf(i_0_3395,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_1756]),
[final] ).
cnf(i_0_3396,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_2011]),
[final] ).
cnf(i_0_3397,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_2011]),
[final] ).
cnf(i_0_3398,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_2080,c_0_1493]),
[final] ).
cnf(i_0_3399,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_2081,c_0_1509]),
[final] ).
cnf(i_0_3400,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oabs__class_Oabs(X1,X3),X2) = c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2))
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2082]),
[final] ).
cnf(i_0_3401,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X3),X2) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2083]),
[final] ).
cnf(i_0_3402,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_2084,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3403,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_2085]),
[final] ).
cnf(i_0_3404,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_1981]),
[final] ).
cnf(i_0_3405,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_2086,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3406,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_1878]),
[final] ).
cnf(i_0_3407,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_2087]),
[final] ).
cnf(i_0_3408,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_2088]),
[final] ).
cnf(i_0_3409,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_2088]),
[final] ).
cnf(i_0_3410,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_2089]),
[final] ).
cnf(i_0_3411,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_2090]),
[final] ).
cnf(i_0_3412,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,X5) = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,X3) != c_Groups_Otimes__class_Otimes(X1,X4,X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3413,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,X5) = c_Groups_Otimes__class_Otimes(X1,X4,X3)
| X5 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Rings_Oinverse__class_Odivide(X1,X4,X5)
| ~ class_Fields_Ofield(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2091]),
[final] ).
cnf(i_0_3414,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_2092,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3415,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_2093,c_0_1509]),c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3416,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk5_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_2094,c_0_1509]),
[final] ).
cnf(i_0_3417,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_2095]),
[final] ).
cnf(i_0_3418,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_2095]),
[final] ).
cnf(i_0_3419,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_1986]),
[final] ).
cnf(i_0_3420,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_2096,c_0_1493]),
[final] ).
cnf(i_0_3421,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_2097,c_0_1493]),
[final] ).
cnf(i_0_3422,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_2098,c_0_1493]),
[final] ).
cnf(i_0_3423,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_2099,c_0_1493]),
[final] ).
cnf(i_0_3424,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_2100,c_0_1493]),
[final] ).
cnf(i_0_3425,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_2101,c_0_1493]),
[final] ).
cnf(i_0_3426,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_2102,c_0_1493]),
[final] ).
cnf(i_0_3427,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_2103,c_0_1493]),
[final] ).
cnf(i_0_3428,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_1876]),
[final] ).
cnf(i_0_3429,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X4,X3)
| c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3430,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_1921]),
[final] ).
cnf(i_0_3431,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_2105]),
[final] ).
cnf(i_0_3432,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_2029]),
[final] ).
cnf(i_0_3433,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_1986]),
[final] ).
cnf(i_0_3434,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_2029]),
[final] ).
cnf(i_0_3435,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_1981]),
[final] ).
cnf(i_0_3436,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_1983]),
[final] ).
cnf(i_0_3437,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_1985]),
[final] ).
cnf(i_0_3438,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_1868]),
[final] ).
cnf(i_0_3439,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,esk17_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),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3440,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),esk15_3(X2,X1,X3))
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3441,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_1877]),
[final] ).
cnf(i_0_3442,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_1986]),
[final] ).
cnf(i_0_3443,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_2106]),
[final] ).
cnf(i_0_3444,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,esk17_3(X2,X1,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,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3445,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,esk15_3(X2,X1,X3),X1)
| X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| epred1_3(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3446,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_1911]),
[final] ).
cnf(i_0_3447,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_2095]),
[final] ).
cnf(i_0_3448,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_2107]),
[final] ).
cnf(i_0_3449,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_2027]),
[final] ).
cnf(i_0_3450,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_2028]),
[final] ).
cnf(i_0_3451,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_2030]),
[final] ).
cnf(i_0_3452,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_2025]),
[final] ).
cnf(i_0_3453,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_2108]),
[final] ).
cnf(i_0_3454,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_2109]),
[final] ).
cnf(i_0_3455,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_2026]),
[final] ).
cnf(i_0_3456,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_2110]),
[final] ).
cnf(i_0_3457,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_1984]),
[final] ).
cnf(i_0_3458,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_2111,c_0_1509]),
[final] ).
cnf(i_0_3459,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_2112]),
[final] ).
cnf(i_0_3460,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_2105]),
[final] ).
cnf(i_0_3461,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X4,X3)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3462,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_2113]),
[final] ).
cnf(i_0_3463,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_2114]),
[final] ).
cnf(i_0_3464,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_2115,c_0_1494]),
[final] ).
cnf(i_0_3465,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_2116,c_0_1494]),
[final] ).
cnf(i_0_3466,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_2117]),
[final] ).
cnf(i_0_3467,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_2118]),
[final] ).
cnf(i_0_3468,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_2119,c_0_1509]),
[final] ).
cnf(i_0_3469,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_2120,c_0_1494]),
[final] ).
cnf(i_0_3470,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_2121,c_0_1494]),
[final] ).
cnf(i_0_3471,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_2122]),
[final] ).
cnf(i_0_3472,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_2123,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3473,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_2124,c_0_1509]),
[final] ).
cnf(i_0_3474,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_2125,c_0_1493]),
[final] ).
cnf(i_0_3475,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_2126]),
[final] ).
cnf(i_0_3476,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_2127]),
[final] ).
cnf(i_0_3477,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_1964]),
[final] ).
cnf(i_0_3478,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_1964]),
[final] ).
cnf(i_0_3479,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_2070]),
[final] ).
cnf(i_0_3480,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_2071]),
[final] ).
cnf(i_0_3481,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_2128]),
[final] ).
cnf(i_0_3482,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_2129]),
[final] ).
cnf(i_0_3483,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_2130]),
[final] ).
cnf(i_0_3484,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_2131]),
[final] ).
cnf(i_0_3485,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_2072]),
[final] ).
cnf(i_0_3486,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_2132]),
[final] ).
cnf(i_0_3487,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_2133,c_0_1509]),
[final] ).
cnf(i_0_3488,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_2134,c_0_1509]),
[final] ).
cnf(i_0_3489,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_2135,c_0_1509]),
[final] ).
cnf(i_0_3490,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_2065]),
[final] ).
cnf(i_0_3491,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_2078]),
[final] ).
cnf(i_0_3492,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_2136,c_0_1509]),
[final] ).
cnf(i_0_3493,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_2137,c_0_1509]),
[final] ).
cnf(i_0_3494,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_2138,c_0_1509]),
[final] ).
cnf(i_0_3495,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_2139,c_0_1509]),
[final] ).
cnf(i_0_3496,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_2140,c_0_1509]),
[final] ).
cnf(i_0_3497,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_2141,c_0_1509]),
[final] ).
cnf(i_0_3498,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_2142]),
[final] ).
cnf(i_0_3499,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_2143]),
[final] ).
cnf(i_0_3500,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_2128]),
[final] ).
cnf(i_0_3501,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_2144]),
[final] ).
cnf(i_0_3502,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_2145]),
[final] ).
cnf(i_0_3503,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_2146]),
[final] ).
cnf(i_0_3504,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_2126]),
[final] ).
cnf(i_0_3505,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_1868]),
[final] ).
cnf(i_0_3506,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_2055]),
[final] ).
cnf(i_0_3507,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) = c_Power_Opower__class_Opower(X1,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2))
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2147]),
[final] ).
cnf(i_0_3508,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)) = X4
| X3 != c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3509,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)) = X4
| X3 != c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3510,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Groups_Otimes__class_Otimes(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3511,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| c_Rings_Oinverse__class_Odivide(X1,X3,c_Int_Onumber__class_Onumber__of(X1,X2)) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3512,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2150]),
[final] ).
cnf(i_0_3513,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X3,X5),hAPP(X4,X5))
| ~ class_Orderings_Oord(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1),X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2151]),
[final] ).
cnf(i_0_3514,plain,
( c_Orderings_Oord__class_Oless__eq(X2,hAPP(X3,X5),hAPP(X4,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1581]),
[final] ).
cnf(i_0_3515,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_2152]),
[final] ).
cnf(i_0_3516,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_2153]),
[final] ).
cnf(i_0_3517,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_2154]),
[final] ).
cnf(i_0_3518,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_2155]),
[final] ).
cnf(i_0_3519,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Odivide(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_b)),v_b)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_th0]),
[final] ).
cnf(i_0_3520,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_2156,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3521,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_2157,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3522,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_2158,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3523,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_2159,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3524,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_2160,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3525,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2161]),
[final] ).
cnf(i_0_3526,plain,
( c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X4)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3527,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,c_Int_Onumber__class_Onumber__of(X1,X2),X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3528,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oabs__class_Oabs(X1,X3),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2164]),
[final] ).
cnf(i_0_3529,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_2165]),
[final] ).
cnf(i_0_3530,plain,
( c_RealVector_Oof__real(X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_RealVector_Oreal__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2166]),
[final] ).
cnf(i_0_3531,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2167]),
[final] ).
cnf(i_0_3532,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X3),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2168]),
[final] ).
cnf(i_0_3533,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_2169,c_0_1493]),
[final] ).
cnf(i_0_3534,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_2170,c_0_1493]),
[final] ).
cnf(i_0_3535,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_2171,c_0_1493]),
[final] ).
cnf(i_0_3536,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_2172,c_0_1493]),
[final] ).
cnf(i_0_3537,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_2173,c_0_1493]),
[final] ).
cnf(i_0_3538,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_2174,c_0_1493]),
[final] ).
cnf(i_0_3539,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_2175,c_0_1493]),
[final] ).
cnf(i_0_3540,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_2176,c_0_1493]),
[final] ).
cnf(i_0_3541,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_2177,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3542,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_2178,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3543,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_2179]),
[final] ).
cnf(i_0_3544,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_2180]),
[final] ).
cnf(i_0_3545,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X1,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X3,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_RealVector_Oof__real(X1,X3),c_RealVector_Oof__real(X1,X2))
| ~ class_RealVector_Oreal__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2181]),
[final] ).
cnf(i_0_3546,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2182]),
[final] ).
cnf(i_0_3547,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2183]),
[final] ).
cnf(i_0_3548,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2184]),
[final] ).
cnf(i_0_3549,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2185]),
[final] ).
cnf(i_0_3550,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2186]),
[final] ).
cnf(i_0_3551,plain,
( c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2187]),
[final] ).
cnf(i_0_3552,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(split_conjunct,[status(thm)],[i_0_2188]),
[final] ).
cnf(i_0_3553,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X4,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2189]),
[final] ).
cnf(i_0_3554,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Rings_Oinverse__class_Odivide(X1,X2,X3)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2190]),
[final] ).
cnf(i_0_3555,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2191]),
[final] ).
cnf(i_0_3556,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Otimes__class_Otimes(X1,X2,X3)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_RealVector_Onorm__class_Onorm(X1,X3))
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2192]),
[final] ).
cnf(i_0_3557,plain,
( c_Rings_Oinverse__class_Odivide(X2,X3,c_Int_Onumber__class_Onumber__of(X2,X4)) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Otimes__class_Otimes(X2,X1,c_Int_Onumber__class_Onumber__of(X2,X4))
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3558,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,c_Int_Onumber__class_Onumber__of(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Otimes__class_Otimes(X2,X1,c_Int_Onumber__class_Onumber__of(X2,X3)) != X4
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3559,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_2193]),
[final] ).
cnf(i_0_3560,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_2194]),
[final] ).
cnf(i_0_3561,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2195]),
[final] ).
cnf(i_0_3562,plain,
( c_RealVector_Oof__real(X1,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X3)) = c_Groups_Otimes__class_Otimes(X1,c_RealVector_Oof__real(X1,X2),c_RealVector_Oof__real(X1,X3))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2196]),
[final] ).
cnf(i_0_3563,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_2197]),
[final] ).
cnf(i_0_3564,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_2198]),
[final] ).
cnf(i_0_3565,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_1921]),
[final] ).
cnf(i_0_3566,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_2199,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3567,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_1980]),
[final] ).
cnf(i_0_3568,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2200]),
[final] ).
cnf(i_0_3569,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_2201]),
[final] ).
cnf(i_0_3570,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_2202]),
[final] ).
cnf(i_0_3571,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_2165]),
[final] ).
cnf(i_0_3572,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_2203]),
[final] ).
cnf(i_0_3573,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_2204]),
[final] ).
cnf(i_0_3574,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_2205]),
[final] ).
cnf(i_0_3575,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_2206]),
[final] ).
cnf(i_0_3576,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_2207]),
[final] ).
cnf(i_0_3577,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_2208]),
[final] ).
cnf(i_0_3578,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_2209,c_0_1509]),
[final] ).
cnf(i_0_3579,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_2210]),
[final] ).
cnf(i_0_3580,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_2210]),
[final] ).
cnf(i_0_3581,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_2211]),
[final] ).
cnf(i_0_3582,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_2212]),
[final] ).
cnf(i_0_3583,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_2211]),
[final] ).
cnf(i_0_3584,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_2212]),
[final] ).
cnf(i_0_3585,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) = c_Int_Onumber__class_Onumber__of(X2,X4)
| X3 != c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X4),X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3586,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X2,X3) = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X3),X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3587,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_2213,c_0_1509]),
[final] ).
cnf(i_0_3588,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_2214,c_0_1509]),
[final] ).
cnf(i_0_3589,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,X1,X3)
| ~ hBOOL(hAPP(X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3590,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,X2),X3,X4)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X1,X2),X3,X4)
| ~ class_Orderings_Oord(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2104]),
[final] ).
cnf(i_0_3591,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_2215]),
[final] ).
cnf(i_0_3592,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_2216]),
[final] ).
cnf(i_0_3593,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_2217,c_0_1509]),
[final] ).
cnf(i_0_3594,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_2218,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3595,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_2219,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3596,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_2220,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3597,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_2221,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3598,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3599,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X2),X1))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3600,plain,
( 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),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2019]),
[final] ).
cnf(i_0_3601,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_2223]),
[final] ).
cnf(i_0_3602,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X3),X1) = X4
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3603,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X2,X4),X1)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) != c_Int_Onumber__class_Onumber__of(X2,X4)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3604,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_2224]),
[final] ).
cnf(i_0_3605,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_2105]),
[final] ).
cnf(i_0_3606,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_2225]),
[final] ).
cnf(i_0_3607,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2226]),
[final] ).
cnf(i_0_3608,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_1986]),
[final] ).
cnf(i_0_3609,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Power_Opower__class_Opower(X1,X2,X3)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),X3)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2227]),
[final] ).
cnf(i_0_3610,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_2228,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3611,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,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),X2)),
inference(split_conjunct,[status(thm)],[i_0_2229]),
[final] ).
cnf(i_0_3612,plain,
( c_RealVector_Oof__real(X1,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,X3)) = c_Power_Opower__class_Opower(X1,c_RealVector_Oof__real(X1,X2),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2230]),
[final] ).
cnf(i_0_3613,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_2179]),
[final] ).
cnf(i_0_3614,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_2180]),
[final] ).
cnf(i_0_3615,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3616,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_2232]),
[final] ).
cnf(i_0_3617,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_2233]),
[final] ).
cnf(i_0_3618,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_2234]),
[final] ).
cnf(i_0_3619,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_2235]),
[final] ).
cnf(i_0_3620,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_2236]),
[final] ).
cnf(i_0_3621,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(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_2237]),
[final] ).
cnf(i_0_3622,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_1981]),
[final] ).
cnf(i_0_3623,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_2238]),
[final] ).
cnf(i_0_3624,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_2165]),
[final] ).
cnf(i_0_3625,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_1983]),
[final] ).
cnf(i_0_3626,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_1984]),
[final] ).
cnf(i_0_3627,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_2055]),
[final] ).
cnf(i_0_3628,plain,
c_Power_Opower__class_Opower(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1),X2) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X2)),
inference(split_conjunct,[status(thm)],[i_0_2239]),
[final] ).
cnf(i_0_3629,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_2240]),
[final] ).
cnf(i_0_3630,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[i_0_2241]),
[final] ).
cnf(i_0_3631,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_2242,c_0_1509]),
[final] ).
cnf(i_0_3632,plain,
( c_Groups_Oabs__class_Oabs(X1,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)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3633,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_2244,c_0_1509]),
[final] ).
cnf(i_0_3634,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_2245,c_0_1509]),
[final] ).
cnf(i_0_3635,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3636,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_2224]),
[final] ).
cnf(i_0_3637,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_2225]),
[final] ).
cnf(i_0_3638,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_2113]),
[final] ).
cnf(i_0_3639,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_2112]),
[final] ).
cnf(i_0_3640,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_2234]),
[final] ).
cnf(i_0_3641,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_2235]),
[final] ).
cnf(i_0_3642,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_2232]),
[final] ).
cnf(i_0_3643,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_2233]),
[final] ).
cnf(i_0_3644,plain,
( X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3645,plain,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2248]),
[final] ).
cnf(i_0_3646,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3647,plain,
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3648,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_2251]),
[final] ).
cnf(i_0_3649,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_2252]),
[final] ).
cnf(i_0_3650,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_1981]),
[final] ).
cnf(i_0_3651,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_2253]),
[final] ).
cnf(i_0_3652,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_2254]),
[final] ).
cnf(i_0_3653,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_2255]),
[final] ).
cnf(i_0_3654,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_2256]),
[final] ).
cnf(i_0_3655,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_2257]),
[final] ).
cnf(i_0_3656,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_2113]),
[final] ).
cnf(i_0_3657,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_2258]),
[final] ).
cnf(i_0_3658,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_2258]),
[final] ).
cnf(i_0_3659,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2259]),
[final] ).
cnf(i_0_3660,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2260]),
[final] ).
cnf(i_0_3661,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2261]),
[final] ).
cnf(i_0_3662,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_3663,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3664,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3665,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3666,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2265]),
[final] ).
cnf(i_0_3667,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3668,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3669,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_2268,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3670,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_2269,c_0_1509]),c_0_1509]),
[final] ).
cnf(i_0_3671,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2)) != X3
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3672,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3673,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_2270]),
[final] ).
cnf(i_0_3674,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_2271,c_0_1509]),
[final] ).
cnf(i_0_3675,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_2272]),
[final] ).
cnf(i_0_3676,plain,
c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2)),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_3677,plain,
c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2)) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2)),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_3678,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_2275]),
[final] ).
cnf(i_0_3679,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_2276]),
[final] ).
cnf(i_0_3680,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_2277]),
[final] ).
cnf(i_0_3681,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_2278]),
[final] ).
cnf(i_0_3682,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_2279]),
[final] ).
cnf(i_0_3683,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_2280]),
[final] ).
cnf(i_0_3684,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_2281]),
[final] ).
cnf(i_0_3685,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,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3686,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_2282]),
[final] ).
cnf(i_0_3687,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_2283]),
[final] ).
cnf(i_0_3688,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_2284]),
[final] ).
cnf(i_0_3689,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_2285,c_0_1509]),
[final] ).
cnf(i_0_3690,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_2286,c_0_1493]),c_0_1493]),
[final] ).
cnf(i_0_3691,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_2287]),
[final] ).
cnf(i_0_3692,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_2288]),
[final] ).
cnf(i_0_3693,plain,
( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Otimes__class_Otimes(X1,X2,X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3694,plain,
( X1 = c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,esk13_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_2290]),
[final] ).
cnf(i_0_3695,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X2),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3696,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_2065]),
[final] ).
cnf(i_0_3697,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_2292,c_0_1509]),
[final] ).
cnf(i_0_3698,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_2293,c_0_1509]),
[final] ).
cnf(i_0_3699,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_2070]),
[final] ).
cnf(i_0_3700,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_2071]),
[final] ).
cnf(i_0_3701,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_2294,c_0_1494]),
[final] ).
cnf(i_0_3702,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_2295,c_0_1494]),
[final] ).
cnf(i_0_3703,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk10_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3704,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3705,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_2117]),
[final] ).
cnf(i_0_3706,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_2298,c_0_1509]),
[final] ).
cnf(i_0_3707,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oabs__class_Oabs(X1,X3),X2) = c_Power_Opower__class_Opower(X1,X3,X2)
| ~ class_Rings_Olinordered__idom(X1)
| ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3708,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_2252]),
[final] ).
cnf(i_0_3709,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_2270]),
[final] ).
cnf(i_0_3710,plain,
( c_Rings_Oinverse__class_Odivide(X2,X3,X4) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Otimes__class_Otimes(X2,X1,X4)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3711,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Otimes__class_Otimes(X2,X1,X3) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3712,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_2302,c_0_1494]),
[final] ).
cnf(i_0_3713,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_2210]),
[final] ).
cnf(i_0_3714,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_2211]),
[final] ).
cnf(i_0_3715,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_2212]),
[final] ).
cnf(i_0_3716,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_2303]),
[final] ).
cnf(i_0_3717,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_2304]),
[final] ).
cnf(i_0_3718,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_2305]),
[final] ).
cnf(i_0_3719,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3720,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3721,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_2258]),
[final] ).
cnf(i_0_3722,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) = X4
| X3 != c_Groups_Otimes__class_Otimes(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3723,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Otimes__class_Otimes(X2,X3,X1) = X4
| X3 != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3724,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X3,X2) = X4
| ~ class_Rings_Odivision__ring(X1)
| X3 != c_Groups_Otimes__class_Otimes(X1,X4,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3725,plain,
( c_Rings_Oinverse__class_Odivide(X2,X1,X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Otimes__class_Otimes(X2,X3,X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3726,plain,
( c_Groups_Otimes__class_Otimes(X2,X1,X4) = X3
| X4 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Rings_Oinverse__class_Odivide(X2,X3,X4)
| ~ class_Rings_Odivision__ring(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3727,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| c_Groups_Otimes__class_Otimes(X2,X3,X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3728,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Otimes__class_Otimes(X2,X4,X1)
| c_Rings_Oinverse__class_Odivide(X2,X3,X1) != X4
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3729,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,X4,X2)
| ~ class_Rings_Odivision__ring(X1)
| c_Groups_Otimes__class_Otimes(X1,X3,X2) != X4 ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3730,plain,
( X2 = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,X2,X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3731,plain,
( X2 = c_Groups_Otimes__class_Otimes(X1,X4,X3)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != X4
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3732,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3733,plain,
( 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),c_NthRoot_Osqrt(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3734,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3735,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3736,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_3737,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3738,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3739,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3740,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3741,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk7_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_2321,c_0_1509]),
[final] ).
cnf(i_0_3742,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3743,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3744,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3745,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3746,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3747,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3748,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3749,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_3750,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3751,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3752,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3753,plain,
( X3 = X2
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3754,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3755,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3756,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3757,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3758,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3759,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3760,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3761,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[final] ).
cnf(i_0_3762,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2333]),
[final] ).
cnf(i_0_3763,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3764,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_3765,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(X1),c_Transcendental_Oarctan(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2335]),
[final] ).
cnf(i_0_3766,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2336]),
[final] ).
cnf(i_0_3767,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3768,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2337]),
[final] ).
cnf(i_0_3769,plain,
( c_Int_Onumber__class_Onumber__of(X2,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X4,X1) != c_Int_Onumber__class_Onumber__of(X2,X3)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3770,plain,
( c_Int_Onumber__class_Onumber__of(X2,X3) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3771,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3772,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3773,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2338]),
[final] ).
cnf(i_0_3774,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2231]),
[final] ).
cnf(i_0_3775,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_2339,c_0_1509]),
[final] ).
cnf(i_0_3776,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_2340]),
[final] ).
cnf(i_0_3777,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_2340]),
[final] ).
cnf(i_0_3778,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| X2 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3779,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2342]),
[final] ).
cnf(i_0_3780,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_2211]),
[final] ).
cnf(i_0_3781,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_2212]),
[final] ).
cnf(i_0_3782,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_2210]),
[final] ).
cnf(i_0_3783,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2343]),
[final] ).
cnf(i_0_3784,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_2290]),
[final] ).
cnf(i_0_3785,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_2344]),
[final] ).
cnf(i_0_3786,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_2345]),
[final] ).
cnf(i_0_3787,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_2346]),
[final] ).
cnf(i_0_3788,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_2347]),
[final] ).
cnf(i_0_3789,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_2348]),
[final] ).
cnf(i_0_3790,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_2349]),
[final] ).
cnf(i_0_3791,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_2296]),
[final] ).
cnf(i_0_3792,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_2297]),
[final] ).
cnf(i_0_3793,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_2344]),
[final] ).
cnf(i_0_3794,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_2345]),
[final] ).
cnf(i_0_3795,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_2346]),
[final] ).
cnf(i_0_3796,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_2350]),
[final] ).
cnf(i_0_3797,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_2351]),
[final] ).
cnf(i_0_3798,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_2348]),
[final] ).
cnf(i_0_3799,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_2349]),
[final] ).
cnf(i_0_3800,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_2223]),
[final] ).
cnf(i_0_3801,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_2223]),
[final] ).
cnf(i_0_3802,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_2352]),
[final] ).
cnf(i_0_3803,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_2353,c_0_1509]),
[final] ).
cnf(i_0_3804,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_2252]),
[final] ).
cnf(i_0_3805,plain,
( c_Rings_Oinverse__class_Odivide(X2,X4,c_Int_Onumber__class_Onumber__of(X2,X3)) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2148]),
[final] ).
cnf(i_0_3806,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,c_Int_Onumber__class_Onumber__of(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Int_Onumber__class_Onumber__of(X2,X3) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2)
| ~ class_Int_Onumber(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2149]),
[final] ).
cnf(i_0_3807,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3808,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_2355]),
[final] ).
cnf(i_0_3809,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_2355]),
[final] ).
cnf(i_0_3810,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_2356]),
[final] ).
cnf(i_0_3811,plain,
( hBOOL(hAPP(X2,X3))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ epred1_3(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1624]),
[final] ).
cnf(i_0_3812,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3813,plain,
c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[i_0_2357]),
[final] ).
cnf(i_0_3814,plain,
( c_Rings_Oinverse__class_Odivide(X1,X4,X3) = c_Int_Onumber__class_Onumber__of(X1,X2)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2162]),
[final] ).
cnf(i_0_3815,plain,
( c_Int_Onumber__class_Onumber__of(X1,X2) = c_Rings_Oinverse__class_Odivide(X1,X4,X3)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2163]),
[final] ).
cnf(i_0_3816,plain,
( X1 = X2
| c_Orderings_Oord__class_Oless(X3,X1,X2)
| c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3817,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2359]),
[final] ).
cnf(i_0_3818,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2360]),
[final] ).
cnf(i_0_3819,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2361]),
[final] ).
cnf(i_0_3820,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2362]),
[final] ).
cnf(i_0_3821,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| X2 = X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3822,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_2363]),
[final] ).
cnf(i_0_3823,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2364]),
[final] ).
cnf(i_0_3824,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2365]),
[final] ).
cnf(i_0_3825,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_2366,c_0_1509]),
[final] ).
cnf(i_0_3826,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_2356]),
[final] ).
cnf(i_0_3827,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2367]),
[final] ).
cnf(i_0_3828,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2368]),
[final] ).
cnf(i_0_3829,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2267]),
[final] ).
cnf(i_0_3830,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2369]),
[final] ).
cnf(i_0_3831,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2266]),
[final] ).
cnf(i_0_3832,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2370]),
[final] ).
cnf(i_0_3833,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2371]),
[final] ).
cnf(i_0_3834,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_2372]),
[final] ).
cnf(i_0_3835,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_2373]),
[final] ).
cnf(i_0_3836,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_2374]),
[final] ).
cnf(i_0_3837,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_2375]),
[final] ).
cnf(i_0_3838,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_2376,c_0_1509]),
[final] ).
cnf(i_0_3839,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_2278]),
[final] ).
cnf(i_0_3840,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_2279]),
[final] ).
cnf(i_0_3841,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_2276]),
[final] ).
cnf(i_0_3842,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_2377]),
[final] ).
cnf(i_0_3843,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_2378]),
[final] ).
cnf(i_0_3844,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_2379]),
[final] ).
cnf(i_0_3845,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_2380]),
[final] ).
cnf(i_0_3846,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_2381]),
[final] ).
cnf(i_0_3847,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_2382]),
[final] ).
cnf(i_0_3848,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_2381]),
[final] ).
cnf(i_0_3849,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_2383]),
[final] ).
cnf(i_0_3850,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_2384]),
[final] ).
cnf(i_0_3851,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_2385]),
[final] ).
cnf(i_0_3852,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X4,X1) != X3
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3853,plain,
( X3 = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Rings_Oinverse__class_Odivide(X2,X4,X1)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3854,plain,
( X2 = X3
| X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X3) != c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3855,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_2387]),
[final] ).
cnf(i_0_3856,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_2388]),
[final] ).
cnf(i_0_3857,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_2389]),
[final] ).
cnf(i_0_3858,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_2390]),
[final] ).
cnf(i_0_3859,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_2391]),
[final] ).
cnf(i_0_3860,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_2392]),
[final] ).
cnf(i_0_3861,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_2393]),
[final] ).
cnf(i_0_3862,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_2394]),
[final] ).
cnf(i_0_3863,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_2395]),
[final] ).
cnf(i_0_3864,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_2396]),
[final] ).
cnf(i_0_3865,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_2397]),
[final] ).
cnf(i_0_3866,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_2398]),
[final] ).
cnf(i_0_3867,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_2399]),
[final] ).
cnf(i_0_3868,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_2399]),
[final] ).
cnf(i_0_3869,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_2399]),
[final] ).
cnf(i_0_3870,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_2399]),
[final] ).
cnf(i_0_3871,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_NthRoot_Osqrt(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2400]),
[final] ).
cnf(i_0_3872,plain,
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2337]),
[final] ).
cnf(i_0_3873,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_2401]),
[final] ).
cnf(i_0_3874,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_2355]),
[final] ).
cnf(i_0_3875,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_NthRoot_Osqrt(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2402]),
[final] ).
cnf(i_0_3876,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),c_Groups_Oabs__class_Oabs(X2,X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3877,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2,X1),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2343]),
[final] ).
cnf(i_0_3878,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3879,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2264]),
[final] ).
cnf(i_0_3880,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2403]),
[final] ).
cnf(i_0_3881,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2404]),
[final] ).
cnf(i_0_3882,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2405]),
[final] ).
cnf(i_0_3883,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3884,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2358]),
[final] ).
cnf(i_0_3885,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_2406]),
[final] ).
cnf(i_0_3886,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_2407]),
[final] ).
cnf(i_0_3887,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2408]),
[final] ).
cnf(i_0_3888,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_2409]),
[final] ).
cnf(i_0_3889,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2341]),
[final] ).
cnf(i_0_3890,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_2410]),
[final] ).
cnf(i_0_3891,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2411]),
[final] ).
cnf(i_0_3892,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_2399]),
[final] ).
cnf(i_0_3893,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2412]),
[final] ).
cnf(i_0_3894,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_2413]),
[final] ).
cnf(i_0_3895,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_2414]),
[final] ).
cnf(i_0_3896,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_2415,c_0_1509]),
[final] ).
cnf(i_0_3897,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_2416,c_0_1509]),
[final] ).
cnf(i_0_3898,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_2417,c_0_1509]),
[final] ).
cnf(i_0_3899,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_2418,c_0_1509]),
[final] ).
cnf(i_0_3900,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_2419,c_0_1509]),
[final] ).
cnf(i_0_3901,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_2420,c_0_1509]),
[final] ).
cnf(i_0_3902,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_2421]),
[final] ).
cnf(i_0_3903,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_2421]),
[final] ).
cnf(i_0_3904,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_2422]),
[final] ).
cnf(i_0_3905,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_2422]),
[final] ).
cnf(i_0_3906,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_2423]),
[final] ).
cnf(i_0_3907,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_2423]),
[final] ).
cnf(i_0_3908,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_2424]),
[final] ).
cnf(i_0_3909,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_2425,c_0_1509]),
[final] ).
cnf(i_0_3910,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_2426,c_0_1509]),
[final] ).
cnf(i_0_3911,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2))
| ~ class_Int_Onumber__ring(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2427]),
[final] ).
cnf(i_0_3912,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X2))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2428]),
[final] ).
cnf(i_0_3913,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_2429]),
[final] ).
cnf(i_0_3914,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_2430]),
[final] ).
cnf(i_0_3915,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_2431]),
[final] ).
cnf(i_0_3916,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_2432]),
[final] ).
cnf(i_0_3917,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Oabs__class_Oabs(X1,X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2433]),
[final] ).
cnf(i_0_3918,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2344]),
[final] ).
cnf(i_0_3919,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2346]),
[final] ).
cnf(i_0_3920,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2434]),
[final] ).
cnf(i_0_3921,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2435]),
[final] ).
cnf(i_0_3922,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2349]),
[final] ).
cnf(i_0_3923,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3924,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2385]),
[final] ).
cnf(i_0_3925,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_2436]),
[final] ).
cnf(i_0_3926,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_2437]),
[final] ).
cnf(i_0_3927,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_2438]),
[final] ).
cnf(i_0_3928,plain,
( c_Int_OPls = X1
| c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) ),
inference(rw,[status(thm)],[i_0_2439,c_0_1493]),
[final] ).
cnf(i_0_3929,plain,
( X1 = c_Int_OPls
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_2440,c_0_1493]),
[final] ).
cnf(i_0_3930,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(split_conjunct,[status(thm)],[i_0_2354]),
[final] ).
cnf(i_0_3931,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_2441]),
[final] ).
cnf(i_0_3932,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2442]),
[final] ).
cnf(i_0_3933,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2443]),
[final] ).
cnf(i_0_3934,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) != c_Int_OMin,
inference(rw,[status(thm)],[i_0_2444,c_0_1493]),
[final] ).
cnf(i_0_3935,plain,
c_Int_OMin != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(rw,[status(thm)],[i_0_2445,c_0_1493]),
[final] ).
cnf(i_0_3936,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_2441]),
[final] ).
cnf(i_0_3937,plain,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)),
inference(split_conjunct,[status(thm)],[fact_i__mult__eq]),
[final] ).
cnf(i_0_3938,plain,
( c_Rings_Oinverse__class_Odivide(X2,X4,X3) = X1
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3939,plain,
( X1 = c_Rings_Oinverse__class_Odivide(X2,X4,X3)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3940,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2446]),
[final] ).
cnf(i_0_3941,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2447]),
[final] ).
cnf(i_0_3942,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(split_conjunct,[status(thm)],[i_0_2448]),
[final] ).
cnf(i_0_3943,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(split_conjunct,[status(thm)],[i_0_2449]),
[final] ).
cnf(i_0_3944,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_3945,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_2406]),
[final] ).
cnf(i_0_3946,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_2407]),
[final] ).
cnf(i_0_3947,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_2450]),
[final] ).
cnf(i_0_3948,plain,
( c_Rings_Oinverse__class_Odivide(X3,X1,X2) = c_Groups_Oone__class_Oone(X3)
| X2 = c_Groups_Ozero__class_Ozero(X3)
| X1 != X2
| ~ class_Rings_Odivision__ring(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2386]),
[final] ).
cnf(i_0_3949,plain,
( c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_3950,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_2395]),
[final] ).
cnf(i_0_3951,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_2377]),
[final] ).
cnf(i_0_3952,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_2377]),
[final] ).
cnf(i_0_3953,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_2397]),
[final] ).
cnf(i_0_3954,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_2452]),
[final] ).
cnf(i_0_3955,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_2453]),
[final] ).
cnf(i_0_3956,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_2454]),
[final] ).
cnf(i_0_3957,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2455]),
[final] ).
cnf(i_0_3958,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2456]),
[final] ).
cnf(i_0_3959,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_2457]),
[final] ).
cnf(i_0_3960,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_2458]),
[final] ).
cnf(i_0_3961,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_2459]),
[final] ).
cnf(i_0_3962,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_2460]),
[final] ).
cnf(i_0_3963,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_2461]),
[final] ).
cnf(i_0_3964,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_2462]),
[final] ).
cnf(i_0_3965,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2463]),
[final] ).
cnf(i_0_3966,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_2464]),
[final] ).
cnf(i_0_3967,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_3968,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_2466]),
[final] ).
cnf(i_0_3969,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_2467]),
[final] ).
cnf(i_0_3970,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_2401]),
[final] ).
cnf(i_0_3971,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Odivide(X2,X1,X1) = c_Groups_Oone__class_Oone(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2451]),
[final] ).
cnf(i_0_3972,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2468]),
[final] ).
cnf(i_0_3973,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_2469]),
[final] ).
cnf(i_0_3974,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_2470]),
[final] ).
cnf(i_0_3975,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_3976,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_2472]),
[final] ).
cnf(i_0_3977,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_2473]),
[final] ).
cnf(i_0_3978,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_2474]),
[final] ).
cnf(i_0_3979,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_2475]),
[final] ).
cnf(i_0_3980,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_2476]),
[final] ).
cnf(i_0_3981,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_3982,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_2478]),
[final] ).
cnf(i_0_3983,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2479]),
[final] ).
cnf(i_0_3984,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_2480]),
[final] ).
cnf(i_0_3985,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_2481]),
[final] ).
cnf(i_0_3986,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_2482]),
[final] ).
cnf(i_0_3987,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_2483]),
[final] ).
cnf(i_0_3988,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_2484]),
[final] ).
cnf(i_0_3989,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_2485]),
[final] ).
cnf(i_0_3990,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_2422]),
[final] ).
cnf(i_0_3991,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_2399]),
[final] ).
cnf(i_0_3992,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_2421]),
[final] ).
cnf(i_0_3993,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_2423]),
[final] ).
cnf(i_0_3994,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_2486]),
[final] ).
cnf(i_0_3995,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_2487]),
[final] ).
cnf(i_0_3996,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_2488]),
[final] ).
cnf(i_0_3997,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3998,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3999,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2489]),
[final] ).
cnf(i_0_4000,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_4001,plain,
( c_RealVector_Oof__real(X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X2)) = c_Int_Onumber__class_Onumber__of(X1,X2)
| ~ class_Int_Onumber__ring(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2490]),
[final] ).
cnf(i_0_4002,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_2414]),
[final] ).
cnf(i_0_4003,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X2)
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2491]),
[final] ).
cnf(i_0_4004,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_2492,c_0_1509]),
[final] ).
cnf(i_0_4005,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_2409]),
[final] ).
cnf(i_0_4006,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_2409]),
[final] ).
cnf(i_0_4007,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X2)) = c_Groups_Oabs__class_Oabs(X1,X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2493]),
[final] ).
cnf(i_0_4008,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_2494]),
[final] ).
cnf(i_0_4009,plain,
c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex,c_Complex_Oii,c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(split_conjunct,[status(thm)],[fact_i__squared]),
[final] ).
cnf(i_0_4010,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_2410]),
[final] ).
cnf(i_0_4011,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_2495]),
[final] ).
cnf(i_0_4012,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2496]),
[final] ).
cnf(i_0_4013,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2497]),
[final] ).
cnf(i_0_4014,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_4015,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_4016,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_4017,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_2498]),
[final] ).
cnf(i_0_4018,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_2499]),
[final] ).
cnf(i_0_4019,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_2500]),
[final] ).
cnf(i_0_4020,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_2501]),
[final] ).
cnf(i_0_4021,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_2502]),
[final] ).
cnf(i_0_4022,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_2503]),
[final] ).
cnf(i_0_4023,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_2504]),
[final] ).
cnf(i_0_4024,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_2505]),
[final] ).
cnf(i_0_4025,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_2506]),
[final] ).
cnf(i_0_4026,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_2507]),
[final] ).
cnf(i_0_4027,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_2508]),
[final] ).
cnf(i_0_4028,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_2509]),
[final] ).
cnf(i_0_4029,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2345]),
[final] ).
cnf(i_0_4030,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2350]),
[final] ).
cnf(i_0_4031,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2510]),
[final] ).
cnf(i_0_4032,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2348]),
[final] ).
cnf(i_0_4033,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_2511]),
[final] ).
cnf(i_0_4034,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_2512]),
[final] ).
cnf(i_0_4035,plain,
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1) = c_Int_OPls
| X1 != c_Int_OPls ),
inference(rw,[status(thm)],[i_0_2513,c_0_1493]),
[final] ).
cnf(i_0_4036,plain,
( c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1)
| c_Int_OPls != X1 ),
inference(rw,[status(thm)],[i_0_2514,c_0_1493]),
[final] ).
cnf(i_0_4037,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_2515]),
[final] ).
cnf(i_0_4038,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2516]),
[final] ).
cnf(i_0_4039,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_4040,plain,
( X2 = X3
| c_RealVector_Oof__real(X1,X2) != c_RealVector_Oof__real(X1,X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2517]),
[final] ).
cnf(i_0_4041,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2518]),
[final] ).
cnf(i_0_4042,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2519]),
[final] ).
cnf(i_0_4043,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2520]),
[final] ).
cnf(i_0_4044,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2521]),
[final] ).
cnf(i_0_4045,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[i_0_2522]),
[final] ).
cnf(i_0_4046,plain,
c_Groups_Otimes__class_Otimes(tc_Int_Oint,c_Int_OPls,X1) = c_Int_OPls,
inference(split_conjunct,[status(thm)],[i_0_2523]),
[final] ).
cnf(i_0_4047,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_4048,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_4049,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_4050,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_4051,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
inference(rw,[status(thm)],[i_0_2524,c_0_1493]),
[final] ).
cnf(i_0_4052,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2525]),
[final] ).
cnf(i_0_4053,plain,
( X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4054,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_RealVector_Onorm__class_Onorm(X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_4055,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2528]),
[final] ).
cnf(i_0_4056,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2529]),
[final] ).
cnf(i_0_4057,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2530]),
[final] ).
cnf(i_0_4058,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2531]),
[final] ).
cnf(i_0_4059,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_4060,plain,
( c_Groups_Oabs__class_Oabs(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2525]),
[final] ).
cnf(i_0_4061,plain,
( c_RealVector_Onorm__class_Onorm(X2,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2527]),
[final] ).
cnf(i_0_4062,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2532]),
[final] ).
cnf(i_0_4063,plain,
( c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2533]),
[final] ).
cnf(i_0_4064,plain,
( c_RealVector_Oof__real(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2526]),
[final] ).
cnf(i_0_4065,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Oone__class_Oone(X1)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2534]),
[final] ).
cnf(i_0_4066,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2535]),
[final] ).
cnf(i_0_4067,plain,
( c_RealVector_Oof__real(X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2536]),
[final] ).
cnf(i_0_4068,plain,
( c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2537]),
[final] ).
cnf(i_0_4069,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_2538]),
[final] ).
cnf(i_0_4070,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[i_0_2539]),
[final] ).
cnf(i_0_4071,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_4072,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_4073,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_2542]),
[final] ).
cnf(i_0_4074,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_2543]),
[final] ).
cnf(i_0_4075,plain,
c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X1),
inference(split_conjunct,[status(thm)],[i_0_2544]),
[final] ).
cnf(i_0_4076,plain,
~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
inference(split_conjunct,[status(thm)],[i_0_2545]),
[final] ).
cnf(i_0_4077,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_4078,plain,
( X1 = X2
| c_NthRoot_Osqrt(X1) != c_NthRoot_Osqrt(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2546]),
[final] ).
cnf(i_0_4079,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2547]),
[final] ).
cnf(i_0_4080,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2548]),
[final] ).
cnf(i_0_4081,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_4082,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_4083,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_4084,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_2549]),
[final] ).
cnf(i_0_4085,plain,
( c_NthRoot_Osqrt(X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2547]),
[final] ).
cnf(i_0_4086,plain,
( c_NthRoot_Osqrt(X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[i_0_2548]),
[final] ).
cnf(i_0_4087,plain,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_arctan__zero__zero]),
[final] ).
cnf(i_0_4088,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__one]),
[final] ).
cnf(i_0_4089,plain,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__zero]),
[final] ).
cnf(i_0_4090,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_4091,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_4092,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_complex__i__not__one]),
[final] ).
cnf(i_0_4093,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_complex__i__not__zero]),
[final] ).
cnf(i_0_4094,plain,
v_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_b]),
[final] ).
cnf(i_0_4095,plain,
v_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_assms_I2_J]),
[final] ).
cnf(i_0_4096,plain,
v_na____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_n]),
[final] ).
cnf(i_0_4097,plain,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__algebra__1]),
[final] ).
cnf(i_0_4098,plain,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__algebra__1]),
[final] ).
cnf(i_0_4099,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4100,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
[final] ).
cnf(i_0_4101,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__field]),
[final] ).
cnf(i_0_4102,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__field]),
[final] ).
cnf(i_0_4103,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
[final] ).
cnf(i_0_4104,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_4105,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_4106,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]),
[final] ).
cnf(i_0_4107,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]),
[final] ).
cnf(i_0_4108,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]),
[final] ).
cnf(i_0_4109,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]),
[final] ).
cnf(i_0_4110,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_4111,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_4112,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_4113,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_4114,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]),
[final] ).
cnf(i_0_4115,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_4116,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]),
[final] ).
cnf(i_0_4117,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_4118,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_4119,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]),
[final] ).
cnf(i_0_4120,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]),
[final] ).
cnf(i_0_4121,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]),
[final] ).
cnf(i_0_4122,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]),
[final] ).
cnf(i_0_4123,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]),
[final] ).
cnf(i_0_4124,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]),
[final] ).
cnf(i_0_4125,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
[final] ).
cnf(i_0_4126,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
[final] ).
cnf(i_0_4127,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_4128,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_4129,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_4130,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_4131,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_4132,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add__abs]),
[final] ).
cnf(i_0_4133,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_4134,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_4135,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_4136,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_4137,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_4138,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_4139,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_4140,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_4141,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_4142,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_4143,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_4144,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_4145,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_4146,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_4147,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_4148,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_4149,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_4150,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_4151,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_4152,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_4153,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_4154,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_4155,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_4156,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_4157,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_4158,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4159,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4160,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4161,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_4162,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_4163,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_4164,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_4165,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_4166,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_4167,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_4168,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_4169,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_4170,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_4171,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_4172,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_4173,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_4174,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_4175,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_4176,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_4177,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_4178,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_4179,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_4180,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_4181,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_4182,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_4183,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_4184,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_4185,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_4186,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_4187,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_4188,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4189,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4190,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_4191,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4192,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_4193,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_4194,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_4195,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_4196,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_4197,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_4198,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_4199,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_4200,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_4201,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_4202,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_4203,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4204,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4205,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4206,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_4207,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_4208,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_4209,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_4210,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_4211,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_4212,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_4213,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4214,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4215,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_4216,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_4217,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_4218,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_4219,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4220,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_4221,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_4222,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_4223,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_4224,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_4225,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_4226,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4227,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4228,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_4229,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_4230,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_4231,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4232,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_4233,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4234,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4235,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4236,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_4237,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_4238,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_4239,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_4240,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_4241,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_4242,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_4243,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_4244,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_4245,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_4246,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_4247,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_4248,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4249,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4250,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4251,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
[final] ).
cnf(i_0_4252,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_4253,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_4254,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_4255,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_4256,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_4257,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_4258,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_4259,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_4260,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_4261,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_4262,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_4263,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_4264,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_4265,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_4266,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_4267,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_4268,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_4269,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_4270,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_4271,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4272,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4273,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4274,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_4275,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]),
[final] ).
cnf(i_0_4276,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]),
[final] ).
cnf(i_0_4277,plain,
class_Int_Onumber(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
[final] ).
cnf(i_0_4278,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
[final] ).
cnf(i_0_4279,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_4280,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_4281,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_4282,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]),
[final] ).
cnf(i_0_4283,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]),
[final] ).
cnf(i_0_4284,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
[final] ).
cnf(i_0_4285,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[fact_Pls__def]),
[final] ).
cnf(i_0_4286,plain,
c_Int_OPls != c_Int_OMin,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
[final] ).
cnf(i_0_4287,plain,
c_Int_OMin != c_Int_OPls,
inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
[final] ).
cnf(i_0_4288,axiom,
X1 = X1 ).
cnf(i_0_4289,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4290,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4291,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_4292,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_4293,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_4294,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4295,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4296,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4297,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4298,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4299,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4300,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4301,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4302,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4303,axiom,
( X1 != X2
| c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X2) ) ).
cnf(i_0_4304,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_4305,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_4306,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_4307,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_4308,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_4309,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4310,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4311,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4312,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4313,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4314,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4315,axiom,
( X1 != X2
| c_Transcendental_Oarctan(X1) = c_Transcendental_Oarctan(X2) ) ).
cnf(i_0_4316,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4317,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4318,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4319,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_4320,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_4321,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4322,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4323,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4324,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4325,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4326,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4327,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4328,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4329,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4330,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4331,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4332,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4333,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4334,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4335,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4336,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4337,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4338,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4339,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4340,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4341,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4342,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4343,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4344,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4345,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4346,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4347,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4348,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4349,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4350,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4351,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4352,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4353,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4354,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4355,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4356,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4357,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4358,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4359,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_4360,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4361,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4362,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4363,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4364,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4365,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4366,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4367,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4368,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4369,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4370,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4371,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4372,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4373,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__field(X1)
| class_RealVector_Oreal__field(X2) ) ).
cnf(i_0_4374,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4375,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4376,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4377,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4378,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4379,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4380,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4381,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4382,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4383,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4384,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4385,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4386,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4387,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4388,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4389,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4390,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4391,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4392,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4393,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4394,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_4395,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_4288_001,axiom,
X1 = X1 ).
cnf(i_0_4289_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_4290_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_4291_004,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1,X3,X4) = c_Power_Opower__class_Opower(X2,X3,X4) ) ).
cnf(i_0_4292_005,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X1,X4) = c_Power_Opower__class_Opower(X3,X2,X4) ) ).
cnf(i_0_4293_006,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X3,X4,X1) = c_Power_Opower__class_Opower(X3,X4,X2) ) ).
cnf(i_0_4294_007,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_4295_008,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).
cnf(i_0_4296_009,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).
cnf(i_0_4297_010,axiom,
( X1 != X2
| c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).
cnf(i_0_4298_011,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_4299_012,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_4300_013,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_4301_014,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_4302_015,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_4303_016,axiom,
( X1 != X2
| c_NthRoot_Osqrt(X1) = c_NthRoot_Osqrt(X2) ) ).
cnf(i_0_4304_017,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_4305_018,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_4306_019,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X1,X3,X4) = c_Groups_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_4307_020,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X1,X4) = c_Groups_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_4308_021,axiom,
( X1 != X2
| c_Groups_Otimes__class_Otimes(X3,X4,X1) = c_Groups_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_4309_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_4310_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_4311_024,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_4312_025,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_4313_026,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_4314_027,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_4315_028,axiom,
( X1 != X2
| c_Transcendental_Oarctan(X1) = c_Transcendental_Oarctan(X2) ) ).
cnf(i_0_4316_029,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X1,X3,X4) = c_Rings_Oinverse__class_Odivide(X2,X3,X4) ) ).
cnf(i_0_4317_030,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X1,X4) = c_Rings_Oinverse__class_Odivide(X3,X2,X4) ) ).
cnf(i_0_4318_031,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Odivide(X3,X4,X1) = c_Rings_Oinverse__class_Odivide(X3,X4,X2) ) ).
cnf(i_0_4319_032,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_4320_033,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_4321_034,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4322_035,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4323_036,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4324_037,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4325_038,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4326_039,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_4327_040,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__1(X1)
| class_Rings_Osemiring__1(X2) ) ).
cnf(i_0_4328_041,axiom,
( X1 != X2
| ~ epred1_3(X1,X3,X4)
| epred1_3(X2,X3,X4) ) ).
cnf(i_0_4329_042,axiom,
( X1 != X2
| ~ epred1_3(X3,X1,X4)
| epred1_3(X3,X2,X4) ) ).
cnf(i_0_4330_043,axiom,
( X1 != X2
| ~ epred1_3(X3,X4,X1)
| epred1_3(X3,X4,X2) ) ).
cnf(i_0_4331_044,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4332_045,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4333_046,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4334_047,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4335_048,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4336_049,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4337_050,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4338_051,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4339_052,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4340_053,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4341_054,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4342_055,axiom,
( X1 != X2
| ~ class_Divides_Osemiring__div(X1)
| class_Divides_Osemiring__div(X2) ) ).
cnf(i_0_4343_056,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4344_057,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4345_058,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4346_059,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4347_060,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4348_061,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4349_062,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_4350_063,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4351_064,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4352_065,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4353_066,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4354_067,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4355_068,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4356_069,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4357_070,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4358_071,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4359_072,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_4360_073,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4361_074,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4362_075,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4363_076,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4364_077,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4365_078,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4366_079,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4367_080,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4368_081,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4369_082,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4370_083,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4371_084,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4372_085,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4373_086,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__field(X1)
| class_RealVector_Oreal__field(X2) ) ).
cnf(i_0_4374_087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4375_088,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4376_089,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4377_090,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4378_091,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4379_092,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4380_093,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4381_094,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4382_095,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4383_096,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4384_097,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4385_098,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4386_099,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4387_100,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4388_101,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4389_102,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4390_103,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4391_104,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4392_105,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4393_106,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4394_107,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X1,X3)
| c_Parity_Oeven__odd__class_Oeven(X2,X3) ) ).
cnf(i_0_4395_108,axiom,
( X1 != X2
| ~ c_Parity_Oeven__odd__class_Oeven(X3,X1)
| c_Parity_Oeven__odd__class_Oeven(X3,X2) ) ).
cnf(i_0_4396,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_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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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))),X2))) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X2),
inference(equality_inference,[],[2588]) ).
cnf(i_0_4397,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,[],[2596]) ).
cnf(i_0_4398,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,[],[2598]) ).
cnf(i_0_4399,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,[],[2599]) ).
cnf(i_0_4400,plain,
( c_NthRoot_Osqrt(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))))) = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(equality_inference,[],[2630]) ).
cnf(i_0_4401,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,[],[2634]) ).
cnf(i_0_4402,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,[],[2649]) ).
cnf(i_0_4403,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,[],[2661]) ).
cnf(i_0_4404,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,[],[2662]) ).
cnf(i_0_4405,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,[],[2667]) ).
cnf(i_0_4406,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2717]) ).
cnf(i_0_4407,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,[],[2787]) ).
cnf(i_0_4408,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,[],[2825]) ).
cnf(i_0_4409,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,[],[2851]) ).
cnf(i_0_4410,plain,
( ~ epred1_3(X1,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4))
| ~ 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,[],[2857]) ).
cnf(i_0_4411,plain,
( ~ epred1_3(X1,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Otimes__class_Otimes(tc_Int_Oint,X2,X3),X4))
| ~ 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,[],[2858]) ).
cnf(i_0_4412,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,[],[2916]) ).
cnf(i_0_4413,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,[],[2943]) ).
cnf(i_0_4414,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,[],[2964]) ).
cnf(i_0_4415,plain,
X1 = X1,
inference(equality_inference,[],[3008]) ).
cnf(i_0_4416,plain,
X1 = X1,
inference(equality_inference,[],[3009]) ).
cnf(i_0_4417,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,[],[3048]) ).
cnf(i_0_4418,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,[],[3300]) ).
cnf(i_0_4419,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,[],[3323]) ).
cnf(i_0_4420,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_inference,[],[3327]) ).
cnf(i_0_4421,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,[],[3399]) ).
cnf(i_0_4422,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,[],[3404]) ).
cnf(i_0_4423,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X3,X2) = c_Rings_Oinverse__class_Odivide(X1,X3,X2) ),
inference(equality_inference,[],[3412]) ).
cnf(i_0_4424,plain,
( ~ class_Fields_Ofield(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,X3,X2) = c_Groups_Otimes__class_Otimes(X1,X3,X2) ),
inference(equality_inference,[],[3413]) ).
cnf(i_0_4425,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,[],[3414]) ).
cnf(i_0_4426,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,[],[3415]) ).
cnf(i_0_4427,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,[],[3442]) ).
cnf(i_0_4428,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[3443]) ).
cnf(i_0_4429,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,[],[3466]) ).
cnf(i_0_4430,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[3467]) ).
cnf(i_0_4431,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,[],[3520]) ).
cnf(i_0_4432,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,[],[3521]) ).
cnf(i_0_4433,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,[],[3522]) ).
cnf(i_0_4434,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,[],[3523]) ).
cnf(i_0_4435,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Power_Opower__class_Opower(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_inference,[],[3599]) ).
cnf(i_0_4436,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,[],[3608]) ).
cnf(i_0_4437,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,[],[3610]) ).
cnf(i_0_4438,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,[],[3633]) ).
cnf(i_0_4439,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,[],[3634]) ).
cnf(i_0_4440,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,[],[3650]) ).
cnf(i_0_4441,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3652]) ).
cnf(i_0_4442,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3653]) ).
cnf(i_0_4443,plain,
( ~ class_Groups_Ocancel__semigroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3655]) ).
cnf(i_0_4444,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3678]) ).
cnf(i_0_4445,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3679]) ).
cnf(i_0_4446,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3680]) ).
cnf(i_0_4447,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3682]) ).
cnf(i_0_4448,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,[],[3689]) ).
cnf(i_0_4449,plain,
X1 = X1,
inference(equality_inference,[],[3690]) ).
cnf(i_0_4450,plain,
X1 = X1,
inference(equality_inference,[],[3691]) ).
cnf(i_0_4451,plain,
X1 = X1,
inference(equality_inference,[],[3692]) ).
cnf(i_0_4452,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,[],[3696]) ).
cnf(i_0_4453,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,[],[3697]) ).
cnf(i_0_4454,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,[],[3700]) ).
cnf(i_0_4455,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,[],[3701]) ).
cnf(i_0_4456,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,[],[3702]) ).
cnf(i_0_4457,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) = X3 ),
inference(equality_inference,[],[3722]) ).
cnf(i_0_4458,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) = X3 ),
inference(equality_inference,[],[3723]) ).
cnf(i_0_4459,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) = X3 ),
inference(equality_inference,[],[3725]) ).
cnf(i_0_4460,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) = X3 ),
inference(equality_inference,[],[3726]) ).
cnf(i_0_4461,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(equality_inference,[],[3727]) ).
cnf(i_0_4462,plain,
( ~ class_Fields_Ofield__inverse__zero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(equality_inference,[],[3728]) ).
cnf(i_0_4463,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Otimes__class_Otimes(X1,X3,X2),X2) ),
inference(equality_inference,[],[3730]) ).
cnf(i_0_4464,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Otimes__class_Otimes(X1,c_Rings_Oinverse__class_Odivide(X1,X3,X2),X2) ),
inference(equality_inference,[],[3731]) ).
cnf(i_0_4465,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3740]) ).
cnf(i_0_4466,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,[],[3775]) ).
cnf(i_0_4467,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1))) ),
inference(equality_inference,[],[3778]) ).
cnf(i_0_4468,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,[],[3784]) ).
cnf(i_0_4469,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3792]) ).
cnf(i_0_4470,plain,
( ~ epred1_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| hBOOL(hAPP(X1,X2)) ),
inference(equality_inference,[],[3811]) ).
cnf(i_0_4471,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X2)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3812]) ).
cnf(i_0_4472,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,[],[3825]) ).
cnf(i_0_4473,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,[],[3840]) ).
cnf(i_0_4474,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,[],[3841]) ).
cnf(i_0_4475,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1)) ),
inference(equality_inference,[],[3872]) ).
cnf(i_0_4476,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,[],[3874]) ).
cnf(i_0_4477,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(equality_inference,[],[3877]) ).
cnf(i_0_4478,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3880]) ).
cnf(i_0_4479,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3882]) ).
cnf(i_0_4480,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3883]) ).
cnf(i_0_4481,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3884]) ).
cnf(i_0_4482,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3908]) ).
cnf(i_0_4483,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3918]) ).
cnf(i_0_4484,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3919]) ).
cnf(i_0_4485,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3923]) ).
cnf(i_0_4486,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3924]) ).
cnf(i_0_4487,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_inference,[],[3930]) ).
cnf(i_0_4488,plain,
( ~ class_Power_Opower(X1)
| ~ class_Rings_Osemiring__0(X1)
| c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3931]) ).
cnf(i_0_4489,plain,
( ~ class_Rings_Odivision__ring(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1) ),
inference(equality_inference,[],[3948]) ).
cnf(i_0_4490,plain,
( ~ class_Rings_Odivision__ring__inverse__zero(X1)
| c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3949]) ).
cnf(i_0_4491,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,[],[3950]) ).
cnf(i_0_4492,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,[],[3951]) ).
cnf(i_0_4493,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,[],[3952]) ).
cnf(i_0_4494,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,[],[3953]) ).
cnf(i_0_4495,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,[],[3970]) ).
cnf(i_0_4496,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3998]) ).
cnf(i_0_4497,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3999]) ).
cnf(i_0_4498,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[4000]) ).
cnf(i_0_4499,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,[],[4005]) ).
cnf(i_0_4500,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,[],[4006]) ).
cnf(i_0_4501,plain,
( ~ class_Int_Onumber__ring(X1)
| ~ class_Int_Oring__char__0(X1)
| X2 = X2 ),
inference(equality_inference,[],[4008]) ).
cnf(i_0_4502,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[4029]) ).
cnf(i_0_4503,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[4032]) ).
cnf(i_0_4504,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls) = c_Int_OPls,
inference(equality_inference,[],[4035]) ).
cnf(i_0_4505,plain,
c_Int_OPls = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(equality_inference,[],[4036]) ).
cnf(i_0_4506,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = X2 ),
inference(equality_inference,[],[4040]) ).
cnf(i_0_4507,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(X1)
| c_Groups_Oabs__class_Oabs(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[4060]) ).
cnf(i_0_4508,plain,
( ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[4061]) ).
cnf(i_0_4509,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[4064]) ).
cnf(i_0_4510,plain,
X1 = X1,
inference(equality_inference,[],[4078]) ).
cnf(i_0_4511,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(equality_inference,[],[4085]) ).
cnf(i_0_4512,plain,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(equality_inference,[],[4086]) ).
cnf(i_0_4513,plain,
$false,
inference(scs_inference,[],[i_0_2601,i_0_4076,i_0_2616]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW198+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.13 % 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
% 0.17/0.34 % Computer : n008.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 06:24:28 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 3.09/3.80 % Version : CSE_E---1.7
% 3.09/3.80 % Problem : theBenchmark.p
% 3.09/3.80 % SZS status Theorem for theBenchmark.p
% 3.09/3.80 % SZS output start CNFRefutation
% See solution above
% 3.19/3.95 % Total time : 3.443s
%------------------------------------------------------------------------------